The Structure of the Universe in the Quasar Absorption Spectra

Abstract

An analysis of the absorption lines observed in the spectra of quasars makes it possible to study the evolution of the structure of the Universe up to redshifts $z \sim 5$. The observed clustering of C IV lines demonstrates the multiple birth of low-mass galaxies in separate structural elements—filaments and “pancakes.” This ensures their subsequent regular hierarchical merger in the central galaxy or group of galaxies. Remnants of the early “pancakes” are observed today as the Local Group, groups around the Andromeda and Centaurus galaxies, and other small groups of galaxies. In turn, the observed clustering of Lyman-alpha lines shows that starless dark matter (DM) halos are also formed in structural elements and their hierarchical clustering leads to the formation of massive starless dark matter halos of moderate density, which also appear in numerical models.

Appendix

STATISTICAL CHARACTERISTICS OF THE STRUCTURE OF THE UNIVERSE

As was shown in [33], in the linear theory of gravitational instability there is a “natural” length scale,

$$\begin{gathered} {{L}_{0}} = \frac{1}{{{{k}_{0}}}} = \frac{{{\text{Mpc}}}}{{{{\Omega }_{m}}{{h}^{2}}}} \simeq 7.29\;{\text{Mpc}}\frac{{0.14}}{{{{\Omega }_{m}}{\kern 1pt} {{h}^{2}}}}{\kern 1pt} , \\ {{M}_{L}} = \frac{\pi }{6}\langle {{\rho }_{m}}\rangle L_{0}^{3} \simeq 7.5 \times {{10}^{{12}}}{\kern 1pt} {{M}_{ \odot }}{\kern 1pt} . \\ \end{gathered} $$

(11)

Several characteristic scales appear in Zel’dovich’s theory, associated with the “natural” scale and the processes of formation of structural elements—“pancakes” and filaments. These scales are directly related to the moments of the perturbation spectrum

$${{Q}_{n}} = \int\limits_0^\infty \,{{k}^{n}}P(k{\text{/}}{{k}_{0}})dk{\kern 1pt} ,$$

(12)

where $P(k)$ is the spectrum of perturbations, normalized by the usual condition

$$\sigma _{8}^{2} = \int\limits_0^\infty \,{{k}^{2}}P(k{\text{/}}{{k}_{0}}){{W}^{2}}(k{\kern 1pt} {{R}_{8}})dk \simeq 0.64,$$

and $W(x)$,

$$W(x) = 3(\sin x - x\cos x){\text{/}}{{x}^{3}}{\kern 1pt} ,$$

is the filter corresponding to a spherical halo with radius ${{R}_{8}} = 8{\kern 1pt} {{h}^{{ - 1}}}$ Mpc.

As was shown in [4, 67], in cosmological models with “cold” DM, the evolution of the structure is determined by the displacement of DM particles from the unperturbed position and the characteristic length

$$\begin{gathered} {{l}_{0}} = \sqrt {{{Q}_{0}}} \simeq 13{\text{ Mpc}}, \\ {{M}_{0}} = {{M}_{L}}{{({{l}_{0}}{\text{/}}{{L}_{0}})}^{3}} \simeq 4 \times {{10}^{{13}}}{\kern 1pt} {{M}_{ \odot }}. \\ \end{gathered} $$

(13)

This scale appears in observations of galaxy clusters and in the parameters of the structure of the Universe at low redshifts [24].

At earlier stages of the evolution of the Universe, smaller scales appear. Thus, for the standard spectrum [33] limited by the region

$$\begin{gathered} 0 \leqslant k \leqslant {{k}_{{mn}}} = 170{\kern 1pt} {{k}_{0}} \simeq 23{\text{ Mp}}{{{\text{c}}}^{{ - 1}}}, \\ {{M}_{{mn}}} = {{M}_{0}}{{({{k}_{0}}{\text{/}}{{k}_{{mn}}})}^{3}} \simeq {{10}^{5}}{\kern 1pt} {{M}_{ \odot }}, \\ \end{gathered} $$

(14)

$$\begin{gathered} {{l}_{1}} = \sqrt {{{Q}_{0}}{\text{/}}{{Q}_{2}}} \simeq 2{\text{ Mpc}}, \\ {{M}_{1}} = 1.33{\kern 1pt} \pi \langle \rho \rangle l_{1}^{3} \simeq 1.3 \times {{10}^{{12}}}{\kern 1pt} {{M}_{ \odot }}. \\ \end{gathered} $$

(15)

These values are close to the observed group sizes (7). The same scales are visible in the mass distribution of observed galaxies and clusters of galaxies. Using the standard methods of the theory of random processes [4, 68, 69], one can roughly estimate the average linear density of “pancakes” along a random straight line as

$${{\sigma }_{1}} = \frac{{{{f}_{m}}}}{{2\pi {{l}_{1}}}}{\kern 1pt} ,$$

(16)

where ${{f}_{m}}$ is the fraction of the mass included in the observed objects. The observed mean free path between C IV absorption systems $\langle {{d}_{{sys}}}\rangle$ (9) at fraction $\langle {{f}_{m}}\rangle \sim 0.6 \times {{10}^{{ - 3}}}$ corresponds to the characteristic length ${{l}_{1}} \simeq \langle {{f}_{m}}{{d}_{{sys}}}\rangle {\text{/}}2\pi \simeq 0.6$ Mpc, which is close to the estimate of ${{l}_{1}}$ (15). In the model [65], such a spectrum corresponds to the mass of DM particles ${{M}_{{{\text{DM}}}}} \sim 2$ keV.