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Intergalactic Matter

Lyman α forest

1) What is it?

The Lyman α forest is an absorption phenomenon in the spectra of background quasistellar objects (QSOs) which can be observed in the ultraviolet (UV) and optical wavelength range. Following the today's picture, there exists an intergalactic medium collapsing under the influence of dark matter gravity into filamentary structures. While this gaseous medium essentially consists of hydrogen and is heated and highly photoionized by the intergalactic QSO radiation field (T ~ 30,000 K, H I / H ~ 10-4, at the intersections of the filaments the matter compresses and may form proto-galaxies (see Fig. 1).

Fig. 1 - Simulation of the distribution of hydrogen in a comoving box size with a border length of nine million light years. The filamentary structures can be seen: The brighter the colour of a region, the hotter and denser is the gas contained in that region. From the hot and dense structure in the center of the box a galaxy could arise. (Simulation: Yu Zhang, Peter Anninos, Michael L. Norman, National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign)

Any line of sight to a QSO will intersect the gaseous filaments causing absorption of the QSO continuum by the Lyman α resonance line (λ = 1215.67 Å) of neutral hydrogen. Based on Hubble's Law describing the overall expansion of the universe (v = H0 * r, v escape velocity of an object, r its distance from earth, H0 Hubble constant) and the doppler effect shifting the absorption lines in the spectra (Δ λ / λrest = v/c, Δ λ wavelength shift, λrest rest wavelength, v escape velocity, c velocity of light), the Lyman α lines of the absorbing systems can not be seen at the Lyman α rest wavelength, but they are rather shifted to higher wavelengths. That is the more distant the Lyman α absorbing structures (or just "clouds") are, the faster they move away from us (due to the Hubble expansion of the universe), and the more redshifted are the corresponding absorption lines found in the spectrum. Thus in a typical high resolution quasar spectrum the Lyman α lines are sorted according to the distances of the clouds causing the absorption, giving rise to the label "Lyman α forest". Fig. 2 shows examples for this forest seen in the spectra of two quasars with different redshifts z.

Fig. 2 - Illustration of the evolution of the Lyman α forest: higher redshift quasars exhibit a considerably denser forest of lines. (From Charlton, J.C. and Churchill, C.W. 2000, Encyclopedia of Astronomy and Astrophysics)

Because receiving information of objects in cosmological distances always means to look back in the past, the forest contains information not only about the distribution of the intergalactic Medium (IGM) in space, but also about its evolution .

A small fraction of the absorption lines detected in QSO spectra is not caused by hydrogen but belongs to various ionization stages of heavier elements, e.g., C IV, Si IV, C II, C III, N V, Fe I, Fe II, O VI. These so-called "metal" lines are associated with strong Lyman α lines, i.e., they are detected at nearly the same redshift.

2) Quantitative analysis of the Lyman α forest

For spectra with sufficient resolution (i.e. resolving the intrinsic widths of Lyman α lines [> 10 km/s]) synthetic Voigt profiles can be constructed to match individual lines or line ensembles. The fit procedure is based on three parameters per line profile:

  • the redshift z = (λobs - λrest) / λrest of the absorbing material (λobs denotes the observed wavelength),
  • the column density N (usually given logarithmically), and
  • the doppler parameter b [km/s], expressing the width of the line.
In an iterative procedure these parameters can be adjusted by minimizing the so-called χ2, which measures the difference between the observed and the synthetic line. The values for the column density of the Lyman α lines span a wide range, the lower limit being confined by the detection limit of the respective telescope (a few times 1011 cm-2) and the upper limit lying at ~ 1022 cm-2. The high column density absorbers are much more rare than the low column density ones. Typical values for the doppler parameter b lie at ~ 30 km/s. The redshift reaches from ~ 0 for the local universe to ~ 6 found in the spectra of the most distant quasars. If z > 1.5, the Lyman α lines are shifted in the optical.

Therefore, for an extensive investigation of the evolution of the Lyman α forest data from optical telescopes are required as well as UV data. In the past years, progress has especially come from the Hubble Space Telescope (HST) with its high resolution UV spectrographs, the Hopkins Ultraviolet Telescope (HUT) and, in the optical, from the 10m Keck Telescope on Hawaii and the ESO Very Large Telescope (VLT) in Chile with their powerful High Resolution Spectrograph (HIRES) and Ultraviolet-Visual Echelle Spectrograph (UVES), respectively.

3) Observational results

There are several observed quantities in the spectra of QSOs describing the properties of the Lyman α forest:

The column density distribution

The distribution function f(N) of the column densities in the Lyman α forest (i.e., the number of absorbers in a given column density bin) can be well approximated by a power law over several orders of magnitude: f(N) = A * N, A, β positive constants, thus the number of absorbers increases with decreasing column density. Numerous studies have examined the slope β and restricted it to 1.5 < β < 2. This seems to be valid for at least the linear part of the curve of growth (describing the dependence of the equivalent width from the column density) where the equivalent width is proportional to the number of absorbing atoms (log N ~ 12 - 14.5). There is some evidence for a departure from a single power law going to higher column density absorbers, in the sense that the distribution function steepens. However, for the strongest absorbers (log N > 16) f(N) flattens and the so-called damped Lyman α systems (DLAs) are more abundant than expected, judging from an extrapolation of the lower column density distribution.
There exist some hints for an evolution of f(N), but the results regarding this are still vague.

