Annu. Rev. Astron. Astrophys. 1998. 36: 267-316
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3.6. Spatial Structure Across the Sky: Multiple Lines of Sight

The lack of two-dimensional information is one of the main shortcomings of high redshift QSO spectroscopy. This problem makes it hard to understand the geometry of the absorbers, and to disentangle positions in velocity and real space. Through observations of common absorption systems in spatially separated LOS (multiple images of gravitationally lensed QSOs, or QSO pairs) the spatial dimension(s) across the sky can be restored to some degree. Gravitationally lensed QSOs have maximum image separations up to a few arcseconds, giving information on scales < 100 kpc. In contrast, QSO pairs rarely occur closer to each other than a few arcminutes, which limits the scale that can be probed at high redshift to larger than a few hundred kpc. The presence or absence of common absorption in two LOS gives an indication of the coherence length of the absorber. Obviously, common absorption systems must be at least as large as the transverse separation between the beams to appear in both LOS. If some of the systems are missing in one image, a maximum likelihood estimate based on the binomial probability distribution for the fraction of "hits" and "misses" can be used to estimate the mean extent of the absorbing cloud across the sky (McGill 1990).

GRAVITATIONALLY LENSED QSOS     The first gravitational lens discovered, the z = 1.39 QSO Q0957+561 (Walsh et al 1979) enabled Young et al (1981) to put a lower limit of ~ 7 kpc on the size of an intervening CIV absorption system common to both LOS. Another notorious lensed QSO, 2345+007 A,B yielded lower limits to the size of Lyalpha clouds of 1-11 h-1 kpc (at z ~ 2) (Foltz et al 1984; McGill 1990); the uncertainty comes from the unknown position of the lensing object. This scale, though strictly an upper limit, came to be considered as a typical "size" for several years, until the observations of UM 673 (z = 2.73; lens at z ~ 0.5, LOS angular separation 2.2 arcseconds) by Smette et al (1992) showed two virtually identical Lyalpha forests in the A and B images, with equivalent width and velocity differences consistent with the measurement errors. With LOS proper separations ranging up to 1h-1 kpc for Lyalpha systems a 2-sigma lower limit of 12h-1 kpc to the diameter of the clouds (which were assumed to be spherical) was obtained. Observations of another bright lensed QSO (HE 1104-1805A, B) by Smette et al (1995a) produced even more stringent lower limits to cloud diameters of 25h-1 kpc. These remarkable results seem to indicate that the Lyalpha forest absorbers are not consistent with the relatively small clouds envisaged in the pressure confined model, nor are they consistent with the possibility that the absorption of a significant fraction of the systems could arise in the virialized regions of galaxies, or could exhibit the small scale variations typical of the interstellar medium.

Unfortunately, very few lensed objects are suitable targets for Lyalpha spectroscopy: At least two images must be bright enough to be observed at high resolution; the image separation must exceed typical seeing conditions (> 1.5 arcseconds); the emission redshift must be sufficient to shift the Lyalpha forest into the optical wavelength range. The apparent lack of structure of the forest over several kpc and the limited angular separation of lensed LOS make observations of QSO pairs more suited for studying the large scale structure of the Lyalpha forest proper. Lensed QSOs however, should become increasingly useful for the study of metal absorption systems and high redshift galaxies, a topic which is beyond the scope of this review (see Smette 1995b).

QSO PAIRS     In view of the crowding in the high redshift Lyalpha forest and the relatively large separations between most QSO pairs, the cross-identification of individual absorption systems in the two LOS can be difficult, and detections of coherent absorption across the sky may be significant only in a statistical sense. Sargent et al (1982) applied a cross-correlation analysis to the spectra of the QSO pair near 1623+26 (Sramek & Weedman 1978; see also Crotts (1989), who included two additional QSOs near this pair). With transverse separations ~ 1-2h-1 Mpc the LOS were well-suited for searching for the large coherent absorption pattern predicted by some theories. Oort (1981), for example, had suggested that the Lyalpha forest was caused by intergalactic gas distributed like low redshift "superclusters". Sargent et al (1982) concluded that there is too little coherence between the systems across the plane of the sky to agree with the large "pancake" structures envisaged by Oort.

However, evidence for very large structures seen in the much less densely populated CIV forest suggests that some of the coherent absorption in the Lyalpha forest is being missed because of the difficulty of cross-identifying absorbers. Therefore, examples of gaseous structures with large coherence usually have come from high column density systems. Shaver & Robertson (1983) saw common absorption over ~ 380 h-1 kpc at z ~ 2 in metal absorption systems (Q0307-195A,B). Francis & Hewett (1993) found coincident damped Lyalpha absorption over ~ 3h-1 Mpc across the sky. Considering the firm lower limits from gravitational lensing there was reason to expect large sizes for the low column density forest as well, and such evidence was eventually found: Optical MMT data of the unusually close QSO pair Q1343+266A,B (also known as Q1343+264A,B; separation of 9.5 arcseconds) showed absorbers extending over several hundred kpc at redshifts just below 2 (Bechtold et al 1994; Dinshaw et al 1994). Even larger sizes appear to occur at somewhat lower redshift. Dinshaw et al (1995) deduced a most probable diameter of 360 h-1 kpc for 0.5 < z < 0.9.from HST FOS spectra of the Q0107-25A,B pair. A later re-analysis points to a median diameter of ~ 0.5h-1 Mpc for Q1343+266 and and ~ 1 h-1 Mpc for the lower z Q0107-25A,B (Fang et al 1996). The velocity difference between lines in different LOS assumed to belong to the same absorption system however, are small, with a intrinsic mean difference of only ~ 50 kms-1. Fang et al (1996) found a trend for the size estimate to increase with separation between the LOS, which is indicative of spatial coherence on a range of scales, the upper end of which may not have been sampled yet. Most of these studies assumed spherical clouds, but from photoionization arguments spherical objects consistent with the measured sizes and column densities would be so highly ionized as to easily overfill the universe with baryons. The simplest explanation, which allows for a denser and more neutral gas while remaining consistent with the transverse sizes assumes that typical Lyalpha clouds are flattened, with a thickness on the order of ~ 30 h-1 kpc, for transverse sizes of 1 h-1 Mpc (Rauch & Haehnelt 1995).

The large sizes, the small velocity and column density differences, the possible absence of a unique size scale, the apparent flatness of the clouds found at high and intermediate redshifts, and the general absence of voids all argue against an origin of the typical (i.e., low column density, log N ltapprox 14) Lyalpha forest line in potential wells of already formed galaxies.

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