Broadening is due both to the natural width of the transition and to the velocity spread of the absorbing atoms along the line of sight.
= velocity of the cloud relative to the observer.
This full expression (1) is denoted as a ``Maxwell + damping wing'' or ``Voigtian'' profile in the program.
In the case of low column density ( 1)
can be approximated to:
= NS
This simplified expression (2) is denoted as a ``Maxwellian'' profile in the
program.
Finally if the line of sight crosses N clouds then, the resulting optical depth is:
In cases where the source has a (cosmological) velocity.
Let z be the redshift of the source.
An absorption is measured in the spectrum at = corresponding to a rest wavelength .
This yields for the redshift of the cloud:
The velocity of the cloud relative to the source is:
In practice the program computes the absorption profile in the cloud reference
frame
( = 0) and shifts the result into the observer's rest frame