ISAP Line fitting module

Overview:

This module has three basic functions: it allows you to fit models to your flux continuum and spectral line data and reports the salient results; it allows you to replot your data on a velocity axis with respect to a given rest wavelength; and it will assist you in identifying spectral lines.

If your source velocity (V_helio) is significantly different from 0 km/s, we recommend entering the source velocity as your first action upon entering this module. (The three functions above will provide more useful information if the source velocity is entered.)

Three warnings: 1) We recommend averaging your data prior to entering this module: unaveraged data may have spurious points that can throw-off the convergence of fits. 2) If you have SWS data, or any other data in the units of Jy, use the Special Functions button "Change Units" and convert your fluxes to W/cm^2/um. (Future versions of Line Fit will accept Jy. 3) If you have LWS FP data, we recommend that you first use the "arithm" routine to divide your spectrum by the resolution element of the LWS (in microns), which may be found in the LWS User's Manual. This will put your data into flux density units (W/cm^2/um) although it will not change the label, which are units that are natural to the module. (The module also accepts flux density in Jys as from SWS.)

Note: there is a message sub-window at the bottom of this window, and when fits do not converge, etc., there will be a message there saying why.

In fitting lines, you may choose one of the two fitting method: Gaussian (also multiple components) or Lorentzian. you may follow one of three paths: The first path is the "composite fit," where you fit the Gaussian line and polynomial baseline simultaneously. The second possible path is "two-step baseline and Gaussian or Lorentzian fit," where you first identify baselines regions for the fit and remove (subtract) a polynomial baseline from the data, and then you identify line(s) region and fit a desired profile to this. The third path, "two-step baseline and moment fit" is much like the second, but here, after removing the baseline, you determine the "moments" of the data. The details of these operations are discussed below.

Setting Source Velocity:

Redshift:

This sub-window allows you to set a v_helio velocity, or specify a source redshift, z (z = V_helio / c).

The redshift law used in this module is always the non-relativistic optical definition of redshift:

lambda_shifted = lambda_rest x (1 + V_helio/c),

and likewise:

lambda_shifted = lambda_rest x (1 + z)

The source velocity is used in many places in this module. When a fit is performed, any cataloged lines found within 1 HPBW of the fitted line center in the source's velocity frame are reported. The nearest is referred to as the "identified line." The velocity associated with the line's fitted center (with respect to the rest wavelength of the identified line) is also reported. When the user plots the data against heliocentric velocity (the "Plot in V-space" option) the velocities shown on the x-axis are velocities with respect to the rest wavelength of the identified line. The identified line wavelength is indicated on the wavelength plots with a pointer and a label. The wavelength pointed to is the redshifted wavelength using the entered source velocity.

When velocities are reported, they are always computed using the law:

V = c x (lambda - lambda_rest) / lambda_rest

no matter how large the velocity. Note that the ISO satellite always reports wavelengths in the V_helio frame.

Three Methods of Fitting the Continuum and Line:

1) The Composite Fit: Here a polynomial baseline and a Gaussian line are fitted simultaneously to the data. The advantage of the composite fit is that no assumptions are made as to where the line ends and the baseline begins. For this reason more data points are used for each component than would available were the dataset separated, and so the results are more accurate.

The steps in this mode are :

Select the "Order of Baseline Fit" for the polynomial baseline fit. Using order 0 or order 1 for the Baseline is strongly recommended. Higher order baselines tend to not be separable from the Gaussian component, and the fits will usually not converge.
Select region for Composite Fit : When this button is set, any subsequent right mouse selection of spectrum will be used for the composite fit. If the button is not set, or no right mouse selection is made, then the whole input spectrum will be used in the fit (which is often the fastest method).
Method of Fit : You must have selected the Gaussian (single line) option or an error message will result.
Line Parameters : you may chose to fix any of the three Gaussian line parameters (height, width, and center) and thus exclude them as free parameters in the fit.
Fit Baseline and Line (Composite Fit) : The actual fit is done when this button is set. The window containing Line Fit Results pop up if the fit is successful and convergence achieved.

How the method works: An initial baseline guess (zeroeth or first order only) is made from the endpoints of the data set, and this function is subtracted from the data to guess the Gaussian line parameters. The Gaussian height and center are guessed from the extreme data point (negative or positive flux) and the lambda variance with respect to this guessed center provides a guess for the width. A modified interactive IDL curvefit routine, equipped with the parameter partial derivatives is set to work on the original data to perform a gradient search on the chi-square of the fit. Convergence is determined by a non-changing chi-square and uncertainties are determined from the product of the central diagonal of the covariance matrix of the parameters and the reduced chi-square. The data are not weighted by their own standard deviations as these are often unreliable.

2) Two-Step Baseline and Line Fit: Here the user specifies baseline regions, fits and removes the baseline, then specifies a line region , and fits a Gaussian or Lorentzian to this, or select multi Gaussian fit menu to identify and fit multiple regions The advantages to this method are that the user may avoid poor segments of the baseline in the fit, and may judge the results of baseline fitting before removing it and proceeding. If the user wants to fit a single or multiple lines in this two step method, the user must remove the baseline fit from the data. The user also records the baseline fit, and it is remembered by the module so that the user may overplot the data, baseline fit and line fit when finished. The user may also look back at the line fit reports or write them to disk.

