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The dimming of the flux received from molecular emission with distance renders the measurement of molecular abundances at redshifts larger than a few tenths increasingly difficult with current sensitivities. Until now, only CO, HCN, HCO+, HNC and CN (plus OH and H2O masers and fine structure lines of CI and C+) have been detected at z > 0.1; and the few detections of HCN and HCO+ do not reveal much differences from local ULIRGs (see section 9).

In contrast to emission lines, the independence of absorption line strength with distance makes absorption line studies an ideal tool to study the ordinary, widespread molecular gas at high redshift. However, it requires a strong background continuum source just aligned with the molecular gas. Such a coincidence is currently known in a few high-z lines of sight in two main domains: UV lines of molecular hydrogen in diffuse clouds in front of high-z quasars; millimetre and radio lines in denser clouds in front of high-z radio galaxies. The number of such rare cases is expected to considerably grow in the future with large surveys and increased sensitivities of large facilities.

7.1. H2 UV absorption lines in Damped Lyman-alpha systems of quasars

Damped Ly-alpha (DLA) absorption systems seen in quasar spectra correspond to relatively large neutral hydrogen column densities: N(HI) gtapprox 2 × 1020 cm-2. There are various arguments supporting the case that DLA systems arise from galactic or proto-galactic disks, occur very close (within 10-15 kpc) to the center of typical L* galaxies (see Schechter 1976 for the definition of standard L* galaxies), and are the main neutral gas reservoir for star formation at high redshift (see e.g. Wolfe et al. 2005, Srianand et al. 2005a). DLA absorption lines are thus an essential tool to study the diffuse interstellar gas at high redshift and its evolution with respect to the redshift and type of galaxies. Although there is a major difficulty for directly detecting the emission of the corresponding dim high-z galaxies just in front of very bright QSOs, the (atomic) absorption lines by themselves may provide a rich diagnostic of their interstellar medium (e.g. Wolfe et al. 2005).

H2 UV lines of the strong Lyman and Werner bands are known as ubiquitous along lines of sight of the Galactic disk and a large proportion of those in the Magellanic Clouds (Section 6.2). The number of different H2 lines detectable along a line of sight allows a diagnostic of the column density and the abundance of H2, as well as its rotational excitation, and hence of the ratio ortho- to para-H2 and the kinetic temperature, the dust abundance and the intensity of the UV radiation field in the DLA molecular gas (see e.g. Savage et al. 1977, Tumlinson et al. 2002, Tielens 2005, Srianand et al. 2005a, b). Until a few years ago, the number of confirmed H2 detections in DLAs remained extremely low after the first detection by Levshakov & Varshalovich (1985) (see references in Ledoux et al. 2003 and Curran et al. 2004). The major problem is the need to detect very weak absorptions in H2 lines and especially to disentangle them from ubiquitous HI multi-line absorption in the Lyman-alpha forest. A major advance has been achieved by the systematic programme of Ledoux, Petitjean and Srianand and collaborators using ultra-sensitive high-resolution spectroscopy with UVES/VLT (Ledoux et al. 2003, Srianand et al. 2005a, Petitjean et al 2006). Reaching a detection limit of typically N(H2) = 2 × 1014 cm-2, they have brought the total number of current detections of H2 in DLAs and sub-DLAs to 14, all at z > 1.8, including one system at z = 4.2 (Ledoux et al. 2006). H2 is detected in about 20% of the DLAs, and the H2 column density is always small, mainly in the range 1016 - 1018 cm-2, with very low H2 / HI abundance ratio, ~ 10-3. The detection probability is practically independent of the total HI column density, but it has a very good correlation with the dust abundance. The latter is well traced by the degree of depletion of heavy elements in the gas and strongly depends on the metallicity, so that the probability of detecting H2 exceeds 50% in DLAs with metallicity larger than 0.1 solar (Ledoux et al. 2003, Petitjean et al. 2006, Noterdaeme et al. 2007).

Such properties are similar to those found by H2 studies in the LMC and SMC (Tumlinson et al. 2002) and in the Galactic halo (see Richter 2006 and references therein). Models of physical conditions in DLAs inferred from these H2 detections (Srianand et al. 2005a, b, Hirashita & Ferrara 2005), imply TK = 100-300 K, nH = 10-200 cm-3, and internal UV radiation 1-100 times larger, and dust-to-gas ratio 10-100 times smaller than the respective standard Galactic disk values. Such high value of the UV intensity, derived from the excitation of the high-J rotational levels, is in agreement with the excitation of CII derived from the CII* absorption line which is detected in all the components where H2 absorption lines are seen (Wolfe et al. 2003, Srianand et al. 2005a). It is consistent with such H2-detected DLAs being mainly located in the outskirts of high-z Lyman-Break star forming galaxies.

