Emission-Line Measurements

Emission-Line Parameters

The table below provides a compilation of emission-line parameters gathered through the development of the DAP. Many of them have not actually been fit by the DAP in any survey-level runs of the software and are simply collected here for reference.

Rest wavelengths are Ritz wavelengths in vacuum, collected from the NIST Atomic Spectra Database.

The “M1” and “E2” values are the Einstein \(A_{ki}\) coefficients for the magnetic dipole and electric quadrupole transitions, respectively. These are collected to fix the expected flux ratio between specific line doublets. The expected flux ratio is:

\[\frac{f_1}{f_2} = \frac{\lambda_2}{\lambda_1}\ \cdot\ \frac{M1_1+E2_1}{M1_2+E2_2}\]

where, e.g., \(\lambda_1\) is the rest wavelength of the first line in the doublet.

Additionally, we have defined some nominal passbands used for calculations of the line equivalent width (EW), including the main passband centered on the line and blue and red sidebands that are used to construct a linear continuum beneath the emission line.

Name	Rest \(\lambda\) (Å)	M1	E2	EW Passband (Å)	Blue Passband (Å)	Red Passband (Å)
HeII [3]	3204.019
NeIII	3343.14
NeV	3346.783	1.38e-1	6.2e-5
NeV	3426.864	3.82e-1	3.9e-4
NI [3]	3467.513
H25	3670.5155
H24	3672.5279
H23	3674.8110
H22	3677.4160
H21	3680.4065
H20	3683.8627
H19	3687.8871
H18	3692.6119
H17	3698.2103
H16	3704.9132
H15	3713.0334
H14	3723.0035			[1]	3706.3 – 3716.3	3738.6 – 3748.6
OII	3727.092	1.59e-4	1.86e-5	3716.3 – 3738.3	3706.3 – 3716.3	3738.6 – 3748.6
OII	3729.875	1.98e-6	2.86e-5	[1]	3706.3 – 3716.3	3738.6 – 3748.6
H13	3735.4365			[1]	3706.3 – 3716.3	3738.6 – 3748.6
H12 [4]	3751.2174			3746.2 – 3756.2	3738.6 – 3748.6	3756.6 – 3766.6
H11 [4]	3771.7012			3761.7 – 3781.7	3756.6 – 3766.6	3779.1 – 3789.1
\({\rm H}\theta\) [4]	3798.9757			3789.0 – 3809.0	3776.5 – 3791.5	3806.5 – 3821.5
\({\rm H}\eta\) [4]	3836.4720			3826.5 – 3846.5	3806.5 – 3826.5	3900.2 – 3920.2
NeIII	3869.86	1.74e-1		3859.9 – 3879.9	3806.5 – 3826.5	3900.2 – 3920.2
HeI [3]	3889.749			[1]	3806.5 – 3826.5	3900.2 – 3920.2
\({\rm H}\zeta\) [4]	3890.1506			3880.2 – 3900.2	3806.5 – 3826.5	3900.2 – 3920.2
NeIII	3968.59	5.40e-2		[1]	3938.6 – 3958.6	3978.6 – 3998.6
\({\rm H}\epsilon\) [4]	3971.1951			3961.2 – 3981.2	3941.2 – 3961.2	3981.2 – 4001.2
HeI [3]	4027.328			4017.3 – 4037.3	3997.3 – 4017.3	4037.3 – 4057.3
SII	4069.749	1.92e-1	9.53e-8	4062.7 – 4073.6	4049.7 – 4062.7	4082.0 – 4092.9
SII	4077.500	7.72e-2	1.16e-6	4073.6 – 4084.5	4049.7 – 4062.7	4082.0 – 4092.9
\({\rm H}\delta\) [4]	4102.8922			4092.9 – 4112.9	4082.0 – 4092.9	4112.9 – 4132.9
\({\rm H}\gamma\) [4]	4341.6837			4331.7 – 4351.7	4311.7 – 4331.7	4349.7 – 4358.7
OIII	4364.436	1.71e+0		4358.7 – 4374.4	4349.7 – 4358.7	4374.4 – 4384.4
HeI [3]	4472.734			4462.7 – 4482.7	4442.7 – 4462.7	4482.7 – 4502.7
HeII [3]	4687.015			4677.0 – 4697.0	4667.0 – 4677.0	4697.0 – 4707.0
ArIV [2]	4712.58	9.6e-3
