Multi-line diagnostics for the optical identification of Supernova Remnants

These are diagnostics for the optical identification of Supernova Remnants (SNRs). In Kopsacheili et al. 2020 multi-line diagnostics are presented for the separation of SNRs from HII regions. They have been built using shock (2008) and photoionization or starburst (2001, 2010) models from MAPPINGS III modeling code that are considered as SNRs and HII regions respectively.

The separation of these two types of nebulae is based on the different emission-line ratios of lines presented in their spectra. In the multi-line diagnostics the emission-line ratios predicted by the models are combined in 2 and 3 dimensions (where each dimension is an emission-line ratio), and using a Support Vector Machine (SVM) model, the line (in the case of 2D) or the surface (in the case of 3D) that best separates shock from photoionization models (or SNRs from HII regions) has been calculated.

The diagnostics are basically the functions that describe the aforementioned lines or surfaces. They combine the following emission-line ratios in 2 and 3 dimensions: $\rm [N\,II](6583)/H\alpha,\, [S\,II](6716,6731)/H\alpha,\, [O\,I](6300)/H\alpha,\, [O\,II](3727,3729)/H\beta,\,[O\,III](5008)/H\beta $.

In Kopsacheili et al. 2020 the functions are presented in tables where one can find the coefficients combined with polynomials of 2nd and 3rd order and construct them. Here, these functions can be found in python format and used directly. In every case, in order for a source to be considered as a SNR$^*$ the function $f$ should be positive. Apart from the functions, the schematic respesantation of the diagnostics is presented. In every case, red color corresponds to the starburst models (HII regions) and green to the shock models (SNRs). The black lines and the blue surfaces are the lines and surfaces that best separate the two classes (i.e. the decision functions of SVM).

The scripts '2D_SNR_diagsotics.py' and '3D_SNR_diagsotics.py' are also provided, along with the ascii files 'factors_2d.txt' and 'factors_3d.txt'. The latters contain the factors axx and axxx (as presented below) that are used by the polynomials that describe the diagnostics. The '2D_SNR_diagsotics.py' and '3D_SNR_diagsotics.py' use these files in order to calculate the diagnostics. These scripts can be run directly and return if a source satisfies a given diagnostic or not. In the case of 2D diagnostics, one can run:

python 2D_SNR_diagntostics.py -ha [x1] -sii [x2] -nii [x3] -oi [x4] -oii [x5] -oiii [x6] -hb [x7] -diag [diagntostic] 

where [x1], [x2], ....., [x7] is the observed flux/luminosity of a source of: $\rm H\alpha(6563), [S\,II](6717,6731), [N\,II](6583), [O\,I](6300), [O\,II](3729,3731), [O\,III](5007), H\beta(4681)$ respectively.

The parameter 'diag' refers to the 2D-diagnostics of interest and it should be one of the following:

1. 'SII-NII', 2. 'NII-OIII', 3. 'SII-OIII', 4. 'OI-OIII', 5. 'NII-OI',
6. 'OII-OIII', 7. 'NII-OII', 8. 'SII-OI', 9. 'OI-OII', 10. 'SII-OII'

Those are the diagntostics that combine the emission line ratios:
1. [S II]/$\rm H\alpha$-[N II]/$\rm H\alpha$, 2. [N II]/$\rm H\alpha$-[O III]/$\rm H\beta$, 3. [S II]/$\rm H\alpha$-[O III]/$\rm H\beta$, 4. [O I]/$\rm H\alpha$-[O III]/$\rm H\beta$, 5. [N II]/$\rm H\alpha$-[O I]/$\rm H\alpha$
6. [O II]/$\rm H\beta$-[O III]/$\rm H\beta$, 7. [N II]/$\rm H\alpha$-[O II]/$\rm H\beta$, 8. [S II]/$\rm H\alpha$-[O I]/$\rm H\alpha$, 9. [O I]/$\rm H\alpha$-[O II]/$\rm H\beta$, 10. [S II]/$\rm H\alpha$-[O II]/$\rm H\beta$,
respectively.

