Running the program

`gauss' requires an input spectrum in which the data points are equally spaced in wavelength. If you supply a spectrum with unequally spaced points it will abort with an error message. A spectrum with unequally spaced points can be converted to one with equally spaced points using Figaro command `scrunch' (see Section ).

Before running `gauss' make sure that a soft and a hard plot device have been allocated using the Figaro commands `soft' and `hard'. These are required for graphics (although use of the `hard' device is not mandatory). The program will fail if `soft' has not been specified.

The program will prompt for the following:

• Name of spectrum file
  Name of spectrum file to be fitted. Must be 1-d. If no errors are available (.VARIANCE) then a message is written to the terminal to this effect and the goodness of fit will be in terms of rms only. If `soft' and `hard' have not been set, then the program will terminate at this point.
• Label for plot
  Label written to top of soft and hard plot, and recorded in the results data file.
• Are Gaussian fit results to be recorded on a file
  If `yes' then name of file is prompted for. If `no' results will be written to terminal only.
• Name of data file for results
  This is the name of the data file (.dat) to which results are written. If a file of this name already exists then the results are simply appended to this file. If not, then a new file of this name is created.
• Use whole of spectrum for line analysis
  If `yes' then all the spectrum is displayed. If `no' the `xstart' and `xend' of the region to be displayed is prompted for (cf. `splot').
• Scale so all of spectrum fits
  If `yes' then whole Y extent plotted. If not `high', `low' and `bias' are prompted for (cf. `splot').

The spectrum is then plotted on the soft device in the lower box. If errors are available, then these are displayed in the upper box. The upper box is used for residuals on line and continuum fit. The scalar for the residuals indicates the ratio between the range of spectrum data to the range of residuals data, i.e. smaller errors and residuals have a larger scalar on the residuals box.

The continuum fitting menu next appears. The line or lines are demarcated from the continuum using the cursor, the parameters of the polynomial fitting set, and the fit performed. When satisfactory the fit and residuals are plotted ready for Gaussian fitting.

The options are as follows:

• CUR: Use the cursor to indicate the left and right edges of one or more regions of continuum. There is no limit to the number of continuum regions that can be so demarcated. Usually these regions will bracket the lines of interest.

• ORD: Order of polynomial fit to continuum points.

• SIG: Factor times sigma on last continuum fit such that points whose deviation from the last fit exceed this value are not used for the subsequent fits.

• ERR: Factor times the individual error on a point such that a point whose deviation from the last fit exceeds this value is not used in subsequent fits (only usable if errors are available)

• ITN: Number of iterations performed for rejecting points with deviations exceeding the rejection value

• FIT: Apply the polynomial fit specified by ORD,ITN and SIG/ERR to the continuum. (CUR must have been set for this to occur.) If ORD, SIG, ERR, or ITN have not been set then the default values are 3, 2.0, 1.0, and 1 respectively. For each iteration, the iteration number, the rms on the fit for each order (up to a maximum of 7), the number of rejected points and the number of fitted points are printed to the terminal (cf. `abline'). In the case when errors are available, the mean value of the deviation as a factor times the actual error bar is printed out as a function of the order. The aim is to take the lowest order and minimum number of iterations so that the rms (or mean fractional error) and number of rejected points level out. The values of SIG/ERR, ORD and ITN can be altered until this condition is achieved. The continuum fit highest order, highest iteration number fit is plotted on the `soft' device from the left edge of the left section to the right edge of the right section. The residuals on the continuum fit appear in the residuals box over the extent of the fitted continuum (excluding the line(s)).

• GAU: Continuum fitting complete; move to GAUssian fitting.

The Gaussian fitting menu now appears. The line or lines are simulated by one or more Gaussians.

The options are as follows:

• LIM: Left and right edges of observed profile to be fitted are indicated by the cursor. If this option is omitted the profile edges are taken as the nearest edges of the continuum sections, and a warning to this effect is issued.

• SIN: Fit a single Gaussian to a profile. This is a quick way to fit a line by a single Gaussian involving minimum user interaction. With the cursor the peak position of the line is indicated. The peak height of this line is found and the half height points taken to get the line width. These initial values are then used to optimise the fit. If the fit is successful then the results-peak position, peak height, sigma (= FWHM/2.3540), flux in the line, equivalent width of the line and the rms deviation on the fit (mean deviation in terms of the error bars if errors are available) are written to the screen and to the data file if appropriate. See OPT below for details of what happens if the optimisation fails.

• NEW: Introduce a Gaussian at a cursor defined position, of height the same as the data value and width 4 X channels.