The first step of this method is baseline removal. Note, if this step is skipped, then when the user subsequently fits a line (Gaussian , Lorentzian, or Moment), the routine will consider any underlying continuum as part of the line shape. The steps are:

Select Baseline region(s) : when this button is set, the plot works in the "Baseline selection mode", which means that all successive right-mouse selections are recorded for further baseline fit. If none is selected the baseline is fitted on the whole spectrum.
Reset selection : to start the selection from scratch (ignores all the previous selections).
Order of Baseline Fit : choose the order of the polynomial fit :
Fit Baseline : The baseline fit is performed when this button is set. The fitted baseline is plotted over the input spectrum, and a window pops-up showing the Baseline Fit Report. At this point, you have an option either to Cancel the fit and try another one, or Record or Remove/Record the current fit and go on to the Line Fit.

After performing the baseline fit, "Select Line Region" is automatically set, which means that all subsequent right-mouse selections will be used to select line range and identify possible lines in this wavelength from the line database.

The second set of the method is line fitting:

Select region for Line Fit : when this is set then any subsequent right mouse selection of spectrum will be used for line fit. If none is selected then the whole spectrum will be used.
Order of Baseline Fit : choose the order of the polynomial fit :
Method of Fit : choose the Gaussian or Lorentzian Fit for single line, Multi Gaussian for multiple lines, or Moment.
Line Parameters : choose the line parameters to hold frozen (if any); note that a dedicated widget for initial fit parameters will pop-up if the multiple gaussian line fit option is chosen.
Fit Line : The actual fit is done when this button is set. The window containing Line Fit Results will pop-up if the fit is successful and convergence is achieved.

When fit is done, the baseline fit (green) and line fit (blue) are overplotted on the spectrum and the line residual is shown in red. A plot with the residual absent may be acquired by pressing the Replot Line and Fit button. The plot is also labeled with the nearest line in the source velocity frame found in line database, but if one is found within 1 HPBW of the fitted line center. The data range used for the line fit used marked with two vertical cyan bars. The results of the line fit are displayed in a pop-up window.

lines parameters (height, width, center and flux) and their errors, equivalent width.
Note - the equivalent width is determined from the formula: EW = integral { (feature - continuum) / continuum } where the feature is comprised of the data points (line and continuum), and the continuum is the point by point baseline fit, taken from plus to minus 5-sigma from the line center.
baseline flux density w.r.t line center, Mean baseline flux density in Jy, RMS, SNR.
Delta V_helio w.r.t nearest line found
list of existing element or molecules who emits inside this line width, if a redshift is given, it is taken into account before extracting this list.

The user can then Record these parameters into Line Fit Results or Cancel and try to fix some parameters or select a new range.

Note that when the multiple gaussian option is chosen, an additional possibility is offered: a set of lines (2 up to 8) can be fitted keeping the distance between line centers fixed. This mode can be activated pressing the 'yes' button at the option 'Bounded Gaussians'. In this case, the linecenters for the selected number of gaussians will be held to a fixed distance from the linecenter of the first gaussian and the whole pattern can float as a whole during the fitting procedure. IMPORTANT: when this option is active, the numbers given in input in the 'linecenter' text field of the mutigaussian widget, which normally are the absolute linecenter values, will instead hold the distance of the linecenters with respect to the first gaussian (in microns). If this option is selected, the errors on the linecenters of the multiple gaussians will be equal to the error on the linecenter determination of the first gaussian.

Main Functions :

Baseline Fit : fit a baseline and remove it (four possible polynomials patterns)
Line Fit : fit a line on baseline removed data and record/remove it
Composite Fit : fit a baseline & line on data and record it
Select region to show Cataloged Lines: search for existing lines into given range
Show Linelist : show entries in line data base, select/plot/write

Input Options :

Order of Baseline Fit : Desired order of baseline polynomial, 0 to 3 allowed
Line Fit Method : Gaussian(single or multiple line) , Lorentzian (single line)or Moment
Fix/Free Line Height : fix line height for fit
Fix/Free Line Center : fix line wavelength for fit
Fix/Free Line Width fix line width for fit:
Redshift : Velocity or Z shift on wavelength (for database access)

Spectrum Region(s) of Interest:

All selections are done by pressing the right mouse button.