For the 3D diagnostics:

python 3D_SNR_diagntostics.py -ha [x1] -sii [x2] -nii [x3] -oi [x4] -oii [x5] -oiii [x6] -hb [x7] -diag [diagntostic]  

The [x1], [x2], ....., [x7] are same as in the 2D case, however now, the parameter 'diag' refers to the 3D diagnostics and it should be one of the following:

1.'NII-SII-OIII', 2.'NII-SII-OI', 3.'NII-SII-OII', 4.'NII-OII-OIII', 5.'NII-OI-OII',
6.'NII-OI-OIII', 7.'SII-OI-OII', 8.'SII-OII-OIII', 9.'SII-OI-OIII', 10.'OI-OII-OIII',

Those are the diagntostics that combine the emission line ratios:
1. [N II]/$\rm H\alpha$-[S II]/$\rm H\alpha$-[O III]/$\rm H\beta$, 2. [N II]/$\rm H\alpha$-[S II]/$\rm H\alpha$-[O I]/$\rm H\alpha$, 3. [N II]/$\rm H\alpha$-[S II]/$\rm H\alpha$-[O II]/$\rm H\beta$, 4. [N II]/$\rm H\alpha$-[O II]/$\rm H\beta$-[O III]/$\rm H\beta$,
5. [N II]/$\rm H\alpha$-[O I]/$\rm H\alpha$-[O II]/Hb,
6. [N II]/$\rm H\alpha$-[O I]/$\rm H\alpha$-[O III]/$\rm H\beta$, 7. [S II]/$\rm H\alpha$-[O I]/$\rm H\alpha$-[O II]/$\rm H\beta$, 8. [S II]/$\rm H\alpha$-[O II]/$\rm H\beta$-[O III]/$\rm H\beta$, 9. [S II]/$\rm H\alpha$-[O I]/$\rm H\alpha$-[O III]/$\rm H\beta$,
10. [O I]/$\rm H\alpha$-[O II]/$\rm H\beta$-[O III]/$\rm H\beta$,
respectively.

In both cases, the default value of the emission lines is 0.01. This means that if one or more emission lines are not available they can be skipped (of course in this case the diagnsotics that use these lines are not valid). There is no default diagnostic so it should be always defined.

$^*$ By using these diagnostics someone should be aware that false positives can be identified. For this reason it is more safe to consider them all as candidate SNRs.

$\rm {\bf{[S\,II]/H\alpha - [N\,II]/H\alpha}}$

a30 = -0.043
a21 = 0.175
a20 = -0.257
a12 = 0.029
a11 = -2.452
a10 = 2.244
a03 = -0.217
a02 = 1.388
a01 = 1.116
a00 = 2.763

$\rm f\_SII\_NII(x, y) = a30x^3 + a21x^2y + a20x^2 + a12xy^2 + a11xy + a10x + a03y^3 + a02y^2 + a01y + a00$

where $\rm x = log_{10}([S\,II]/H\alpha)$ and $\rm y = log_{10}([N\,II]/H\alpha).$
So, in this case if f_SII_NII(x, y) > 0, the source can be considered as a SNR.

f_SII_NII = lambda x, y: (a30*x**3.0 + a21*x**2.0*y + a20*x**2.0 + a12*x*y**2.0 + a11*x*y + a10*x + 
                          a03*y**3.0 + a02*y**2.0 + a01*y + a00)

$\rm {\bf{[N\,II]/H\alpha - [O\,III]/H\beta}}$

a10 = 0.939
a01 = 1.000
a00 = 0.469

$\rm f\_NII\_OIII(x, y) = a10x + a01y + a00 $

where $\rm x = log_{10}([N\,II]/H\alpha)$ and $ \rm y = log_{10}([O\,III]/H\beta)$.
If f_NII_OIII(x, y) > 0, the source can be considered as a SNR.

f_NII_OIII = lambda x, y: (a10*x + a01*y + a00)

$\rm {\bf{[S\,II]/H\alpha - [O\,III]/H\beta}}$

a30 = 0.079
a21 = 0.148
a20 = -1.821
a12 = -0.318
a11 = -0.781
a10 = 4.66
a03 = 0.255
a02 = -0.479
a01 = 4.433
a00 = 3.403

