3.4. Discussion of surveys for faint Ly emitting candidates at z 2.4
3.4.1. Assembling giant galaxies from fragments?
The redshift at which P96b find their z 2.4 candidates is close to the peak redshift of star formation in disk galaxies of z 1-2 (M96). These sub-galactic-sized objects likely existed throughout the entire redshift range z 1-4, and could have grown into the luminous giant galaxies (ellipticals and early-type spirals) that we see today through the process of repeated hierarchical merging (cf. NW94). An epoch-dependent merger rate proportional to (1 + z)2.5 would result in a time integral of ~ 10-20 mergers of compact objects from z ~ 3.5 to z = 0 (B94). This process of repeated merging would have to be largely complete by z ~ 1 if ellipticals and early-type spirals were in fact formed from such subgalactic clumps, as their HST morphological counts show little evolution since z 1 (Fig. 3; D95, O96, Mu94). The 18 z 2.4 candidates could thus have merged to produce a few L* galaxies today, given that objects separated by several hundred kiloparsecs will have many crossing times in the interval z 2.39 to z = 0. The total V606 luminosity for the 18 z 2.4 candidates is MV -24.7 mag at z 2.39 (Fig. 5b), which agrees rather well with the combined luminosities of a few typical L* galaxies today of MV -24.3 mag (again including the expected ~ -2 mag from their K-corrections plus evolution, W91).
In models of hierarchical galaxy formation, the luminous galaxies we see today were built up through the repeated merging of smaller protogalactic pieces. Such subgalactic clumps appear to have been found at z 2.4 by P96b and P97. In addition, there have been recent reports of high redshift, "normal" star-forming galaxies with possibly larger scale-lengths and higher luminosities (e.g., H96, G94, S96a, F97, Low97, Tr97). About 40-50% of the S96a, b & Low97 samples are Ly emitters, the remainder are Ly absorbers or show no Ly at all, and may be more extinguished by dust and possibly be a more evolved population of objects that has gone through more generations of star-formation. The relatively stronger Ly emitters like the subgalactic clumps of P96b and the objects of H96, Y96, and F97 may have had fewer generations of O stars, and so fewer supernovae to produce significant dust to resonantly scatter the Ly light. These findings suggest that galaxies likely formed over a large range of redshift rather than at one special time, and likely according to several different formation scenarios. If a large percentage of galaxies did in fact form hierarchically, one would expect to find their building blocks at high redshifts (z > 1-2), consistent with the large number of star-forming objects currently being found at such high redshifts. Many studies seem to point toward a merger rate that was significantly higher in the past, following (1 + z)m with m 2-3 (B94), and suggesting that there must have been many more subgalactic clumps around at earlier epochs in order to produce the observed local luminosity function. Taken together with the fact that most luminous early-type galaxies appear to have been "in place" by z ~ 1 (Mu94, D95a, O96, L95, H97), these two points imply that a large fraction of today's luminous ellipticals and early- to mid-type spirals formed at z 1, possibly from the merging of these sub-galactic sized objects. Indeed, it has been shown that disks can be regenerated (or generated) after such mergers (HM95).
3.4.2. How much large scale structure could there be at z ~ 2.4?
Currently, eight z 2.4 candidates have been spectroscopically confirmed with the MMT or the KPNO 4 meter out of the 17 candidates surrounding 53W002 (P96b). In total, there are two negative confirmations. Deeper Keck spectroscopy is presented by A97 on the F410M fields. If one assumes this same 70% success rate for the Cycle 6 parallel fields, for which spectroscopy is in progress, then the yield will be about two z 2.4 candidates (out of the three candidates found) from the 21-hour field and about eight z 2.4 candidates (out of the 12 candidates found) from the 16-hour field. The latter is consistent with the 53W002 field, while the former has a much lower density, given the relative exposure times. The difference in the numbers of candidates from the two (approximately) equally-deep Cycle 6 F410M fields is only significant at the ~ 2 level. There are two possible reasons for this discrepancy. First, it may be an indication that the 53W002 region is not representative for the general field, but that it could be a ~ 2 fluctuation compared to other random fields, based on the numbers estimated above (see P97). Given that the Cycle 6 parallel F410M fields are only ~ 40% as deep as the original 53W002 observations, one would expect to find 11-12 z 2.4 candidates in any random part of the sky if these objects are indeed a widespread population. If the existence of the weak radio source or the other two z 2.4 AGN surrounding 53W002 (see Section 4) make the W02 field not representative of the universe at z 2.4 then one should find very few (if any) significant z 2.4 candidates in any of the random F410M searches, not consistent with the number of z 2.4 candidates found in the F410M parallel fields. If there were large-scale structure at high-redshift as has been found at z 1, one would expect to find ~ 10 z 2.4 candidates in a random field whose F410M line-of-sight is approximately tangential to a sheet or passing through the intersection of two sheets or a particularly rich sheet, as possibly in 53W002 field. Conversely, if one happens to choose a field whose F410M line-of-sight passes in between sheets, one should find very few (although not necessarily zero) candidates, consistent with the observed statistics. The F410M parallel fields of P97 allow both of the latter possibilities.
