and Cosmology

8. Cosmology III: The Cosmological Parameters
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In recent years, QSOs at redshifts > 6 have been
discovered, not least by careful color selection in data
from the Sloan Digital Sky Survey (see Sect. 8.1.2). The
spectrum of one of these QSOs is displayed in Fig. 5.42.
For this QSO, we can see that virtually no radiation
bluewards of the Lyα emission line is detected. After
this discovery, it was speculated whether the redshift had
been identified at which the Universe was reionized.
The situation is more complicated, though. First, the
Lyα forest is so dense at these redshifts that lines blend
together, making it very difficult to draw conclusions
about a homogeneous absorption. Second, in spectra of
QSOs at even higher redshift, radiation bluewards of the
Lyα emission line has been found. As we will soon see,
the reionization of the Universe probably took place at
a redshift significantly higher than z ∼ 6.
8.5.2 Phenomenology of the Lyman-α Forest
Neutral hydrogen in the IGM is being observed in the
Lyα forest. For the observation of this Lyα forest, spectra
of QSOs with high spectral resolution are required
because the typical width of the lines is very small, corresponding
to a velocity dispersion of ∼ 20 km/s. To
obtain spectra of high resolution and of good signal-tonoise
ratio, very bright QSOs are selected. In this field,
enormous progress has been made since the emergence
of 10 m-class telescopes.
As mentioned before, the line density in the Lyα
forest is a strong function of the absorption redshift. The
number density of Lyα absorption lines with equivalent
width (in the rest-frame of the absorber) W ≥ 0.32 Å at
z 2 is found to follow
dN
dz ∼ k(1 + z)γ , (8.17)
with γ ∼ 2.5andk ∼ 4, which implies a strong redshift
evolution. At lower redshift, where the Lyα forest is
located in the UV part of the spectrum and therefore
is considerably more difficult to observe (only by UVsensitive
satellites like the IUE, FUSE, and the HST),
the evolution is slower and the number density deviates
from the power law given above.
From the line strength and width, the HI column
density N HI of a line can be measured. The number
density of lines as a function of N HI is
dN
dN HI
∝ N −β
HI , (8.18)
with β ∼ 1.6. This power law approximately describes
the distribution over a wide range of column densities,
10 12 cm −2 N HI 10 22 cm −2 , including Ly-limit
systems and damped Lyα systems.
The temperature of the absorbing gas can be estimated
from the line width as well, by identifying the
width with the thermal line broadening. As typical values,
one obtains ∼ 10 4 Kto2× 10 4 K which, however,
are somewhat model-dependent.
The Proximity Effect. The statistical properties of the
Lyα forest depend only on the redshift of the absorption
lines, and not on the redshift of the QSO in the spectrum
of which they are measured. This is as expected
if the absorption is not physically linked to the QSO,
and this observational fact is one of the most important
indicators for an intergalactic origin of the absorption.
However, there is one effect in the statistics of Lyα
absorption lines which is directly linked to the QSO.
One finds that the number density of Lyα absorption
lines at those redshifts which are only slightly smaller
than the emission line redshift of the QSO itself, is
lower than the mean absorption line density at this redshift
(averaged over many different QSO lines-of-sight).
This effect indicates that the QSO has some effect on the
absorption lines, if only in its immediate vicinity; for
this reason, it is named the proximity effect. An explanation
of this effect follows directly from considering
the ionization stages of hydrogen. The gas is ionized
by energetic photons which originate from hot stars and
AGNs and which form an ionizing background. On the
other hand, ionized hydrogen can recombine. The degree
of ionization results from the equilibrium between
these two processes.
The number of photoionizations of hydrogen atoms
per volume element and unit time is proportional to the
density of neutral hydrogen atoms and given by
ṅ ion = Γ HI n HI , (8.19)
where Γ HI , the photoionization rate, is proportional
to the density of ionizing photons. The corresponding
number of recombinations per volume and time is