$\rm f\_SII\_OIII(x, y) = a30x^3 + a21x^2y + a20x^2 + a12xy^2 + a11xy + a10x + a03y^3 + a02y^2 + a01y + a00$

where $\rm x = log_{10}([S\,II]/H\alpha)$ and $\rm y = log_{10}([O\,III]/H\beta).$
In this case if f_SII_OIII(x, y) > 0, the source can be considered as a SNR.

f_SII_OIII = lambda x, y: (a30*x**3.0 + a21*x**2.0*y + a20*x**2.0 + a12*x*y**2.0 + a11*x*y + 
                           a10*x + a03*y**3.0 + a02*y**2.0 + a01*y + a00)

$\rm {\bf{[O\,I]/H\alpha - [O\,III]/H\beta}}$

a30 = 0.465
a21 = -0.245
a20 = -0.432
a12 = 1.067
a11 = -0.887
a10 = -0.701
a03 = 0.049
a02 = -1.610
a01 = 2.096
a00 = 2.710

$\rm f\_OI\_OIII(x, y) = a30x^3 + a21x^2y + a20x^2 + a12xy^2 + a11xy + a10x + a03y^3 + a02y^2 + a01y + a00$

where $\rm x = log_{10}([O\,I]/H\alpha)$ and $\rm y = log_{10}([O\,III]/H\beta).$
In this case if f_OI_OIII(x, y) > 0, the source can be considered as a SNR.

f_OI_OIII = lambda x, y: (a30*x**3.0 + a21*x**2.0*y + a20*x**2.0 + a12*x*y**2.0 + a11*x*y + 
                           a10*x + a03*y**3.0 + a02*y**2.0 + a01*y + a00)

$\rm {\bf{[N\,II]/H\alpha - [O\,I]/H\alpha}}$

a30 = -2.159
a21 = 4.249
a20 = -0.874
a12 = 0.067
a11 = 4.330
a10 = -0.0007
a03 = 1.162
a02 = 1.263
a01 = 0.382
a00 = 1.285

$\rm f\_NII\_OI(x, y) = a30x^3 + a21x^2y + a20x^2 + a12xy^2 + a11xy + a10x + a03y^3 + a02y^2 + a01y + a00$

where $\rm x = log_{10}([N\,II]/H\alpha)$ and $\rm y = log_{10}([O\,I]/H\alpha).$
In this case if f_NII_OI(x, y) > 0, the source can be considered as a SNR.

f_NII_OI = lambda x, y: (a30*x**3.0 + a21*x**2.0*y + a20*x**2.0 + a12*x*y**2.0 + a11*x*y + 
                           a10*x + a03*y**3.0 + a02*y**2.0 + a01*y + a00)

$\rm {\bf{[O\,II]/H\beta - [O\,III]/H\beta}}$

a30 = -0.008
a21 = 0.416
a20 = 1.952
a12 = -0.616
a11 = -1.133
a10 = 4.591
a03 = 0.347
a02 = 1.344
a01 = 3.356
a00 = -2.904

$\rm f\_OII\_OIII(x, y) = a30x^3 + a21x^2y + a20x^2 + a12xy^2 + a11xy + a10x + a03y^3 + a02y^2 + a01y + a00$

where $\rm x = log_{10}([Ο\,II]/H\beta)$ and $\rm y = log_{10}([O\,III]/H\beta).$
In this case if f_OII_OIII(x, y) > 0, the source can be considered as a SNR.

f_OII_OIII = lambda x, y: (a30*x**3.0 + a21*x**2.0*y + a20*x**2.0 + a12*x*y**2.0 + a11*x*y + 
                           a10*x + a03*y**3.0 + a02*y**2.0 + a01*y + a00)

$\rm {\bf{[N\,II]/H\alpha - [O\,II]/H\beta}}$

a10 = 1.262
a01 = 1.000
a00 = 0.581

$\rm f\_NII\_OII(x, y) = a10x + a01y + a00$

where $\rm x = log_{10}([N\,II]/H\alpha)$ and $\rm y = log_{10}([O\,II]/H\beta).$
In this case if f_NII_OIII(x, y) > 0, the source can be considered as a SNR.