HeI [3]	4714.466			4707.0 – 4722.0	4697.0 – 4707.0	4722.0 – 4732.0
ArIV	4741.45	7.2e-2	5.1e-3
\({\rm H}\beta\) [4]	4862.6830			4852.7 – 4872.7	4798.9 – 4838.9	4885.6 – 4925.6
HeI	4923.3051			4913.3 – 4933.3	4898.3 – 4913.3	4933.3 – 4948.3
OIII	4960.295	6.21e-3	4.57e-6	4950.3 – 4970.3	4930.3 – 4950.3	4970.3 – 4990.3
OIII	5008.240	1.81e-2	3.52e-5	4998.2 – 5018.2	4978.2 – 4998.2	5028.2 – 5048.2
HeI	5017.0769			[1]	4988.2 – 4983.2	5028.2 – 5048.2
ArIII	5193.27		3.10e+0
NI	5199.349	1.60e-5	4.34e-6	5189.3 – 5209.3	5169.4 – 5189.3	5211.7 – 5231.7
NI	5201.705	9.71e-7	6.59e-6	[1]	5169.4 – 5189.4	5211.7 – 5231.7
OI	5578.887		1.26e+0
NII	5756.19		1.14e+0
HeI [3]	5877.252			5867.2 – 5887.2	5847.2 – 5867.2	5887.2 – 5907.2
NaI	5891.583
NaI	5897.558
OI	6302.046	5.63e-3	2.11e-5	6292.0 – 6312.0	6272.0 – 6292.0	6312.0 – 6332.0
OI	6365.536	1.82e-3	3.39e-6	6355.5 – 6375.5	6335.5 – 6355.5	6375.5 – 6395.5
NII	6549.86	9.84e-4	9.22e-7	6542.9 – 6556.9	6483.0 – 6513.0	6623.0 – 6653.0
HeII [3]	6561.890
\({\rm H}\alpha\) [4]	6564.608			6557.6 – 6571.6	6483.0 – 6513.0	6623.0 – 6653.0
NII	6585.27	2.91e-3	8.65e-6	6575.3 – 6595.3	6483.0 – 6513.0	6623.0 – 6653.0
HeI	6679.9956			6670.0 – 6690.0	6652.0 – 6670.0	6690.0 – 6708.0
SII	6718.295	1.39e-5	1.88e-4	6711.3 – 6725.3	6690.0 – 6708.0	6748.0 – 6768.0
SII	6732.674	5.63e-4	1.21e-4	6725.7 – 6739.7	6690.0 – 6708.0	6748.0 – 6768.0
HeI [3]	7067.144			7057.1 – 7077.1	7037.1 – 7057.1	7077.1 – 7097.1
HeI	7067.65683
ArIII	7137.76	3.21e-1	1.4e-3	7127.8 – 7147.8	7107.8 – 7127.8	7147.8 – 7167.8
ArIV	7172.67	8.1e-1	9.8e-2
ArIV	7239.77	4.44e-1	2.26e-1
ArIV	7265.33	4.88e-1	1.90e-1
HeI	7283.3571
OII	7320.94		5.19e-2	[1]	7291.0 – 7311.0	7342.8 – 7362.8
OII	7322.01	8.37e-3	9.07e-2	7313.8 – 7326.8	7291.0 – 7311.0	7342.8 – 7362.8
OII	7331.68	9.32e-3	7.74e-2	7326.8 – 7339.8	7291.0 – 7311.0	7342.8 – 7362.8
OII	7332.75	1.49e-2	3.85e-2	[1]	7291.0 – 7311.0	7342.8 – 7362.8
ArIV	7334.17		1.22e-1
ArIII	7753.24	8.3e-2	1.3e-4	7743.2 – 7763.2	7703.2 – 7743.2	7763.2 – 7803.2
ArIII	8038.73		2.9e-5
P20	8394.703
P19	8415.630
P18	8440.274
P17	8469.581
P16	8504.819			8494.8 – 8514.8	8474.8 – 8494.8	8514.8 – 8534.8
P15	8547.731			8534.8 – 8557.7	8514.8 – 8534.8	8557.7 – 8587.7
P14	8600.754			8587.7 – 8610.8	8557.7 – 8587.7	8610.8 – 8650.8
P13	8667.398			8657.4 – 8677.4	8617.4 – 8657.4	8677.4 – 8717.4
P12	8752.876			8742.9 – 8762.9	8702.9 – 8742.9	8762.9 – 8802.9
SIII	8831.8		5.25e-6
\({\rm P}\theta\)	8865.216			8855.2 – 8875.2	8815.2 – 8855.2	8875.2 – 8915.2
\({\rm P}\eta\)	9017.384			9007.4 – 9027.4	8977.4 – 9007.4	9027.4 – 9057.4
SIII	9071.1	1.85e-2	3.94e-5	9061.1 – 9081.1	9026.1 – 9061.1	9081.1 – 9116.1
HeI [3]	9212.862
\({\rm P}\zeta\)	9231.546			9221.5 – 9241.5	9181.5 – 9221.5	9241.5 – 9281.5
SIII	9533.2	4.78e-2	2.09e-4	9525.5 – 9540.9	9483.2 – 9523.2	9558.6 – 9598.6
\({\rm P}\epsilon\)	9548.588			9540.9 – 9556.3	9483.2 – 9523.2	9558.6 – 9598.6
HeI [3]	9528.778
HeI [3]	10030.470
\({\rm P}\delta\)	10052.123			10042.1 – 10062.1	10002.1 – 10042.1	10062.1 – 10102.1