Select Baseline region(s) : select different parts of spectrum where baseline will be fitted.
Reset Baseline selection(s) : Reset baseline selection regions to none
Select region for Line fit : select region for line fitting
Select region for Composite Fit : select region for baseline & line fitting together
Select region to show Cataloged Lines: search for existing lines into given range

Plot Buttons

Set Plotstyle : select plot styles
Plot in V-Space : copy of main window plot in Velocity space
Reset original data : plot original data and delete all baseline selections
Replot original data and fit: plot original data and the latest fit
Replot fitted data : plot wave, flux from working AAR
ISAP plot buttons, environment, hardcopy, replot max and unzoom, (see ISAP main window)

Line Fit Output:

Line FIT Results : access to the list of recorded lines (print, show, erase)
Write Ascii Fit : write (wave, flux) data of fitted line to an ascii file

Line Fit Additional Buttons:

Help : this html
Exit : quit Line Fit window and save current AAR
Quit : quit Line Fit window

WARNINGS : Crazy fits

The selection is not large (short) enough

Wrong line shape

Wrong fixed parameters

Wrong baseline

Noise

Fit Parameters :

Baseline Polynomial :

poly 0 : Baseline fit is constant.
poly 1 : Baseline fit is linear.
poly 2 : Baseline fit is a 2 degree polynomial.
poly 3 : Baseline fit is a 3 degree polynomial.

Line fit method :

Gauss (single line) : line is fitted with a gauss function (like IDL routine Gaussfit)

flux = exp(-((wavelength - line_center)/line_width)^2/2) * line_height

+ a0 + a1*wavelength + a2*wavelength^2 + a3*wavelength^3

where a0, a1, a2, a3 are the baseline coefficients. For non-composite fits, these parameters are set to zero.

Lorentzian (single line) : line is fitted with a Lorentzian function. Note that this method does not allow the baseline fit and line fit together as in Gaussian method.

flux = (1. /(1. + 0.5 * (wavelength - line_center)/line_width)^2 ) ) * line_height

Moment : Statistical Parameters on selected line region

Line Parameters : Single Lines have 3 parameters :

line height (flux) can be set writing it manually in "Fix/Free Line Height" text window.
line position (wavelength) can be set writing it manually in "Fix/Free wavelength" text window.

Wavelengths are fitted if 0, or outside plot window current range.

Full Width Half Max (FWHM) can be set by selecting the following buttons in "Fix/free line width" .

LWS : Line Fit will compute the value of FWHM for LWS as follows:

For AOT 1,2 det 0 - 4 , FWHM = 0.29
For AOT 1,2 det 5 - 9 , FWHM = 0.6
For AOT 3,4 (FP) table look up

SWS : Line Fit will compute the value of FWHM from the calibration file "cal19.fits". The program computes the mean AAR data point of selected range, obtains aot band, speed, name and aotname, finds the entries in cal19 using these parameters, and interpolates the value of FWHM for the given wavelength.
Free : reset to zero (width will be fitted). Default
Enter : Type the FWHM value in the text window

The gaussian width is = FWHM/2.354

The Lorentzian width is = FWHM/2.*sqrt(2.)

Line Database Access:

Show Linelist : when this button is set, all entries of the Line list database are displayed (as non exclusive toggle buttons) with both rest and shifted wavelengths. If the line is already fitted, the button containing the nearest line will be selected upon entering into this window. The user has a choice to select/ deselect, select similar species, plot and write the selected entries to disk file.
Show Cataloged Lines in region : when this mode is set, you can select a wavelength range (right mouse selection), then a window appears with the list of existing lines inside the range (corrected with redshift on wavelength : Velocity window)

Line database :

The database currently records a list of about 800 lines. Each line is defined by a wavelength (in microns), an element or molecule formula, a transition name (when available) and a precision (not currently used). It has been created merging three lists available from MPE web server (http://www.mpe-garching.mpg.de/iso/linelists/index.html)

HI, DI and HeII Lines : 1-196 microns (Peter van Hoof)
Fine-Structure Lines : 2-205 microns (D.Lutz)
Selected Molecular Lines : 53-186 microns (compiled by E.F. van Dishoeck)
Unidentified Lines/Bands. (refer to http://www. ipac.caltech.edu/iso/lws/unidentified.html)

Warnings :
The database is not complete, it contains only the most frequently observed molecules or elements. Moreover, possible lines from sources with very high redshift may not be recorded as we limit the list to the ISO range. People who are looking for specific elements (or who observe sources with high redshift) are kindly requested to use their own line list. Some are available at ISO centers e.g. (http://www.mpe-garching.mpg.de/iso/linelists/index.html).

Line Fit Output:

Line Fit Results: Recorded lines are stored inside a report handled by 3 buttons :

show recorded lines : display a window with the list of lines and their parameters,
print recorded lines : print the list of recorded lines (same format and as show button) on a file,
clean recorded lines : erase all recorded information.

Write Ascii Fit: writes the (wave, flux) values of the latest fit to a disk file.

Line Fit specific plots buttons:

Set Plotstyle: choose Line style, Color, Symbol, Error bars, Masked data, Linear/log
Plot in V-Space : Plot the latest fit in V-space w.r.t Rest Wavelength of nearest line
Reset original data : Replots original AAR spectrum and deletes all baseline selections
Replot original data and fit : Replots original spectrum, overplot the last recorded baseline, line fit, and write the nearest line name.
Replot fitted data : plots spectrum from working AAR (may be original, or baseline removed, or /baseline & line removed)

GUI Buttons
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Last update: 03-December-1999