f_NII_OIII = lambda x, y: (a10*x + a01*y + a00)

$\rm {\bf{[S\,II]/H\alpha - [O\,I]/H\alpha}}$

a30 = 0.461
a21 = 2.197
a20 = -0.089
a12 = -1.036
a11 = 1.932
a10 = -0.449
a03 = 1.446
a02 = 1.371
a01 = 0.145
a00 = 1.218

$\rm f\_SII\_OI(x, y) = a30x^3 + a21x^2y + a20x^2 + a12xy^2 + a11xy + a10x + a03y^3 + a02y^2 + a01y + a00$

where $\rm x = log_{10}([S\,II]/H\alpha)$ and $\rm y = log_{10}([O\,I]/H\alpha).$
In this case if f_SII_OI(x, y) > 0, the source can be considered as a SNR.

f_SII_OI = lambda x, y: (a30*x**3.0 + a21*x**2.0*y + a20*x**2.0 + a12*x*y**2.0 + a11*x*y + 
                           a10*x + a03*y**3.0 + a02*y**2.0 + a01*y + a00)

$\rm {\bf{[O\,I]/H\alpha - [O\,II]/H\beta}}$

a30 = 0.701
a21 = 4.291
a20 = -0.842
a12 = 0.124
a11 = 3.095
a10 = 0.719
a03 = 0.432
a02 = -1.170
a01 = -2.274
a00 = 5.017

$\rm f\_OI\_OII(x, y) = a30x^3 + a21x^2y + a20x^2 + a12xy^2 + a11xy + a10x + a03y^3 + a02y^2 + a01y + a00$

where $\rm x = log_{10}([O\,I]/H\alpha)$ and $\rm y = log_{10}([O\,II]/H\beta).$
In this case if f_OI_OII(x, y) > 0, the source can be considered as a SNR.

f_OI_OII = lambda x, y: (a30*x**3.0 + a21*x**2.0*y + a20*x**2.0 + a12*x*y**2.0 + a11*x*y + 
                           a10*x + a03*y**3.0 + a02*y**2.0 + a01*y + a00)

$\rm {\bf{[S\,II]/H\alpha - [O\,II]/H\beta}}$

a30 = -0.403
a21 = -0.511
a20 = -0.575
a12 = -0.225
a11 = -0.332
a10 = 4.283
a03 = 1.185
a02 = 0.981
a01 = -0.283
a00 = 2.777

$\rm f\_SII\_OII(x, y) = a30x^3 + a21x^2y + a20x^2 + a12xy^2 + a11xy + a10x + a03y^3 + a02y^2 + a01y + a00$

where $\rm x = log_{10}([S\,II]/H\alpha)$ and $\rm y = log_{10}([O\,II]/H\beta).$
In this case if f_SII_OII(x, y) > 0, the source can be considered as a SNR.

f_SII_OII = lambda x, y: (a30*x**3.0 + a21*x**2.0*y + a20*x**2.0 + a12*x*y**2.0 + a11*x*y + 
                           a10*x + a03*y**3.0 + a02*y**2.0 + a01*y + a00)

$\rm {\bf{[N\,II]/H\alpha - [S\,II]/H\alpha - [O\,III]/H\beta}}$

a300 = -2.913
a201 = -0.638
a210 = 1.568
a200 = 0.407
a102 = -0.866
a111 = -2.264
a101 = 1.508
a120 = 1.753
a110 = -6.913
a100 = 0.001
a003 = 1.463
a012 = -1.325
a002 = -2.732
a021 = 1.823
a011 = -2.697
a001 = 4.377
a030 = -1.585
a020 = 0.770
a010 = 1.267
a000 = 2.413

$\rm f\_NII\_SII\_OIII(x, y, z) = a300x^3 + a201x^2z + a210x^2y + a200x^2 + a102xz^2 + a111xyz + a101xz + a120xy^2 + a110xy + a100x $
$ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\, \rm + a003z^3 + a012yz^2 + a002z^2 + a021y^2z + a011yz + a001z + a030y^3 + a020y^2+ a010y + a000$

where $\rm x = log_{10}([N\,II]/H\alpha)$, $\rm y = log_{10}([S\,II]/H\alpha)$, and $\rm z = log_{10}([O\,III]/H\beta).$
If f_NII_SII_OIII(x, y) > 0, the source can be considered as a SNR.

