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2.1. Introduction: Changing Paradigms of Galaxy Formation

We now turn to the interesting history of how our views of galaxy formation have changed over the past 20-30 years. It is convenient to break this into 3 eras

  1. The classical era (pre-1985) as articulated for example in the influential articles by Beatrice Tinsley and others. Galaxies were thought to evolve in isolation with their present-day properties governed largely by one function - the time-dependent star formation rate psi(t). Ellipticals suffered a prompt conversion of gas into stars, whereas spirals were permitted a more gradual consumption rate leading to a near-constant star formation rate with time.

  2. The dark matter-based era (1985-): in hierarchical models of structure formation involving gravitational instability, the ubiquity of dark matter halos means that merger driven assembly is a key feature. If mergers redistribute angular momentum, galaxy morphologies are transformed.

  3. Understanding feedback and the environment (1995-): In the most recent work, the evolution of the morphology-density relation (Dressler et al 1997) and the dependence of the assembly history on galactic mass (`downsizing', Cowie et al 1996) have emphasized that star formation is regulated by processes other than gas cooling and infall associated with DM-driven mergers.

2.2. Galaxy Morphology - Valuable Tool or Not?

In the early years, astronomers placed great stock on understanding the origin of the morphological distribution of galaxies, sometimes referred to as the Hubble sequence (Hubble 1936). Despite this simple categorization 70 years ago, the scheme is evidently still in common use. In its support, Sandage (e.g. 2005) has commented on this classification scheme as describing `a true order among the galaxies, not one imposed by the classifier'. However, many contemporary modelers and observers have paid scant attention to morphology and placed more emphasis on understanding stellar population differences. What value should we place on accurately measuring and reproducing the morphological distribution?

The utility of Hubble's scheme, at least for local galaxies, lies in its ability to distinguish dynamically distinct structures - spirals and S0s are rotating stellar disks, whereas luminous spheroids are pressure-supported ellipsoidal or triaxial systems with anisotropic velocity fields. This contains key information on the degree of dissipation in their formation (Fall & Efstathiou 1980).

There are also physical variables that seem to underpin the sequence, including (i) gas content and color which relate to the ratio of the current to past average star formation ratio psi(t0) / bar{psi} (Figure 8) and (ii) inner structures including the bulge-to-disk ratio. Various modelers (Baugh et al 1996) have argued that the bulge-to-disk ratio is closely linked to the merger history and attempted to reproduce the present distribution as a key test of hierarchical assembly.

Figure 8a Figure 8b

Figure 8. A succinct summary of the classical view of galaxy formation (pre-1985): (Left) The monotonic distribution of Hubble sequence galaxies in the U - V vs V-K color plane (Aaaronson 1978). (Right) A simple model which reproduces this trend by changing only the ratio of the current to past average star formation rate (Struck-Marcell & Tinsley 1978). Galaxies with constant star formation permanently occupy the top left (blue) corner; galaxies with an initial burst rapidly evolve to the bottom right (red) corner.

Much effort has been invested in attempting to classify galaxies at high redshift, both visually and with automated algorithms. This is a challenging task because the precise appearance of diagnostic features such as spiral arms and the bulge/disk ratio depends on the rest-wavelength of the observations. An effect termed the `morphological k-correction' can thus shift galaxies to apparently later types as the redshift increases for observations conducted in a fixed band. A further limitation, which works in the opposite sense, is surface brightness dimming, which proceeds as propto (1 + z)4, rendering disks less prominent at high redshift and shifting some galaxies to apparent earlier types.

The most significant achievements from this effort has been the realization that, despite the above quantitative uncertainties, faint star-forming galaxies are generally more irregular in their appearance than in local samples (Glazebrook et al 1995, Driver et al 1995). Moreover, HST images suggest on-going mergers with an increasing frequency at high redshift (Le Fevre et al 2000) although quantitative estimates of the merging fraction as a function of redshift remain uncertain (see Bundy et al 2004).