Non-parametric Emission-Line Measurements

The DAP performs non-parametric measurements of the emission lines using a simple moment analysis. See mangadap.proc.emissionlinemoments and Emission-line Moments. In survey-level runs of the DAP, we have typically paired the set of moment measurements and Gaussian models; however, the number of emission-line moment measurements need not be matched to the number of emission-line Gaussian models and vice versa.

Input Data Format

The parameters that define the emission-line moments to calculate are provided via the EmissionMomentsDB object, which is built using an SDSS-style parameter file.

The columns of the parameter file are:

Parameter	Format	Description
index	int	Unique integer identifier of the emission line. Must be unique.
name	str	Name of the transition.
lambda	float	Rest frame wavelength of the emission line to analyze.
waveref	str	The reference frame of the wavelengths; must be either ‘air’ for air or ‘vac’ for vacuum.
primary	float[2]	A two-element vector with the starting and ending wavelength for the primary passband surrounding the emission line(s).
blueside	float[2]	A two-element vector with the starting and ending wavelength for a passband to the blue of the primary band.
redside	float[2]	A two-element vector with the starting and ending wavelength for a passband to the red of the primary band.

and an example file might look like this:

typedef struct {
    int index;
    char name[6];
    double lambda;
    char waveref[3];
    double primary[2];
    double blueside[2];
    double redside[2];
} DAPELB;

DAPELB   2  OIId    3728.4835  vac  { 3716.3  3738.3 } { 3706.3  3716.3 } { 3738.6  3748.6 }
DAPELB   3  OII     3729.875   vac  {   -1      -1   } {   -1      -1   } {   -1      -1   }

Note in the above example that the second set of parameters define nonsensical passbands with limits of {-1 -1}. This is used to signify that the moment parameters are “dummy” or placeholder parameters. This is used to create an empty channel in the output MAPS file and is used just to synchronize the channel indices between the non-parametric and Gaussian-fit results. That is, it’s used to ensure that, e.g., the \({\rm H}\alpha\) measurements are in the same channel for both the EMLINE_SFLUX and EMLINE_GFLUX extensions in the DAP MAPS file.

Changing the moment parameters

The moment measurements are performed by EmissionLineMoments; see Emission-line Moments. A set of parameter files that define a list of emission-line moment sets are provided with the DAP source distribution and located at $MANGADAP_DIR/mangadap/data/emission_bandpass_filters. The database you wish to use is selected by the passbands parameter in the relevant parameter block of the Analysis Plans file. The keyword is simply the capitalized name of the file without the “.par” extension. For example, to use the elbmpl9.par database, the plan file would include

[default.eline_moments]
 passbands = 'ELBMPL9'

To provide a user-defined database, simply replace the passbands keyword with the name of the local file defining the database (in the format given above). For example,

[default.eline_moments]
 passbands = '/path/to/my/local/file/my_elb_database.par'

Gaussian Emission-Line Modeling

The DAP models the emission lines using single-component Gaussian functions. See mangadap.proc.emissionlinemoments and Emission-line Modeling. In survey-level runs of the DAP, we have typically paired the set of moment measurements and Gaussian models; however, the number of emission-line moment measurements need not be matched to the number of emission-line Gaussian models and vice versa.

Input Data Format

The parameters that define the emission-line models to fit are provided via the EmissionLineDB object, which is built using an SDSS-style parameter file.

