Fitting Multiple Components in Auto mode

If LONGSLIT, when in auto mode, comes across a fit defined as multiple, it will attempt to fit it with as many lines as it thinks are needed! It uses the tolerance settings for minimum and maximum width, and minimum height. These are used for the guesses and the final answers, and will probably need some tweaking. Also it will of course still need checking afterwards. It may well have more than one attempt at fitting. This checking is easily carried out using the CHECK option in MANUAL mode--it is best to use this to produce hardcopy plots which can be kept beside the terminal while you go through checking (you may find 20% of the profiles need re-fitting, but this will depend upon the line profiles, as well as the values of the tolerances). You may also need to investigate cross-sections for which no fit is given--this may be because there is no emission at that point, or the fit may have failed for some reason, even with strong emission (it may guess too many components for example, and then crash in the fitting). Note that LONGSLIT outputs to the screen the reason why the next component was not accepted when it searches for components. The display also contain details of any re-fitting. Thus if the fits are not acceptable after the first attempt at using this the user can alter the tolerances accordingly.

The option AIC in the fit defining menu determines whether Akaike's information criterion (Akaike 1973) is used during multiple fitting to decide how many components to fit. This is true by default. The guesses are made in the same way, whether or not this is true, except that the widths are allowed to be a little larger--in both cases the guesses to the widths are allowed to the value in the tolerances array, to allow for errors in guessing (the fits are only accepted if they are actually within the tolerances), this ratio is larger if AIC is true. The value of the criterion is then calculated, and the best value is selected after progressively removing components to the fit. Thus if the guessing produces three components, the program will also ``see what happens'' with two components, one component and just a base. The criterion is

$$C = M \times \ln S + 2 \times N$$ (5)

where $C$ is Akaike's information criterion, $M$ is the number of data points, $S$ is the weighted sum of squares, and $N$ is the number of fit parameters. The fit with the lowest value of $C$ is used.

For fitting the tolerances should be as close as possible to the expected values of the parameters.

The user is encouraged to learn to use this option, since it can give considerable time savings.

N.B. To refit a cube which has already been fitted, but the values changed, e.g. flux-calibrated, use the keyword COPY, which will use scaled existing values as first guesses, repeating all the fits in the ``cube''. If used with CLONE, it enables similar spectra to be easily fitted.