f_NII_SII_OIII = lambda x, y, z:(a300*x**3 + a201*x**2*z + a210*x**2*y + a200*x**2 + a102*x*z**2 + a111*x*y*z + 
                                 a101*x*z + a120*x*y**2 + a110*x*y + a100*x + a003*z**3 + a012*y*z**2 + 
                                 a002*z**2 + a021*y**2*z + a011*y*z + a001*z + a030*y**3 + a020*x*y**2+  
                                 a010*y + a000)

$\rm {\bf{[N\,II]/H\alpha - [S\,II]/H\alpha - [O\,I]/H\alpha}}$

a300 = 0.025
a201 = 0.253
a210 = 0.250
a200 = -0.350
a102 = 0.196
a111 = 0.379
a101 = 0.149
a120 = 0.127
a110 = -0.795
a100 = -1.821
a003 = 0.223
a012 = 0.014
a002 = -0.804
a021 = -0.021
a011 = 0.658
a001 = 0.214
a030 = -0.002
a020 = 0.151
a010 = -1.822
a000 = 2.382

$\rm f\_NII\_SII\_OI(x, y, z) = a300x^3 + a201x^2z + a210x^2y + a200x^2 + a102xz^2 + a111xyz + a101xz + a120xy^2 + a110xy + a100x $
$ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\, \rm + a003z^3 + a012yz^2 + a002z^2 + a021y^2z + a011yz + a001z + a030y^3 + a020y^2+ a010y + a000$

where $\rm x = log_{10}([N\,II]/H\alpha)$, $\rm y = log_{10}([S\,II]/H\alpha)$, and $\rm z = log_{10}([O\,I]/H\alpha).$
If f_NII_SII_OI(x, y) > 0, the source can be considered as a SNR.

f_NII_SII_OI = lambda x, y, z:(a300*x**3 + a201*x**2*z + a210*x**2*y + a200*x**2 + a102*x*z**2 + a111*x*y*z + 
                                 a101*x*z + a120*x*y**2 + a110*x*y + a100*x + a003*z**3 + a012*y*z**2 + 
                                 a002*z**2 + a021*y**2*z + a011*y*z + a001*z + a030*y**3 + a020*x*y**2+  
                                 a010*y + a000)

$\rm {\bf{[N\,II]/H\alpha - [S\,II]/H\alpha - [O\,II]/H\beta}}$

a300 = -0.140
a201 = -0.388
a210 = 0.231
a200 = 1.460
a102 = 0.067
a111 = -0.460
a101 = 2.639
a120 = 0.283
a110 = -2.699
a100 = -0.610
a003 = 0.361
a012 = 0.141
a002 = 0.283
a021 = 0.098
a011 = -1.050
a001 = 1.626
a030 = -0.055
a020 = -0.038
a010 = 2.202
a000 = 1.520

$\rm f\_NII\_SII\_OII(x, y, z) = a300x^3 + a201x^2z + a210x^2y + a200x^2 + a102xz^2 + a111xyz + a101xz + a120xy^2 + a110xy + a100x $
$ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\, \rm + a003z^3 + a012yz^2 + a002z^2 + a021y^2z + a011yz + a001z + a030y^3 + a020y^2+ a010y + a000$

where $\rm x = log_{10}([N\,II]/H\alpha)$, $\rm y = log_{10}([S\,II]/H\alpha)$, and $\rm z = log_{10}([O\,II]/H\beta).$
If f_NII_SII_OII(x, y) > 0, the source can be considered as a SNR.

f_NII_SII_OII = lambda x, y, z:(a300*x**3 + a201*x**2*z + a210*x**2*y + a200*x**2 + a102*x*z**2 + a111*x*y*z + 
                                 a101*x*z + a120*x*y**2 + a110*x*y + a100*x + a003*z**3 + a012*y*z**2 + 
                                 a002*z**2 + a021*y**2*z + a011*y*z + a001*z + a030*y**3 + a020*x*y**2+  
                                 a010*y + a000)

