Annu. Rev. Astron. Astrophys. 1998. 36:
267-316
Copyright © 1998 by Annual Reviews. All rights reserved |

**2.4. High Resolution Spectroscopy: Voigt Profile Decomposition**

If the Ly forest is seen as
an assemblage of redshifted lines
the standard arsenal of notions and techniques from stellar
spectroscopy becomes applicable. For lower resolution data, the
equivalent width provides a combined measure of line width and
strength. In high resolution spectra (FWHM < 25 kms^{-1})
where the
typical Ly line is resolved,
the line shapes are found to be reasonably well approximated by Voigt
profiles
(Carswell et al 1984).
Then line width (Doppler parameter *b*
(= 2
)), column density
*N*(*HI*), and redshift *z* of an absorption line are the
basic observables. The
statistics of the Ly forest
from high resolution studies largely have
been cast in terms of the distribution functions of these three
quantities and their correlations. The main advantage of the high
resolution approach is the opportunity of determining the shape of these
distribution functions without parametric prejudices, by directly
counting lines with parameters in a certain range.

The standard approach to Voigt profile fitting
(Webb 1987;
Carswell et al. 1987)
relies on ^{2}
minimization to achieve a complete
decomposition of the spectrum into as many independent Voigt profile
components as necessary to make the
^{2} probability consistent
with random fluctuations.
For stronger Ly lines the
higher order Lyman lines can provide
additional constraints when fitted simultaneously.
The absorption lines are measured against a
QSO continuum estimated locally from polynomial fits to spectral
regions deemed free of absorption. A local high order continuum fit
(as compared to a global extrapolation with a physical model for the
QSO continuum) is necessary because the spectra are patched together
from many individual echelle orders with strong variations in
sensitivity. These variations do not divide out completely when dividing
by the flux of a standard star because the light going through a slit narrow
enough to ensure slit-width limited resolution varies with the
seeing conditions and with the position of the object on the slit.
When applying a local fit to the continuum the
zeroth order contribution tends to be underestimated, i.e., the continuum
is drawn too low, which is the main drawback of this method.

Given sufficient spectral resolution, and assuming that Ly clouds are discrete entities (in the sense of some of the models to be discussed below) the profile fitting approach is the most physically meaningful way of extracting information from the Ly forest. If the absorber is a gas cloud with a purely Gaussian velocity dispersion (a thermal Maxwell-Boltzmann distribution, plus any Gaussian contributions from turbulence) a Voigt profile provides an exact description of the absorption line shape. The Doppler parameter can then be written as the quadratic sum of its individual contributions:

(5) |

Unfortunately, in most more realistic models of the absorbing gas finite velocity and density gradients invalidate the assumptions underlying Voigt profile fitting, and the line parameters may have less immediate physical meaning. Departures of the absorption line shape from a Voigt profile may contain valuable information about the underlying nature of the absorption systems, and different scenarios may have quite different observational signatures. Rotational motion (Weisheit 1978; Prochaska & Wolfe 1997), gravitational collapse (McGill 1990; Meiksin 1994; Rauch 1996) and galactic outflows (Fransson & Epstein 1982; Wang 1995) have been discussed in terms of the likely absorption line shapes they produce. As yet, the quantitative application of these results has proven difficult, because of the lack of realistic prototypical models for the actual line formation, the rather subtle departures from Voigt profiles expected, and the wide variety of profiles actually encountered.

Non-Voigt profiles can still be fitted as blends of several Voigt profiles, but the information about the non-thermal motion is encoded in the spatial correlations between the individual profiles (Rauch 1996). Also, there is no guarantee that the number of components necessary for a good fit converges with increasing signal-to-noise ratio. Clearly, for more general line formation models, global techniques of extraction the velocity information may be more appropriate.