Broadening Function

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.

• In the ideal case of atoms at rest.

  

  

  

• Let be the normalized distribution of atoms with velocity between v and
  v + dv, then:

  

• In the program the velocity is assumed to be gaussian, thus:

= 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