$\rm {\bf{[N\,II]/H\alpha - [O\,II]/H\beta - [O\,III]/H\beta}}$

a300 = -1.704
a201 = -0.879
a210 = 8.080
a200 = -1.549
a102 = -3.772
a111 = -0.877
a101 = 0.788
a120 = -0.372
a110 = 3.313
a100 = 7.034
a003 = 3.011
a012 = -2.641
a002 = -2.798
a021 = 1.264
a011 = -1.968
a001 = 5.176
a030 = 0.576
a020 = 2.729
a010 = -1.199
a000 = 3.478

$\rm f\_NII\_OII\_OIII(x, y, z) = a300x^3 + a201x^2z + a210x^2y + a200x^2 + a102xz^2 + a111xyz + a101xz + a120xy^2 + a110xy + a100x $
$ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\, \rm + a003z^3 + a012yz^2 + a002z^2 + a021y^2z + a011yz + a001z + a030y^3 + a020y^2+ a010y + a000$

where $\rm x = log_{10}([N\,II]/H\alpha)$, $\rm y = log_{10}([O\,II]/H\beta)$, and $\rm z = log_{10}([O\,III]/H\beta).$
If f_NII_SII_OII(x, y) > 0, the source can be considered as a SNR.

f_NII_OII_OIII = lambda x, y, z:(a300*x**3 + a201*x**2*z + a210*x**2*y + a200*x**2 + a102*x*z**2 + a111*x*y*z + 
                                 a101*x*z + a120*x*y**2 + a110*x*y + a100*x + a003*z**3 + a012*y*z**2 + 
                                 a002*z**2 + a021*y**2*z + a011*y*z + a001*z + a030*y**3 + a020*x*y**2+  
                                 a010*y + a000)

$\rm {\bf{[N\,II]/H\alpha - [O\,I]/H\alpha - [O\,II]/H\beta}}$

a300 = -1.085
a201 = -0.268
a210 = 3.986
a200 = 0.863
a102 = 4.071
a111 = -2.792
a101 = 3.889
a120 = 0.609
a110 = 6.108
a100 = -3.186
a003 = 0.139
a012 = -0.459
a002 = -0.768
a021 = 4.849
a011 = 1.608
a001 = -1.437
a030 = 0.326
a020 = -2.053
a010 = 1.578
a000 = 3.734

$\rm f\_NII\_OI\_OII(x, y, z) = a300x^3 + a201x^2z + a210x^2y + a200x^2 + a102xz^2 + a111xyz + a101xz + a120xy^2 + a110xy + a100x $
$ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\, \rm + a003z^3 + a012yz^2 + a002z^2 + a021y^2z + a011yz + a001z + a030y^3 + a020y^2+ a010y + a000$

where $\rm x = log_{10}([N,II]/H\alpha)$, $\rm y = log_{10}([O,I]/H\alpha)$, and $\rm z = log_{10}([O,II]/H\beta).$
If f_NII_OI_OII(x, y) > 0, the source can be considered as a SNR.

f_NII_OI_OII = lambda x, y, z:(a300*x**3 + a201*x**2*z + a210*x**2*y + a200*x**2 + a102*x*z**2 + a111*x*y*z + 
                                 a101*x*z + a120*x*y**2 + a110*x*y + a100*x + a003*z**3 + a012*y*z**2 + 
                                 a002*z**2 + a021*y**2*z + a011*y*z + a001*z + a030*y**3 + a020*x*y**2+  
                                 a010*y + a000)

$\rm {\bf{[N\,II]/H\alpha - [O\,I]/H\alpha - [O\,III]/H\beta}}$

a300 = -1.082
a201 = 0.195
a210 = 1.873
a200 = 0.027
a102 = 2.230
a111 = -3.680
a101 = -0.428
a120 = 1.281
a110 = 2.433
a100 = -1.752
a003 = 1.842
a012 = 1.837
a002 = -1.213
a021 = 0.477
a011 = -2.307
a001 = 1.400
a030 = 0.590
a020 = 0.386
a010 = -0.862
a000 = 0.567

