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

**5.2. The Ly Forest as a
Cosmological Laboratory**

The first generation of simulations was largely aimed at establishing the physical properties of the Ly absorbers. The newly gained understanding of the nature of the Ly forest and the increasing realism of the simulations, together with new semi-analytic methods and novel ways of data analysis have brought quantitative cosmology with the low column density Ly forest within reach.

Aside from the cosmic microwave background, the intergalactic medium is
the only astrophysical environment for which observable properties can (at
least in principle) be calculated from a simple set of cosmological
initial conditions. This is because at z~ 3 the density fluctuations
=
/
- 1 on
spatial scales relevant for detectable
Ly lines (on the order of
10^{2} kpc comoving) are not too far into the non-linear regime,
so the history of the gas causing most of the low column density
Ly
forest has not yet been obliterated by virialization and dissipative
processes. Overdensities between
0 and
~ 15 roughly correspond to
Ly lines on the linear
part of the curve of growth (12
log *N*
14), where spectroscopic
measurements are most sensitive. When observing structures still dominated
by gravity the problem of "bias", one of the
main obstacles to doing cosmology with galaxies, largely can be avoided.

The link between the observable appearance of the Ly forest and the various cosmological input parameters can be described by the Gunn-Peterson relation for the HI optical depth, generalized to include an inhomogenous density and velocity field. As long as the gas is highly ionized and in photoionization equilibrium (not necessarily thermal equilibrium), and the gas is unshocked, the optical depth is given by

(17) |

This equation relates the optical depth for
Ly absorption to
the mean baryonic density (in gas) in units of the critical density,
_{b}, the Hubble
constant at redshift *z*, *H*(*z*), the average gas
temperature *T*, the proper baryon density
, the photoionization
rate _{-12} in units
of 10 ^{-12} *s*^{-1}, and the gradient of
the local peculiar velocity
*dv*_{pec}/*dr* along the LOS. A further
convolution with a Voigt profile is necessary to include the proper
thermal velocity broadening. To turn this relation into a complete
description of the observed
Ly forest, cosmology has to
predict
the cosmic density and velocity fields, the fraction of the closure
density in the form of gas, the equation of state, *T* =
*T*(), and
the ionizing radiation field.
The exponent
(=2 for an isothermal gas)
takes account of the fact that in denser regions of the universe the
gas is typically warmer because it is more effectively heated by
photoionization, but also
depends on the reionization history
of the gas and the amount of adiabatic expansion/compression.
Hui & Gnedin (1997),
and Croft et al (1997a)
find values of
1.6 - 1.8.

Cosmological parameters can now be "measured" by
iterating simulations with different input parameters until the
simulated statistics of
(*z*) (the mean absorption,
correlation
function etc) match the observed ones. Perhaps the simplest
cosmological parameter combination to be obtained is related to the
baryon density,
_{b}.
Given eqn. (17) the optical depth
scales approximately with
(
*h*_{50}^{2})^{} /
_{-12}. Using an
independent estimate of the photoionization rate
_{-12}, e.g., from
the integrated UV radiation of QSOs,
one can determine _{b}.

The simulations show that a rather high
_{b}
*h*^{2} is required to
reproduce the amount of observed absorption, even for a conservatively
low estimate of
(Hernquist et al 1996,
Miralda-Escudé et al
1996).
If the ionizing background is given by the known QSOs alone and
a Haardt & Madau
(1996)
spectrum (scaled to
*J*_{-21}
0.23, at
*z* = 2) is adopted,
_{b}
*h*^{2} > 0.017
(Rauch et al 1997).
Although the observations of
_{eff} on which the result
is based, are still somewhat uncertain, relatively
large _{b} values
appear to be an inherent feature of hierarchical
structure formation and cannot be avoided unless most of the low column
density absorption dominating the
Ly forest has a different
physical origin
(Weinberg et al 1997).