The idea that morphology is driven by mergers took some time for the observational community to accept. Numerical simulations by Toomre & Toomre (1972) provided the initial theoretical inspiration, but the observational evidence supporting the notion that spheroidal galaxies were simple collapsed systems containing old stars was strong (Bower et al 1992). Tell-tale signs of mergers in local ellipticals include the discovery of orbital shells (Malin & Carter 1980) and multiple cores revealed only with 2-D dynamical studies (Davies et al 2001).

2.3. Semi-Analytical Modeling

As discussed by the other course lecturers and briefly in Section 1, our ability to follow the distribution of dark matter and its growth in numerical simulations is well-advanced (e.g. Springel et al 2005). The same cannot be said of understanding how the baryons destined, in part, to become stars are allocated to each DM halo. This remains the key issue in interfacing theory to observations.

Progress has occurred in two stages - according to the eras discussed in Section 2.1. Semi analytic codes were first developed in the 1990's to introduce baryons into DM n-body simulations using prescriptive methods for star formation, feedback and morphological assembly (Figure 9). These codes were initially motivated to demonstrate that the emerging DM paradigm was consistent with the abundance of observational data (Kauffmann et al 1993, Somerville & Primack 1999, Cole et al 2000). Prior to development of these codes, evolutionary predictions were based almost entirely on the `classical' viewpoint with stellar population modeling based on variations in the star formation history psi(t) for galaxies evolving in isolation e.g. Bruzual (1980).

Figure 9

Figure 9. Schematic of the ingredients inserted into a semi-analytical model (from Cole et al 2000). Solid lines refer to mass transfer, dashed lines to the transfer of metals according to different compositions Z. Gas cooling (M) and star formation (psi) is inhibited by the effect of supernovae (beta). Stars return some fraction of their mass to the interstellar medium (R) and to the hot gas phase (e) according to a metal yield p.

Initially these feedback prescriptions were adjusted to match observables such as the luminosity function (whose specific details we will address below), as well as specific attributes of various surveys (counts, redshift distributions, colors and morphologies). In the recent versions, more elaborate physically-based models for feedback processes are being considered (e.g. Croton et al 2006)

The observational community was fairly skeptical of the predictions from the first semi-analytical models since it was argued that the parameter space implied by Figure 9 enabled considerable freedom even for a fixed primordial fluctuation spectrum and cosmological model. Moreover, where different codes could be compared, considerably different predictions emerged (Benson et al 2002). Only as the observational data has moved from colors and star formation rates to physical variables more closely related to galaxy assembly (such as stellar masses) have the limitations of the early semi-analytical models been exposed.

2.4. A Test Case: The Galaxy Luminosity Function

One of the most straightforward and fundamental predictions a theory of galaxy formation can make is the present distribution of galaxy luminosities - the luminosity function (LF) Phi(L) whose units are normally per comoving Mpc3 2.

As the contribution of a given luminosity bin dL to the integrated luminosity density per unit volume is propto Phi(L) L dL, an elementary calculation shows that all luminosity functions (be they for stars, galaxies or QSOs) must have a bend at some characteristic luminosity, otherwise they would yield an infinite total luminosity (see Felton 1977 for a cogent early discussion of the significance and intricacies of the LF). Recognizing this, Schechter (1976) proposed the product of a power law and an exponential as an appropriate analytic representation of the LF, viz:


where Phi* is the overall normalization corresponding to the volume density at the turn-over (or characteristic) luminosity L*, and alpha is the faint end slope which governs the relative abundance of faint and luminous galaxies.

The total abundance of galaxies per unit volume is then:


and the total luminosity density is:


where Gamma is the incomplete gamma function which can be found tabulated in most books with integral tables (e.g. Gradshteyn & Ryzhik 2000). Note that NTOT diverges if alpha < -1, whereas rhoL diverges only if alpha < -2.