$\rm f\_NII\_OI\_OIII(x, y, z) = a300x^3 + a201x^2z + a210x^2y + a200x^2 + a102xz^2 + a111xyz + a101xz + a120xy^2 + a110xy + a100x $
$ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\, \rm + a003z^3 + a012yz^2 + a002z^2 + a021y^2z + a011yz + a001z + a030y^3 + a020y^2+ a010y + a000$

where $\rm x = log_{10}([N\,II]/H\alpha)$, $\rm y = log_{10}([O\,I]/H\alpha)$, and $\rm z = log_{10}([O\,III]/H\beta).$
If f_NII_OI_OIII(x, y) > 0, the source can be considered as a SNR.

f_NII_OI_OIII = lambda x, y, z:(a300*x**3 + a201*x**2*z + a210*x**2*y + a200*x**2 + a102*x*z**2 + a111*x*y*z + 
                                 a101*x*z + a120*x*y**2 + a110*x*y + a100*x + a003*z**3 + a012*y*z**2 + 
                                 a002*z**2 + a021*y**2*z + a011*y*z + a001*z + a030*y**3 + a020*x*y**2+  
                                 a010*y + a000)

$\rm {\bf{[S\,II]/H\alpha - [O\,I]/H\alpha - [O\,II]/H\beta}}$

a300 = 0.042
a201 = -1.707
a210 = 0.359
a200 = -0.172
a102 = 0.762
a111 = -2.236
a101 = 1.342
a120 = -0.096
a110 = 2.439
a100 = -2.305
a003 = 0.266
a012 = -0.094
a002 = -0.747
a021 = 5.000
a011 = 2.587
a001 = -1.758
a030 = 0.826
a020 = -1.274
a010 = 1.213
a000 = 4.108

$\rm f\_SII\_OI\_OII(x, y, z) = a300x^3 + a201x^2z + a210x^2y + a200x^2 + a102xz^2 + a111xyz + a101xz + a120xy^2 + a110xy + a100x $
$ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\, \rm + a003z^3 + a012yz^2 + a002z^2 + a021y^2z + a011yz + a001z + a030y^3 + a020y^2+ a010y + a000$

where $\rm x = log_{10}([S\,II]/H\alpha)$, $\rm y = log_{10}([O\,I]/H\alpha)$, and $\rm z = log_{10}([O\,III]/H\beta).$
If f_SII_OI_OII(x, y) > 0, the source can be considered as a SNR.

f_SII_OI_OII = lambda x, y, z:(a300*x**3 + a201*x**2*z + a210*x**2*y + a200*x**2 + a102*x*z**2 + a111*x*y*z + 
                                 a101*x*z + a120*x*y**2 + a110*x*y + a100*x + a003*z**3 + a012*y*z**2 + 
                                 a002*z**2 + a021*y**2*z + a011*y*z + a001*z + a030*y**3 + a020*x*y**2+  
                                 a010*y + a000)

$\rm {\bf{[S\,II]/H\alpha - [O\,II]/H\beta - [O\,III]/H\beta}}$

a300 = -0.151
a201 = -0.501
a210 = 0.713
a200 = -3.181
a102 = -0.304
a111 = 1.194
a101 = -0.421
a120 = -1.869
a110 = 2.946
a100 = 3.761
a003 = 2.156
a012 = -0.354
a002 = -3.318
a021 = 1.078
a011 = 1.088
a001 = 4.722
a030 = 2.269
a020 = 1.467
a010 = -3.676
a000 = 4.974

$\rm f\_SII\_OII\_OIII(x, y, z) = a300x^3 + a201x^2z + a210x^2y + a200x^2 + a102xz^2 + a111xyz + a101xz + a120xy^2 + a110xy + a100x $
$ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\, \rm + a003z^3 + a012yz^2 + a002z^2 + a021y^2z + a011yz + a001z + a030y^3 + a020y^2+ a010y + a000$

where $\rm x = log_{10}([S\,II]/H\alpha)$, $\rm y = log_{10}([O\,II]/H\beta)$, and $\rm z = log_{10}([O\,III]/H\beta).$
If f_SII_OII_OIII(x, y) > 0, the source can be considered as a SNR.

