FIXED PARAMETERS: On occasion it is useful to fix the redshift or the Doppler parameter because you know them accurately from fits to other lines.. eg z and b from SiII, and you wish to apply these to OI or CII. Fixed parameters are indicated by UPPER CASE letters after the parameters in question. For the input fort.13 file the parameter lines could look like:

O I 14.043 4.382795E 4.25K
O I 14.043 4.382893J 4.25N
O I 12.346 4.383487 13.04

.. in which case the redshifts and the Doppler parameters are fixed, but the column densities are free to vary for the first two, and everything varies in the fit for the third.

TIED PARAMETERS: Another thing you might want to do is to tie parameters -- for example so that SiII and CII are at the same redshift, and have the same Doppler parameters (or Doppler parameters in the ratio set by the square root of their mass ratios to mimic thermal broadening). This is done by the same letter approach, but now one thinks of a reference ion (with lower case letters) and others tied to it (by the corresponding upper case ones), so the ion detail lines in fort.13 become like:

C II 14.043 4.382893j 4.25k 0.00 1.00E+00 0
C II 15.568 4.383865c 11.32n 0.00 1.00E+00 0
SiII 14.043 4.382893J 4.25K 0.00 1.00E+00 0
SiII 13.276 4.383865C 11.32N 0.00 1.00E+00 0

.. here the redshifts and the Doppler parameters are tied. The mysterious 1.00E+00 is the ASSUMED temperature, which is fixed at 1K in this case so that the Doppler parameters are effectively the same, i.e. all the b is turbulent. If you want thermal widths, set the 0.00 to be some small number (like 0.01) -- it is the turbulent Doppler parameter in km/s. If you like 1.0E4K, then change the 1.00E+00 to 1.00E+04, and so on. If there is a number there it fixes the value, and 0.0 means free to fit. (0.00 0.00E+00 gives a thermal fit). You can tie Doppler parameters at different redshifts if you want to, but it is not clear what that would mean.

There are some things to be aware of:

Do not  use the same lower case letter more than once, since then the program does not know what you are trying to link a variable to.  This does not mean you are restricted to 26 linked parameters however - the "j" in the example above could be replaced by a two-letter combination (e.g. "ja"), and in such a case "J" should be changed to "JA". This means there are 676 independent tied or fixed systems possible, which should be plenty!

Note that you can't fix both the turbulent and thermal Doppler parameters at the same time, because this fixes the total b-value (which you can do, as above). If the turbulent value input is non-zero, then the temperature value is ignored, whatever it is, and the program treats it as an input value zero. Note that the letter should be earlier in the alphabet than the 'lastchtied' one in the setup file, since if not it is liable to try fitting a turbulent and thermal component simultaneously using a different prescription.

In this case the column densities are free parameters, but you can fix and tie these as well if you want to. Fixing is obvious, but tied column densities is not something which has been wanted often, so it is a bit primitive. Outline details on how to do this are here.

ESTIMATING TEMPERATURES: Once the Doppler parameters for different elements in the same redshift system are known, then it is possible to estimate the temperature and turbulent components of the Doppler parameter. The safest way of doing this is after the event, when you see if the parameters are consistent with those you would expect from a single system with some thermal broadening. If they are not then either the errors are too large to allow a temperature estimate, or there is some component structure which has been missed. Since this state of affairs is the common one, there used to be no quick way of getting temperature components from the program. However, there is now -- in the same way that characters after some specified one (in the vp_setup.dat file) after the column density values flag that the column densities should be summed, if these late alphabet characters are used after the Doppler parameters they tie the Doppler parameters to a thermal + Gaussian turbulence model. It is best to do this from an input file (if for no other reason than that I have not tried it with interactively entered parameters), which might contain in the ions/guesses list:

   FeII      13.7237    2.910220AA    11.33wa
   SiII      13.5840    2.910220AA    12.85WA
   AlII      12.1005    2.910220AA    12.97WA
   C II      14.2342    2.910220aa    16.25wa
.....

What happens here is that the ones with lower case flags (C II and FeII) provide reference Doppler parameters for the calculation of temperature and turbulent broadening, with the velocities from each added in quadrature, and the ones with upper case flags are tied to follow them according to the ion mass which is in the atom.dat file. All lines included go in to determining the parameters needed for a best fit, so in principle it does not matter which you choose as a reference. However, since the variables held internally are the Doppler parameters for the two ions, it is best to choose ones with fairly different masses, and definitely not to choose two (like C II and C IV) with exactly the same mass! I have no idea what happens if you do, or if you fail to have two lower case flags present.

Note that there are a range of Doppler parameter combinations which are unphysical, such as those requiring a negative temperature or negative value for the square of the turbulent velocity (negative turbulent velocities are equivalent to positive ones, since it is used only as a square in a quadrature sum). These are checked for, and vaguely sensible physical values substituted.

The output on the screen and to fort.18 now gives the temperature and turbulent estimates, where appropriate, and very rough error estimates at the end of the iteration. The fort.26 summary file has the  same numbers.
 

SUMMED COLUMN DENSITIES:  There is another way tieing parameters, and that is to make the ratio of ions within a complex to be the same for all components in the complex while letting the actual ratios be determined by the fit. This can also be used for single ions where you might be interested in the total column density rather than  the individual components -- since the total in close blends may often be determined more accurately than the root sum squared error indicates. The reason for this is that within complexes the uncertainties for individual components may arise because similar profiles can be obtained while trading column density contributions between components while the overall total changes little.  The procedure for doing this is described here, and it involves vp_setup.dat (see 'Optional Extras') parameters, but is reasonably straightforward.

Pretty well everything which can go in the fort.13 file has now been covered except the last item on the line which gives the ion, redshift etc.. which has always shown up as 0. It should be zero in any sensible fit, but occasionally it is useful to have lines of a system appear in one region only. To do this just replace the '0' by the region number (which is just the placement in the list at the beginning of the file). Its main use is as a convenient (?) tool for modifying local continua when you have overlapping spectral regions which don't agree.