diff --git a/adsingestp/parsers/base.py b/adsingestp/parsers/base.py index 790d963..7646f39 100644 --- a/adsingestp/parsers/base.py +++ b/adsingestp/parsers/base.py @@ -543,6 +543,14 @@ def _detag(self, r, tags_keep): for e in elements: if t in self.HTML_TAGS_DANGER: e.decompose() + elif (t == "alternatives") or (t == "inline-formula"): + alt_math_element = e.find_all("mml:math", []) + alt_tex_element = e.find_all("tex-math", []) + if alt_math_element and alt_tex_element: + for ee in alt_tex_element: + ee.decompose() + if t not in tags_keep: + e.unwrap() elif t in tags_keep: continue else: diff --git a/tests/stubdata/input/jats_apj_967_1_35.xml b/tests/stubdata/input/jats_apj_967_1_35.xml new file mode 100644 index 0000000..9162104 --- /dev/null +++ b/tests/stubdata/input/jats_apj_967_1_35.xml @@ -0,0 +1,7877 @@ + + +
+ + + apj + + The Astrophysical Journal + APJ + Astrophys. J. + + 0004-637X + 1538-4357 + + The American Astronomical Society + + + + apjad3c2b + 10.3847/1538-4357/ad3c2b + ad3c2b + AAS52670 + + + 330 + High-Energy Phenomena and Fundamental Physics + + + + Tests of the Kerr Hypothesis with MAXI J1803-298 Using Different RELXILL_NK Flavors + + + + + Liao + Jie + + 1 + 2 + + + 0000-0001-6113-0317 + + Ghasemi-Nodehi + M. + + 1 + + + 0000-0003-0721-5509 + + Cui + Lang + + 1 + 3 + 4 + cuilang@xao.ac.cn + + + 0000-0002-3960-5870 + + Tripathi + Ashutosh + + 1 + 5 + + + 0000-0001-7199-2906 + + Huang + Yong-Feng + + 6 + 7 + + + 0000-0001-9815-2579 + + Liu + Xiang + + 1 + 3 + 4 + + + + Xinjiang Astronomical Observatory, CAS, 150 Science-1 Street, Urumqi 830011, + People's Republic of China; + cuilang@xao.ac.cn + + + +College of Astronomy and Space Science, + University of Chinese Academy of Sciences, No.1 Yanqihu East Road, Beijing 101408, + People's Republic of China + + + + Key Laboratory of Radio Astronomy, CAS, 150 Science 1-Street, Urumqi 830011, + People's Republic of China + + + + Xinjiang Key Laboratory of Radio Astrophysics, 150 Science 1-Street, Urumqi 830011, + People's Republic of China + + + +George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, + Texas A&M University, College Station, TX 77843-4242, + USA + + + +School of Astronomy and Space Science, + Nanjing University, Nanjing 210023, + People's Republic of China + + + + Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education, Nanjing 210023, + People's Republic of China + + + + 01 + 5 + 2024 + + + 16 + 05 + 2024 + + + 16 + 05 + 2024 + + 967 + 1 + 35 + + + 1 + 2 + 2024 + + + 2 + 4 + 2024 + + + 4 + 4 + 2024 + + + 04 + 04 + 2024 + + + + © 2024. The Author(s). Published by the American Astronomical Society. + 2024 + + + + Original content from this work may be used under the terms of the + Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. + + + + + + + Abstract +

Iron line spectroscopy has been one of the leading methods not only for measuring the spins of accreting black holes but also for testing fundamental physics. Basing on such a method, we present an analysis of a data set observed simultaneously by NuSTAR and NICER for the black hole binary candidate MAXI J1803-298, which shows prominent relativistic reflection features. Various + relxill_ + nk flavors are utilized to test the Kerr black hole hypothesis. The results obtained from our analysis provide stringent constraints on Johannsen deformation parameter + α + 13 with the highest precise to date, namely + + + + + + + + α + + + 13 + + + = + + + 0.023 + + + − + 0.038 + + + + + 0.071 + + + + + from + relxillD_ + nk and + + + + + + + + α + + + 13 + + + = + + + 0.006 + + + − + 0.022 + + + + + 0.045 + + + + + from + relxillion_ + nk, respectively, in 3 + σ credible lever, where the Johannsen metric reduces to the Kerr metric when + α + 13 vanishes. Furthermore, we investigate the best model fit results using Akaike information criterion and assess its systematic uncertainties. +

+ + + unified-astronomy-thesaurus + + http://astrothesaurus.org/uat/887 + Kerr metric + 887 + + + http://astrothesaurus.org/uat/641 + General relativity + 641 + + + http://astrothesaurus.org/uat/98 + Astrophysical black holes + 98 + + + http://astrothesaurus.org/uat/1611 + Stellar mass black holes + 1611 + + + http://astrothesaurus.org/uat/1810 + X-ray astronomy + 1810 + + + + + CAS ∣ West Light Foundation, Chinese Academy of Sciences (West Light Foundation of CAS) + https://doi.org/10.13039/501100013494 + + 2021-XBQNXZ-005 + + + + + + + + ccc + 0004-637X/24/35+12$33.00 + + + crossmark + yes + + + + + + + + Introduction +

Since Einstein proposed general relativity in late 1915, it has found applications across various physical phenomena and has undergone numerous tests in the weak field regime (Will + 2014). Over the decades, advancements in instruments and technology have made the testing of general relativity in strong gravitational regimes a prominent and contemporary research focus. Astrophysical black holes (BHs), which can be described by the Kerr solution (Kerr + 1963; Carter + 1971; Robinson + 1975), serve as an ideal laboratory for probing strong gravity. +

+

The presence of an accretion disk, nearby stars, or a potential nonvanishing electric charge of the BH is typically negligible in the strong gravitational field near the event horizon (Bambi et al. + 2009; Bambi + 2018; Cardoso & Pani + 2019). Conversely, certain plausible macroscopic deviations from the Kerr metric arise in the presence of quantum gravity effects (Dvali & Gomez + 2013; Giddings + 2017; Giddings & Psaltis + 2018), exotic matter (Herdeiro et al. + 2016; Giddings & Psaltis + 2018), and various modified theories of gravity (Kleihaus et al. + 2011; Ayzenberg & Yunes + 2014; Sotiriou & Zhou + 2014). Consequently, testing the Kerr metric proves to be an effective approach for exploring the strong gravitational field regime. +

+

Numerous methods for testing the Kerr hypothesis have been explored, primarily encompassing electromagnetic techniques (Johannsen + 2016; Bambi et al. + 2017), and in recent years, gravitational-wave approaches (Glampedakis & Babak + 2006; Yunes & Siemens + 2013; Abbott et al. + 2016; Yunes et al. + 2016). The X-ray reflection spectrum is generally used to study the relativistic effects on the inner part of the accretion disk around BHs and to understand the properties of spacetime (Bambi et al. + 2021). There are many observational constraints already published using X-ray reflection spectrum originated from the accretion disk around BHs to test the Kerr hypothesis (Cao et al. + 2018; Xu et al. + 2018; Tripathi et al. + 2019a, + 2019b, + 2019c; Abdikamalo et al. + 2019). Among these approaches, the disk–corona model is regarded as a phenomenological model describing the relationship between the accretion disk and the ionized corona in a BH system. +

+

The thermal photons emitted from the disk undergo inverse-Compton scattering within the corona, characterized by high temperatures (approximately 100 keV), and some of them are reflected back to the disk, which is the so-called reflection spectrum. The most prominent features of the reflection spectrum are often characterized by the iron + K + α line around 6.4 keV, depending on the ionization of iron atoms, and the Compton hump peaked around 20–30 keV. In the rest frame of the gas, fluorescent emission lines display narrow profiles; however, in a strong-gravity region, the + K + α line undergoes broadening due to relativistic effects, which indicates that it is one of the most potential tools that can be used to test relativistic effects in a strong-gravity region (Cao et al. + 2018; Abdikamalo et al. + 2019; Tripathi et al. + 2020). +

+

The + relxill_ + nk model + + 8 + + + +

+ https://github.com/ABHModels/relxill_nk +

+ (Bambi + 2017; Abdikamalov et al. + 2019), an extension of the + relxill package + + 9 + + + +

+ http://www.sternwarte.uni-erlangen.de/~dauser/research/relxill/ +

+ (Dauser et al. + 2013; García et al. + 2014), is a versatile tool for analyzing the reflection features of a geometrically thin and optically thick disk in non-Kerr spacetimes. The model employs a parametric BH spacetime metric, where a set of deformation parameters parameterizes deviations from the Kerr solution. The Kerr metric is recovered when all the deformation parameters vanish (Cao et al. + 2018; Abdikamalo et al. + 2019; Tripathi et al. + 2020). +

+

This paper details the spectral analysis conducted on the observational data during the outburst of the Galactic BH binary candidate MAXI J1803-298. The outburst of this BH binary candidate was first captured by the Gas Slit Camera of the Monitor of All-sky X-ray Image (MAXI) nova alert system at 19:50 UT on 2021 May 1, located at R.A. = 270.°923, decl. = −29.°804 (J2000; Serino et al. + 2021). A comprehensive multiwavelength follow-up of the discovery outburst and the timing analysis of the BH candidate MAXI J1803−298 are presented in Mata Sánchez et al. ( + 2022) and Zhu et al. ( + 2023). These findings indicate a state transition from the low/hard state to the hard intermediate state, followed by the soft intermediate state, and ultimately reaching the high/soft state. The works of Feng et al. ( + 2022) and Coughenour et al. ( + 2023) previously examined variability and reflection features, revealing a notable, relativistically broadened iron-line component in the spectrum with an extraordinarily high value of spin parameter. +

+

Based on the reflection feature from MAXI J1803-298 within a soft intermediate state, we mainly test the Kerr metric with different flavors of model + relxill_ + nk and then discuss the impact of different + relxill_ + nk flavors in fitting data from NuSTAR and NICER in this work. Stringent constraints on its parameters have been obtained, and these findings reveal no significant distinctions among different flavors of + relxill_ + nk. Subsequently, the AIC was employed to assess the congruence among diverse models for the purpose of selecting the best-fitting model. +

+

The contents of this paper are organized as follows. In Section + 2, we present the observations of MAXI J1803-298 and data reduction from NuSTAR and NICER. In Section + 3, we present our spectrum analysis with different + relxill flavors and + relxill_ + nk flavors. In Section + 4, we discuss our results, estimate the systematic uncertainties, and give conclusions in the end. +

+ + + + Observation and Data Reduction + + + Observations +

MAXI J1803-298 was observed by various X-ray missions, including simultaneous observations by NuSTAR and the X-ray Timing Instrument (XTI) payload on NICER on 2021 May 23. Observation IDs and their exposure times are reported in Table + 1. The focus of this work is the observation with ObsID 90702318002 from NuSTAR/(FPMA and FPMB) and ObsID 4202130110 from NICER/XTI followed by works in Feng et al. ( + 2022). Assuming that the Kerr solution describes the spacetime metric around the BH, Feng et al. ( + 2022) and Coughenour et al. ( + 2023) estimated the BH’s spin and well-constrained features of the reflection spectrum. We followed their works but mainly employed the + relxill_ + nk with different flavors to estimate the deformation parameter + α + 13 of the Johannsen metric. The line element of the Johannsen spacetime is reported in the + Appendix, where we also list the main properties of this BH metric. +

+ + + +

Observations Analyzed in the Present Work

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
MissionObservation IDStart DateExposure
+ + + (s)
NuSTAR907023180022021-05-2312922
NICER42021301102021-05-237508
+ + + +

Typeset image

+ + + + + + + Data Reduction +

The raw data obtained from the NuSTAR detectors, denoted as FPMA and FPMB, are processed by the standard pipeline + + 10 + + + +

+ https://heasarc.gsfc.nasa.gov/docs/nustar/analysis/ +

+ + NUPIPELINE 0.4.9 in + HEASOFT v6.32 using the latest calibration database + CALDB v20230816. The good time interval files are produced using + nuscreen, and we remove some obvious variabilities in the NuSTAR light curve by the tool + fv to preclude the impact of flare and dip events on the spectrum analysis. The source events are extracted from a circular region centered on MAXI J1803-298 with a radius of 120″. The background region is a circle of the same size taken far from the source region to avoid any contribution from the source. We use the + nuproducts to generate the spectra and other products. The FPMA and FPMB spectra are grouped to have a minimum count of 25 photons per bin for the  + χ + 2 statistics to be applicable. The NuSTAR data are modeled over the 3–55 keV band for further analysis. +

+

Based on the latest calibration file, the NICER data are processed following the standard steps. + + 11 + + + +

+ https://heasarc.gsfc.nasa.gov/docs/nicer/analysis_threads/ +

+ We use the tool + nicer12 and + nibackgen3C50 to extract the source and background spectra, respectively. The response matrix and ancillary file are generated by + nicerrmf and + nicerarf. In this work, the spectrum from NICER’s data is fitted over the energy band of 1.0–8.0 keV, ignoring the energy range of 1.7–2.1 keV (calibration residuals remain found in the Si band) and 2.2–2.3 keV (calibration residuals remain in Au edges), respectively. We also group the XTI spectra to have a minimum count of 25 photons per bin. +

+ + + + + Spectrum Analysis +

Spectra are modeled using XSPEC v12.13.1 with + χ + 2 statistics. To fit these spectra simultaneously from FPMA, FPMB, and XTI, a constant multiplicative factor was included in each model, set to 1.0 for XTI, and allowed to vary freely for FPMA and FPMB to eliminate the calibration differences in different instruments in the process of joint fit. To begin with, we fit the NuSTAR spectrum with a galactic absorbed power-law component from the corona and a thermal spectrum from the disk. The normalized residual is shown in Figure + 1. This residual presents a strong reflection feature with a broad iron line around 6.4 keV and a Compton hump with a peak at 20–30 keV, with + + + + + + + + χ + + + ν + + + 2 + + + = + 3127.37 + + / + + 2290 + + + . +

+ + + +

Normalized residuals for an absorbed power-law spectrum + disk blackbody spectrum (in XSPEC language, + tbabs× + (diskbb+powerlaw)). Green crosses are for XTI/NICER data, red crosses are for FPMA/NuSTAR data, and blue crosses are for FPMB/NuSTAR data. Data have been rebinned for visual clarity. +

+ + + + + +

To study the strong relativistic reflection composition in this source, our primary full XSPEC model involves substituting the power-law component with standard reflection models, denoted as + relxill(flavor), which encompasses + relxill, + relxillCP, + relxillp, and + relxillpCP. The initial model is described by + constant × + tbabs × ( + diskbb+ + relxill(flavor)), where the specific flavors are respectively marked as I1-I4. + tbabs describes the galactic absorption and has only one parameter: column density ( + N + H) along the line of sight. + N + H is set to be free while fitting the spectra. + diskbb describes the thermal spectrum from the accretion disk. + relxill(flavor) component describes the power law and reflection composition. As it is widely believed that the accretion disk approaches the ISCO between the intermediate and soft states, we assume that the inner edge of the accretion disk is at the ISCO (equal to 6 + GM/ + c + 2 = 6 + R + + g + for a Schwarzschild BH, or just 1 + R + + g + for a maximally spinning Kerr BH), and the outer radius is set to 400 + R + + g + where + R + + g + is the gravitational radius. The emissivity profile in Models I1–I2 is modeled with a broken power-law emissivity profile with three parameters that are let free. Due to the limited fitting energy range, we additionally set the electron temperature of the corona (kTe) to one-third of the default value of the power-law cutoff energy ( + E + cut = 300 keV), i.e., kTe = 100 keV. Because inclination is measured by a high value from the same and another NuSTAR’s observation from Feng et al. ( + 2022) and Coughenour et al. ( + 2023), we also left it free to vary in the same way. In the lamppost Models I3 and I4, we freeze the spin parameter to 0.998. In addition, a Fe + xxvi absorption line at 7.0 keV has been detected during its intermediate state in Zhang et al. ( + 2024). We also added a + Gaussian component in our Models I1–I4. +

+

After fitting the data with the model, we found the “standard” weighting scheme in XSPEC often resulted in overfitting the data, yielding a reduced + χ + 2 < 1. This is a known issue discussed in Galloway et al. ( + 2020) regarding handling the low-count bins in + XSPEC v.12. The Churazov weighting scheme is an alternative to the standard weighting used for fitting data (Churazov et al. + 1996). It adjusts the weight by taking into account the counts in neighboring channels. This ensures that local extrema are not given disproportionate weight, leading to a smoother overall weighting. The result is a more accurate and reliable data fitting. Our best-fit results of Models I1–I4 are shown in Table + 2, and all errors are reported at the 90% credible level. +

