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

**2.3. Intermediate Resolution Spectroscopy: Line Counting**

At higher
resolution, where it becomes possible to distinguish between discrete
absorption lines, the distribution of the lines in terms of equivalent
width *W* and redshift *z* is the next most sophisticated
tool. Just as the
mean absorption *D* under certain conditions provides a measure of the
mean (gas) density of the universe, so does the number of lines per
unit equivalent width,
*d*^{2} /
*dW dz* essentially measure the clumpiness of the
Ly forest gas. An
exponential distribution in *W* and a power law dependence on (1 +
*z*) have been found to provide a reasonable match
to the observed line counts
(Sargent et al (1980);
Young et al (1982b);
Murdoch et al (1986)).
For lines above a rest
equivalent width threshold *W* > 0.16 Å,

(4) |

with a typical *W*_{*}
0.27 Å
(Bechtold 1994),
and 1.5 < < 3
(see also the discussion on redshift evolution below).
The multiplicative form of Equation (4) is justified by a relatively weak
dependence of *W*_{*} on *z*
(Murdoch et al 1986).
The exponential model fits less well for lines with *W* < 0.3
Å as
the weaker lines are moving off the saturated part of the curve of
growth and become more numerous.

Unfortunately, statistics involving the observed equivalent width
distribution
are not easy to interpret in physical terms. The *W* values are usually
obtained by simply measuring statistically significant downward
excursions from the QSO continuum. Without properly deblending the
lines (impossible at low resolution) the curve of growth cannot be used
to relate *W* to the more meaningful parameters *N* and *b*.