The columns of the parameter file are:

Parameter	Format	Description
index	int	Unique integer identifier of the emission line. Must be unique. Specifically used when tying line parameters.
name	str	Name of the transition.
restwave	float	Rest frame wavelength of the emission line to analyze.
waveref	str	The reference frame of the wavelengths; must be either ‘air’ for air or ‘vac’ for vacuum.
action	str	A single character setting how the line should be treated. See Emission-Line “Actions”.
tie_f	str[2]	A sequence of 2 10-character strings that indicate how the flux of the line should be tied to another line. The first element gives the index of the line to tie (see index above). The second element provides the constraint. Currently fluxes can only be tied by fixing the line flux ratio, and lines with tied fluxes must also have their velocity and velocity dispersions tied by equality. For example, to fix the ratio of the OIII 4959 line to the OIII 5007 line, the entry for the OIII 4959 line should be {  14 =0.34 }, where 14 is the index number of the OIII 5007 in the file and the flux in the OIII 4959 line is always 0.34 times the flux in the OIII 5007 line.
tie_v	str[2]	A sequence of 2 10-character strings that indicate how the velocity of the line should be tied to another line. The first element gives the index of the line to tie (see index above). The second element provides the constraint. Velocities can be tied by equality (using =) or tied by inequality (see below); however, tying by inequality is not well tested.
tie_s	str[2]	A sequence of 2 10-character strings that indicate how the velocity dispersion of the line should be tied to another line. The first element gives the index of the line to tie (see index above). The second element provides the constraint. Velocity dispersions can can be tied by equality (using =) or tied by inequality (see below).
blueside	float[2]	A two-element vector with the starting and ending wavelength for a passband to the blue of the primary band.
redside	float[2]	A two-element vector with the starting and ending wavelength for a passband to the red of the primary band.

and an example file might look like this:

typedef struct {
    int index;
    char name[6];
    double restwave;
    char waveref[3];
    char action;
    char tie_f[2][10];
    char tie_v[2][10];
    char tie_s[2][10];
    double blueside[2];
    double redside[2];
} DAPEML;

DAPEML   2  OII     3727.092   vac  f  { None   None }  {   34      = }  { None   None }  {  3706.3  3716.3 }  {  3738.6  3748.6 }
DAPEML   3  OII     3729.875   vac  f  { None   None }  {    2      = }  {    2      = }  {  3706.3  3716.3 }  {  3738.6  3748.6 }
DAPEML  23  Hb      4862.6830  vac  f  { None   None }  {   34      = }  {   34    1.4 }  {  4798.9  4838.9 }  {  4885.6  4925.6 }
DAPEML  33  NII     6549.86    vac  f  {   35  =0.34 }  {   35      = }  {   35      = }  {  6483.0  6513.0 }  {  6623.0  6653.0 }
DAPEML  34  Ha      6564.608   vac  f  { None   None }  { None   None }  { None   None }  {  6483.0  6513.0 }  {  6623.0  6653.0 }
DAPEML  35  NII     6585.27    vac  f  { None   None }  {   34      = }  { None   None }  {  6483.0  6513.0 }  {  6623.0  6653.0 }

Note

• Both the emission-line moments database and the emission-line modeling database define the sidebands used for the equivalent width calculations. Nominally, these should be the same, but it’s up to the person that writes the two parameter files to make sure that is true.

• Format changes:

  • version 3.1.0: Many parameters removed that were used by the deprecated Elric fitter.

  • version 4.1.0: Added ability to tie the three parameters to different lines; i.e., velocity can be tied to one line while dispersion is tied to a different one.

Emission-Line “Actions”

The action parameter allows the emission-line database to be used both in masking during the stellar-continuum modeling (see SpectralPixelMask) and during the emission-line modeling itself.

The valid actions are:

• i: ignore the line, as if the line were commented out.

• f: fit the line and mask the line when fitting the stellar continuum.

• m: mask the line when fitting the stellar continuum but do not fit the line itself

• s: defines a sky line that should be masked. When masked, the wavelength of the line is not adjusted for the redshift of the object spectrum.

I.e., when using the emission-line database for the emission-line modeling, lines with the action set to f are fit, whereas all other lines are ignored.

Emission-Line Tying

Line tying in the DAP uses the functionality in ppxf in a limited and abstracted way.

Tying fluxes effectively means that the lines are put in the same emission-line template. This is why, currently, any lines with tied fluxes must also tie their velocity and velocity dispersion. Also, the DAP currently does not allow tying fluxes using inequalities.

Tying kinematics can be done with equality or inequality. For equality, use the = character, as in the example file above. Unlike the fluxes, the kinematics cannot be tied to be, e.g., a specific fraction of the value of the tied line. (I.e., you can’t tie the dispersion to be exactly half of the dispersion of the tied line). For inequality, there are a couple of options:

1. Use >N or <N to force the value to be greater or less than the provided fraction of the the value of the tied line. E.g., to force the dispersion of one component to be at least 1.5 times larger than the tied line, use >1.5. Using > or < is equivalent to >1 and <, respectively.