+ + + +

Best-fit Values for the Kerr Models I1–I4

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ ParameterModel I1Model I2Model I2 + + + Model I3Model I4
+ tbabs + + + + + + +
+ N + H(10 + 21 cm + −2) + Hydrogen column density3.68 ± 0.043.39 ± 0.073.54 ± 0.123.31 ± 0.043.16 ± 0.06
+
+
+ diskbb + + + + + + +
+ T + in (keV) + Temperature of disk0.813 ± 0.0170.768 ± 0.0070.822 ± 0.0090.765 ± 0.0050.793 ± 0.010
+ N + diskbb + Normalization425 ± 43612 ± 30433 ± 31598 ± 19546 ± 33
+
+
+ relxill flavor + + + relxill + + relxillCP + + relxillCP + + relxilllp + + relxilllpCP +
+ h + Height of the corona⋯⋯⋯<11.7<10.8
+ q + in + Emissivity index in the inner region10.0 + −4.9 + + + + + + + + + 9.64 + + + − + 2.1 + + + + + + + + + + + + + + + 10.0 + + + − + 5.09 + + + + + + + ⋯⋯
+ q + out + Emissivity index in the outer region5.7 ± 5.76 + ∗ + 6 + ∗ + ⋯⋯
+ R + + r + (M) + Break radius2.13 ± 1.072.37 ± 0.792.15 ± 0.30⋯⋯
+ a + ∗ + BH spin0.989 ± 0.0050.993 ± 0.0070.984 ± 0.0060.998 + ∗ + 0.998 + ∗ +
+ i (deg) + Inclination angle72.5 ± 1.572.5 ± 1.868.2 ± 1.750.3 ± 2.244.1 ± 1.9
+ R + in + Disk inner radius−1 + ∗ + −1 + ∗ + −1 + ∗ + −1 + ∗ + −1 + ∗ +
ΓPhoton Index2.34 ± 0.032.25 ± 0.022.22 ± 0.052.23 ± 0.022.17 ± 0.04
+ + + + + + log + ξ + + + + Ionization state of disk3.78 ± 0.284.44 ± 0.213.35 ± 0.094.70 ± 0.193.97 ± 0.14
log + N + The density of the accretion disk15 + ∗ + 15 + ∗ + 18.3 ± 0.515 + ∗ + 18.0 ± 0.6
FeIron abundance1.17 ± 0.425.63 ± 2.901.30 ± 0.287.07 ± 2.194.35 ± 1.60
+ E + cut( + kT + + e + ) (keV) + Energy cutoff (or + T + corona) + 300 + ∗ + 100 + ∗ + 100 + ∗ + 300 + ∗ + 100 + ∗ +
+ R + + f + + Reflection fraction1.92 ± 0.871.77 ± 0.521.74 ± 0.471.16 ± 0.420.66 ± 0.38
norm (10 + −2) + Normalization1.9 ± 0.41.5 ± 0.21.2 ± 0.32.0 ± 0.72.2 ± 1.2
+
+
+ Gaussian + + + + + + +
+ E + line + Absorption line energy in keV7.12 ± 0.067.11 ± 0.077.11 ± 0.067.33 ± 0.107.06 ± 0.10
+ σ + + E + + Line width in keV0.08 ± 0.090.06 ± 0.100.08 ± 0.080.51 ± 0.110.78 ± 0.07
+
+
+ C + FPMA + Cross-normalization1.0231.0231.0231.0231.024
+ C + FPMB + Cross-normalization0.9960.9970.9970.9970.997
+
+
+ χ + 2/ + ν ( + reduced) + ⋯2520/22792545/22802492/22792509/22822507/2281
+ + =1.106=1.116=1.093=1.099=1.099
+ + + +

Typeset image

+ + + +

+ Note. Best-fit values of initial Models I1–I4: + tbabs × ( + diskbb+ + relxill(flavor)+ + gaussian), in Xspec language ( + relxill, + relxillCP, + relxillp, and + relxillpCP, respectively), with errors calculated within a 90% confidence interval by + χ + 2 statistic. The + ∗ symbol indicates that the parameter is frozen in the fit. The + + symbol indicates that the parameter log + N is free. + R + in = −1 means that + R + in is set at the ISCO radius. The radial coordinate of the outer edge of the accretion disk is fixed at 400. + i is allowed to vary from 3° to 80°. + a + ∗ is allowed to vary from −0.998 to 0.998. log + N in relxillCP flavors is allowed to range from 15 to 19. When the lower/upper uncertainty is not reported, the 90% confidence level reaches the boundary (or the best fit is at the boundary). +

+ + +

We then substitute the + relxill(flavors) model with various + relxill_ + nk flavors: the + relxill_ + nk (default model), + relxillCP_ + nk (nthcomp Comptonization for the coronal spectrum), + relxillD_ + nk (variable disk electron density), and + relxillion_ + nk (the value of the ionization parameter varies as the radial coordinate + r increases). We conduct joint fitting on the data. The models in XSPEC language are + constant × + tbabs × + (diskbb+relxill_ + nk(flavor)+Gaussian), which are respectively marked as A1–A4 (set + α + 13 to 0) and B1–B4 (set + α + 13 to free). More details of the extension of the + relxill_ + nk model can be found in Abdikamalov et al. ( + 2019). We apply the same bounds to the emissivity profile and the break radius as we did for Models I1–I2. +

+

Within the framework of Johannsen spacetime, it is assumed that, with the exception of + α + 13, the remaining three deformation parameters, namely + α + 22, + ϵ + 3, and + α + 52, are held constant at 0 for simplicity in this work. Here, a nonzero former signifies the departure from the Kerr metric. After we free + α + 13, the best-fit results from our Models B1–B4 are shown in Table + 3, and its unfolded spectra and normalized residuals are shown in Figure + 2. +

+ + + +

Summary of the Best-fit Values for Johannsen Models A1–B6 with Only + α + 13 Set Free after the MCMC Runs +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ Model A1Model B1Model A2Model B2Model A3Model B3Model A4Model B4Model B5Model B6
+ tbabs + + + + + + + + + +
+ N + H(10 + 21 cm + −2) + + + + + + + + + 3.35 + + + − + 0.08 + + + + + 0.04 + + + + + + + + + + + + + + 3.34 + + + − + 0.03 + + + + + 0.04 + + + + + + + + + + + + + + 3.22 + + + − + 0.03 + + + + + 0.04 + + + + + + + + + + + + + + 3.20 + + + − + 0.03 + + + + + 0.02 + + + + + + + + + + + + + + 3.33 + + + − + 0.05 + + + + + 0.06 + + + + + + + + + + + + + + 3.33 + + + − + 0.04 + + + + + 0.05 + + + + + + + + + + + + + + 3.60 + + + − + 0.06 + + + + + 0.05 + + + + + + + + + + + + + + 3.58 + + + − + 0.06 + + + + + 0.08 + + + + + + + + + + + + + + 3.50 + + + − + 0.06 + + + + + 0.03 + + + + + + + + + + + + + + 3.28 + + + − + 0.03 + + + + + 0.03 + + + + + +
+
+
+ diskbb + + + + + + + + + + +
+ T + in (keV) + + + + + + + + + 0.765 + + + − + 0.015 + + + + + 0.006 + + + + + + + + + + + + + + 0.783 + + + − + 0.003 + + + + + 0.003 + + + + + + + + + + + + + + 0.746 + + + − + 0.003 + + + + + 0.004 + + + + + + + + + + + + + + 0.745 + + + − + 0.004 + + + + + 0.004 + + + + + + + + + + + + + + 0.774 + + + − + 0.005 + + + + + 0.005 + + + + + + + + + + + + + + 0.777 + + + − + 0.007 + + + + + 0.006 + + + + + + + + + + + + + + 0.808 + + + − + 0.008 + + + + + 0.007 + + + + + + + + + + + + + + 0.804 + + + − + 0.008 + + + + + 0.012 + + + + + + + + + + + + + + 0.787 + + + − + 0.003 + + + + + 0.004 + + + + + + + + + + + + + + 0.755 + + + − + 0.004 + + + + + 0.002 + + + + + +
+ N + diskbb + + + + + + + + + 606 + + + − + 20 + + + + + 53 + + + + + + + + + + + + + + 599 + + + − + 25 + + + + + 14 + + + + + + + + + + + + + + 702 + + + − + 20 + + + + + 14 + + + + + + + + + + + + + + 714 + + + − + 18 + + + + + 15 + + + + + + + + + + + + + + 564 + + + − + 22 + + + + + 27 + + + + + + + + + + + + + + 567 + + + − + 41 + + + + + 16 + + + + + + + + + + + + + + 430 + + + − + 24 + + + + + 31 + + + + + + + + + + + + + + 438 + + + − + 37 + + + + + 36 + + + + + + + + + + + + + + 496 + + + − + 18 + + + + + 15 + + + + + + + + + + + + + + 645 + + + − + 9 + + + + + 14 + + + + + +
+
+
+ relxill_ + nk flavor + + relxill_ + nk + + + relxillCP_ + nk + + + relxillD_ + nk + + + relxillion_ + nk + + + relxill_ + nk + +
+ + α + 13 = 0 + free + α + 13 + + α + 13 = 0 + free + α + 13 + + α + 13 = 0 + free + α + 13 + + α + 13 = 0 + free + α + 13 + + set Fe=1 + + set Fe=5 +
+ q + in + 10 + ∗ + 10 + ∗ + + + + + + + + + 9.76 + + + − + 0.92 + + + + + + + + + + + + + + + 9.73 + + + − + 0.91 + + + + + + + + + + + + + + + 9.94 + + + − + 0.49 + + + + + + + + + + + + + + + 9.94 + + + − + 2.3 + + + + + + + + + + + + + + + 9.73 + + + − + 0.89 + + + + + + + + + + + + + + + 9.96 + + + − + 1.10 + + + + + + + + + + + + + + + 9.94 + + + − + 2.42 + + + + + + + + + + + + + + + 9.94 + + + − + 2.26 + + + + + + +
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norm (10 + −3) + + + + + + + + + 3.9 + + + − + 1.9 + + + + + 2.1 + + + + + + + + + + + + + + 4.1 + + + − + 1.4 + + + + + 2.3 + + + + + + + + + + + + + + 7.0 + + + − + 1.7 + + + + + 1.8 + + + + + + + + + + + + + + 6.2 + + + − + 1.5 + + + + + 1.8 + + + + + + + + + + + + + + 4.7 + + + − + 1.7 + + + + + 2.8 + + + + + + + + + + + + + + 5.6 + + + − + 0.8 + + + + + 1.4 + + + + + + + + + + + + + + 8.3 + + + − + 4.6 + + + + + 4.3 + + + + + + + + + + + + + + 7.5 + + + − + 3.7 + + + + + 4.2 + + + + + + + + + + + + + + 4.2 + + + − + 3.2 + + + + + 2.1 + + + + + + + + + + + + + + 3.9 + + + − + 3.1 + + + + + 2.5 + + + + + +
+
+
+ Gaussian + + + + + + + + + + +
+ σ + line + <0.31<0.47<0.13<0.12<0.33<0.35<0.53<0.56<0.41<0.35
Norm (10 + −4) + −3.1−2.6−3.0−2.3−4.1−3.2−3.1−3.0−2.6−2.2
+
+
+ C + FPMA + 1.0231.0231.0231.0231.0231.0231.0231.0231.0221.023
+ C + FPMB + 0.9960.9970.9970.9950.9970.9970.9970.9970.9970.997
+
+
+ χ + 2/ + ν (reduced) + 2533/22812527/22802563/22802565/22792521/22802513/22792446/22792444/22782567/22802533/2280
+ =1.110=1.108=1.124=1.125=1.105=1.103=1.073=1.072=1.125=1.111
+ + + +

Typeset image

+ + + +

+ Note. Best-fit Values of Models A1–B6 (includes + relxill_ + nk, + relxillCP_ + nk, + relxillD_ + nk, and + relxillion_ + nk). All errors determined through a 90% confidence interval after MCMC runs for the global minimum. The + ∗ symbol indicates that the parameter is frozen in the fit. + R + in = −1 means that + R + in is set at the ISCO radius. The radial coordinate of the outer edge of the accretion disk is fixed to 400. + i is allowed to vary from 3° to 80°. + a + ∗ is allowed to vary from −0.998 to 0.998. The deformation parameter of + α + 13 is allowed to vary from −1 to 1. + E + line in Gaussian is frozen to 7.1 keV. When the lower/upper uncertainty is not reported, the 90% confidence level reaches the boundary (or the best fit is at the boundary). +

+ + + + + +

The best-fit results of unfolded spectra and normalized residuals of Models B1–B4. Upper quadrants show total models (black), + relxill_ + nk (magenta), and diskbb (yellow). For each subgraph, dashed–dotted, dotted, and dashed lines present the same model for NICER/XTI, NuSTAR/FPMA, and NuSTAR/FPMB data, respectively. Lower quadrants show normalized residuals. NICER/XTI, NuSTAR/FPMA, and NuSTAR/FPMB data are plotted in green, red, and blue, respectively. Data have been rebinned for visual clarity. +

+ + + + + +

The + χ + 2 statistic is employed to determine the best-fit parameters, serving as the prior distribution for Markov Chain Monte Carlo (MCMC) analysis in the fitting process. The MCMC samples were generated using the Goodman & Weare algorithm embedded in the XSPEC software. + + 12 + + + +

+ https://github.com/zoghbi-a/xspec_emcee +

+ The chains were run with 40 walkers, each comprising 25000 iterations, with an initial burn-in phase of 1000 steps. Thus, a total of 1 × 10 + 6 samples were obtained. The 90% confidence intervals, indicative of purely statistical uncertainties across the entire parameter chain, for the free parameters within the best-fit results of Models B1–B4 derived from the MCMC simulations, are detailed in Table + 3. Furthermore, Figures + 3, + 4, + 5, and + 6 showcase corner plots illustrating the one- and two-dimensional projections of the posterior probability distributions for the relevant free parameters corresponding to Models B1–B4, respectively, as a result of the MCMC analysis. +

+ + + +

The corner plot for free parameters in Model B1 after MCMC runs are used in this work. The 2D plots report the 1 + σ, 2 + σ, and 3 + σ confidence contours. +

+ + + + + + + + +

The corner plot for free parameters in Model B2 after MCMC runs are used in this work. The 2D plots report the 1 + σ, 2 + σ, and 3 + σ confidence contours. +

+ + + + + + + + +

The corner plot for free parameters in Model B3 after MCMC runs are used in this work. The 2D plots report the 1 + σ, 2 + σ, and 3 + σ confidence contours. +

+ + + + + + + + +

The corner plot for free parameters in Model B4 after MCMC runs are used in this work. The 2D plots report the 1 + σ, 2 + σ, and 3 + σ confidence contours. +

+ + + + + + + + + Discussion and Conclusions +

After scrutinizing the spectra of MAXI J1803-298 from NuSTAR and NICER utilizing state-of-art relativistic reflection models in Section + 3, we derived precise and accurate constraints within these models employed in the present work. Our findings and conclusions are presented below. +

+

In this work, we mainly used the + relxill flavors and + relxill_ + nk flavors to fit the data. Our best-fit values of our employed Models I1–I4 and A1–B6 are shown in Tables + 2 and + 3, respectively. It is essential to recognize that direct comparisons of the + χ + 2 values between Models I1–I4 utilizing + relxill flavors and Models A1–B6 employing + relxill_ + nk flavors cannot definitively ascertain the superior model due to variations in the calculation of the transfer function. As such, the minor discrepancies observed in the + χ + 2 values between these two sets of models will not impact the subsequent discussion. +

+ + + Fitting with + <monospace>Relxill</monospace> Flavors + +

We first compare our best-fit results of Model A with results shown in Feng et al. ( + 2022). Our findings showcase a relatively lower galactic-absorption coefficient∼ 3.0 × 10 + 21 cm + −1, which aligns with results in Homan et al. ( + 2021). However, the best-fit values in Table + 2 show a slightly higher galactic-absorption coefficient than the results in Chand et al. ( + 2022), which may be caused by the outflowing disk winds and the moving clouds during the outburst. +