Ultraviolet lines of deuterated molecular hydrogen, HD, have been identified in one absorption system at z = 2.34 by Varshalovich et al. (2001). However, this is the only detection reported (Petitjean et al. 2003). CO has also been detected in only one system (Petitjean priv. com.), and other heavy-atom molecules have never been detected in UV. This is fully consistent with the low molecular contents of DLA clouds and their low metallicity.

A very important product of such accurate measurements of H2 lines at high redshift is the ability to check possible variation with time of the proton-electron mass ratio µ = mp / me. A recent reanalysis of very good quality H2 spectral lines observed in the sight-lines of two quasars, based on highly accurate laboratory measurements of Lyman bands of H2 and an updated representation of the H2 level structure, may yield a fractional change in the mass ratio of Deltaµ / µ ~ (2 ± 0.6) × 10-5, indicating that µ could have decreased in the past 12 Gyr (Ivanchik et al. 2005, Reinhold et al. 2006).

The rapid development of gamma-ray burst (GRB) observations is opening new prospects for studying high-z absorption systems and H2 in particular. The first tentative evidence for H2 molecules in a GRB absorber at z = 4.05 has been recently found by Fynbo et al. (2006). Very sensitive studies of absorption systems on sight-lines of QSOs and GRBs are one of the major goals of the new generation of extremely large telescopes presently studied (Section 12.3.1).

7.2. Millimetre and radio absorption lines in lensing galaxies and radio-sources

As explained, absorption millimetre molecular lines are easier to detect than emission ones, especially at large distances, since for their detection the sensitivity depends on the intensity of the background continuum source and not on the distance. This is well known with the detection of 21 cm HI absorption in a number of high-z DLAs (see e.g. Gupta et al. 2007 and references therein). While millimetre emission lines mostly probe the dense, warm gas, absorption line measurements are mainly sensitive to cold, diffuse gas where the rotational excitation is concentrated in the lowest energy levels. They are thus complementary to emission line studies to probe molecular abundances and physical conditions in the diffuse molecular interstellar medium not directly implied in star formation, especially at high redshift. They are indeed a very sensitive probe of cold gas at high redshift, able to detect individual clouds of a few solar masses (instead of 1010 Modot for emission). However, they are limited to the molecular clouds which by chance are along the lines of sight of strong background continuum sources. This is a severe limitation outside of the Milky Way. Indeed, such extragalactic molecular line absorptions are detected up to now either directly in the host galaxy itself of a few radio continuum sources, or in a very few strong-lensing galaxies in front of strong radio sources. Such studies are still marginal for local galaxies (see Evans et al. 2005, Liszt & Lucas 2004, and references therein) except in nearby (4 Mpc) Centaurus A where the detections include CO, 13CO, H2CO, C3H2, HCO+, HCN, HNC and CS, with abundances compatible with Galactic values (Wiklind & Combes 1997a and references therein). However, despite their small number, the four systems known and comprehensively studied at z = 0.25-0.89 (see e.g. Wiklind & Combes 1994, 1995, 1996a, b, 1997a, b, 1998, 1999, 2005; Combes & Wiklind 1997a, b, 1998, 1999; Henkel et al. 2005, Muller et al. 2006, Combes 2007, Muller et al. 2007, and references therein) are very important for the direct information on the abundances and the properties of the molecular interstellar gas at high redshift.

In these high-z systems, a total of at least 15 different molecules have been detected, in a total of more than 30 different transitions. These include CO, HCO+, HCN, HNC, CS, CN, C2H, OH, H2O, N2H+, NH3, H2CO, C3H2, HC3N. Many isotopic varieties were also detected especially by Muller et al. (2006), including 13CO, C18O, H13CN, HC18O+, HC17O+, H13CO+, HN13C, HC15N, H15NC, C34S, H234S. Two of the four known absorption systems, PKS 1413+135 and B3 1504+377, are situated within the host galaxy itself of the `background' continuum radio source. The two other absorption systems occur in intervening galaxies acting as strong gravitational lens to the background continuum source: B0218+357 and PKS 1830-211, which are among the most strongly lensed radio galaxies, and were thus among the first objects selected for such studies. These two lines of sight have a very large extinction, Av ~ 10-100, and thus a very high molecular fraction. Several isotopic species are detected there, showing that the main lines are saturated. Nevertheless, the absorption lines do not reach the zero level, indicating that the coverage of the continuum source by obscuring molecular gas is only partial, but this gas is optically thick, as verified by mm-wave interferometry (Menten & Reid 1996, Wiklind & Combes 1998, Frye et al. 1997). Such absorption data are consistent with the presence of a diffuse gas component, dominating the observed opacity, and a dense component, accounting for most of the mass (Wiklind & Combes 1997b). It is clear that without knowledge of the small scale structure of the absorbing molecular gas, one can only derive lower limits to the column density. However, within such limitations, Wiklind & Combes (1997a) have compared the column densities of simple molecules (HCO+, HCN, HNC and CS) in these high-z systems with absorption measurements in Galactic low and high density gas and in Cen A. Despite the presence of a considerable scatter, the most striking impression is the remarkable correlation, over more than three orders of magnitude, in column density. The high-z systems do not show any peculiarites compared to the local values, except maybe for the ratio HNC/HCN, suggesting that the molecular ISM and its chemistry display similar conditions at earlier epochs as it does in the present one.