2. To bound the value between both upper and lower limits, you must use a single fixed fractional bound. For example, setting the tied value for the dispersion to 1.4 means that the best-fitting dispersion must be greater than 1/1.4 and less than 1.4 times the dispersion of the tied line.

Warning

Although line tying has been experimented with for MaNGA data, much of the inequality tying is not well tested.

Emission-Line “Modes”

Warning

This parameter is now DEPRECATED in favor of the tie parameter.

The mode parameter sets how the emission line should be treated with respect of the rest of the lines being modeled.

The valid modes are:

• f: Fit the line independently of all others.

• wN: Used by Elric only. Fit the line with untied parameters, but use a window that includes both this line and the line with index N.

• xN: Used by Elric only. Fit the line with its flux tied to the line with index N.

• vN: Fit the line with the velocity tied to the line with index N.

• sN: Fit the line with the velocity dispersion tied to the line with index N.

• kN: Fit the line with the velocity and velocity dispersion tied to the line with index N.

• aN: Fit the line with the flux, velocity, and velocity dispersion tied to the line with index N.

As noted in the mode description, many of the modes are only available when using the Elric module. For the w mode, this is simply because the preferred module, Sasuke, fits the full spectrum instead of fitting the lines within small spectral windows. The other limitation are because Sasuke is based on the use of template spectra to fit the emission lines (see EmissionLineTemplates): To tie line fluxes, the lines to be tied are included in the same template spectrum, meaning that their kinematics are also automatically tied. That means that, for Sasuke, the x and a modes are identical.

In the Input Data Format example, the modes set the \({\rm H}\alpha\) line as the “reference” line. I.e., there should always be one line whose mode is f. This requirement is simply practical in setting up the tied parameter structure; there is no more weight given to the fit to the reference line than any other line. The blue [OII] and red [NII] lines have their velocities tied to the \({\rm H}\alpha\) line, all kinematics of the red [OII] line are tied to the blue [OII] line, and all parameters of the blue [NII] line are tied to the red [NII] line with a fixed flux ratio of NII-6550/NII-6585 == 0.34. By virtue of being tied to lines that have their velocites tied to the \({\rm H}\alpha\) line, the velocities of the red [OII] and blue [NII] lines are also tied to the \({\rm H}\alpha\) line. Again, this doesn’t mean that the fit to the \({\rm H}\alpha\) line is given any more weight than any other line, it just means that there is one model parameter that defines the velocity of all lines.

Changing the modeling parameters

The moment measurements are performed by EmissionLineMoments; see Emission-line Moments. A set of parameter files that define a list of emission-line moment sets are provided with the DAP source distribution and located at $MANGADAP_DIR/mangadap/data/emission_bandpass_filters. The database you wish to use is selected by the passbands parameters in the relevant parameter block of the Analysis Plans file. The keyword is simply the capitalized name of the file without the “.par” extension. To provide a user-defined database, simply replace the passbands keyword with the name of the local file defining the database (in the format given above).

The emission-line modeling is performed by EmissionLineModel; see Emission-line Modeling. A set of files that define a list of emission-line model parameter sets are provided with the DAP source distribution and located at $MANGADAP_DIR/mangadap/data/emission_lines. The database you wish to use is selected by the emission_lines parameter in the relevant parameter block of the Analysis Plans file. The keyword is simply the capitalized name of the file without the “.par” extension. For example, to use the elpmpl11.par database, the plan file would include

[default.eline_fits.fit]
 emissionpassbands = 'ELPMPL11'

To provide a user-defined database, simply replace the passbands keyword with the name of the local file defining the database (in the format given above). For example,

[default.eline_fits.fit]
 emissionpassbands = '/path/to/my/local/file/my_elp_database.par'

---

[1] (1,2,3,4,5,6,7,8,9)

No primary band defined because it overlaps with another line.

[2]

Provided magnetic dipole coefficient is actually its sum with the electric quadrupole coefficient.

[3] (1,2,3,4,5,6,7,8,9,10,11,12,13)

Wavelength based on a simple average of wavelengths for many fine-structure transitions.

[4] (1,2,3,4,5,6,7,8,9,10)

Center of gravity of the blending of fine-structure lines assuming Boltzmann populations in an optically thin plasma; see, e.g.: https://physics.nist.gov/cgi-bin/ASBib1/get_ASBib_ref.cgi?db=el&db_id=&comment_code=c69&element=H&spectr_charge=1&ref=&type=