Recent comprehensive surveys by the 2dF team (Norberg et al 2002) and by the Sloan Digital Sky Survey (Blanton et al 2001) have provided definitive values for the LF in various bands. Encouragingly, when allowance is made for the various photometric techniques, the two surveys are in excellent agreement. Figure 10 shows the Schechter function is a reasonably good (but not perfect) fit to the 2dF data limited at apparent magnitude bJ < 19.7. Moreover there is no significant difference between the LF derived independently for the two Galactic hemispheres. The slight excess of intrinsically faint galaxies in the northern cap is attributable to a local inhomogeneity in the nearby Virgo supercluster.

Figure 10

Figure 10. Rest-frame bJ luminosity function from the 2dF galaxy redshift survey (Norberg et al 2002). (Top) a comparison of results across the northern and southern Galactic caps; there is only a marginal difference in the abundance of intrinsically faint galaxies. (Bottom) combined from both hemispheres indicating the Schechter function is a remarkably good fit except at the extreme ends of the luminosity distribution.

Fundamental though this function is, despite ten years of semi-analytical modeling, reproducing its form has proved a formidable challenge (as discussed by Benson et al 2003, Croton et al 2006 and de Lucia et al 2006). Early predictions also failed to reproduce the color distribution along the LF. The halo mass distribution does not share the sharp bend at * and too much star formation activity is retained in massive galaxies. These early predictions produced too many luminous blue galaxies and too many faint red galaxies (Bower et al 2006).

As a result, more specific feedback recipes have been created to resolve this discrepancy. Several physical processes have been invoked to regulate star formation as a function of mass, viz:

Benson et al (2003) and Croton et al (2006) illustrate the effects of these more detailed prescriptions for these feedback modes on the predicted LF and find that supernova and reionization feedback largely reduce the excess of intrinsically faint galaxies but, on grounds of energetics, only AGN can inhibit star formation and continued growth in massive galaxies. There remains an excess at the very faint end (Fig. 11).

Figure 11a Figure 11b Figure 11c

Figure 11. The effect of various forms of feedback (dots) on the resultant shape of the blue 2dF galaxy luminosity function (Norberg et al 2002). From left to right: no feedback, supernova feedback only, supernova, reionization & AGN feedback (Courtesy: Darren Croton).

2.5. The Role of the Environment

In addition to recognizing that more elaborate modes of feedback need to be incorporated in theoretical models, the key role of the environment has also emerged as an additional feature which can truncate star formation and alter galaxy morphologies.

The preponderance of elliptical and S0 galaxies in rich clusters was noticed in the 1930's but the first quantitative study of this effect was that of Dressler (1980) who correlated the fraction of galaxies of a given morphology T above some fixed luminosity with the projected galaxy density, Sigma, measured in galaxies Mpc-2.

The local T - Sigma relation was used to justify two rather different possibilities. In the first, the nature hypothesis, those galaxies which formed in high density peaks at early times were presumed to have consumed their gas efficiently, perhaps in a single burst of star formation. Galaxies in lower density environments continued to accrete gas and thus show later star formation and disk-like morphologies. In short, segregation was established at birth and the present relation simply represents different ways in which galaxies formed according to the density of the environment at the time of formation. In the second, the nurture hypothesis, galaxies are transformed at later times from spirals into spheroidals by environmentally-induced processes.

Work in the late 1990's, using morphologies determined using Hubble Space Telescope, confirmed a surprisingly rapid evolution in the T - Sigma relation over 0 < z < 0.5 (Couch et al 1998, Dressler et al 1997) strongly supporting environmentally-driven evolution along the lines of the nurture hypothesis. Impressive Hubble images of dense clusters at quite modest redshifts (z appeq 0.3-0.4) showed an abundance of spirals in their cores whereas few or none exist in similar environs today.