+

In the initial Model I1–I2, the results obtained with + relxill and + relxillCP, which are standard models for relativistic reflection within the Kerr paradigm, incorporate emissivity that can be parameterized through an empirically defined broken power law. Our results shown in Table + 2 are indicative of a BH with extremely high spin and a highly inclined accretion disk (approximately 70°). Particularly, it shows Δ + χ + 2 > 45 when the density of the accretion disk is set free, denoted as Model I2 + +. This suggests a high ionization density disk near ∼10 + 18 cm + −3, within MAXI J1803-298, which aligns with Coughenour et al. ( + 2023). Thus, their fit results with a higher galactic-absorption coefficient ∼5.0 × 10 + 21 cm + −1 with only a low ionization density disk model + relxillCP in Feng et al. ( + 2022) appear to be inconclusive. +

+

We subsequently incorporate lamppost Models I3 and I4, which posit a lamppost source located along the rotational axis, to evaluate the proximity of the corona to the disk, setting the spin parameter to 0.998. The results indicate that the height of the compact corona above the disk is constrained to + h < 10.8 + R + + g + , suggesting a still-pronounced reflection component in the data observed during its SIMS. +

+ + + + Fitting with + <monospace>Relxill</monospace>_ + <monospace>nk</monospace> Flavors + +

Afterwards, we transition to the + relxill_ + nk flavors to investigate the correlation between deformation parameters + α + 13 and the spin parameter + a + ∗ based on its reflection feature. As is shown in Models B1–B4 in Table + 3, it is evident that, when modeling the emissivity profile with a broken power law using the + relxill_ + nk flavors, consistently high spin values ( + a + ∗ > 0.98) are observed. Additionally, there is a notable pattern of high values for the emissivity index + q + in and low values for + q + out. This further supports our fit results of a compact corona near the BH modeled by Models I3–I4 in Section + 4.1. +

+

In Model B2 with + relxillCP_ + nk, in which the parameter + kT + + e + represents the temperature of the corona, we found a stringent constraint on the deformation parameter assuming the Johannsen spacetime (Johannsen + 2013). However, this constraint on + α + 13 should be excluded due to its bad parameter estimation; details are presented in Section + 4.3. In addition, since the electron density is fixed to a low value of 10 + 15 cm + −3 rather than a high disk density in the disk in Model B1 and Model B2, we employed + relxillD_ + nk for data fitting, where the parameter linked to the disk electron density, log + N, was frozen to 18 due to the high disk density we got from Model I2 + + in Section + 4.1. Notably, when the high disk density is set to 18 in Model B3, it shows Δ + χ + 2 > 14, but it will not significantly change the constraint on + α + 13. The contours of spin versus deformation parameter + α + 13 are shown in Figure + 7. +

+ + + +

Constraints on the spin parameter + a + ∗ and the deformation parameter + α + 13 for Models B1–B6 after the MCMC runs. The 2D plots report the 1 + σ, 2 + σ, and 3 + σ confidence contours. +

+ + + + + +

In previous + relxill_ + nk flavors, the ionization parameter + ξ was not considered as a variable. To address this, we also applied the + relxillion_ + nk model (Abdikamalov et al. + 2021), utilizing + xillver table for the reflection spectrum in the rest frame of the gas. In this model, the electron density is assumed to be a constant (10 + 15 cm + −3) across the entire disk. The ionization has instead a radial profile described by a power law: + + + + + + + ξ + ( + r + ) + = + + + ξ + + + in + + + + + + + + + + + + R + + + in + + + + + r + + + + + + + + + + α + + + ξ + + + + + . + + + +

+

For the index of + α + + ξ + = 0, model + relxillion_ + nk is reduced to + relxill_ + nk. Our best-fit result from Model B4 indicates a positive value of + α + + ξ + , which shows the Δ + χ + 2 > 80 compared with Model B1, implying that the ionization parameter decreases as the radial coordinate + r increases within the actual disk. +

+ + + + The Best-fit Model +

Among the initial Models I1–I4 with different + relxill flavors, Model I2 + + shows the best-fit results modeled by a high-density disk, approximately 10 + 18 cm + −3. From the residuals of Models B1–B4 shown in Figure + 2, there are no significant differences among their fits. However, there is a slight elevation in the residuals above 30 keV among Models B1–B4. We attribute this behavior to a low count rate above 30 keV during the soft intermediate state. If we compare their + χ + 2, we see that Model B4 best fits MAXI J1803-298, and its value of the ionization index is near 0.5. However, comparing the minimum of + χ + 2 of different models is not a particularly robust method to determine which model is favored by the data. AIC (Akaike + 1974), which is already applied and discussed in Mall et al. ( + 2022), is a more reliable method to determine the best model in this case of a relatively small size of samples (AICc) for the number of free parameters. As we already have the minimum + χ + 2 for every model by + XSPEC, it can calculate the AICc directly by + + + + + + + AICc + = + + + χ + + + min + + + 2 + + + + + 2 + + + N + + + p + + + + + + + + 2 + + + N + + + p + + + + + + + N + + + p + + + + + 1 + + + + + + + + + N + + + b + + + − + + + N + + + p + + + − + 1 + + + + + + , + + + where + N + + p + is the number of free parameters and + N + + b + is the number of bins. The values of AICc obtained from Models A1–A3 and Models B1–B4 are shown in Table + 4. As a general criterion for AIC, models with ΔAICc > 5 are considered less favored by the data, while those with ΔAICc > 10 are ruled out and can be excluded from further analysis (Burnham & Anderson + 2004). +

+ + + +

AICc Values of the Fits with I1-I4 and A1–B6 of MAXI J1803-298 in Our Study

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Models + + + + + +
+ relxill flavor + I1I2I2 + + + I3I4⋯
+ 2670.02666.42642.02592.32607.0⋯
+
+
+ relxill_ + nk flavor ( + α + 13 = 0) + A1A2A3A4⋯⋯
+ 2633.02683.42642.42596.0⋯⋯
+
+
+ relxill_ + nk flavor ( + α + 13 to free) + B1B2B3B4B5B6
+ 2648.42715.02663.02634.02688.42654.4
+ + + +

Typeset image

+ + + +

By applying this selection criterion, we determine that among Models A1–A3, Model I2 + +, which incorporates a high-density disk, achieves the best fit. Among Models B1–B4, the + relxillion_ + nk model distinctly outperforms the other three in terms of fit quality. Although we found a precise constraint on + + + + + + + + α + + + 13 + + + = + + + 0.002 + + + − + 0.015 + + + + + 0.020 + + + + + with + relxillCP_ + nk, at a 3 + σ confidence level, Model B2 is deemed unsuitable for consideration. This is due to its fixed corona electron temperature at 100 keV and unrealistic estimates of certain parameters, such as + A + Fe and + + + + + + log + ξ + + + . Notably, when the + kT + + e + is allowed to vary, its best-fit value invariably maxes out at 400 keV. Consequently, the outcomes from Models A2 and B2 are excluded from our analysis, not merely because of their elevated reduced + χ + 2 values but also due to the low disk density values inserted. Considering the AICc values presented in Table + 4 and their plausible parameter estimates, Models B3 and B4 are affirmed as providing more reliable constraints on + α + 13. +

+ + + + Constraints on + <italic toggle="yes">α</italic> + <sub>13</sub> with MAXI J1803-298 + +

The constraints on the spin versus deformation parameter plane for Models B1–B4 after MCMC runs are shown in Figure + 7 ( + a + ∗ versus + α + 13). The most precise measurements for + α + 13 are measured as + + + + + + + + + α + + + 13 + + + = + + + 0.023 + + + − + 0.038 + + + + + 0.071 + + + + + from Model B3 with + relxillD_ + nk, and + + + + + + + + + α + + + 13 + + + = + + + 0.006 + + + − + 0.022 + + + + + 0.045 + + + , + + + from Model B4 with + relxillion_ + nk in the 3 + σ confidence level, respectively. These error bounds provided are purely statistical and do not include systematic errors. +

+

The most stringent constraint on + α + 13 to date has been obtained from the analysis of a NuSTAR observation of the BH in GX 339-4 in Tripathi et al. ( + 2021), and its 3 + σ measurement of Johannsen deformation parameter on + α + 13 is + + + + + + + + + α + + + 13 + + + = + − + + + 0.02 + + + − + 0.14 + + + + + 0.03 + + + . + + + +

+

We attribute the notable precision in determining + α + 13 in this investigation to the outstanding energy resolution and extensive effective area of the NICER detector, which excels in capturing reflection features. Furthermore, our fitting process is likely unaffected by jet activities in BHXBs. Leveraging time-dependent visibility modeling of a relativistic jet, Wood et al. ( + 2023) deduced the ejection date for MAXI J1803-298 as MJD 59348.08, predicting a cessation on 2021 May 23, in their radio flux density light curve. This timing corresponds with the data set analyzed in our study, suggesting a significant reduction in jet activities as the system transitioned to the soft state. We argue that such a pause in jet activities could be potentially one of the key factors in enhancing the precision of our + α + 13 constraints. +

+ + + + Iron Abundance +

The variable iron abundance ( + A + Fe) values in our employed Models I1–I4 and A1–B4 appear to be inconclusive; that is because the reliability of iron abundance determinations derived from the analysis of accretion disk reflection spectra is a well-known issue (Bambi et al. + 2021). In particular, estimates of supersolar iron abundances become contentious in scenarios where reflection signatures are influenced by high plasma densities, as detailed by García et al. ( + 2018), and the omission of returning radiation could lead to an underestimation of iron abundance (Riaz et al. + 2021). This concern is pertinent to our analysis of MAXI J1803-298. To mitigate potential biases in iron abundance estimates that could impact our constraints on + α + 13, we incorporated Models B5 (with Fe = 1) and B6 (with Fe = 5) into our fitting process. Its constraints on the spin parameter versus + α + 13 are shown in Figure + 7, which shows no significant change to our results. +

+ + + + + Concluding Remarks +

It is noted that the reflection models we employed are simplified in current versions; see Liu et al. ( + 2019) for the list of simplifications in the current version of the model. In this present work, our model assumes an infinitesimally thin disk, a simplification, whereas actual disks possess finite thickness (Taylor & Reynolds + 2018). To ascertain whether the disk configuration of MAXI J1803-298 aligns with a geometrically thin disk model, Jana et al. ( + 2022) have estimated its accretion rate to be within the range of 6%–10% + L + Edd based on the ionization parameter, which means it is nicely in the 5%–30% range required by a Novikov–Thorne disk with an inner edge at ISCO radius (Steiner et al. + 2010). Despite our choice to position the inner edge of the accretion disk at the ISCO radius during a soft intermediate state, there might still be a discrepancy between our assumption and the actual disk configuration. The ionization parameter + ξ is presumed to be either constant or subject to power-law decline across the disk. However, in reality, it is anticipated to exhibit a complex radial variation influenced by factors such as the X-ray flux from the corona and the disk density (Ingram et al. + 2019; Kammoun et al. + 2019). +

+

In this study, we employ a simplified broken power-law model to characterize the disk–corona geometry, recognizing that this represents a rudimentary approximation. In this approach, the calculation of the emissivity profile is omitted, while a consistent calculation based on the specific geometry between the corona and disk is reported by Dauser et al. ( + 2013). Future work could also consider the impact of returning radiation in this work to obtain a more precise parameter space (Mirzaev et al. + 2024). The launch of next-generation X-ray observatories in the coming years, such as Athena (Nandra et al. + 2013) and eXTP (Zhang et al. + 2019), have the potential to significantly enhance our understanding of accretion processes through their improved instrumentation. Athena will incorporate innovative microcalorimeter technology to provide unprecedented energy resolution around iron emission lines. Meanwhile, eXTP will expand our ability to probe accretion physics. The capabilities of these advanced missions offer the exciting possibility of placing tighter constraints on models, thereby deepening our comprehension of these energetic phenomena. +

+ + + + + Acknowledgments +

We thank the referee for constructive comments that helped us improve the quality of this paper. We thank Cosimo Bambi, Lijun Gou, and Yu Wang for constructive suggestions and fruitful discussions. This work was supported by the CAS “Light of West China” Program (grant No. 2021-XBQNXZ-005) and the National SKA Program of China (grant Nos. 2022SKA0120102 and 2020SKA0120300). M.G.N. acknowledges the support from the CAS Talent Program. L.C. acknowledges the support from the Tianshan Talent Training Program (grant No. 2023TSYCCX0099). M.G.N., A.T., and Y.F.H. acknowledge the support from the Xinjiang Tianchi Talent Program. Y.F.H. also acknowledges the support from the NSFC (grant No. 12233002) and the National Key R&D Program of China (2021YFA0718500). This work was partly supported by the Urumqi Nanshan Astronomy and Deep Space Exploration Observation and Research Station of Xinjiang (XJYWZ2303).

+ + + + + Appendix Information +

The Johannsen metric is a phenomenological deformation from the Kerr metric and is specifically designed for testing the Kerr BH hypothesis with electromagnetic observations of BHs (Johannsen + 2013). In Boyer–Lindquist-like coordinates, the line element is + + + + + + + + + + + + ds + + + 2 + + + = + − + + + + + + Σ + + + ˜ + + + ( + Δ + − + + + a + + + 2 + + + + + C + + + 2 + + + 2 + + + + + sin + + + 2 + + + θ + ) + + + + + B + + + 2 + + + + + + + + dt + + + 2 + + + + + + + + + + Σ + + + ˜ + + + + + Δ + + + C + + + 5 + + + + + + + + dr + + + 2 + + + + + + + Σ + + + ˜ + + + d + + + θ + + + 2 + + + + + + + − + + + + 2 + a + [ + ( + + + r + + + 2 + + + + + + + a + + + 2 + + + ) + + + C + + + 1 + + + + + C + + + 2 + + + − + Δ + ] + + + Σ + + + ˜ + + + + + sin + + + 2 + + + θ + + + + + B + + + 2 + + + + + + dtd + ϕ + + + + + + + + + + [ + + + + + + + r + + + 2 + + + + + + + a + + + 2 + + + + + + + 2 + + + + + C + + + 1 + + + 2 + + + − + + + a + + + 2 + + + Δ + + + sin + + + 2 + + + θ + ] + + + Σ + + + ˜ + + + + + sin + + + 2 + + + θ + + + + + B + + + 2 + + + + + + d + + + ϕ + + + 2 + + + , + + + + + + where + M is the BH mass and + a = + J/ + M is the BH angular momentum. + + + + + + + + Σ + + + ˜ + + + = + Σ + + + f + + + , and + + + + + + + + + + Σ + + + = + + + + + r + + + 2 + + + + + + + a + + + 2 + + + + + cos + + + 2 + + + θ + , + + + + + Δ + + + = + + + + + r + + + 2 + + + − + 2 + Mr + + + + + a + + + 2 + + + , + + + + + B + + + = + + + + + + + r + + + 2 + + + + + + + a + + + 2 + + + + + + + C + + + 1 + + + − + + + a + + + 2 + + + + + C + + + 2 + + + + + sin + + + 2 + + + θ + , + + + + + + in which the functions + f, + C + 1, + C + 2, and + C + 5 are defined as + + + + + + + + + + f + + + = + + + + + + ∑ + + + n + = + 3 + + + ∞ + + + + + + ϵ + + + n + + + + + + + + M + + + n + + + + + + + r + + + n + − + 2 + + + + + + , + + + + + + + C + + + 1 + + + + + = + + + 1 + + + + + + ∑ + + + n + = + 3 + + + ∞ + + + + + + α + + + 1 + n + + + + + + + + + + M + + + r + + + + + + + + n + + + , + + + + + + + C + + + 2 + + + + + = + + + 1 + + + + + + ∑ + + + n + = + 2 + + + ∞ + + + + + + α + + + 2 + n + + + + + + + + + + M + + + r + + + + + + + + n + + + , + + + + + + + C + + + 5 + + + + + = + + + 1 + + + + + + ∑ + + + n + = + 2 + + + ∞ + + + + + + α + + + 5 + n + + + + + + + + + + M + + + r + + + + + + + + n + + + , + + + + + + where { + ϵ + + n + }, { + α + 1 + n + }, { + α + 2 + n + }, and { + α + 5 + n + } are four infinite sets of deformation parameters without constraints from the Newtonian limit and solar system experiments. In this work, we have only considered the deformation parameter + α + 13, which has the strongest impact on the reflection spectrum, and all other deformation parameters are assumed to vanish. To work with a regular metric, some constraints are imposed on the BH spin parameter + a + ∗ and the deformation parameter + α + 13 + + + + + + + − + 1 + ≤ + + + a + + + ∗ + + + ≤ + 1 + , + + + + α + + + 13 + + + > + − + + + + 1 + + + 2 + + + + + + + + 1 + + + + + 1 + − + + + a + + + ∗ + + + 2 + + + + + + + + + 4 + + + , + + + as discussed in Tripathi et al. ( + 2018). +

