© CAMBRIDGE UNIVERSITY PRESS 1999

1.7.5 CHDM: Early Structure Troubles?

Aside from the possibility mentioned at the outset that the Hubble constant is too large and the universe too old for any = 1 model to be viable, the main potential problem for CHDM appears to be forming enough structure at high redshift. Although, as mentioned above, the prediction of CHDM that the amount of gas in damped Lyman systems is starting to decrease at high redshift z 3 seems to be in accord with the available data, the large velocity spread of the associated metal-line systems may indicate that these systems are more massive than CHDM would predict (see e.g., (Lu et al. 1996, Wolfe 1997). Also, results from a recent CDM hydrodynamic simulation (Katz et al. 1996) in which the amount of neutral hydrogen in protogalaxies seemed consistent with that observed in damped Lyman systems (DLAS) led the authors to speculate that CHDM models would produce less than enough DLAS; however, since the regions identified as DLAS in these simulations were not actually resolved gravitationally, this will need to be addressed by higher resolution simulations for all the models considered.

Finally, Steidel et al. (1996) have found objects by their emitted light at redshifts z = 3-3.5 apparently with relatively high velocity dispersions (indicated by the equivalent widths of absorption lines), which they tentatively identify as the progenitors of giant elliptical galaxies. Assuming that the indicated velocity dispersions are indeed gravitational velocities, Mo & Fukugita (1996, hereafter MF96) have argued that the abundance of these objects is higher than expected for the COBE-normalized = 1 CDM-type models that can fit the low-redshift data, including CHDM, but in accord with predictions of the CDM model considered here. (In more detail, the MF96 analysis disfavors CHDM with h = 0.5 and 0.2 in a single species of neutrinos. They apparently would argue that this model is then in difficulty since it overproduces rich clusters - and if that problem were solved with a little tilt n_p 0.9, the resulting decrease in fluctuation power on small scales would not lead to formation of enough early objects. However, if 0.2 is shared between two species of neutrinos, the resulting model appears to be at least marginally consistent with both clusters and the Steidel objects even with the assumptions of MF96. The CDM model with h = 0.7 consistent with the most restrictive MF96 assumptions has ₀ 0.5, hence t₀ 12 Gyr. CDM models having tilt and lower h, and therefore more consistent with the small-scale power constraint discussed above, may also be in trouble with the MF96 analysis.) But in addition to uncertainties about the actual velocity dispersion and physical size of the Steidel et al. objects, the conclusions of the MF96 analysis can also be significantly weakened if the gravitational velocities of the observed baryons are systematically higher than the gravitational velocities in the surrounding dark matter halos, as is perhaps the case at low redshift for large spiral galaxies (Navarro, Frenk, & White 1996), and even more so for elliptical galaxies which are largely self-gravitating stellar systems in their central regions.

Given the irregular morphologies of the high-redshift objects seen in the Hubble Deep Field (van den Bergh et al. 1996) and other deep HST images, it seems more likely that they are mostly relatively low mass objects undergoing starbursts, possibly triggered by mergers, rather than galactic protospheroids (Lowenthal et al. 1996). Since the number density of the brightest of such objects may be more a function of the probability and duration of such starbursts rather than the nature of the underlying cosmological model, it may be more useful to use the star formation or metal injection rates (Madau et al. 1996) indicated by the total observed rest-frame ultraviolet light to constrain models (Somerville et al. 1997). The available data on the history of star formation (Gallego et al. 1995, Lilly et al. 1996, Madau et al. 1996, Connolly et al. 1997) suggests that most of the stars and most of the metals observed formed relatively recently, after about redshift z ~ 1; and that the total star formation rate at z ~ 3 is perhaps a factor of 3 lower than at z ~ 1, with yet another factor of ~ 3 falloff to z ~ 4 (although the rates at z 3 could be higher if most of the star formation is in objects too faint to see). This is in accord with indications from damped Lyman systems (Fall, Charlot, & Pei 1996) and expectations for = 1 models such as CHDM, but perhaps not with the expectations for low-₀ models which have less growth of fluctuations at recent epochs, and therefore must form structure earlier. But this must be investigated using more detailed modeling, including gas cooling and feedback from stars and supernovae (e.g., Kauffmann 1996, Somerville et al. 1997), before strong conclusions can be drawn.

There is another sort of constraint from observed numbers of high-redshift protogalaxies that would appear to disfavor CDM. The upper limit on the number of z 4 objects in the Hubble Deep Field (which presumably correspond to smaller-mass galaxies than most of the Steidel objects) is far lower than the expectations in low-₀ models, especially with a positive cosmological constant, because of the large volume at high redshift in such cosmologies (Lanzetta et al. 1996). Thus evidence from high-redshift objects cuts both ways, and it is too early to tell whether high- or low-₀ models will ultimately be favored by such data.