4.6 Discussion
4.6.3 Reconciling Downsizing with the Hierarchical Structure Forma-
massive galaxies but, as it is currently implemented, does not reproduce observations of the decline in MQ (Croton, priv. communication). Moreover, some environmental dependence is apparently expected as the triggering of AGN is accelerated in dense environs (De Lucia et al. 2005).
The model described in Scannapieco et al. (2005) presents a hybrid solution that combines internal AGN feedback with properties of the immediate environment. Here the AGN feedback efficiency also depends on the density of the local intergalac- tic medium (IGM). As the IGM density decreases with the expansion of the uni- verse, smaller AGN in less massive halos become capable of quenching star formation, thereby producing a downsizing signal. With this cooling mechanism, Scannapieco et al. (2005) find a redshift dependence of (1 +z)3/4, significantly less than the ob- served dependence of MQ ∝ (1 +z)4.5. In addition to this problem, a key question is how the IGM density relates to the environmental density we use in this study.
The answer is likely to be quite complicated, but if the two are proportional, then downsizing in this scenario would be slowed in overdense regions and accelerated in underdense regions. The predicted trend seems to work in the opposite sense to that observed (Figure 4.10).
Regardless of the physical explanation (and several may be necessary), it is clear that precise quantitative measures of the evolving mass distribution and its depen- dence on the basic parameters explored here will provide the ultimate test of these theories.
4.6.3 Reconciling Downsizing with the Hierarchical Struc-
the small fluctuations present in the early universe. In the CDM model halos grow through constant, hierarchical merging with other halos. Both the masses of indi- vidual systems and the total amount of matter in halos over a given mass increase monotonically with time. At any epoch, halos are growing and merging most actively on the largest mass scales, and the most massive halos are also the most recently assembled ones. Thus, at first examination downsizing seems completely at variance with the CDM picture.
Several processes contribute to reversing the bottom-up trend in structure for- mation, producing what appears to be to a top-down pattern to galaxy formation.
The first is simply the gradual effect of the dark energy, or cosmological constant, which causes halo growth rates to slow once the universe reaches a scale factor (1 +z)−1 >Ωm. The second is the physics of gas cooling, which has been known since well before the CDM model was introduced to select out a characteristic mass scale for galaxy formation (Rees & Ostriker 1977; Silk 1977; White & Rees 1978). Gas cannot cool rapidly, and by implication stars cannot form efficiently, until structure formation produces virial temperatures in excess of 104 K within halos. This sets the epoch for the onset of galaxy formation at z ∼15–20. Once gas temperatures reach 106–107 K, cooling again becomes inefficient, turning off star formation in the most massive halos. This then marks the end of the era of galaxy formation, as more and more mass builds up in group and cluster halos over this cooling limit.
More detailed numerical or semi-analytic models of galaxy formation show that the cooling delay alone is insufficient to reduce star formation to observed levels, particularly in massive halos, and that other forms of feedback are required, although the exact details remain controversial (e.g., Benson et al. 2003). Nonetheless, the net effect of this feedback is to place an upper limit on the range of halo mass over which active star formation can take place. This limit, taken together with the decline in the global structure formation rate at late times, can certainly explain why star formation in galaxies is rarer at the present-day than it was at z ∼1–2. As discussed in §4.6.2, it is less obvious how to explain the observed decline in the mass scale of star-forming objects.
To help gain insight into this question, we can attempt to relate various galaxies in our sample to dark matter halos. Models of halo occupation, or similar attempts to reconcile observed luminosity functions and correlation functions with theoretical halo mass functions, predict that galaxies with the range of stellar masses sampled here (log(M/M⊙)∼10–12, corresponding to logLbJ ∼10–11.2) should reside in dark matter halos of mass 1012–1015M⊙ (e.g., Yang et al. 2003; Cooray & Milosavljevi´c 2005a) and furthermore that 75-80% of these galaxies will be “central,” that is the dominant galaxies within their halo rather than satellites of a brighter galaxy (Cooray
& Milosavljevi´c 2005b). Thus, these models suggest that the objects in the three mass bins in Figure 4.11 correspond approximately to central galaxies in galaxy, group, and cluster halos.
In the top panel of Figure 4.12 we show the comoving number density of halos of mass log(M/M⊙) = 12.5,13.5, and 14.5 as a function of redshift (three lines from top to bottom). The numbers are roughly consistent with the comoving number densities of galaxies in our three mass bins, although the most massive stellar objects are more abundant than 1014.5M⊙ halos and may therefore reside in slightly less massive systems. The bottom panel shows the mean ages of halos in the three mass bins as a function of observed redshift. The mean age here is defined as the time elapsed since half of the halos in that mass range had first built up 90% or 50% of their current mass in a single progenitor (solid and dashed curves respectively), calculated using equation 2.26 from Lacey & Cole (1993).
Regardless of which criterion one uses for defining the formation epoch, the timescales for the low-mass halos are roughly twice those for the massive systems, and the change in age between z = 1.4 andz = 0.4 is roughly 2.5 times that between z = 1.4 and z = 1.0. Combining these results, we conclude that if the observed decline in star formation is related to or triggered by halo growth, then the timescale for this process is at least 5 times longer in the low-mass systems than it is in the high-mass systems. Since global dynamical timescales should be independent of halo mass at a given redshift, this suggests that the quenching mechanism is strongly mass-dependent with the potential for different physical processes acting in different
Figure 4.12 (Upper panel) The abundance of halos likely to host central galaxies in the three mass ranges plotted in Figure 4.11 versus redshift. The curves are labeled with log(M/M⊙). (Lower panel) Mean age of these systems as a function of their observed redshift. The mean age is defined as the time elapsed since half of the systems had built up a fraction f of the mass they have at zobs. Solid curves show the age for f = 0.9 and dashed curves f = 0.5.
mass ranges. As discussed previously, we note that environment is normally the most obvious explanation for downsizing, with numerical simulations of structure forma- tion indicating that dense environments evolve somewhat like high-density, high-σ8
universes, producing older and more massive halos at any given epoch, while struc- ture formation in voids is retarded (e.g., Gottl¨ober et al. 2001). The lack of a strong environmental dependence in our results, however, suggests that environment alone cannot be responsible for the observed trends in the quenching timescale with mass.