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diff --git a/tests/stubdata/input/jats_springer_SoPh_s11207-023-02231-5_mathtex.xml b/tests/stubdata/input/jats_springer_SoPh_s11207-023-02231-5_mathtex.xml new file mode 100644 index 0000000..30b1693 --- /dev/null +++ b/tests/stubdata/input/jats_springer_SoPh_s11207-023-02231-5_mathtex.xml @@ -0,0 +1,6432 @@ + + +
+ + + + 11207 + 10.1007/11207.1573-093X + + Solar Physics + A Journal for Solar and Solar-Stellar Research and the Study of Solar-Terrestrial Physics + Sol Phys + + 0038-0938 + 1573-093X + + Springer Netherlands + Dordrecht + + + + s11207-023-02231-5 + 2231 + 10.1007/s11207-023-02231-5 + + + Research + + + + Derived Electron Densities from Linear Polarization Observations of the Visible-Light Corona During the 14 December 2020 Total Solar Eclipse + + + + http://orcid.org/0000-0002-9222-8648 + + Edwards + Liam + + 1 + a + + + + Bunting + Kaine A. + + 1 + + + http://orcid.org/0000-0002-6845-1698 + + Ramsey + Brad + + 1 + + + http://orcid.org/0000-0002-1366-678X + + Gunn + Matthew + + 1 + + + http://orcid.org/0000-0002-0500-5789 + + Fearn + Tomos + + 2 + + + + Knight + Thomas + + 1 + + + http://orcid.org/0000-0003-0581-1278 + + Muro + Gabriel Domingo + + 1 + 3 + + + http://orcid.org/0000-0002-6547-5838 + + Morgan + Huw + + 1 + + + + + https://ror.org/015m2p889 + grid.8186.7 + 0000 0001 2168 2483 + Department of Physics + Aberystwyth University + + SY23 3BZ + Ceredigion + Cymru + UK + + + + + https://ror.org/015m2p889 + grid.8186.7 + 0000 0001 2168 2483 + Department of Computer Science + Aberystwyth University + + SY23 3DB + Ceredigion + Cymru + UK + + + + + https://ror.org/05dxps055 + grid.20861.3d + 0000 0001 0706 8890 + Space Radiation Lab + California Institute of Technology + + 91125 + Pasadena + CA + USA + + + + + + lie6@aber.ac.uk + + + + 5 + 12 + 2023 + + + 12 + 2023 + + 298 + 12 + 140 + + + 17 + 11 + 2023 + + + 12 + 5 + 2023 + + + 17 + 11 + 2023 + + + 5 + 12 + 2023 + + + + © The Author(s) 2023 + 2023 + + + Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit + http://creativecommons.org/licenses/by/4.0/. + + + + + Abstract +

A new instrument was designed to take visible-light (VL) polarized brightness ( + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + ) observations of the solar corona during the 14 December 2020 total solar eclipse. The instrument, called the + Coronal Imaging Polarizer (CIP), consisted of a 16 MP CMOS detector, a linear polarizer housed within a piezoelectric rotation mount, and an f-5.6, 200 mm DSLR lens. Observations were successfully obtained, despite poor weather conditions, for five different exposure times (0.001 s, 0.01 s, 0.1 s, 1 s, and 3 s) at six different orientation angles of the linear polarizer ( + + + + + 0 + ∘ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$0^{\circ}$\end{document} + + + , + + + + + 30 + ∘ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$30^{\circ}$\end{document} + + + , + + + + + 60 + ∘ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$60^{\circ}$\end{document} + + + , + + + + + 90 + ∘ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$90^{\circ}$\end{document} + + + , + + + + + 120 + ∘ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$120^{\circ}$\end{document} + + + , and + + + + + 150 + ∘ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$150^{\circ}$\end{document} + + + ). The images were manually aligned using the drift of background stars in the sky and images of different exposure times were combined using a simple signal-to-noise ratio cut. The polarization and brightness of the local sky were also estimated and the observations were subsequently corrected. The + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + of the K-corona was determined using least-squares fitting and radiometric calibration was done relative to the + Mauna Loa Solar Observatory (MLSO) K-Cor + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + observations from the day of the eclipse. The + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + data was then inverted to acquire the coronal electron density, + + + + + n + e + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$n_{e}$\end{document} + + + , for an equatorial streamer and a polar coronal hole, which agreed very well with previous studies. The effect of changing the number of polarizer angles used to compute the + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + is also discussed and it is found that the results vary by up to + + + + ≈ + 13 + % + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\approx 13\%$\end{document} + + + when using all six polarizer angles versus only a select of three angles. +

+ + + Keywords + Eclipse observations + Polarization + Optical + Instrumentation and data management + Spectrum + Visible + + + + + + Coleg Cymraeg Cenedlaethol + http://dx.doi.org/10.13039/501100003507 + + + + + + + Science and Technology Facilities Council + http://dx.doi.org/10.13039/501100000271 + + + ST/N002962/1 + ST/N002962/1 + ST/N002962/1 + + + + + publisher-imprint-name + Springer + + + volume-issue-count + 12 + + + issue-article-count + 1 + + + issue-toc-levels + 0 + + + issue-pricelist-year + 2023 + + + issue-copyright-holder + Springer Nature B.V. + + + issue-copyright-year + 2023 + + + article-contains-esm + No + + + article-numbering-style + ContentOnly + + + article-registration-date-year + 2023 + + + article-registration-date-month + 11 + + + article-registration-date-day + 17 + + + article-toc-levels + 0 + + + toc-levels + 0 + + + volume-type + Regular + + + journal-product + ArchiveJournal + + + numbering-style + ContentOnly + + + article-grants-type + OpenChoice + + + metadata-grant + OpenAccess + + + abstract-grant + OpenAccess + + + bodypdf-grant + OpenAccess + + + bodyhtml-grant + OpenAccess + + + bibliography-grant + OpenAccess + + + esm-grant + OpenAccess + + + online-first + false + + + pdf-file-reference + BodyRef/PDF/11207_2023_Article_2231.pdf + + + pdf-type + Typeset + + + target-type + OnlinePDF + + + issue-type + Regular + + + article-type + OriginalPaper + + + journal-subject-primary + Physics + + + journal-subject-secondary + Astrophysics and Astroparticles + + + journal-subject-secondary + Atmospheric Sciences + + + journal-subject-secondary + Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics) + + + journal-subject-collection + Physics and Astronomy + + + open-access + true + + + + + + + Introduction +

A total solar eclipses (TSE) provides a unique opportunity to observe the visible-light (VL) corona down to the solar limb for a few minutes during totality, and allow continuous observations from the limb out to several solar radii. Not only does the Moon block out the solar disk, but it also lowers the local sky brightness along the eclipse path, which makes it perfect for observing the significantly fainter corona (Lang, + 2010). This lower coronal region ( + + + + < + 2 + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$< 2$\end{document} + + + + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + ) is the origin of the solar wind and is therefore crucial to observe in order to better understand how the solar wind is formed and accelerates to supersonic speeds (Habbal, + 2020; Strong et al., + 2017; McComas et al., + 2007). TSEs have been used to obtain valuable information about a variety of solar phenomena, including coronal streamers (Pasachoff and Rušin, + 2022), coronal mass ejections (CMEs) (Boe et al., + 2021c; Filippov, Koutchmy, and Lefaudeux, + 2020; Koutchmy et al., + 2004), coronal holes (Pasachoff and Rušin, + 2022), plasma flows (Sheeley and Wang, + 2014; De Pontieu et al., + 2009), prominences (Jejčič et al., + 2014), and coronal jets (Hanaoka et al., + 2018). Physical properties of the coronal plasma have also been studied extensively during TSEs; typically, temperature, density, and velocity (Del Zanna et al., + 2023; Muro et al., + 2023; Bemporad, + 2020; Reginald et al., + 2014; Habbal et al., + 2011, + 2010; Reginald, Davila, and Cyr C, + 2009; Habbal et al., + 2007). +

+

A coronagraph is required in order to observe the VL corona outside of a total solar eclipse. First designed by Bernard Lyot in the 1930s (Lyot and Marshall, + 1933), it consists of a telescope with an opaque disk that is positioned to block out the bright disk of the Sun. This is crucial because the photosphere is + + + + ≈ + + + 10 + + + 6 + + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\approx 10^{6}$\end{document} + + + times brighter than the corona itself. In fact, the Earth’s sky is also much brighter than the corona – of the order + + + + ≈ + + + 10 + + + 5 + + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\approx 10^{5}$\end{document} + + + times brighter at 20 + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + – therefore, any ground-based coronagraph, such as the + COronal Solar Magnetism Observatory’s (COSMO) + K-Coronagraph (K-Cor: Hou, de Wijn, and Tomczyk, + 2013), is affected by the Earth’s own atmosphere. To overcome this issue, several space-based coronagraphs have been launched in recent decades, for example, the + Large Angle Spectrometric Coronagraph (LASCO: Brueckner et al., + 1995) onboard the + Solar and Heliospheric Observatory (SOHO: Domingo, Fleck, and Poland, + 1995) and the + Sun-Earth Connection Coronal and Heliospheric Investigation (SECCHI: Howard et al., + 2008) COR1/2 instruments onboard the + Solar Terrestrial Relations Observatory (STEREO: Kaiser et al., + 2008). However, despite the unprecedented access to the corona they have given the field of solar physics, there is still a fundamental issue for any type of coronagraph to overcome, which is the stray light resulting from the diffraction of incoming light at the occulter edge. In order to mitigate this, most occulters will block not only the solar disk but also a portion of the very lower solar corona – out to around 1.5 + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + for internally occulted coronagraphs (Verroi, Frassetto, and Naletto, + 2008). One way to circumvent this issue is to increase the distance between the detector and the occulter, which is possible to achieve in space by the use of formation-flying cube satellites (e.g., the Association of Spacecraft for Polarimetric and Imaging Investigation of the Corona of the Sun, ASPIICS: Lamy et al., + 2010), however, these type of instruments are still in their infancy. As a result, observations of the inner corona during a TSE are unmatched in the VL regime. +

+

The VL corona is composed of light from several different sources, primarily from the scattering of photospheric light by free electrons in the corona and dust in the interplanetary plane, termed the K- and F-corona, respectively. In the case of the K-corona, the scattering process – known as Thomson scattering – produces a strongly tangentially polarized component to the total VL brightness (for an indepth overview of this mechanism see Inhester, + 2015), whereas the F-corona is considered to be unpolarized below + + + + ≈ + 3 + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\approx 3$\end{document} + + + + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + (Morgan and Habbal, + 2007). As a result, observing the VL corona below this height with a linear polarizer during a TSE can be considered to be a measurement of the K-coronal brightness only. There are also other types of brightness contributions to the total coronal brightness, namely the E-corona (emission) that consists of spectral-line emission from highly ionized atoms, but these are considered to be negligible for the purposes of this work. The K-coronal brightness component, + + + + + B + K + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$B_{K}$\end{document} + + + , represents the structure and amount of coronal plasma irrespective of its temperature, unlike EUV or X-ray observations. The K-coronal component of the polarized brightness ( + + + + + pB + k + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit {pB}_{k}$\end{document} + + + ) gives the electron density ( + + + + + n + e + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$n_{e}$\end{document} + + + ) that is calculated using an inversion method first developed by van de Hulst ( + 1950) and later improved upon by Hayes, Vourlidas, and Howard ( + 2001) and Quémerais and Lamy ( + 2002). Equation + 1 describes the relationship between the polarized brightness of the K-corona and the electron density that is used to acquire the electron density from the TSE images: + + + + + p + + B + k + + ∝ + + ∫ + LOS + + + n + e + + ( + r + ) + ⋅ + G + ( + s + , + ρ + ) + + d + s + , + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$$ pB_{k} \propto \int _{\mathrm{LOS}} n_{e}(r) \cdot G(s, \rho) \, ds, $$\end{document} + + + where + + + + G + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$G$\end{document} + + + is a geometrical weighting function, + + + + ρ + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\rho $\end{document} + + + is the distance between the Sun and the intercept between the line-of-sight (LOS) and the plane-of-sky (POS), and + + + + s + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$s$\end{document} + + + is the distance between the intercept point on the POS and an arbitrary point in the corona along the LOS (see Figure 1 in Quémerais and Lamy, + 2002 for more detail). This is a well-established technique and several studies have used this inversion of + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + to obtain coronal electron densities (e.g. Liang et al., + 2022; Bemporad, + 2020; Skomorovsky et al., + 2012; Hayes, Vourlidas, and Howard, + 2001; Raju and Abhyankar, + 1986; Saito, Poland, and Munro, + 1977). Several studies have also been conducted attempting to separate the K- and F-components of the solar corona (e.g. Boe et al., + 2021a; Fainshtein, + 2009; Morgan and Habbal, + 2007; Dürst, + 1982; Calbert and Beard, + 1972). Most of the previous studies involving TSE observations require some level of image processing as a result of several factors – primarily the sharp decrease in brightness with radial height from the Sun. For example, since the Moon and the Sun move relative to each other with respect to the background stars, all TSE images need to be coaligned and there are a number of different methods that can be used to do this. One of the most common of these methods over the past decade or so has been to use a modified phase-correlation technique by Druckmüller ( + 2009), whereas others have used more manual methods such as using the drift of background stars as they move relative to the TSE (Bemporad, + 2020). There are also many different image-processing techniques that have been developed to better reveal various structures and phenomena (Patel et al., + 2022; Qiang et al., + 2020; Morgan and Druckmüller, + 2014; Druckmüller, + 2013; Byrne et al., + 2012; Druckmüllerová, Morgan, and Habbal, + 2011). The outline of this paper is as follows. Section  + 1.1 describes the 2020 TSE in more detail. Section  + 2 summarizes the design of the instrument ( + 2.1), and the calibrating, processing, coaligning, and inversion to derive the coronal electron densities (Sections  + 2.2.3 –  + 2.2.7). Section  + 3 presents the results of the study, with Sections  + 4 and + 5 disseminating and concluding the results of this work, respectively. +

+ + 14 December 2020 Total Solar Eclipse +

The TSE on 14 December 2020 was observed by a team from Aberystwyth University at a site in Neuquén province, Argentina. The observation site was located at 39 + ∘ 42′ 40.4″ S, 70 + ∘ 23′ 57.6″ W, and an altitude of + + + + ≈ + 1082 +  m + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\approx 1082\text{ m}$\end{document} + + + (3550 ft). Totality lasted + + + + ≈ + 129 +  s + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\approx 129\text{ s}$\end{document} + + + with the time of maximum eclipse at 13:07:58 local time (16:07:58 UTC) and the apparent altitude of the Sun above the horizon was + + + + ≈ + + 75 + ∘ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\approx 75^{\circ}$\end{document} + + + . The weather conditions at the time of observation were not optimal with intermittent cloud cover and very strong gusts of up to 70 km/h that resulted in a lot of airborne dust. Furthermore, a small, wispy cloud passed across the Sun’s disk for + + + + ≈ + 12 +  s + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\approx 12\text{ s}$\end{document} + + + . This had an adverse effect on the quality of the data but, despite the conditions, the data captured during totality were still usable. Figure  + 1 shows the location of the observation site (white marker) along with the cloud cover at approximately the time of the eclipse. During this eclipse, a CME had erupted from the eastern limb of the Sun + + + + ≈ + 110 + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\approx 110$\end{document} + + +  min before totality, providing a truly unique opportunity to study CME dynamics right down to the solar limb. The LASCO CME catalog (Gopalswamy et al., + 2009) states that the CME first appeared in the C2 field-of-view (FOV) at 15:12:10 UT with an estimated linear speed of 437 km/s, mass of + + + + 3 + × + + + 10 + + + 12 + + +  kg + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$3 \times 10^{12}\text{ kg}$\end{document} + + + , and a central position angle of 121 + ∘. The CME is discussed in detail by Boe et al. ( + 2021c). + + + +

Satellite image of cloud cover above the observation site in Neuquén province, denoted by the white marker, taken at approximately 13:30 local time (Credit: Zoom Earth).

