Algorithms - Emission and absorption line fitting
Overview of line fits, result tables, and line "
Spectro1D fits spectral features at three separate stages during
the pipeline. The first two fits are fits to emission lines
only. They are done in the process of determining an emission line
redshift and these are referred to as
final fitting of the complete line list, i.e. both emission and
absorption lines, occurs after the object's classification has been
made and a redshift has been measured. These fits are known as
measuredLines. In all cases a single Gaussian is fitted
to a given feature, therefore the quality of the fit is only good
where this model holds up.
The first line fit is done when attempting to measure the object's
emission line redshift. Wavelet filters are used to locate emission
lines in the spectrum. The goal of these filters is to find strong
emission features, which will be used as the basis for a more careful
search. The lines identified by the wavelet filter are stored in the
specLine table as
foundLines, i.e., with the
category set to 1. They are stored without any
identifications, i.e., they have
restWave = 0.
Every one of these features is then tentatively matched to each of
a list of candidate emission lines as given in the line table below, and a system of lines is
searched for at the position indicated by the tentative matching. The
best system of emission lines (if any) found in this process is used
to calculate the object's emission-line redshift. The lines from this
system and their parameters are stored in the
foundLines, i.e., with the parameter
category set to 1. These lines are identified by their
restWave as given in the line table below.
The final line fitting is done for all features (both
emission and absorption) in the line list
below, and occurs after the object has been classified and a redshift
has been determined. This allows for a better continuum estimation and
thus better line fits. This latter fit is stored in HDU 2 of the
spSpec*.html files in the DAS, and in the
specLine view in the CAS (those rows from the
specLineAll table with the parameter
category set to 2).
Types of line fits stored in
|Type of fit
|"Found" emission lines from wavelet filter
|"Found" emission lines from best-fit system to
restWave from line list
|"Measured" emission and absorption lines according to the
object's classification and best redshift
restWave from line list
For almost all purposes we recommend the use of the
category=2 stored in HDU 2 of
spSpec files or the specLine view) since these result from the most
careful continuum measurement and precise line fits.
Spectral line indices (Lick indices)
Separate continuum and flux windows are used to determine spectral
line indices analogous to the Lick indices. These are stored in Line index HDU (HDU 5) of
spSpec*.fits files (this link also shows the
continuum and line windows used for these indices) and in the
specLineIndex table in the CAS.
Details of continuum fitting and line measurements
All of the line parameters are measured in the observed frame, and
no correction has been made for the instrumental resolution. Line
indices are invariant under transforming from observed to rest frame.
The results of the line fit are returned in the parameters:
wave: The central wavelength of the Gaussian in Angstroms.
height: The height of the fitted Gaussian in units of 10E-17 erg/s/cm^2/Ang
sigma: The dispersion(observed frame) of the Gaussian measured in units of Angstroms.
ew: The integrated equivalent width of the line (observed frame) in Angstroms. The equivalent width can also be estimated from the Gaussian fit.
The continuum is fit using a median/mean filter. A sliding window is
created of length 300 pixels for galaxies and stars or 1000 pixels for
quasars. Pixels closer than 8 pixels(560km/s) for galaxies and stars
or 30 pixels (2100 km/s) for QSOs to any reference line are masked and
not used in the continuum measurement. The remaining pixels in the
filter are ordered and the values between the 40th and 60th percentile
are averaged to give the continuum. The category=1 lines are fit with
a cruder continuum which is given by a fifth order polynomial fit
which iteratively rejects outlying points.
Reference Line List
The list of lines which are fit are given as ASCII line list and as HTML line table below. Note that many times that a
single line in the table actually represents multiple features. Since
the line fits are allowed to drift in wavelength somewhat, the exact
precision of the lines are not important. The wavelength precision
does become important for the emission line determination.
Every line in the reference list is fit as a single Gaussian on top of
the continuum subtracted spectrum. Lines that are deemed close enough
are fitted simultaneously as a blend. The basic line fitting is
performed by the SLATEC common mathematical library routine SNLS1E
which is based on the Levenberg-Marquardt method. Parameters are
constrained to fall within certain values by multiplying the returned
chi-squared values by a steep function. Any lines with parameters
falling close to these constraints should be treated with caution.
The constraints are: sigma > 0.5 Angstrom, sigma < 100 Angstrom, and
the center wavelength is allowed to drift by no more than 450 km/sec
for stars and galaxies or 1500 km/sec for QSOs, except for the CIV
line which is allowed to be shifted by as much as 3000 km/sec.
Testing the results
There are a number of ways that the line fitting can fail. If the
continuum is bad the line fits will be compromised. The median/mean
filtering routine will always fail for white dwarfs, some A stars as
well as late-type stars. In addition is has trouble for galaxies with
a strong 4000 Angstrom break. Likewise the line fitting will have
trouble when the lines are not really Gaussian. The
Levenberg-Marquardt routine can fall into local minima, which can
happen when there is self-absorption in a QSO line or both a narrow
and broad component for example. One should always check the
chi-squared values to evaluate the quality of the fit. Examples of
the quality of the line fits for over 100 spectra can be found in ps file with sample line fits (.ps.gz,
16 MB). In these plots, the red line is the continuum and the blue
line is the continuum plus the sum of the Gaussian fits.
You can download the line list as ASCII table.
|1399.8|| SiIV+OIV |
Last modified: Mon Sep 27 13:29:36 CDT 2004