As noted in P96b, the confirmed 53W002 candidates show a remarkably small velocity dispersion (at z 2.391 ± 0.004 with v 286 km s-1, corrected to z = 0), despite the much larger width of the F410M filter. Ly emission could have been seen in the F410M filter from objects at z 2.28-2.45, although some dropoff in transmission would occur for z 2.30 and z 2.42. This implies that the subgalactic clumps may have existed to some extent in groups or proto-clusters at high redshift, or else we should have seen a larger number of objects at other redshifts (z 2.391 ± 0.004) inside the F410M filter. Currently, only one object was found (out of eight) which has a discrepant redshift (z = 2.451), surprisingly far out into the red wing of the filter.
The 16-hour field could be a factor of 4-10x more dense than the 21-hour field, far in excess of any effect from its 1.2x greater F410M exposure time. The variation in number density among the Cycle 5 and 6 fields, if real, is indeed suggestive of some kind of structure (e.g., groups, clusters, or "sheets"). This structure may have been hit with the F410M filter "face-on" in the 53W002 and 16-hour fields, but we are perhaps looking "in between" any such major structures in the 21-hour field. A picture is beginning to develop which is quite consistent with that of RHS97, in which luminous galaxies at z = 0 are broken up into several individual Ly emitting chumps at higher redshifts, and are embedded in sheet-like structures, often lying along filaments or ribbons where these sheets intersect (cf. RHS97; Ostriker, this volume). These sheets appear to be group or sub-cluster size, and may represent the preferred environment for high-redshift objects.
The extremely narrow redshift distribution for the spectroscopically confirmed objects thus far (z 2.391 ± 0.003), as compared to the much broader width of the F410M filter (z = 0.12) leads one to question why objects at other redshifts in the range 2.30 z 2.42 were not seen in the MMT or KPNO spectroscopy samples thus far. There are no major ground-based night-sky lines hampering the spectroscopic follow-up around 4100 Å. There is good agreement of the space density ( 0.027 Mpc-3) and velocity dispersion ( 286 km s-1) of the objects with measured MMT & KPNO redshifts with models based on the Press-Schechter theory (see Fig. 1 of WF91) - which predict the abundance of dark-matter halos as a function of redshift - suggesting that galaxies may have existed preferentially in groups or "proto"-clusters at z 2.4. In redshift surveys out to z 1 (B90; Co94); LF94), and most recently to z 1 (CHS95a, C96, Cohen et al., this volume) with the Keck 10-meter telescope, often more than a few objects were found at very similar redshifts in these small survey fields, supporting the possible existence of clumpiness in the redshift distribution in small fields out to z 1. In addition, groups or other large structures have recently been found at redshifts comparable to the P96b group (F96), It is possible that the "spikes" or "frothiness" observed in the redshift distribution of small fields out to z ~ 1 may have also existed at some level out to z ~ 1-3, although the clustering amplitude at higher redshift would have to be lower according to most CDM models. Recent deep KPNO 4m imaging in the F410M filter (K97) and spectroscopy (Co97) shows that the that the 53W002 "cluster" stretches over 7'(~ 5 Mpc), with two more spectroscopic confirmations at z 2.39 (again out of an entire allowed redshift range of 233 z 2.46!), and may be part of some larger-scale structure at z 2.39. Further investigations are needed to see if such large scale structure at these high redshifts are inconsistent with all CDM models.
