and Cosmology

8.5 Origin of the Lyman-α Forest
proportional to the density of free protons and electrons,
ṅ rec = α n p n e , (8.20)
where the recombination coefficient α depends on the
gas temperature. The Gunn–Peterson test tells us that
the intergalactic medium is essentially fully ionized, and
thus n HI ≪ n p = n e ≈ n b (we disregard the contribution
of helium in this consideration). We then obtain for
the density of neutral hydrogen in an equilibrium of
ionization and recombination
n HI =
α n 2 p
Γ . (8.21)
HI
This results shows that n HI is inversely proportional to
the number density of ionizing photons. However, the
intergalactic medium in the vicinity of the QSO does not
only experience the ionizing background radiation field
but, in addition, the energetic radiation from the QSO
itself. Therefore, the degree of ionization of hydrogen
in the immediate vicinity of the QSO is higher, and
consequently less Lyα absorption can take place there.
Since the contribution of the QSO to the ionizing
radiation depends on the distance of the gas from the
QSO (∝ r −2 ), and since the spectrum and ionizing flux
of the QSO is observable, examining the proximity effect
provides an estimate of the intensity of the ionizing
background radiation as a function of redshift. This
value can then be compared to the total ionizing radiation
which is emitted by QSOs and young stellar
populations at the respective redshift. This comparison,
in which the luminosity function of AGNs and the starformation
rate in the Universe are taken into account,
yields good agreement, thus confirming our model for
the proximity effect.
8.5.3 Models of the Lyman-α Forest
Since the discovery of the Lyα forest, various models
have been developed in order to explain its nature. Since
about the mid-1990s, one model has been established
that is directly linked to the evolution of large-scale
structure in the Universe.
The “Old” Model of the Lyman-α Forest. Prior to this
time, models were designed in which the Lyα forest was
caused by quasi-static hydrogen clouds. These clouds
(Lyα clouds) were postulated and were initially seen as
a natural picture given the discrete nature of the absorption
lines. From the statistics of the number density of
lines, the cloud properties (such as radius and density)
could then be constrained. If the line width represented
a thermal velocity distribution of the atoms, the temperature
and, together with the radius, also the mass of the
clouds could be derived (e.g., by utilizing the density
profile of an isothermal sphere). The conclusion from
these arguments was that such clouds would evaporate
immediately unless they were gravitationally bound in
a dark matter halo (mini-halo model), or confined by
the pressure of a hot intergalactic medium. 5
The New Picture of the Lyman-α Forest. For about
a decade now, a new paradigm has existed for the
nature of the Lyα forest. Its establishment became possible
through advances in hydrodynamic cosmological
simulations.
We discussed structure formation in Chap. 7, where
we concentrated mainly on dark matter. After recombination
at z ∼ 1100 when the Universe became neutral
and therefore the baryonic matter no longer experienced
pressure by the photons, baryons were, just like dark
matter, only subject to gravitational forces. Hence the
behavior of baryons and dark matter became very similar
up to the time when baryons began to experience
significant pressure forces by heating (e.g., due to photoionization)
and compression. The spatial distribution
of baryons in the intergalactic medium thus followed
that of dark matter, as is also confirmed by numerical
simulations. In these simulations, the intensity of ionizing
radiation is accounted for – it is estimated, e.g., from
the proximity effect. Figure 8.21 shows the column density
distribution of neutral hydrogen which results from
such a simulation. It shows a structure similar to the
distribution of dark matter, however with a higher density
contrast due to the quadratic dependence of the HI
density on the baryon density – see (8.21).
From the distribution of neutral gas simulated this
way, synthetic absorption line spectra can then be computed.
For these, the temperature of the gas and its
peculiar velocity are used, the latter resulting from
the simulation as well. Such a synthetic spectrum is
5 The latter assumption was excluded at last by the COBE measurements
of the CMB spectrum, because such a hot intergalactic medium
would cause deviations of the CMB spectrum from its Planck shape,
by Compton scattering of the CMB photons.
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