*COSMOLOGICAL PARAMETERS WITHOUT HYDRODYNAMICS *
Rerunning the simulations with different input parameters and/or
evolving them over a long time span is expensive, as is the analysis of
large observed and simulated datasets. A number of new
semi-analytical techniques have been developed to avoid these
difficulties. Although not "hydrodynamically correct" they can give
new insights into important aspects of the sometimes obscure dependence
of the observational properties on the underlying physical
environment. Such techniques compensate for the absent hydrodynamics
by various analytical recipes:
Petitjean et al
(1995), and
Croft et al (1997b)
used dark matter simulations and assume that baryons (furnished
with a suitable analytical thermal history) trace the dark matter directly;
Bi et al (1992),
and Hui et al (1997)
applied power spectra with various forms of cutoff to mimic the smoothing
introduced by the Jeans length;
Gnedin & Hui (1998),
using a dark
matter code, simulate the effects of the gas pressure by modifying the
gravitational potential.

*THE LYMAN ALPHA FOREST AS A RECORD OF PRIMORDIAL
FLUCTUATIONS* Semianalytical work by
Gnedin & Hui (1996) and
Hui et al (1997)
has elucidated the relation between column
density peaks ("absorption lines") and the statistics of density
peaks, and has given analytical expressions for the dependence of the
shape of the column density distribution function *f* (*N*) on
cosmological parameters. The slope of *f* (*N*) was found
largely to be determined by the normalization and the slope of the initial
mass power spectrum, with changes in the equation of state *T* =
*T*()
having an additional, but smaller impact. The overall normalization of
*f* (*N*) is given by
(_{b}
*h*^{2})^{2} /
; a change in this quantity
shifts *f* (*N*) horizontally to larger *N*.

Croft et al (1997b)
have suggested a technique for recovering the
initial power spectrum of density fluctuations directly from the
fluctuations of the optical depth. The distribution function of pixel
fluxes in a Ly forest
spectrum on larger scales is assumed to
have originated via gravitational collapse from an initially Gaussian
probability distribution of overdensities
. Then the flux
probability function can be mapped monotonically according to the rank of
the flux values back onto a Gaussian probability function for the initial
. The density power spectrum
(width of the Gaussian) *P*(*k*) is
then known up to a normalization, which can be derived from iterative
cosmological simulations with the same *P*(*k*) but different
normalization until the right flux power spectrum is obtained from
simulated spectra. The flux power spectrum is unique up to a
normalization which can be fixed by observing the mean absorption
.

*POTENTIAL PROBLEMS - UNSOLVED QUESTIONS* The
new paradigm for the Ly
forest has considerable explanatory
power, but that does not mean that it is correct. The interpretation of
the absorption
systems, and the cosmological measurements planned or already performed
to date depend on gravitational collapse as the dominant source of
structure in the intergalactic medium. Even if the hierarchical models
are basically correct, it is conceivable that
local physical effects may upset some of the
cosmological conclusions. A fluctuating radiation field may be a
source of non-gravitational structure in the forest, as may be stellar
feedback. How much of the absorption is caused by gas blown out by
supernova explosions or stellar winds, and how robust are the
cosmological conclusions in that case ? Metal enrichment has been
found to be common for absorption systems with HI column densities as
low as log *N*(*HI*) ~ 14
(Tytler et al 1995;
Cowie et al 1995).
If this is not due to a very early phase of metal enrichment we have to
worry that some process other than gravitational collapse may have
formed the metal enriched Ly
clouds. The origin of the ionizing radiation
and the spectral slope are another source of uncertainty. When and how
do reionization and reheating happen, and where do the photons come
from ? Is collisional reheating important, and how much do stars
contribute to the UV flux, as a function of time ?
On the technical side: Do hydrodynamic codes already converge, or how
much do the inferred cosmological parameters
(_{b}, the amount of
small scale structure present) depend on the resolution and size of the
simulations, and the numerical technique ?

Finally, the cosmological picture itself could be wrong, and the interpretation of the forest as absorption mostly by the intergalactic medium (as opposed to distinct galaxies) may be doubtful. Galaxy halos or disks could be big/numerous enough to produce the low column density Ly forest as well. For low redshift absorption lines, this last possibility has received much attention, and we will briefly consider this question next.