The distribution of the b parameter

By measuring the line width, insights into the kinematics of the Lyman α clouds can be gained. The distribution of the doppler parameter is roughly Gaussian with a mean of ~ 30 km/s.
On small spatial scales, the intergalactic gas is expected to be in photoionization equilibrium, i.e., the photoionization heating by the UV background balances the adiabatic cooling due to the expansion of the universe. This results in temperatures of the IGM of ~ 30,000 K being consistent with the derived doppler parameters. However, the issue is more complex, and there might be other physical effects than the thermal motion of the gas making a contribution to the b parameter.
There has also been suggested a possible evolution with z of the b value distribution: b may increase with decreasing z.

The log N - b distribution

Distributions of the doppler parameter and the column density are one way to gain information about the equation of state correlating the temperature and the density of the IGM. Occasionally, a correlation between the doppler parameter and the column density has been noted, but this result is very preliminary.

Clusters and voids

It is well-known that galaxies are not distributed homogeneously in the universe but are clustering strongly. Therefore, it suggests itself to suppose the Lyman α clouds to do the same. However, previous results indicate that they are distinct from galaxies concerning this point.
Clustering was searched for on different scales up to a velocity difference of 30,000 km/s (calculated from the distance according to the Hubble Law, see above) of two clouds and in dependence of z and log N, but only weak clustering signals have been detected, first of all for the stronger lines and on small scales, as is expected.
However, it is hard to detect clustering at a high level of significance in an individual QSO spectrum because of the short redshift path length. Besides, the broad Lyman α lines (compared with the narrow line widths of the heavier metals) are often blended (which means that two or more lines overlap) especially in low resolution data and in the optical with its much higher Lyman α line density (see below), blurring signals in the clustering function very strongly.
The question if there are voids in the Lyman α forest analogous to those seen in the galaxy distribution is still unsolved, too. The forest seems to show sporadic gaps in its distribution, but the void structure apparent in the galaxy population can not be seen.

The number density evolution

A very interesting subject examined by a wealth of authors is the number density evolution of Lyman α clouds. Lyman α lines in QSO spectra show a strong evolution in their rate of incidence with the redshift z (see Fig. 3). This evolution is usually expressed in the form

dn/dz = (dn/dz)0 (1+z)γ,

n being the number of Lyman α clouds and (dn/dz)0 being the local number density. Much observational effort has been devoted to studying the evolution by calculating the exponent γ. Summarizing the more secure results, there is no significant change in the comoving number density of clouds for 0 < z < 1, at least concerning the strong lines (defined by 13.64 < log N < 16.00) and probably also not for the weak lines (13.10 < log N < 14.00). Between 1 < z < 2 a steep rise sets in with 2 < γ < 3, the weak lines evolving much slower than their stronger counterparts. At redshifts approaching z ~ 4, the increase appears to steepen further.

Fig. 3 - The number density evolution of the Lyman α forest, comparison of different studies. Shown are the results for the column density ranges 13.10 < log N < 14.00 (upper panel) and 13.64 < log N < 16.00 (lower panel).

In general, the evolution is interpreted qualitatively as follows: On the one hand, the number density of the lines (their number per unit redshift) dn/dz decreases with decreasing z according to the expansion of the universe which forces any initial baryon overdensity to thin out. Furthermore, the expansion results in a decrease of recombinations of the free electrons with the ionized hydrogen atoms and thus in an additional decline in the number of Lyman α lines. On the other hand, the ionizing background intensity is expected to decrease rapidly from z ~ 2 to z = 0 due to the decline in the population of quasars and star-bursting galaxies generating the ionizing radiation field, allowing Lyman α clouds to become less ionized. Thus for z < 2 the decline dn/dz caused by the expansion of the universe is countered by a decreasing photoionization rate and a correspondingly increasing fraction of neutral hydrogen, resulting in a dramatic break in the evolution of dn/dz which can be seen in the evolution diagram for the stronger Lyman α lines at 1 < z < 1.5. The question if there exists an analogous slow-down for the weaker lines is still open. If so, it should be less sharp. In general, there is strong evidence for a different evolution of stronger and weaker Lyman α lines illustrated by Fig. 3.

4) Observational results from the Hamburg IGM group

Most recently we investigated the bright QSOs HE 0515-4414 (z = 1.73, B = 15.0) and HS 0747+4259 (z = 1.90, V = 15.8) discovered by the Hamburg quasar surveys (HQS and HES, respectively), using UV spectra from the high-resolution spectrograph STIS onboard the HST combined with optical spectra from VLT/UVES and Keck/HIRES, respectively. With these spectra, we could explore the Lyman α forest in the redshift range 0.9 < z < 1.9 at a resolution < 10 km/s. The main results are as follows:

  1. The number density evolution of the Lyman α lines is well described by the above given power law approach. The best fit for the weak absorbers yields γ = -0.13 +/- 0.33 and thus indicates that there is no significant evolution in the investigated redshift region. Compared with the earlier optical observations at z > 1.6 (e.g., Hu et al. (1995), Kim et al. (2001), see Fig. 3) our data possibly mark the transition to a flat evolution.
    In contrast, the strong lines show a steeper gradient in the evolution diagram with γ = 1.22 +/- 0.59. Thus we see a correlation between the strength of the evolution and the column density range in the sense that the higher column density clouds evolve faster.
    However, the expected slow-down in the evolution of the stronger absorbers cannot be recognized in our data. This break in the evolution might not occur earlier than at z ~ 1, rather than at z ~ 1.5 - 1.7 as was previously claimed in the literature.

  2. The column density distribution of the Lyman α lines can be approximated over several orders of magnitude (13.0 < log N < 16.0) by a power law. The (negative) slope is described by β = 1.61 +/- 0.04 for ~ 1.4.

  3. We searched for clustering of the Lyman α lines, but no significant signal on scales up to 10,000 km/s was detected.
For more details, see Janknecht, E., Baade, R., and Reimers D. 2002, A&A, 391, L11


02/10/02 | ej