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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:
|
(8.1) |
- In the program the velocity is assumed to be gaussian, thus:
vo = 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
|
(8.2) |
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
(vo = 0) and shifts the result into the observer's rest frame
Next: Summary of the parameters
Up: Basic Equations
Previous: Optical Depth
Petra Nass
1999-06-15