+ +

+ +

+ +

+ + + + Instrument Design and Data Processing + + The Coronal Imaging Polarizer (CIP) +

The instrument used to observe the corona during the total solar eclipse was a VL linear polarization imager designed and built at Aberystwyth University. The + Coronal Imaging Polarizer (CIP) – shown in Figure + 3 – was designed to be relatively cheap and simple to build, easy to assemble, and lightweight in order to be able to be relocated quickly on the day of an eclipse if necessary. It consisted of an objective lens, a VL bandpass filter, + 1 a linear polarizer + 2 housed in a rotating mount, + 3 and a CMOS sensor. + 4 The objective lens, an f-5.6, 200 mm focal length DSLR lens, can be adjusted to give different fields of view if required. The VL bandpass filter has a center wavelength of 520 nm (denoted by the vertical dashed black line in Figure  + 2) where transmission is + + + + > + 90 + % + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$>90\%$\end{document} + + + , and a bandwidth (FWHM) of 10 nm. Since the peak of the Sun’s emission is around 500 nm, the filter is well placed to collect the maximum amount of light possible. + + + +

Extinction ratio and transmissions for both the bandpass filter and linear polarizer measured by their respective manufacturers. The dotted horizontal lines correspond to the extinction ratio (blue) and transmission (red) of the polarizer at the center wavelength of the bandpass filter (data from Thorlabs.)

+ +

+ +

+ +

+

Traditionally, when taking VL polarization observations of the corona, a polarizer is either manually rotated through a set of polarization angles (typically 3 – 5) or several different instruments are set up, each designed to capture the light of a single polarizer orientation angle. In contrast, CIP used a piezoelectrically driven rotation mount from Thorlabs to automatically rotate the polarizer through six different polarization angles (0 + ∘, 30 + ∘, 60 + ∘, 90 + ∘, 120 + ∘, and 150 + ∘). The motorized rotation mount allows for 360 + ∘ rotation with a maximum rotation speed of 430 + ∘/s and has an accuracy of ± 0.4 + ∘, resulting in high precision and fast rotation. The energy requirement of the motor is very low, needing only a maximum of 5.5 V DC input with a typical current consumption of 800 and 50 mA during movement and standby, respectively. +

+

The camera used for CIP (see Figure  + 3) was the Horizon II – a 16 mega-pixel CMOS camera developed by Atik. It uses the Panasonic MN34230 4/3″ CMOS sensor with a + + + + 4644 + × + 3506 + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$4644 \times 3506$\end{document} + + + resolution and has a very low readout noise ( + + + + ≈ + 1 + +  e + − + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\approx 1\text{ e}^{-}$\end{document} + + + ). It is powered by a 12 V 2 A DC input and has a minimum exposure time of 18 μs and unlimited maximum exposure. It is also cooled via an internal fan and can maintain a + + + + Δ + T + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\Delta T$\end{document} + + + of −40  + ∘C, meaning that the camera can still maintain low thermal noise even at high ambient background temperatures. It is a black-and-white camera since using an RGB camera requires extra steps when processing the data (e.g. demosaicking), and the correction and alignment must be done individually for each RGB channel, see Bemporad ( + 2020), for example. In order for the instrument to run in the most efficient way possible, the data-collection process was fully automated. The rotation mount rotates the polarizer to a specific angle, then the camera collects a sequence of images of varying exposure times from 0.001 – 3 s, then the polarizer is rotated to the next angle, and the camera would run through the same sequence as before, and so on for all six polarization angles. The time taken for one complete cycle of data collection is around 30 s, which resulted in two full datasets and a third partial dataset. + + + +

+ The Coronal Imaging Polarizer (CIP) – + + A: + f-5.6, 200 mm objective lens. + + B: + housing containing the rotation mount, polarizer, and VL filter. + + C: + Atik Horizon II 16 MP CMOS camera. + + D: + housing for the interface board of the rotation mount. +

+ +

+ +

+ +

+ + + Data Processing + + Linearity +

The response of the imaging sensor to incoming light intensity is measured by using an integrating sphere, where the level of illumination in the sphere is measured by a photodiode (in Amps). The integrating sphere is not calibrated to give the light levels in SI units but it is linear, so if the photodiode current doubles the light level in the sphere is doubled. The illumination of the sphere was gradually increased by 1 μA until it reached the saturation point. Five measurements were taken and an average intensity was calculated for each photodiode reading. Figure  + 4 presents the results of this linearity test and it clearly shows that the sensor used in CIP had a linear response. The linearity begins to break down close to the saturation limit ( + + + + ≈ + 4096 + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\approx 4096$\end{document} + + + counts), which is to be expected and is accounted for when the images taken at different exposure times are combined for each polarization angle (Section  + 2.2.4). The linearity of the sensor was quantified using Equation + 2: + + + + + Linearity + + ( + % + ) + = + + + ( + MPD + + + MND + ) + + MI + + × + 100 + , + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$$ \mathrm{Linearity} \, (\%) = \frac{(\mathrm{MPD} + \mathrm{MND})}{\mathrm{MI}} \times 100, $$\end{document} + + + where MPD, MND, and MI are the maximum positive deviation, maximum negative deviation, and maximum intensity, respectively. The maximum positive and negative deviations were found from the line of best fit. This calculation was performed twice – once including the last data point where the linearity begins to break down, and a second time without including the aforementioned data point. These calculations result in linearities of 2.99% and 0.96%, respectively. Both of these values are excellent linearities since most CMOS sensors have linearities on the order of several percent (Wang and Theuwissen, + 2017). + + + +

Average pixel intensity as a function of the integrating sphere’s photodiode reading (black dots) and the calculated line of best fit (dashed line) giving an R + 2 value of 0.99956. +

+ +

+ +

+ +

+ + + Flat-Field and Dark-Frame Correction +

Five flat-field images were taken at an exposure time of 0.01 s for each polarization angle using an integrating sphere. A master flat-field image was then produced for each polarization angle using the open-source plugin AstroImageJ – an example of one of these is seen in Figure  + 5 along with an intensity profile taken at the midpoint of the image. + + + +

Master flat-field image for a polarization angle of 0 + ∘ (top) and a normalized intensity profile taken at the midpoint of the image shown by the red horizontal line (bottom). +

+ +

+ +

+ +

+

Two different types of dark-field images were attempted: first, setting the exposure time of the camera to zero and taking several pictures to obtain an average; and secondly, blocking the front of the instrument with the lens cap and running the full eclipse sequence five times. Unfortunately, the Atik Horizon II has a minimum exposure time of 18 μs so the first method was not able to be carried out. For the second method, the instrument was taken to a dark room with the lens cap taped over the lens. Several dark frames were taken in this way for each polarization angle and exposure time used in the eclipse sequence. It is expected that the mean values of the intensity (along with their standard deviations) should be similar for each polarization angle and exposure time and this is indeed what was seen. Figure  + 6 shows the dark noise, + + + + + σ + dark + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\sigma _{\mathrm{dark}}$\end{document} + + + , calculated by taking the average standard deviation of all dark frames taken at each exposure time and polarization angle. It is clear that pixels in the detector follow the same pattern and behave uniformly across all polarization angles. + + + +

Average dark noise for all polarization angles as a function of the exposure time.

+ +

+ +

+ +

+

Once the master flat-field and dark-frame images were produced, the raw eclipse images were calibrated using Equation + 3: + + + + + + C + + θ + , + t + + + = + + + ( + + R + + θ + , + t + + + − + + D + t + + ) + × + m + + + ( + + F + θ + + − + + D + t + + ) + + + , + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$$ C_{\theta ,t} = \frac{(R_{\theta ,t} - D_{t})\times m}{(F_{\theta} - D_{t})}, $$\end{document} + + + where + + + + + C + + θ + , + t + + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$C_{\theta ,t}$\end{document} + + + is the reduced image, + + + + + R + + θ + , + t + + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$R_{\theta ,t}$\end{document} + + + is the raw image taken at a specific polarization angle ( + + + + θ + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\theta $\end{document} + + + ) and exposure time ( + + + + t + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$t$\end{document} + + + ), + + + + + D + t + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$D_{t}$\end{document} + + + is the dark frame for that particular exposure, + + + + + F + θ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$F_{\theta}$\end{document} + + + is the flat field for that particular polarization angle, and + + + + m + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$m$\end{document} + + + is the image-averaged value of + + + + ( + + F + θ + + − + + D + t + + ) + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$(F_{\theta} - D_{t})$\end{document} + + + . At this stage, the scale of the image was calculated. The radius of the Moon was found to be + + + + 255.5 + ± + 0.5 + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$255.5 \pm 0.5$\end{document} + + + pixels by fitting a circle to points plotted along the lunar limb using ImageJ. One of the lowest exposure images was used to obtain this radius in order to reduce the brightness from the lower corona to obtain the most accurate value possible. The Moon’s apparent radius at the time of the eclipse was found to be 1000.145″ using the Stellarium software (Zotti et al., + 2021), therefore, the full-resolution images provided a spatial resolution of + + + + 3.92 + ± + 0.01 + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$3.92 \pm 0.01$\end{document} + + + arcsec/pixel. +

+ + + Image Coalignment +

After the initial calibration of the raw images with the dark and flat frames, they were coaligned before the images with different exposure times could be combined. This step was crucial because, although a motorized tracking mount was used to track the solar center, there were still some factors that needed to be accounted for and corrected. The two main factors were the high winds at ground level throughout the eclipse and the fact that the Moon was moving with respect to the Sun. The effect of the wind on the tracking mount can be seen in Figures  + 7 and + 8. As discussed in Section  + 1, there are several different methods of coaligning eclipse images such as the use of phase correlation (e.g. Druckmüller, + 2009) or by using the positions of stars visible in the exposures (e.g. Bemporad, + 2020). In this study, three stars were visible in the images taken at longer exposure times (see Figure  + 7) and were identified using Stellarium to be HD 157056 (star 1), HD 157792 (star 2), and HD 158643 (star 3), respectively. The images were initially coaligned using the brightest of these stars (HD 157056), which is star 1 in Figure  + 7, since its drift in both the + + + + x + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$x$\end{document} + + + - and + + + + y + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$y$\end{document} + + + -direction was fairly consistent (Figures  + 7 and + 8). For the shorter exposure images, where the stars were not visible, it was assumed that the star did not move much relative to its position in the 1 and 3 s exposures. Shifts in both the + + + + x + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$x$\end{document} + + + - and + + + + y + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$y$\end{document} + + + -pixels were calculated for each image, based on their respective exposure times, using the equations found, in Figure  + 8 and all of the images were coaligned accordingly. The images were then rebinned through + + + + 8 + × + 8 + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$8\times 8$\end{document} + + + pixel averaging to improve the signal quality, which reduced the resolution of the images to + + + + 31.25 + ± + 0.01 + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$31.25 \pm 0.01$\end{document} + + + arcsec/pixel. + + + +

Left: Locations of the three visible stars in a 3 s exposure time image. Right: Locations of the brightest pixel in star 1 for all 1 and 3 s exposures.

+ +

+ +

+ + + + +

Pixel drifts in both the + + + + x + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$x$\end{document} + + + - and + + + + y + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$y$\end{document} + + + -coordinates for star 1. The data points represent the pixel coordinate of the brightest pixel during the 1 and 3 s exposures. The darker and lighter shaded regions show one and two standard deviations, respectively. +

+ +

+ +

+ +

+ + + Image Combination +

The next step was to combine all the images of different exposure times for each individual polarization angle. First, all negative pixel values were set to zero and the images were normalized by their respective exposure times (DN/s) using Equation + 4: + + + + + + I + p + ′ + + = + + + I + p + + + Δ + + t + e + + + + , + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$$ I_{p}' = \frac{I_{p}}{\Delta t_{e}}, $$\end{document} + + + where + + + + + I + p + ′ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$I_{p}'$\end{document} + + + is the pixel intensity ( + + + + + I + p + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$I_{p}$\end{document} + + + ) for each polarization angle + + + + p + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$p$\end{document} + + + , normalized by exposure time ( + + + + Δ + + t + e + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\Delta t_{e}$\end{document} + + + ). Since the eclipse images have a very high dynamic range between the brightest and darkest pixels, they need to be combined together in a way that takes the pixel value itself into account. In the shorter exposure images, the inner coronal signal is strong but the outer coronal signal is too weak, whereas, in the longer-exposure images, the outer coronal signal is strong but the inner corona is overexposed. Thus, the images need to be combined in such a way that the inner and outer corona are adequately exposed in the final image. This is done by using a signal-to-noise ratio (SNR) cut based on the square root of the intensity, thus providing a lower boundary wherein any pixels with a value less than this threshold are excluded. The SNR cut used in this work was + + + + I + > + + I + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$I > \sqrt{I}$\end{document} + + + where + + + + I + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$I$\end{document} + + + is the intensity of the pixel. An upper threshold of 3900 counts is also used since the linearity of the CMOS sensor breaks down around this value (see Figure  + 4). This process was done for each image taken at a given polarization angle, which means that each composite image consists of two sets of different exposure times. +

+ + + Sky-Brightness Removal +

During a TSE, the local sky brightness is significantly lowered to + + + + ≈ + + 10 + + − + 9 + + + + – + + + 10 + + − + 10 + + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\approx 10^{-9}\,\text{--}\,10^{-10}$\end{document} + + +  B + ⊙ that allows unmatched VL observations of the corona out to greater heliocentric heights than without a TSE. However, the sky brightness during a TSE is not negligible and must be removed from the data. As Figure  + 9 shows, a box was defined in each corner of each combined TSE image. There is a considerable amount of noise present in the image as a result of the poor weather conditions, despite the rebinning to improve the signal-to-noise ratio. There is also an optical artifact that takes the form of two parallel lines spanning the width of the image, the cause of which is unknown but is most probably instrumental. The mean intensity in each box was then calculated and the process was repeated for each polarizer angle. The result of this can be seen in Figure  + 10 which seems to show that the intensity at the right-hand side of the image (corresponding to solar north) is greater than that of the left-hand side (corresponding to solar south). A map is then created to estimate the sky brightness at each point in the image by interpolating the mean counts between each of the four boxes for each polarizer angle separately. Two examples of these interpolated sky-brightness maps are shown in Figure  + 11 for 0 + ∘ and 90 + ∘. The polarization of the background sky lies at around 10% of the overall polarization of the image and this component is subsequently removed as a result of this sky-brightness removal step. Finally, the F-coronal component has a noticeable impact on + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + data from heliocentric heights of + + + + ≈ + 2.5 + + – + + 3.0 + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\approx 2.5\,\text{--}\,3.0$\end{document} + + + + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + (Boe et al., + 2021b) but since this study limited observations to a heliocentric height of 1.5  + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + , the F-coronal component can be neglected at such low heights. + + + +

Location of each box used to determine the sky brightness overlaid on the combined 0 + ∘ image. The image has not been rotated so that solar north aligns with the top of the image. L, T, B, and R correspond to the left, top, bottom, and right sides of the image, respectively. +

+ +

+ +

+ + + + +

Mean intensity for each box in Figure  + 9 at each polarizer angle. The fit to Equation + 5 is shown as a solid line for each of the four boxes where the results from the top-left, top-right, bottom-left, and bottom-right boxes are shown in black, red, green, and blue, respectively. The mean polarization of each box is also expressed as a percentage of the total polarization. +

+ +

+ +

+ + + + +

Examples of interpolated sky-brightness maps subtracted from the respective TSE images for polarizer orientation angles of 0 + ∘ (left) and 90 + ∘ (right). +

+ +

+ +

+ +

+ + + Determining the Polarized Brightness +

A standard inversion method used to acquire coronal electron densities was initially developed by van de Hulst ( + 1950) and further developed by Newkirk ( + 1967), Saito, Poland, and Munro ( + 1977), Hayes, Vourlidas, and Howard ( + 2001), and Quémerais and Lamy ( + 2002), among others. The original model assumes both spherical symmetry and that the + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + is produced purely by the Thomson scattering of photospheric light from free coronal electrons and it is proportional to the integrated LOS density of the electrons, as shown in Equation + 1. Most similar studies use three or four different polarization angles to determine the + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + – typically + + + + − + + 60 + ∘ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$-60^{\circ}$\end{document} + + + , 0 + ∘, 60 + ∘ (Hanaoka, Sakai, and Takahashi, + 2021), and 0 + ∘, 45 + ∘, 90 + ∘, 135 + ∘ (Vorobiev et al., + 2020). However, CIP captured images taken at different exposure times for six different polarization angles (0 + ∘, 30 + ∘, 60 + ∘, 90 + ∘, 120 + ∘, and 150 + ∘). As a result, in order to invert the calibrated intensities to find the + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + at each pixel, an approach involving least-squares fitting was used. For a polarizer angle, + + + + + θ + i + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\theta _{i}$\end{document} + + + , where + + + + i + = + 0 + , + 1 + , + 2 + , + … + , + n + − + 1 + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$i=0,1,2,\ldots,n-1$\end{document} + + + (with + + + + n + = + 6 + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$n=6$\end{document} + + + for this study), the measured intensity, + + + + + I + i + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$I_{i}$\end{document} + + + , is described by Equation + 5: + + + + + + I + i + + = + + I + 0 + + + + a + cos + 2 + + θ + i + + + + b + sin + 2 + + θ + i + + , + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$$ I_{i} = I_{0} + a \cos{2\theta _{i}} + b \sin {2\theta _{i}}, $$\end{document} + + + where the coefficients to be fitted are the unpolarized background intensity, + + + + + I + 0 + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$I_{0}$\end{document} + + + , and the polarized components, + + + + a + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$a$\end{document} + + + and + + + + b + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$b$\end{document} + + + . The polarized brightness is then given by + + + + + p + B + = + + + + a + 2 + + + + + b + 2 + + + + . + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$$ pB = \sqrt{a^{2}+b^{2}}. $$\end{document} + + + +