Among the other important information brought by observations of high-z molecular absorption lines, let us note: i) the high sensitivity to the detection of the fundamental sub-mm transition of ortho-water (Combes & Wiklind 1997a, Wiklind & Combes 2005), which should lead to important studies with Herschel and ALMA; ii) the detection of NH3 absorption lines (Henkel et al. 2005); iii) measurements of isotopic ratios (Section 6.4, Table 3; Muller et al. 2006). The last work is particularly remarkable, with the high sensitivity of the IRAM interferometer making it possible to measure reliably the C, N, O and S isotopic abundance ratios in HCO+, HCN, HNC, CS and H2S. These ratios are much more reliable than those which result from the observation of weak and broad emission lines, showing the power of the observation of absorption lines; iv) the number of significant limits for undetected molecules, including particularly important ones such as O2 and LiH (Combes et al. 1997, Combes & Wiklind 1998); v) the surprising absence of detection of molecules with heavy atoms in the sight-line of another radio galaxy, PMN J0134-0931, where the four 18 cm lines of OH are detected (Kanekar et al. 2005), while there is a good correlation between OH and HCO+ in the other four absorption systems (see also Curran et al. 2007).

The narrow widths of the lines, 1-30 km/s, imply depths of parsec scale for the sampled clouds. This situation is favourable to detect time variations in the absorption profile, if there exists knots in the radio source moving close to the velocity of light. Variations on time-scales of a month then correspond to structures of > 103 AU. Wiklind & Combes (1997b) have reported possible time variation affecting the relative ratio of two absorbing components. High-z absorption may thus be used to probe very small scale structures in the molecular gas. In gravitationaly lensed systems, such a variability might also be used to measure the time delay between lensed components. Monitorings were carried out for this purpose, with reasonable results for the value of the Hubble constant, in spite of possible micro-lensing events in one of the lines of sight (Wiklind & Combes 2001). In the diffuse gas the rotational excitation temperature should be close to the cosmic background temperature Tbg. Multi-line observations of absorption systems could thus provide a direct measurement of the variation of Tbg with redshift. However, line saturation effects make accurate determinations difficult (Combes & Wiklind 1999).

High-z radio molecular absorption lines also offer an alternative method than using UV atomic and molecular lines for probing possible time variation of the fundamental constants. The 18 cm OH lines are probably the best for this purpose because of the strong dependence on both the fine structure constant alpha and the mass ratio µ = mp / me, and the possibility to cross-check the four OH 18 cm lines and the HI 21 cm line. Kanekar et al. (2005) have detected the four 18 cm OH lines from the z = 0.765 gravitational lens toward PMN J0134-0931. Their measurements have a 2-sigma sensitivity of [Deltaalpha / alpha] < 6.7 × 10-6 or [Deltaµ / µ] < 1.4 × 10-5 to fractional changes in alpha and µ over a period of ~ 6.5 Gyr. These are among the most sensitive constraints on changes in µ (see Reinhold et al. 2006), and complement the measurements using atomic lines on the alpha variation (e.g. Murphy et al. 2003, Chand et al. 2006 and references therein).

It is surprising that only four high-z millimetre and radio absorption systems are known (e.g. Wiklind & Combes 1999), plus one with only OH (Kanekar et al. 2005), despite the considerable efforts to discover additional ones (e.g. Xanthopoulos et al. 2001, Murphy et al. 2003). This probably reflects various difficulties (see e.g. Curran et al. 2006): the need for the alignment of a molecular cloud with a strong millimetre continuum source, just by chance along the line of sight, or even in the host galaxy of the continuum source; the fact that, while the chance of such an alignment is much enhanced in lensing galaxies, most strong lenses are achieved by massive elliptical galaxies without much gas; the absence of tight correlation with 21 cm HI absorption; the large extinctions of such molecular clouds which prevent using optical data for finding them; the rarity of exceptionally bright high-z lensed millimetre continuum sources which are required with the present sensitivity of millimetre facilities. Such reasons probably also mostly explain why the presently known systems are limited to z < 1, although the lower average metallicity at higher z may also play a defavorable role for molecular abundances, including H2. However, one may expect much progress in this field, especially at high redshift, with the gain in sensitivity in the continuum of one or two orders of magnitude of ALMA enabling a larger number of sources to be observed.

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