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There are considerable differences between the heavy-element and single Ly-alpha redshift systems. The typical column density is N(HI) approx 1015 cm-2. There is a power-law distribution of column densities of the form n(HI) approx N-1.5. (This is the area-weighted observed distribution which translates into a true distribution n(HI) approx N-3.5). The line widths are in the range 10 < b < 40 km s-1; b approx 25 km s-1 is typical. There are several limits on the sizes of the absorbing clouds. The observation of common Ly-alpha absorption lines in the spectra of the two brighter components of the gravitationally lensed QSO, Q1115+080, implies that D > 0.4 kpc. An upper limit of D < 400 kpc is inferred from the absence of common Ly-alpha forest lines in the spectra of the QSOs UM 680 and UM 681 referred to above. In a critical measurement, Foltz et al. (1984) showed that most, but not all, Ly-alpha forest lines were observed in both components of the pair Q2345+007 which is thought to be a gravitational lens, although the lensing galaxy has not been observed. Making a plausible assumption about the redshift of the lensing galaxy, Foltz et al. deduced that the minimum size of the Ly-alpha clouds was 8 kpc; this is likely to be close to the actual value if it is true that some strong lines are not seen in both lines of sight. If the pair is not a lens then the value of D would be about 15 kpc. Statistical methods have been used to set limits on the abundances of any heavy-elements associated with the Ly-alpha clouds. Norris et al. (1983) found marginal evidence for absorption in the OVI lambdalambda 1034, 1038 doublet to be statistically associated with Ly-alpha absorption lines in the spectra of several high-redshift QSOs. They derived an abundance ratio 0/H approx 10-2(O/H)sun on the assumption (see below) that the Ly-alpha clouds are photo-ionized by the meta-galactic flux of radiation from QSOs. Later, Chaffee et al. (1985) conducted an analysis of a single high column density system in the QSO Q0014+81 and deduced that they had detected SiIII lambda1206 line. The problem is that this line lies in the Ly-alpha forest. More detailed calculations of the expected ionization conditions in the clouds indicated that SiIII lambda1206 would be the strongest observable heavy-element line in their spectral range. The inferred abundance was (Si/H) = 0.001 (Si/H)sun. A Lyman limit system with no detectable lines of heavier elements was discovered in the QSO Q2126-158 (zem = 3.30) by Boksenberg and Sargent (1983). This system has zabs = 2.99 and the HI column density is well determined to be N(HI) = 3 x 1017 cm-2. The limit on the possible heavy-element abundance, as reinterpreted by Chaffee et al. in the light of their improved calculations, was Z = 0.001 Zsun. In summary, it is still not established in my opinion that any lines of heavier elements have been detected associated with the Ly-alpha forest lines. This is true for both the weaker lines when added together and for single strong systems. In this respect the Ly-alpha forest redshifts are clearly different from the heavy-element redshifts.

Only weak clustering has been detected in the 2-point correlation function of the Ly-alpha clouds (Webb 1987, personal communication). An earlier study by Sargent, Young and Schneider (1982) revealed no clustering either in the correlation function of a single QSO, Q1623+268 (zem = 2.55), or in the cross-correlation between the Ly-alpha forest lines in this QSO and a second object, Q1623+269, separated from Q1623+268 by 3 arcmin (or approx 1 Mpc) on the plane of the sky. If the local, galaxian correlation function is written as dP = N0[1 + xi(r)]dV where xi(r) = (r/rc)-1.77 and where rc = 5 Mpc, the simplest hierarchical clustering model predicts that rc changes with redshift according to the relation rc(z) = rc(0)(1 + z)-5/3. In fact, the limit obtained by Sargent et al. was rc = 0.2 Mpc at z = 2.5 as compared with rc = 1 Mpc predicted by the simple theory. The marginal clustering detected by Webb is consistent with the upper limit obtained earlier. Rees and Carswell (1987) also pointed out that there is no evidence for voids in the Ly-alpha cloud redshift distribution.

The Ly-alpha clouds exhibit strong evolution in redshift (Peterson 1978; Young, Sargent and Boksenberg 1982; Murdoch et al. 1986). According to the latest work, the number density of the absorption lines evolves as dN / dz approx (1 + z)2.3±0.1 and that for lines with rest equivalent width above 0.36 Å, dN / dz approx 60 at z = 2.5.

Thus, the Ly-alpha lines differ qualitatively from the heavy-element redshifts in at least three important respects: composition, clustering and evolution in number density.

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