+

In order to find a solution for + + + + + I + 0 + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$I_{0}$\end{document} + + + and + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + at each pixel, the squared sum is then minimized as follows: + + + + + + ∑ + + i + = + 0 + + + n + − + 1 + + + + + [ + + I + i + + − + ( + + I + 0 + + + + a + cos + 2 + + θ + i + + + + b + sin + 2 + + θ + i + + ) + ] + + 2 + + . + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$$ \sum _{i=0}^{n-1} [I_{i} - (I_{0} + a \cos{2\theta _{i}} + b \sin {2 \theta _{i}})]^{2}. $$\end{document} + + + +

+

This least-squares fitting method was tested against the standard Mueller matrix-inversion method for three polarization angles (0 + ∘, 60 + ∘, and 120 + ∘) and it agreed within a few percent. As a result, CIP can theoretically take images of the corona for any number of polarizer angles in the future. +

+ + + Relative Radiometric Calibration +

A relative radiometric calibration step converts the polarized brightness measured by CIP (recorded as DN/s) to units relative to the mean solar brightness (MSB). The instrument used in this step was the + Mauna Loa Solar Observatory’s (MLSO) COSMO + K-Coronagraph (doi: + 10.5065/D69G5JV8) that provides + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + data with a field-of-view from 1.05 to + + + + ≈ + 3 + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\approx 3$\end{document} + + + + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + and a spatial resolution of 11.3”. The 10-min averaged K-Cor data was used for this calibration step with the first observation occurring at 17:56:41 UTC and the last at 18:10:20 UTC. Figure  + 12 shows the 10-minute averaged + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + observations taken by MLSO/K-Cor instrument on the day of the TSE, processed using the Multi-scale Gaussian Normalization technique (Morgan and Druckmüller, + 2014) in order to enhance the fine-scale coronal structure, and the concentric rings represent heliocentric heights of 1.0, 1.5, 2.0, and 2.5  + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + , respectively. It is clear that consistent + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + data is restricted to + + + + ≈ + 1.7 + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\approx 1.7$\end{document} + + + + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + with the data extending further out in the equatorial regions. As a result, the relative radiometric calibration in this study was limited to a heliocentric height of 1.5  + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + . + + + +

10-min averaged + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + observations taken by MLSO/K-Cor instrument on the day of the eclipse, processed using the Multi-scale Gaussian Normalization technique, with the concentric circles corresponding to heliocentric heights of 1.0, 1.5, 2.0, and 2.5  + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + , respectively. +

+ +

+ +

+ +

+

The images from both CIP and K-Cor are then coaligned and an intensity profile is taken for a thin slice of the corona at a specified height for both images. Some examples of these intensity profiles can be seen in Figure  + 13 for a range of heliocentric heights. A calibration factor is temporarily applied to the CIP data in order to visualize both latitudinal profiles on the same axis scale, which is denoted in each plot as CF. The mean ratio of the data from both instruments is then computed at intervals of 0.025  + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + between 1.1 and 1.5  + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + and these values are shown in Figure  + 14. This linear increase in the intensity ratio with height is then applied to the TSE data, thus converting the + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + observations taken with CIP from units of DN/s to units of solar brightness ( + + + + + B + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$B_{\odot }$\end{document} + + + ). A crosscorrelation was also performed on the intensity profiles to find the angle needed to rotate the CIP data in order to align it with that taken by K-Cor (i.e. solar north upwards). + + + +

Latitudinal distribution of intensity profiles from both CIP (red) and K-Cor (black) for a range of heliocentric heights. A calibration factor (CF), noted in each plot, is temporarily applied to the CIP data in order to see both profiles on the same axis scale.

+ +

+ +

+ + + + +

Mean intensity ratio between the CIP and K-Cor intensity profiles for each height interval (black) along with the linear fit used to perform the relative radiometric calibration of the TSE data (red).

+ +

+ +

+ +

+ + + + + Results +

Figure  + 15 shows the final calibrated + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + image of the 14 December 2020 TSE. It has been further processed using the Multi-Scale Gaussian Normalization (MGN) technique to enhance the fine-scale coronal detail. Due to the poor viewing conditions at the observation site adversely affecting the data, the data analysis has been limited to a heliocentric height of 1.5  + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + , but the image in Figure  + 15 has been extended out to 2  + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + to show more of the corona. + + + +

Final MGN-processed + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + image of the 14 December 2020 TSE after relative radiometric calibration with respect to MLSO/K-Cor. +

+ +

+ +

+ +

+

Figure  + 16 shows a comparison of + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + data as a function of heliocentric height for the north polar coronal hole and west equatorial streamer chosen for this study (at position angles 12 + ∘ and 245 + ∘ counterclockwise from solar north, respectively). As would be expected, the + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + is highest in the solar equatorial region and lower in the polar region. It is clear to see that the relative radiometric calibration with respect to MLSO/K-Cor is optimal at the equator but the polar + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + observed by CIP is still greater than that of K-Cor. This is believed to be due to the poor weather conditions at the time of observation having a greater effect on the fainter coronal signal in the polar regions. However, the K-Cor instrument has to contend with a much higher sky brightness in comparison to TSE observations and Boe et al. ( + 2021a) found that K-Cor data were unreliable as low as + + + + ≈ + 1.2 + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\approx 1.2$\end{document} + + + or 1.3  + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + in the coronal hole regions when compared with TSE data, which could also explain the discrepancy between the two instruments. There could also be some wavelength-dependent effect causing the discrepancy since CIP’s central wavelength is at 520 nm and K-Cor is centered in the far red ( + + + + ≈ + 800 +  nm + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\approx 800\text{ nm}$\end{document} + + + ). It is, therefore, difficult to say with absolute certainty what is causing the discrepancy. + + + +

Calibrated and corrected + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + profiles from CIP (black) and K-Cor (red) for both the polar coronal hole and equatorial streamer. +

+ +

+ +

+ +

+

Figure  + 17 shows the latitudinal distribution of the + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + for heliocentric heights of 1.2, 1.3, 1.4, and 1.5  + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + in black, red, blue, and green, respectively. The + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + decreases with increasing distance from the limb, which is to be expected, and all four latitudinal distributions have a similar shape, but there is a noticeable offset between corresponding maxima and minima as heliocentric height increases. The dotted vertical lines represent the position angles at which the densities are calculated for the polar coronal hole and the equatorial streamer, as well as the position angle for the CME where its presence becomes increasingly apparent in the 1.4 and 1.5  + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + distributions. + + + +

Latitudinal distribution of + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + for the heliocentric heights of 1.2 (black), 1.3 (red), 1.4 (blue), and 1.5  + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + (green). Vertical dotted lines are included to represent the position angles for the polar coronal hole (left), CME (middle), and equatorial streamer (right). +

+ +

+ +

+ +

+

Figure  + 18 shows the coronal electron densities, derived by inverting the + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + , as a function of heliocentric height for both the polar coronal hole (left) and equatorial streamer (right). Both plots also show comparisons to data from previous works that agree very well with the data from this study. As expected, the density of the streamer is greater than that of the coronal hole by an average factor of + + + + ≈ + 4 + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\approx 4$\end{document} + + + between 1.1 – 1.5  + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + . For the coronal-hole comparison, density profiles from Baumbach ( + 1937), Doyle, Teriaca, and Banerjee ( + 1999), and Guhathakurta et al. ( + 1999) were used. The latter two in particular were selected because they represent observations of polar coronal holes taken at the start of Solar Cycle 24 (solar minimum) and, since the 2020 TSE occurred exactly a year after the start of Solar Cycle 25, they are reasonable comparisons to make. For the equatorial streamer, the densities obtained in this study are compared with Gibson et al. ( + 1999), Liang et al. ( + 2022), and Gallagher et al. ( + 1999). Again, these are reasonable comparisons to make since the compared works represent observations of a streamer (Gibson et al., + 1999) and equatorial regions (Liang et al., + 2022; Gallagher et al., + 1999) taken at or near solar minimum. + + + +

Coronal electron densities as a function of heliocentric height for the coronal hole (left) compared with Baumbach ( + 1937), Doyle, Teriaca, and Banerjee ( + 1999), and Guhathakurta et al. ( + 1999), and the equatorial streamer (right) compared with Gibson et al. ( + 1999), Liang et al. ( + 2022), and Gallagher et al. ( + 1999). The black data points show the densities acquired by inverting the + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + and the solid black line shows the fit to Equation + 9. +

+ +

+ +

+ +

+ + + Discussion + + Number of Polarizer Angles +

Typically, similar studies and space-based coronagraphs use polarizer angles of 0 + ∘, 60 + ∘, and 120 + ∘ to infer the coronal electron density. As mentioned previously, CIP is designed to efficiently take polarized observations for any number of predefined polarizer angles. For this study, six polarizer angles were chosen in an attempt to see if increasing the number of polarizer angles leads to better constraints on the + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + observations and the inferred coronal electron densities. Figure  + 19 shows the mean percentage difference between the coronal electron densities derived using all six polarizer angles (henceforth referred to as angle set A) and only the 0 + ∘, 60 + ∘, and 120 + ∘ polarizer angles (angle set B) with the error bars representing the standard error in the mean. The difference is shown as a function of the position angle between the heliocentric heights 1.1 – 1.5  + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + and ranges from + + + + − + 12.8 + % + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$-12.8\%$\end{document} + + + to 9.44% with the overall mean at 0.56%. For the position angles chosen to represent the coronal hole and equatorial streamer, the mean difference is −8.26% and 8.04%, respectively. This is a very important result. The difference, which is on the order of 10%, implies that the accuracy of + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + observations can benefit greatly from increasing the number of polarizer angles, with direct improvements to density diagnostics. This error has significant implications for the design and development of future TSE observing instruments and, more importantly, space-based coronagraphs. + + + +

Mean difference between the coronal electron densities derived using all six polarizer angles (angle set A) and only the 0 + ∘, 60 + ∘, and 120 + ∘ polarizer angles (angle set B). The mean difference ranges from + + + + ≈ + − + 13 + % + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\approx -13\%$\end{document} + + + to + + + + 10 + % + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$10\%$\end{document} + + + and the mean in the difference is also shown (red line). The error bars show the standard error in the mean. +

+ +

+ +

+ +

+

Figure  + 20 shows the difference in density between both angle sets A (red) and B (black) as a function of heliocentric height for both the coronal hole (left) and equatorial streamer (right). It is clear to see that the densities found using set A (all polarizer angles) are lower in the coronal hole and higher in the equatorial streamer in comparison to those found using only set B (0 + ∘, 60 + ∘, 120 + ∘). Furthermore, the difference between the two calculated densities clearly becomes greater with increasing heliocentric height, which is shown more clearly in Figure  + 21. Since the difference increases with increasing heliocentric height, it is unfortunate that the weather conditions on the day of the TSE were suboptimal because it would be interesting to see how this difference evolves beyond the inner coronal region. However, the existence of this difference confirms that changing the number of polarizer angles used does provide a better constraint on the inferred coronal electron densities, particularly for heliocentric heights above + + + + ≈ + 1.5 + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\approx 1.5$\end{document} + + + + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + . This result has even more important implications for space-based coronagraphs, such as LASCO C2 whose field-of-view begins at 1.5  + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + and extends out to 6  + + + + + R + ⊙ + + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathrm {R}_{\odot }$\end{document} + + + . For the remainder of the analysis of these results, set A (all polarizer angles) was used. + + + +

Difference in coronal electron densities between using + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + data from angle sets A (red) and B (black) for both the coronal hole and equatorial streamer. +

+ +

+ +

+ + + + +

Mean difference (expressed as a percentage) between using + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + data from angle sets A and B for both the coronal hole (black) and equatorial streamer (red) with the error bars representing one standard deviation in both cases. +

+ +

+ +

+ +

+ + + Radial Density Fitting +

Several studies (Saito, Poland, and Munro, + 1977; Guhathakurta et al., + 1999; Hayes, Vourlidas, and Howard, + 2001; Thernisien and Howard, + 2006) state that the radial dependence of the coronal electron density can be expressed in the form of a polynomial: + + + + + + N + e + + ( + r + ) + = + + Σ + i + + + α + i + + + r + + − + i + + + , + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$$ N_{e} (r) = \Sigma _{i} \alpha _{i} r^{-i}, $$\end{document} + + + where + + + + r + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$r$\end{document} + + + is given in solar radii and + + + + α + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\alpha $\end{document} + + + and + + + + β + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\beta $\end{document} + + + are coefficients fitted to the data. Since the analysis of the data obtained in this study extended from below + + + + ≈ + 1.1 + + – + + 1.5 + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\approx 1.1\,\text{--}\,1.5$\end{document} + + +  R + ⊙, three terms are sufficient to provide a good fit to the data, thus, the equation used to fit the data and determine the coefficients was: + + + + + + N + e + + ( + r + ) + = + a + + r + + − + b + + + + + c + + r + + − + d + + + + + e + + r + + − + f + + + . + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$$ N_{e}(r) = ar^{-b} + cr^{-d} + er^{-f}. $$\end{document} + + + +

+

The coefficients for both coronal features of interest are shown in Table  + 1 and they agree well with previous studies. + + + +

Coefficients for Equation + 9. +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +

+ a +

+ 		+

+ b +

+ 		+

+ c +

+ 		+

+ d +

+ 		+

+ e +

+ 		+

+ f +

+
+

Coronal Hole

+ 		+

1.12 × 10 + 6 +

+ 		+

0.107

+ 		+

2.27 × 10 + 8 +

+ 		+

10.4

+ 		+

1.50 × 10 + 8 +

+ 		+

560

+
+

Equatorial Streamer

+ 		+

8.56 × 10 + 5 +

+ 		+

83.8

+ 		+

3.80 × 10 + 7 +

+ 		+

7.91

+ 		+

4.70 × 10 + 8 +

+ 		+

7.91

+
+ +

+ + + + Conclusion +

The primary aim of this study was to present a new design for a lightweight polarization instrument capable of observing using more polarization angles than is typically used, called the + Coronal Imaging Polarizer (CIP). The instrument was designed and built at Aberystwyth University to observe the polarized brightness of the solar corona during the 14 December 2020 TSE for six orientation angles of the linear polarizer. Due to the design of the instrument, it is very easy to increase or decrease the number of polarization angles depending on the time available during the totality phase of an eclipse. One of the main design elements of CIP was that it would be lightweight in order to be easily transported to an observing site. This element was not only met but was also needed as the team had to relocate to a new observing site on the morning of the eclipse. The new site was a few hours’ drive from the original site and with the instrument itself weighing only + + + + ≈ + 1.59 +  kg + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\approx 1.59\text{ kg}$\end{document} + + + , the bulk of the transporting was due to the tripod and tracking mount. Consequently, the entire instrument was easily transported and the simplicity of the design meant that the team could set it up very quickly at the new observing site. However, the weather conditions at the new site still impacted the data – primarily the strong gusts of wind that can be clearly seen in Figure  + 7, along with airborne dust and high humidity. The instrument was also designed to capture data fully autonomously and efficiently and, again, this aim was met. +

+

The raw VL images were successfully corrected using flat-field and dark frame subtraction (see Section  + 2.2.2) and the corrected images were then manually coaligned by tracking the drift of a star in the background of the data throughout the duration of totality (see Section  + 2.2.3). The images were then rebinned to be + + + + 8 + × + 8 + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$8\times8$\end{document} + + + times smaller in order to improve the signal-to-noise ratio that might not be needed in future eclipses given better viewing conditions. The images of different exposure times were combined by using a simple signal-to-noise ratio cut to create composite images of the eclipse for each individual angle of polarization (see Section  + 2.2.4). These composite images were then combined to give the + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + image using a simple least-squares fitting method (see Section  + 2.2.6) and relative radiometric calibration was successfully done by crosscalibration with MLSO/K-COR (see Section  + 2.2.7). The final + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + image was then inverted, assuming a locally spherically symmetric corona, to produce radial density profiles for a polar coronal hole and an equatorial streamer. These densities were then compared with previous studies and were found to be in good agreement (see Section  + 3). The key finding of this study was the effect that varying the number of polarizer angles has on the inferred coronal electron densities. Densities were inferred for two datasets: one consisting of images taken at all six polarizer angles and the other with only three polarizer angles, which resulted in a difference of approximately ± 10% in the densities. It is hoped that CIP can be sent to observe future TSEs to provide better quality constraints on + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + and coronal electron densities and build upon the results of this study, particularly with regard to studying the impact of more polarization angles on the quality of TSE data. The authors plan to observe the “Great North American Eclipse” on 8 April 2024 with CIP but using 12 polarizer angles instead of 6 due to an extended totality of over 4 min. This should help provide better constraints on the effect of increasing the number of polarizer angles on the inferred coronal electron densities. +

+ + + + + Acknowledgments +

A special note of appreciation must go to the members of the team who braved the COVID-19 pandemic in order to observe this eclipse, without whom this work would not be possible. We acknowledge the valuable advice of the Solar Wind Sherpa team of collaborators led by Prof Shadia Habbal at the University of Hawaii. This research has made use of the Stellarium planetarium.