What physical processes drive this relation and how has the T - Sigma relation evolved in quantitative detail? Recent work (Smith et al 2005, Postman et al 2005, Figure 12) has revealed that the basic relation was in place at z appeq 1, but that the fraction fE+S0 of Es and S0s has doubled in dense environments since that time. Smith et al suggest that a continuous, density-dependent, transformation of spirals into S0s would explain the overall trend. Treu et al (2003) likewise see a strong dependence of the fraction as a function of Sigma (and to a lesser extent with cluster-centric radius) within a well-studied cluster at z appeq 0.4; they review the various physical mechanisms that may produce such a transformation.

Figure 12

Figure 12. The fraction of observed E and S0 galaxies down to a fixed rest-frame luminosity as a function of lookback time and projected density Sigma from the study of Smith et al (2005). Although the morphology density relation was already in place at z appeq 1, there has been a continuous growth in the fraction subsequently, possibly as a result of the density-dependent transformation of spirals into S0s.

Figure 12 encapsulates much of what we now know about the role of the environment on galaxy formation. The early development of the T - Sigma relation implies dense peaks in the dark matter distribution led to accelerated evolution in gas consumption and stellar evolution and this is not dissimilar to the nature hypothesis. However, the subsequent development of this relation since z appeq 1 reveals the importance of environmentally-driven morphological transformations.

2.6. The Importance of High Redshift Data

This glimpse of evolving galaxy populations to z appeq 1 has emphasized the important role of high redshift data. In the case of the local morphology-density relation, Hubble morphologies of galaxies in distant clusters have given us a clear view of an evolving relationship, partly driven by environmental processes. Indeed, the data seems to confirm the nurture hypothesis for the origin of the morphology-density relation.

Although we can place important constraints on the past star formation history from detailed studies of nearby galaxies, as the standard model now needs several additional ingredients (e.g. feedback) to reproduce even the most basic local properties such as the luminosity function (Figure 11), data at significant look-back times becomes an essential way to test the validity of these more elaborate models.

Starting in the mid-1990's, largely by virtue of the arrival of the Keck telescopes - the first of the new generation of 8-10m class optical/infrared telescopes - and the refurbishment of the Hubble Space Telescope, there has been an explosion of new data on high redshift galaxies.

It is helpful at this stage to introduce three broad classes of distant objects which will feature significantly in the next few lectures. Each gives a complementary view of the galaxy population at high redshift and illustrates the challenge of developing a unified vision of galaxy evolution.

2.7. Lecture Summary

We have seen in this brief tour that galaxy formation is a process involving gravitational instability driven by the hierarchical assembly of dark matter halos; this component we understand well. However, additional complexities arise from star formation, dynamical interactions and mergers, environmental processes and various forms of feedback which serve to regulate how star formation continues as galaxies grow in mass.

Theorists have attempted to deal with this complexity by augmenting the highly-successful numerical (DM-only) simulations with semi-analytic tools for incorporating these complexities. As the datasets have improved so it is now possible to consider `fine-tuning' these semi-analytical ingredients. Ab initio modeling is never likely to be practical.

I think it fair to say that many observers have philosophical reservations about this `fine-tuning' process in the sense that although it may be possible to reach closure on models and data, we seek a deeper understanding of the physical reality of many of the ingredients. This is particularly the case for feedback processes. Fortunately, high redshift data forces this reality check as it gives us a direct measure of the galaxy assembly history which will be the next topics we discuss.

As a way of illustrating the importance of high redshift data, I have introduced three very different populations of galaxies each largely lying in the redshift range 2 < z < 4. When these were independently discovered, it was (quite reasonably) claimed by their discoverers that their category represented a major, if not the most significant, component of the distant galaxy population. We now realize that UV-selected, sub-mm selected and non-star forming galaxies each provide a complementary view of the complex history of galaxy assembly and the challenge is to complete the `jig-saw' from these populations.

2 If Hubble's constant is not assumed, it is quoted in units of h-3 Mpc-3. Back

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