3.4.3. Relation to Ly PG searches arid chain galaxies
It is possible that the P96b sub-galactic clumps, and possibly a large fraction of the elusive primeval galaxies, may be hiding as many of the compact FBGs (Fig. 1), and have escaped proper recognition from the ground until now because they are so small and faint. The P96b group of faint, compact star-forming subsystems at z 2.39 could thus be the galactic building blocks long sought after by proponents of the 'bottom-up' galaxy formation models. Recent ground-based narrow-band Ly imaging surveys (TDT95) may have missed any such groups or structures because the filters used were generally too narrow (~ 30 Å) to detect one by chance, unless some previous knowledge of the redshift already existed from, for example, one or more known quasars or radio galaxies. The WFPC2 medium-band filter F410M would sample typically one or two such redshift structures (discussed in Section 3.4.2) at z 2.39 (and is not limited by sky-noise as most ground-based images are). Together with the extreme compactness of the P96b z 2.4 candidates, this explains the higher detection rate of faint Ly emitting candidates with HST/WFPC2 in F410M.
Comparing the P96b findings to those of CHS95a, one finds that about 5% of the faint blue objects in the 53W002 WFPC2 field can be classified as 'chain galaxies,' which is lower than the 20%-50% estimated in their sample. We believe that such objects are likely the short-lived ( 3 x 108 years out of a total of 5 x 109 years available for z 1) merger events among time many faint blue sub-galactic clumps, in which the gas is drawn out of the merging objects during the encounter (NW94; MH95).
Figure 7. Luminosity function of the Cycle 5 & 6 Ly emitting candidates (filled triangles) together with the LF at z ~ 2-3 in the HDF from SLY97 (filled squares). The data were converted to AB magnitudes, and space densities were calculated using the comoving volume defined by the depth of the F410M passband and the size of the WFPC2 field at z 2.4. The solid line is the best fit Schechter HDF LF of SLY97. Dashed and dotted lines are fiducial photometric LFs of SLY97 at z ~ 0.2-3. The Cycle 6 F410M Ly LF becomes incomplete for MB -18.5 mag.
3.4.4. The luminosity function of Ly z 2.4 emitting candidates
The space density of the confirmed z 2.4 candidates from P96b is ~ 0.19 Mpc-3 (assuming a gravitationally-bound group). If one assumes a similar velocity dispersion for the Cycle 6 fields, the space densities would be ~ 0.064 Mpc-3 and ~ 0.29 Mpc-3 for the 21-hour and 16-hour fields respectively. Making no assumptions about the existence of any structure or groupings at z 2.4, the entire width of the F410M filter is used to derive a space density of subgalactic clumps for the 53W002 field (again, assuming a 70% success rate) of ~ 0.041 Mpc-3. In the same way, space densities are derived for the Cycle 6 fields of ~ 0.0058 Mpc-3 and ~ 0.026 Mpc-3 for the 21-hour and 16-hour fields respectively.
The LF of the z 2.4 candidates was derived from the candidates in all three Cycles 5 and 6 fields together (Fig. 7), and binned according to their F450W luminosities following SLY97. The z 2.4 Ly LF is quite steep ( ~ 1.8-2.0), despite the small-number statistics involved. SLY97 show a similar LF from photometric redshifts in the HDF that changes with redshift, in agreement galaxy redshift surveys at z 1 (e.g., L95), showing both a brightening and steepening with increasing redshift up to z ~ 3, a result expected in hierarchical models of galaxy formation in which merging plays an important role in removing the subgalactic clumps at lower redshifts. The LF at z 2.4 of P97 is consistent with that of the HDF for 2 < z < 3 (Fig. 8 of SLY97), given the following two caveats from the F410M selection: (a) time completeness limit of MF450WAB -19.5 at z 2.4 is imposed by the shallower F410M observations; and (b) given these completeness limits in F410M and B450, the F410M selection allows to only detect significant Ly emitters, not absorbers (the KPNO F410M images of K97 are deeper compared to B, and do allow to detect Ly absorbers). According to the Keck spectroscopy of S96a, b and Low97, ~ 40-50% of the higher luminosity U-band drop-out objects at z = 2-3 have (weak) Ly in emission. If we assume the same fraction of Ly emitters for the fainter z 2.4 candidates of P96a & P97, we may correct the F410M LF upwards by ~ 0.3 dex for the fact that it was selected by Ly in emission only, which would put the F410M points exactly on top of the SLY97 LF at z 2-3.