+ + + Author contributions +

L.E. wrote the main manuscript text and performed the majority of the data analysis and processing. K.B., B.R., and G.M. collected the data at the eclipse. T.F. wrote the automation code for the instrument to take the data. T.K. contributed to the mathematical formulation of the calculation of + + + + p + B + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$pB$\end{document} + + + . M.G. contributed to the design of the instrument and assembled it. H.M. contributed to the writing of the manuscript, data analysis, image processing, and reviewed the manuscript. +

+ + + Funding +

We acknowledge studentship funding from the Coleg Cymraeg Cenedlaethol, STFC grant ST/N002962/1 and STFC studentships ST/T505924/1 and ST/V506527/1 to Aberystwyth University that made this instrument and work possible.

+ + + Data Availability +

The data generated and/or analyzed during the current study are available from the corresponding author upon reasonable request. Some of the + + + + pB + + \documentclass[12pt]{minimal} + \usepackage{amsmath} + \usepackage{wasysym} + \usepackage{amsfonts} + \usepackage{amssymb} + \usepackage{amsbsy} + \usepackage{mathrsfs} + \usepackage{upgreek} + \setlength{\oddsidemargin}{-69pt} + \begin{document}$\mathit{pB}$\end{document} + + + data and coronal images used in this work are courtesy of the Mauna Loa Solar Observatory, operated by the High Altitude Observatory, as part of the National Center for Atmospheric Research (NCAR). NCAR is supported by the National Science Foundation. +

+ + + Declarations + + Competing interests +

The authors declare no competing interests.

