9 Emission Line Fitting (ELF)

DIPSO has access to a suite of subroutines which are designed to fit a variety of line profiles to observed data. The commands really need a bit more explanation than can readily be put into the alphabetical reference list which follows; so here’s a bit more explanation...

The primary purpose of the ELF routines is to separate blends by fitting multiple profiles. Gaussian profiles are the most commonly used, but other analytic forms are possible, as are ‘numerical’ profiles. Facilities are provided for constraining line centre positions, widths, and relative fluxes, so that known atomic data (such as relative wavelengths or intensities within multiplets) can be utilised. The option of relative flux constraint is particularly useful when analysing optically thin emission lines (hence Emission Line Fitting), but the package is entirely happy with absorption lines (which it treats as emission lines with negative fluxes), or any other form of data that can be reasonably approximated with the available profile forms.

Fits are made to the spectrum data stored in the DIPSO ‘current’ arrays. The continuum level may be set to zero by manipulations within DIPSO, or a polynomial fit to the continuum can be made simultaneously with the profile fitting. (The former option is strongly recommended.) Specification of constraints and starting values for the fit parameters is done in a command language (invoked by the DIPSO command ELFINP) which is described below. After optimisation of parameters (DIPSO command ELFOPT), the full specification of the fit and the results may be stored. The resulting fit, in spectrum form, can be pushed on the DIPSO stack (ELFPUSH).

9.1 ELF commands

The complete set of ELF commands are described in detail in appendixA. They are:

As you can see, they are all of the form ELF..., so that they can easily be found in the documentation.

9.2 ELF data storage

The ELF package takes a COPY of the DIPSO ‘current’ spectrum. The maximum space available is 1000 datum points. This number is deliberately rather smaller than the space available in DIPSO itself, since fitting to large numbers of datum points is prohibitively time consuming.

Fit data are maintained in three storage areas:

• A ‘current’ area (not to be confused with the DIPSO current arrays) contains the specification of the fit in progress. If an optimisation has been carried out, the results (in the sense of optimised coefficients) are also kept in this ‘current’ array.
• A stack of fit coefficients. Data may be interchanged between this stack (again, not to be confused with the main DIPSO stack) and the ELF ‘current’ area. Space is provided for a maximum of 20 lines in each fit.
• A stack of input numerical profiles. These must be spectrum data without internal breaks (gaps), stored in VELOCITY space.

The stack of profile types has space for up to ten entries. The first five of these are reserved for analytically specified profiles, and the last five for numerical profiles. Profile definition is as follows:

9.3 ELF general procedures

Although the command descriptions given later describe functionality in detail, it is probably worth just summarising how to do a simple Gaussian fit, for illustration. The steps would typically be:

• POP the data of interest into the current arrays. Use (e.g.) RXR to restrict the number of data points to the minimum consistent with adequately defining the line(s) of interest and a small amount of continuum.
• Although you can represent the continuum by a polynomial with free parameters, convergence is enormously improved if you first subtract a continuum (using PF, or CDRAW, for example, together with ASUB). If you really must incorporate a background polynomial in the fit, keep the degree as low as possible (e.g. zero) to avoid indeterminacy.
• Type ELFINP to invoke ELFs special command language, and input your first guesses at the values of the parameters to be optimised. Make life easier for yourself by keeping the number of non-linear parameters (line centre positions and widths) as small as possible, and try to make your guesses good ones. Type QELF to leave the command language processor.
• Type ELFOPT to start the ELF Fit Coefficient OPTimisation. If you have many free parameters, and the machine is being heavily used, go for a cup of tea, after you’ve checked the first iteration of the optimisation to make sure everything is as you expect.
• Later…you can push a copy of the ‘best fit’ model onto the DIPSO stack using ELFPUSH. You can also save the fit coefficients on the separate fit coefficient stack, for later use or reference, with ELFPUSHC.

A serious program crash while optimising, such as divide by zero or overflow, may occur occasionally. Such problems are usually caused by overspecified fits, or starting values that are grossly in error.