• NEX: Introduce another Gaussian to a profile where one or more Gaussians have been fitted. A new Gaussian is introduced at the peak of the residuals (observed - fitted). This can have negative height (absorption line) in an emission profile, or vice versa, if residuals are small, so watch out. At any time at most ten Gaussian lines can be kept, an attempt to specify more lines is rejected.

• INCH: Interactively alter the position, height or width of a Gaussian. The latest Gaussian introduced, or the one SELected (see below) is changed thus:
  • P: position
  • H: height; followed by a number to give additive modification
  • W: width
  • S: stop the alteration

  For example: `P100' shifts a Gaussian right by the profile extent; `H-20' decreases the Gaussian height by 20% of the peak height of the original line; W10 widens the line by 10% of the total profile extent. At each change the old fit is erased and the new fit is redrawn.

  S stops the alteration and re-plots the whole display, including residuals, on the latest fit. The rms (or mean fractional deviation in terms of the error bars) on the fit is written to the terminal.

• LIS: Lists the fitting Gaussians in order of introduction, giving position, height, sigma and flux (proportional to height x FWHM).

• SEL: Set index number to that of the Gaussian whose parameters are to be modified. The list of fitting Gaussians is printed and selection made.

• DEL: Set index number to that of the Gaussian which is to be deleted. The list of fitting Gaussians is printed and selection made. The display is redrawn and the new sum of fitting Gaussians and their residuals are plotted.

• OPT: Optimises the fit. Any of the Gaussian parameters-position, height or width-can be constrained so that the value does not change during the optimisation process. If such single constraints are required then the index number of the Gaussian and the parameter to be constrained are entered in response to the `npcon' prompt. Sets of Gaussians can also be `chained' so that their values vary together: for example the separation of two Gaussians can be kept fixed when fitting a doublet with known separation. The index number of the Gaussians, the parameter to be chained and relation between the parameters is entered in reply to the `ichain', `chain' and `rchain' prompts. Different sets of parameters can be chained, e.g. in a three Gaussian fit the positions of Gaussians 1 and 2 could be chained and the relative heights of Gaussians 2 and 3. However if a parameter of a Gaussian is already constrained it cannot be included in a chain.

  The form of weighting for the residuals are prompted. Three options are available:

  • a) no weighting (i.e. unit weights);
  • b) weighting by signal value (without continuum subtraction);
  • c) weighting by inverse square of errors (when available).

  By employing weights more emphasis on points with either higher value or lower errors can help to constrain the fit. Method c is analogous to minimising chi-squared. Success cannot be guaranteed with the minimisation routine. In particular if constraints or chaining are employed then the optimisation can be more troublesome.

  Usually a small change to the interactive fit will enable a minimum to be found if a failure occurs. However don't expect miracles. The algorithm only finds a local minimum. If you don't believe the fit, try another interactive fit and optimise again. The general rule is to try for a fit by a minimum number of Gaussians and to check that the deviations on the line fit are greater than or equal to the error bars, or the deviations on the continuum fit if errors not available.

  If the optimisation is successful or the interactive fit is adopted, then position of peak, peak height, sigma and flux in each fitting Gaussian as well as the equivalent width on the whole profile and the simple (i.e. unweighted) rms deviation on the fit (mean deviation in terms of the error bars if errors are available) are written to the terminal and recorded on the data file (if applicable). On the `soft' display, the fitting Gaussians, their sum and the residuals on the fit are displayed.

• REC: Recall a previous Gaussian fit to the profile. The name of the data file on which the fit was recorded is prompted for. The position, height and width of the recalled Gaussians, equivalent width and rms/mean error on the fit are written to the terminal and the individual Gaussians and their sum and residuals displayed. Any of the individual lines can then be altered by SEL and INCH. If any recalled line falls outside the line extent (which must have been set previously) a warning is issued and the line ignored. There is no safeguard against the case where more than ten lines are read from the file. You have to take care that this does not happen, otherwise the internal storage of `gauss' gets messed up in an unpredictable way.

• HARD: Plot final fit on the specified hard-copy device. Produces a file which needs to be sent to the appropriate printer.

• SAV: Save the continuum and Gaussian fit spectrum. The sum of the Gaussian fit on the continuum is saved as a spectrum file. The name of this file will be prompted for on quitting from the Gaussian fitting menu.

• CON: Move on to next section of the spectrum for more line and continuum fitting (returns to point where `xstart' and `xend' are specified).

• QUIT: Quit from program (fit finished). If the fit is to be saved then the name of the output spectrum is prompted for:
  • Fitted spectrum to be saved
    Name of 1-d spectrum file to be produced. Note that the continuum on this spectrum only extends from the minimum to the maximum X values delimited in the continuum fitting (CUR), but the range of the X values is the same as that of the input spectrum.