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diff --git a/tests/stubdata/output/jats_apj_967_1_35.json b/tests/stubdata/output/jats_apj_967_1_35.json new file mode 100644 index 0000000..957141a --- /dev/null +++ b/tests/stubdata/output/jats_apj_967_1_35.json @@ -0,0 +1,296 @@ +{ + "abstract": { + "textEnglish": "Iron line spectroscopy has been one of the leading methods not only for measuring the spins of accreting black holes but also for testing fundamental physics. Basing on such a method, we present an analysis of a data set observed simultaneously by NuSTAR and NICER for the black hole binary candidate MAXI J1803-298, which shows prominent relativistic reflection features. Various relxill_ nk flavors are utilized to test the Kerr black hole hypothesis. The results obtained from our analysis provide stringent constraints on Johannsen deformation parameter \u03b1 13 with the highest precise to date, namely \u03b1 13 = 0.023 \u2212 0.038 + 0.071 from relxillD_ nk and \u03b1 13 = 0.006 \u2212 0.022 + 0.045 from relxillion_ nk, respectively, in 3 \u03c3 credible lever, where the Johannsen metric reduces to the Kerr metric when \u03b1 13 vanishes. Furthermore, we investigate the best model fit results using Akaike information criterion and assess its systematic uncertainties." + }, + "authors": [ + { + "affiliation": [ + { + "affPubID": "affiliation01", + "affPubRaw": "Xinjiang Astronomical Observatory, CAS, 150 Science-1 Street, Urumqi 830011, People's Republic of China" + }, + { + "affPubID": "affiliation02", + "affPubRaw": "College of Astronomy and Space Science, University of Chinese Academy of Sciences, No.1 Yanqihu East Road, Beijing 101408, People's Republic of China" + } + ], + "name": { + "given_name": "Jie", + "surname": "Liao" + } + }, + { + "affiliation": [ + { + "affPubID": "affiliation01", + "affPubRaw": "Xinjiang Astronomical Observatory, CAS, 150 Science-1 Street, Urumqi 830011, People's Republic of China" + } + ], + "attrib": { + "orcid": "0000-0001-6113-0317" + }, + "name": { + "given_name": "M.", + "surname": "Ghasemi-Nodehi" + } + }, + { + "affiliation": [ + { + "affPubID": "affiliation01", + "affPubRaw": "Xinjiang Astronomical Observatory, CAS, 150 Science-1 Street, Urumqi 830011, People's Republic of China" + }, + { + "affPubID": "affiliation03", + "affPubRaw": "Key Laboratory of Radio Astronomy, CAS, 150 Science 1-Street, Urumqi 830011, People's Republic of China" + }, + { + "affPubID": "affiliation04", + "affPubRaw": "Xinjiang Key Laboratory of Radio Astrophysics, 150 Science 1-Street, Urumqi 830011, People's Republic of China" + } + ], + "attrib": { + "email": "cuilang@xao.ac.cn", + "orcid": "0000-0003-0721-5509" + }, + "name": { + "given_name": "Lang", + "surname": "Cui" + } + }, + { + "affiliation": [ + { + "affPubID": "affiliation01", + "affPubRaw": "Xinjiang Astronomical Observatory, CAS, 150 Science-1 Street, Urumqi 830011, People's Republic of China" + }, + { + "affPubID": "affiliation05", + "affPubRaw": "George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, TX 77843-4242, USA" + } + ], + "attrib": { + "orcid": "0000-0002-3960-5870" + }, + "name": { + "given_name": "Ashutosh", + "surname": "Tripathi" + } + }, + { + "affiliation": [ + { + "affPubID": "affiliation06", + "affPubRaw": "School of Astronomy and Space Science, Nanjing University, Nanjing 210023, People's Republic of China" + }, + { + "affPubID": "affiliation07", + "affPubRaw": "Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education, Nanjing 210023, People's Republic of China" + } + ], + "attrib": { + "orcid": "0000-0001-7199-2906" + }, + "name": { + "given_name": "Yong-Feng", + "surname": "Huang" + } + }, + { + "affiliation": [ + { + "affPubID": "affiliation01", + "affPubRaw": "Xinjiang Astronomical Observatory, CAS, 150 Science-1 Street, Urumqi 830011, People's Republic of China" + }, + { + "affPubID": "affiliation03", + "affPubRaw": "Key Laboratory of Radio Astronomy, CAS, 150 Science 1-Street, Urumqi 830011, People's Republic of China" + }, + { + "affPubID": "affiliation04", + "affPubRaw": "Xinjiang Key Laboratory of Radio Astrophysics, 150 Science 1-Street, Urumqi 830011, People's Republic of China" + } + ], + "attrib": { + "orcid": "0000-0001-9815-2579" + }, + "name": { + "given_name": "Xiang", + "surname": "Liu" + } + } + ], + "copyright": { + "statement": "\u00a9 2024. The Author(s). Published by the American Astronomical Society.", + "status": true + }, + "editorialHistory": { + "acceptedDate": "2024-04-04", + "receivedDates": [ + "2024-02-01" + ], + "revisedDates": [ + "2024-04-02" + ] + }, + "funding": [ + { + "agencyid": { + "idschema": "doi", + "idvalue": "https://doi.org/10.13039/501100013494" + }, + "agencyname": "CAS \u2223 West Light Foundation, Chinese Academy of Sciences (West Light Foundation of CAS)\n\t\t\t\t\t\t\n", + "awardnumber": "2021-XBQNXZ-005" + } + ], + "keywords": [ + { + "keyID": "887", + "keyString": "Kerr metric", + "keySystem": "UAT" + }, + { + "keyID": "641", + "keyString": "General relativity", + "keySystem": "UAT" + }, + { + "keyID": "98", + "keyString": "Astrophysical black holes", + "keySystem": "UAT" + }, + { + "keyID": "1611", + "keyString": "Stellar mass black holes", + "keySystem": "UAT" + }, + { + "keyID": "1810", + "keyString": "X-ray astronomy", + "keySystem": "UAT" + } + ], + "openAccess": { + "license": "\n\nOriginal content from this work may be used under the terms of the\n\t\t\t\t\t\tCreative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.\n\t\t\t\t\t", + "licenseURL": "http://creativecommons.org/licenses/by/4.0/", + "open": true + }, + "pagination": { + "electronicID": "35", + "pageCount": "12" + }, + "persistentIDs": [ + { + "DOI": "10.3847/1538-4357/ad3c2b" + } + ], + "pubDate": { + "electrDate": "2024-05-16", + "printDate": "2024-05-01" + }, + "publication": { + "ISSN": [ + { + "issnString": "0004-637X", + "pubtype": "ppub" + }, + { + "issnString": "1538-4357", + "pubtype": "epub" + } + ], + "issueNum": "1", + "pubName": "The Astrophysical Journal", + "pubYear": "2024", + "publisher": "The American Astronomical Society", + "volumeNum": "967" + }, + "publisherIDs": [ + { + "Identifier": "apjad3c2b", + "attribute": "publisher-id" + }, + { + "Identifier": "ad3c2b", + "attribute": "manuscript" + }, + { + "Identifier": "AAS52670", + "attribute": "other" + } + ], + "recordData": { + "createdTime": "", + "loadFormat": "JATS", + "loadLocation": "", + "loadType": "fromFile", + "parsedTime": "", + "recordOrigin": "" + }, + "references": [ + " Abbott B. 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Wang W. 2023 MNRAS 523 4394 2023MNRAS.523.4394Z 10.1093/mnras/stad1656 " + ], + "title": { + "textEnglish": "Tests of the Kerr Hypothesis with MAXI J1803-298 Using Different RELXILL_NK Flavors" + } +} diff --git a/tests/stubdata/output/jats_springer_EPJC_s10052-023-11699-1.json b/tests/stubdata/output/jats_springer_EPJC_s10052-023-11699-1.json index ac73e8d..a19ff9e 100644 --- a/tests/stubdata/output/jats_springer_EPJC_s10052-023-11699-1.json +++ b/tests/stubdata/output/jats_springer_EPJC_s10052-023-11699-1.json @@ -1,6 +1,6 @@ { "abstract": { - "textEnglish": "The flavour-tagging algorithms developed by the ATLAS Collaboration and used to analyse its dataset of s = 13 \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{s} = 13$$\\end{document} TeV pp collisions from Run 2 of the Large Hadron Collider are presented. These new tagging algorithms are based on recurrent and deep neural networks, and their performance is evaluated in simulated collision events. These developments yield considerable improvements over previous jet-flavour identification strategies. At the 77% b-jet identification efficiency operating point, light-jet (charm-jet) rejection factors of 170 (5) are achieved in a sample of simulated Standard Model t t \u00af \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t\\bar{t}$$\\end{document} events; similarly, at a c-jet identification efficiency of 30%, a light-jet ( b-jet) rejection factor of 70 (9) is obtained." + "textEnglish": "The flavour-tagging algorithms developed by the ATLAS Collaboration and used to analyse its dataset of s = 13 TeV pp collisions from Run 2 of the Large Hadron Collider are presented. These new tagging algorithms are based on recurrent and deep neural networks, and their performance is evaluated in simulated collision events. These developments yield considerable improvements over previous jet-flavour identification strategies. At the 77% b-jet identification efficiency operating point, light-jet (charm-jet) rejection factors of 170 (5) are achieved in a sample of simulated Standard Model t t \u00af events; similarly, at a c-jet identification efficiency of 30%, a light-jet ( b-jet) rejection factor of 70 (9) is obtained." }, "authors": [ { diff --git a/tests/stubdata/output/jats_springer_EPJC_s10052-023-11733-2.json b/tests/stubdata/output/jats_springer_EPJC_s10052-023-11733-2.json index 3c59cde..3afa500 100644 --- a/tests/stubdata/output/jats_springer_EPJC_s10052-023-11733-2.json +++ b/tests/stubdata/output/jats_springer_EPJC_s10052-023-11733-2.json @@ -1,6 +1,6 @@ { "abstract": { - "textEnglish": "The Pandora Software Development Kit and algorithm libraries provide pattern-recognition logic essential to the reconstruction of particle interactions in liquid argon time projection chamber detectors. Pandora is the primary event reconstruction software used at ProtoDUNE-SP, a prototype for the Deep Underground Neutrino Experiment far detector. ProtoDUNE-SP, located at CERN, is exposed to a charged-particle test beam. This paper gives an overview of the Pandora reconstruction algorithms and how they have been tailored for use at ProtoDUNE-SP. In complex events with numerous cosmic-ray and beam background particles, the simulated reconstruction and identification efficiency for triggered test-beam particles is above 80% for the majority of particle type and beam momentum combinations. Specifically, simulated 1 GeV/ c charged pions and protons are correctly reconstructed and identified with efficiencies of 86.1 \u00b1 0.6 \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm 0.6$$\\end{document} % and 84.1 \u00b1 0.6 \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm 0.6$$\\end{document} %, respectively. The efficiencies measured for test-beam data are shown to be within 5% of those predicted by the simulation." + "textEnglish": "The Pandora Software Development Kit and algorithm libraries provide pattern-recognition logic essential to the reconstruction of particle interactions in liquid argon time projection chamber detectors. Pandora is the primary event reconstruction software used at ProtoDUNE-SP, a prototype for the Deep Underground Neutrino Experiment far detector. ProtoDUNE-SP, located at CERN, is exposed to a charged-particle test beam. This paper gives an overview of the Pandora reconstruction algorithms and how they have been tailored for use at ProtoDUNE-SP. In complex events with numerous cosmic-ray and beam background particles, the simulated reconstruction and identification efficiency for triggered test-beam particles is above 80% for the majority of particle type and beam momentum combinations. Specifically, simulated 1 GeV/ c charged pions and protons are correctly reconstructed and identified with efficiencies of 86.1 \u00b1 0.6 % and 84.1 \u00b1 0.6 %, respectively. The efficiencies measured for test-beam data are shown to be within 5% of those predicted by the simulation." }, "authors": [ { diff --git a/tests/stubdata/output/jats_springer_JHEP_JHEP07_2023_200.json b/tests/stubdata/output/jats_springer_JHEP_JHEP07_2023_200.json index 5fda103..1fad0bc 100644 --- a/tests/stubdata/output/jats_springer_JHEP_JHEP07_2023_200.json +++ b/tests/stubdata/output/jats_springer_JHEP_JHEP07_2023_200.json @@ -1,6 +1,6 @@ { "abstract": { - "textEnglish": "This article reports measurements of the angle between differently defined jet axes in pp collisions at s \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 5 .02 TeV carried out by the ALICE Collaboration. Charged particles at midrapidity are clustered into jets with resolution parameters R = 0 .2 and 0.4. The jet axis, before and after Soft Drop grooming, is compared to the jet axis from the Winner-Takes-All (WTA) recombination scheme. The angle between these axes, \u2206 R axis, probes a wide phase space of the jet formation and evolution, ranging from the initial high-momentum-transfer scattering to the hadronization process. The \u2206 R axis observable is presented for 20 < p T ch jet \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {p}_{\\textrm{T}}^{\\textrm{ch}\\ \\textrm{jet}} $$\\end{document} < 100 GeV/ c, and compared to predictions from the PYTHIA 8 and Herwig 7 event generators. The distributions can also be calculated analytically with a leading hadronization correction related to the non-perturbative component of the Collins-Soper-Sterman (CSS) evolution kernel. Comparisons to analytical predictions at next-to-leading-logarithmic accuracy with leading hadronization correction implemented from experimental extractions of the CSS kernel in Drell-Yan measurements are presented. The analytical predictions describe the measured data within 20% in the perturbative regime, with surprising agreement in the non-perturbative regime as well. These results are compatible with the universality of the CSS kernel in the context of jet substructure.\n" + "textEnglish": "This article reports measurements of the angle between differently defined jet axes in pp collisions at s = 5 .02 TeV carried out by the ALICE Collaboration. Charged particles at midrapidity are clustered into jets with resolution parameters R = 0 .2 and 0.4. The jet axis, before and after Soft Drop grooming, is compared to the jet axis from the Winner-Takes-All (WTA) recombination scheme. The angle between these axes, \u2206 R axis, probes a wide phase space of the jet formation and evolution, ranging from the initial high-momentum-transfer scattering to the hadronization process. The \u2206 R axis observable is presented for 20 < p T ch jet < 100 GeV/ c, and compared to predictions from the PYTHIA 8 and Herwig 7 event generators. The distributions can also be calculated analytically with a leading hadronization correction related to the non-perturbative component of the Collins-Soper-Sterman (CSS) evolution kernel. Comparisons to analytical predictions at next-to-leading-logarithmic accuracy with leading hadronization correction implemented from experimental extractions of the CSS kernel in Drell-Yan measurements are presented. The analytical predictions describe the measured data within 20% in the perturbative regime, with surprising agreement in the non-perturbative regime as well. These results are compatible with the universality of the CSS kernel in the context of jet substructure.\n" }, "authors": [ { @@ -12254,6 +12254,6 @@ " Gieseke S Rohr C Siodmok A Colour reconnections in Herwig++ Eur. Phys. J. C 2012 72 2225 2012EPJC...72.2225G 10.1140/epjc/s10052-012-2225-5 [arXiv:1206.0041] [INSPIRE] " ], "title": { - "textEnglish": "Measurement of the angle between jet axes in pp collisions at s \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 5 .02 TeV" + "textEnglish": "Measurement of the angle between jet axes in pp collisions at s = 5 .02 TeV" } } diff --git a/tests/stubdata/output/jats_springer_SoPh_s11207-023-02231-5_mathtex.json b/tests/stubdata/output/jats_springer_SoPh_s11207-023-02231-5_mathtex.json new file mode 100644 index 0000000..29e80f8 --- /dev/null +++ b/tests/stubdata/output/jats_springer_SoPh_s11207-023-02231-5_mathtex.json @@ -0,0 +1,297 @@ +{ + "abstract": { + "textEnglish": "A new instrument was designed to take visible-light (VL) polarized brightness ( pB ) observations of the solar corona during the 14 December 2020 total solar eclipse. The instrument, called the Coronal Imaging Polarizer (CIP), consisted of a 16 MP CMOS detector, a linear polarizer housed within a piezoelectric rotation mount, and an f-5.6, 200 mm DSLR lens. Observations were successfully obtained, despite poor weather conditions, for five different exposure times (0.001 s, 0.01 s, 0.1 s, 1 s, and 3 s) at six different orientation angles of the linear polarizer ( 0 \u2218 , 30 \u2218 , 60 \u2218 , 90 \u2218 , 120 \u2218 , and 150 \u2218 ). The images were manually aligned using the drift of background stars in the sky and images of different exposure times were combined using a simple signal-to-noise ratio cut. The polarization and brightness of the local sky were also estimated and the observations were subsequently corrected. The pB of the K-corona was determined using least-squares fitting and radiometric calibration was done relative to the Mauna Loa Solar Observatory (MLSO) K-Cor pB observations from the day of the eclipse. The pB data was then inverted to acquire the coronal electron density, n e , for an equatorial streamer and a polar coronal hole, which agreed very well with previous studies. The effect of changing the number of polarizer angles used to compute the pB is also discussed and it is found that the results vary by up to \u2248 13 % when using all six polarizer angles versus only a select of three angles." + }, + "authors": [ + { + "affiliation": [ + { + "affPubID": "Aff1", + "affPubRaw": "Department of Physics Aberystwyth University SY23 3BZ Ceredigion Cymru UK" + } + ], + "attrib": { + "email": "lie6@aber.ac.uk", + "orcid": "0000-0002-9222-8648" + }, + "name": { + "given_name": "Liam", + "surname": "Edwards" + } + }, + { + "affiliation": [ + { + "affPubID": "Aff1", + "affPubRaw": "Department of Physics Aberystwyth University SY23 3BZ Ceredigion Cymru UK" + } + ], + "name": { + "given_name": "Kaine A.", + "surname": "Bunting" + } + }, + { + "affiliation": [ + { + "affPubID": "Aff1", + "affPubRaw": "Department of Physics Aberystwyth University SY23 3BZ Ceredigion Cymru UK" + } + ], + "attrib": { + "orcid": "0000-0002-6845-1698" + }, + "name": { + "given_name": "Brad", + "surname": "Ramsey" + } + }, + { + "affiliation": [ + { + "affPubID": "Aff1", + "affPubRaw": "Department of Physics Aberystwyth University SY23 3BZ Ceredigion Cymru UK" + } + ], + "attrib": { + "orcid": "0000-0002-1366-678X" + }, + "name": { + "given_name": "Matthew", + "surname": "Gunn" + } + }, + { + "affiliation": [ + { + "affPubID": "Aff2", + "affPubRaw": "Department of Computer Science Aberystwyth University SY23 3DB Ceredigion Cymru UK" + } + ], + "attrib": { + "orcid": "0000-0002-0500-5789" + }, + "name": { + "given_name": "Tomos", + "surname": "Fearn" + } + }, + { + "affiliation": [ + { + "affPubID": "Aff1", + "affPubRaw": "Department of Physics Aberystwyth University SY23 3BZ Ceredigion Cymru UK" + } + ], + "name": { + "given_name": "Thomas", + "surname": "Knight" + } + }, + { + "affiliation": [ + { + "affPubID": "Aff1", + "affPubRaw": "Department of Physics Aberystwyth University SY23 3BZ Ceredigion Cymru UK" + }, + { + "affPubID": "Aff3", + "affPubRaw": "Space Radiation Lab California Institute of Technology 91125 Pasadena CA USA" + } + ], + "attrib": { + "orcid": "0000-0003-0581-1278" + }, + "name": { + "given_name": "Gabriel Domingo", + "surname": "Muro" + } + }, + { + "affiliation": [ + { + "affPubID": "Aff1", + "affPubRaw": "Department of Physics Aberystwyth University SY23 3BZ Ceredigion Cymru UK" + } + ], + "attrib": { + "orcid": "0000-0002-6547-5838" + }, + "name": { + "given_name": "Huw", + "surname": "Morgan" + } + } + ], + "copyright": { + "statement": "\u00a9 The Author(s) 2023", + "status": true + }, + "editorialHistory": { + "acceptedDate": "2023-11-17", + "receivedDates": [ + "2023-05-12" + ] + }, + "funding": [ + { + "agencyid": { + "idschema": "doi", + "idvalue": "http://dx.doi.org/10.13039/501100003507" + }, + "agencyname": "Coleg Cymraeg Cenedlaethol" + }, + { + "agencyid": { + "idschema": "doi", + "idvalue": "http://dx.doi.org/10.13039/501100000271" + }, + "agencyname": "Science and Technology Facilities Council", + "awardnumber": "ST/N002962/1" + } + ], + "keywords": [ + { + "keyString": "Eclipse observations", + "keySystem": "misc" + }, + { + "keyString": "Polarization", + "keySystem": "misc" + }, + { + "keyString": "Optical", + "keySystem": "misc" + }, + { + "keyString": "Instrumentation and data management", + "keySystem": "misc" + }, + { + "keyString": "Spectrum", + "keySystem": "misc" + }, + { + "keyString": "Visible", + "keySystem": "misc" + } + ], + "openAccess": { + "license": "\nOpen Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article\u2019s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article\u2019s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit\n\t\t\t\t\t\thttp://creativecommons.org/licenses/by/4.0/.\n\t\t\t\t\t", + "licenseURL": "http://creativecommons.org/licenses/by/4.0/", + "open": true + }, + "pagination": { + "electronicID": "140" + }, + "persistentIDs": [ + { + "DOI": "10.1007/s11207-023-02231-5" + } + ], + "pubDate": { + "electrDate": "2023-12-05", + "printDate": "2023-12-00" + }, + "publication": { + "ISSN": [ + { + "issnString": "0038-0938", + "pubtype": "ppub" + }, + { + "issnString": "1573-093X", + "pubtype": "epub" + } + ], + "issueNum": "12", + "pubName": "Solar Physics", + "pubYear": "2023", + "publisher": "Springer Netherlands", + "volumeNum": "298" + }, + "publisherIDs": [ + { + "Identifier": "s11207-023-02231-5", + "attribute": "publisher-id" + }, + { + "Identifier": "2231", + "attribute": "manuscript" + } + ], + "recordData": { + "createdTime": "", + "loadFormat": "JATS", + "loadLocation": "", + "loadType": "fromFile", + "parsedTime": "", + "recordOrigin": "" + }, + "references": [ + " Baumbach S. 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Skyscape Archaeol. 2021 6 2 221 10.1558/jsa.17822 https://journal.equinoxpub.com/JSA/article/view/17822 " + ], + "title": { + "textEnglish": "Derived Electron Densities from Linear Polarization Observations of the Visible-Light Corona During the 14 December 2020 Total Solar Eclipse" + } +} diff --git a/tests/stubdata/output/jats_springer_ZaMP_s00033-023-02064-z.json b/tests/stubdata/output/jats_springer_ZaMP_s00033-023-02064-z.json index 663def7..1cb5d1b 100644 --- a/tests/stubdata/output/jats_springer_ZaMP_s00033-023-02064-z.json +++ b/tests/stubdata/output/jats_springer_ZaMP_s00033-023-02064-z.json @@ -1,6 +1,6 @@ { "abstract": { - "textEnglish": "This paper is concerned with the time-asymptotic stability of a nonlinear wave for the outflow problem of the isentropic compressible Navier\u2013Stokes\u2013Korteweg equations in the half space. Under some suitable assumptions on the spatial-asymptotic states and boundary data, the time-asymptotic profile is a nonlinear wave which is the superposition of a stationary solution and a rarefaction wave. Employing the L 2 \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^{2}$$\\end{document} -energy method and the decay (in both time and space variables) estimates of each component of the nonlinear wave, we prove that this nonlinear wave is time asymptotically stable under a small initial perturbation." + "textEnglish": "This paper is concerned with the time-asymptotic stability of a nonlinear wave for the outflow problem of the isentropic compressible Navier\u2013Stokes\u2013Korteweg equations in the half space. Under some suitable assumptions on the spatial-asymptotic states and boundary data, the time-asymptotic profile is a nonlinear wave which is the superposition of a stationary solution and a rarefaction wave. Employing the L 2 -energy method and the decay (in both time and space variables) estimates of each component of the nonlinear wave, we prove that this nonlinear wave is time asymptotically stable under a small initial perturbation." }, "authors": [ { diff --git a/tests/stubdata/output/jats_springer_jhep_2022_05_05.json b/tests/stubdata/output/jats_springer_jhep_2022_05_05.json index b076504..d3cfef3 100644 --- a/tests/stubdata/output/jats_springer_jhep_2022_05_05.json +++ b/tests/stubdata/output/jats_springer_jhep_2022_05_05.json @@ -1,6 +1,6 @@ { "abstract": { - "textEnglish": "A search for new heavy resonances decaying to a pair of Higgs bosons (HH) in proton-proton collisions at a center-of-mass energy of 13 TeV is presented. Data were collected with the CMS detector at the LHC in 2016\u20132018, corresponding to an integrated luminosity of 138 fb \u22121 . Resonances with a mass between 0.8 and 4.5 TeV are considered using events in which one Higgs boson decays into a bottom quark pair and the other into final states with either one or two charged leptons. Specifically, the single-lepton decay channel HH \u2192 b b \u00af WW \u2217 \u2192 b b \u00af \u2113 v q q \u00af \u2032 \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathrm{HH}\\to \\mathrm{b}\\overline{\\mathrm{b}}{\\mathrm{WW}}^{\\ast}\\to \\mathrm{b}\\overline{\\mathrm{b}}\\ell v\\mathrm{q}{\\overline{\\mathrm{q}}}^{\\prime } $$\\end{document} and the dilepton decay channels HH \u2192 b b \u00af WW \u2217 \u2192 b b \u00af \u2113 v \u2113 v \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathrm{HH}\\to \\mathrm{b}\\overline{\\mathrm{b}}{\\mathrm{WW}}^{\\ast}\\to \\mathrm{b}\\overline{\\mathrm{b}}\\ell v\\ell v $$\\end{document} and HH \u2192 b b \u00af \u03c4\u03c4 \u2192 b b \u00af \u2113 vv \u2113 vv \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathrm{HH}\\to \\mathrm{b}\\overline{\\mathrm{b}}\\uptau \\uptau \\to \\mathrm{b}\\overline{\\mathrm{b}}\\ell vv\\ell vv $$\\end{document} are examined, where \u2113 in the final state corresponds to an electron or muon. The signal is extracted using a two-dimensional maximum likelihood fit of the H \u2192 b b \u00af \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathrm{H}\\to \\mathrm{b}\\overline{\\mathrm{b}} $$\\end{document} jet mass and HH invariant mass distributions. No significant excess above the standard model expectation is observed in data. Model-independent exclusion limits are placed on the product of the cross section and branching fraction for narrow spin-0 and spin-2 massive bosons decaying to HH. The results are also interpreted in the context of radion and bulk graviton production in models with a warped extra spatial dimension. The results provide the most stringent limits to date for X \u2192 HH signatures with final-state leptons and at some masses provide the most sensitive limits of all X \u2192 HH searches.\n[graphic not available: see fulltext]" + "textEnglish": "A search for new heavy resonances decaying to a pair of Higgs bosons (HH) in proton-proton collisions at a center-of-mass energy of 13 TeV is presented. Data were collected with the CMS detector at the LHC in 2016\u20132018, corresponding to an integrated luminosity of 138 fb \u22121 . Resonances with a mass between 0.8 and 4.5 TeV are considered using events in which one Higgs boson decays into a bottom quark pair and the other into final states with either one or two charged leptons. Specifically, the single-lepton decay channel HH \u2192 b b \u00af WW \u2217 \u2192 b b \u00af \u2113 v q q \u00af \u2032 and the dilepton decay channels HH \u2192 b b \u00af WW \u2217 \u2192 b b \u00af \u2113 v \u2113 v and HH \u2192 b b \u00af \u03c4\u03c4 \u2192 b b \u00af \u2113 vv \u2113 vv are examined, where \u2113 in the final state corresponds to an electron or muon. The signal is extracted using a two-dimensional maximum likelihood fit of the H \u2192 b b \u00af jet mass and HH invariant mass distributions. No significant excess above the standard model expectation is observed in data. Model-independent exclusion limits are placed on the product of the cross section and branching fraction for narrow spin-0 and spin-2 massive bosons decaying to HH. The results are also interpreted in the context of radion and bulk graviton production in models with a warped extra spatial dimension. The results provide the most stringent limits to date for X \u2192 HH signatures with final-state leptons and at some masses provide the most sensitive limits of all X \u2192 HH searches.\n[graphic not available: see fulltext]" }, "authors": [ { @@ -33602,6 +33602,6 @@ " Gouzevitch M Oliveira A Rojo J Rosenfeld R Salam GP Sanz V Scale-invariant resonance tagging in multijet events and new physics in Higgs pair production JHEP 2013 07 148 2013JHEP...07..148G 10.1007/JHEP07(2013)148 [arXiv:1303.6636] [INSPIRE] " ], "title": { - "textEnglish": "Search for heavy resonances decaying to a pair of Lorentz-boosted Higgs bosons in final states with leptons and a bottom quark pair at s \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV" + "textEnglish": "Search for heavy resonances decaying to a pair of Lorentz-boosted Higgs bosons in final states with leptons and a bottom quark pair at s = 13 TeV" } } diff --git a/tests/test_jats.py b/tests/test_jats.py index d257264..ffeb908 100644 --- a/tests/test_jats.py +++ b/tests/test_jats.py @@ -77,7 +77,10 @@ def test_jats(self): "mdpi_galaxies-11-00090", "mdpi_symmetry-15-00939", "mdpi_universe-08-00651", + "jats_springer_SoPh_s11207-023-02231-5_mathtex", + "jats_apj_967_1_35", ] + for f in filenames: test_infile = os.path.join(self.inputdir, f + ".xml") test_outfile = os.path.join(self.outputdir, f + ".json")