f_SII_OII_OIII = lambda x, y, z:(a300*x**3 + a201*x**2*z + a210*x**2*y + a200*x**2 + a102*x*z**2 + a111*x*y*z + 
                                 a101*x*z + a120*x*y**2 + a110*x*y + a100*x + a003*z**3 + a012*y*z**2 + 
                                 a002*z**2 + a021*y**2*z + a011*y*z + a001*z + a030*y**3 + a020*x*y**2+  
                                 a010*y + a000)

$\rm {\bf{[S\,II]/H\alpha - [O\,I]/H\alpha - [O\,III]/H\beta}}$

a300 = -0.598
a201 = 0.403
a210 = -0.896
a200 = 0.873
a102 = -1.329
a111 = -3.664
a101 = 1.687
a120 = 1.766
a110 = 0.285
a100 = -1.227
a003 = 1.874
a012 = 2.312
a002 = -1.495
a021 = 1.356
a011 = -1.854
a001 = 1.197
a030 = 0.696
a020 = 0.815
a010 = -1.357
a000 = 0.303

$\rm f\_SII\_OI\_OIII(x, y, z) = a300x^3 + a201x^2z + a210x^2y + a200x^2 + a102xz^2 + a111xyz + a101xz + a120xy^2 + a110xy + a100x $
$ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\, \rm + a003z^3 + a012yz^2 + a002z^2 + a021y^2z + a011yz + a001z + a030y^3 + a020y^2+ a010y + a000$

where $\rm x = log_{10}([S\,II]/H\alpha)$, $\rm y = log_{10}([O\,I]/H\alpha)$, and $\rm z = log_{10}([O\,III]/H\beta).$
If f_SII_OI_OIII(x, y) > 0, the source can be considered as a SNR.

f_SII_OI_OIII = lambda x, y, z:(a300*x**3 + a201*x**2*z + a210*x**2*y + a200*x**2 + a102*x*z**2 + a111*x*y*z + 
                                 a101*x*z + a120*x*y**2 + a110*x*y + a100*x + a003*z**3 + a012*y*z**2 + 
                                 a002*z**2 + a021*y**2*z + a011*y*z + a001*z + a030*y**3 + a020*x*y**2+  
                                 a010*y + a000)

$\rm {\bf{[O\,I]/H\alpha - [O\,II]/H\beta - [O\,III]/H\beta}}$

a300 = 0.768
a201 = -0.419
a210 = 1.134
a200 = -0.166
a102 = 1.842
a111 = -2.650
a101 = -0.174
a120 = -1.075
a110 = 0.932
a100 = -0.871
a003 = 0.964
a012 = -0.771
a002 = -1.476
a021 = 0.185
a011 = 2.248
a001 = 0.824
a030 = 0.452
a020 = -0.554
a010 = -2.228
a000 = 3.070

$\rm f\_OI\_OII\_OIII(x, y, z) = a300x^3 + a201x^2z + a210x^2y + a200x^2 + a102xz^2 + a111xyz + a101xz + a120xy^2 + a110xy + a100x $
$ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\, \rm + a003z^3 + a012yz^2 + a002z^2 + a021y^2z + a011yz + a001z + a030y^3 + a020y^2+ a010y + a000$

where $\rm x = log_{10}([O\,I]/H\alpha)$, $\rm y = log_{10}([O\,II]/H\beta)$, and $\rm z = log_{10}([O\,III]/H\beta).$
If f_OI_OII_OIII(x, y) > 0, the source can be considered as a SNR.

f_OI_OII_OIII = lambda x, y, z:(a300*x**3 + a201*x**2*z + a210*x**2*y + a200*x**2 + a102*x*z**2 + a111*x*y*z + 
                                 a101*x*z + a120*x*y**2 + a110*x*y + a100*x + a003*z**3 + a012*y*z**2 + 
                                 a002*z**2 + a021*y**2*z + a011*y*z + a001*z + a030*y**3 + a020*x*y**2+  
                                 a010*y + a000)