2. GALAXY FORMATION AND COSMOLOGY

Traditionally faint galaxies were studied in order to constrain the cosmological world model ([Sandage 1961]); their evolution was considered just one more tedious correction (the so-called evolutionary correction) in the path to the Holy Grail of the deceleration parameter q₀ ( _M / 2 in = 0 Friedmann models). The most useful galaxies in this respect were giant ellipticals in rich clusters. Tinsley (1976) demonstrated how sensitive the derived q₀ was to the assumed main sequence brightening with look-back time in these populations.

The traditional view for the formation history of an elliptical followed Eggen, Lynden-Bell & Sandage (1962). Monolithic collapse and rapid star formation leads to a subsequent track known as `passive evolution' (i.e. without further star formation). Tinsley showed that main sequence brightening in such a stellar population is largely governed by the rate at which stars evolve off the main sequence, i.e. the slope x ( 1) of the initial mass function at the typical turnoff mass 0.4-1 M. Whence:

(2.1)

and, in terms of its bias on q₀:

(2.2)

Tinsley argued that one would have to know the evolutionary correction to remarkable precision get a secure value of q₀. In fact, noting that the difference in apparent magnitude for a standard candle at z = 1 between an empty and Einstein-de Sitter Universe is only 0.5 mag, the relative importance of cosmology and evolution can be readily gauged.

Despite the above, it is always a mystery to me why several of our most eminent astronomers ([Kristian et al 1978, Gunn & Oke 1975]) continued to pursue the Hubble diagram as a cosmological probe using first-ranked cluster galaxies, in some cases for several years after the challenge of resolving the evolutionary correction became known. Tammann (1985) estimated about 400 nights nights of Palomar 200-inch time was consumed by the two competing groups whose resulting values of q₀ fundamentally disagreed. Recently Aragón-Salamanca (1998) showed, in a elegant summary of the situation, how the modern K-band Hubble diagram is most likely complicated further by the fact that first-ranked cluster galaxies are still assembling their stars over the redshift interval 0 < z < 1, offsetting the main sequence brightening (Figure 2).

Figure 2. A recent appraisal of the prospects of securing cosmological constraints from the Hubble diagram of brightest cluster galaxies ([Aragón-Salamanca et al 1998]). Luminosity evolution is parameterised as L = L(0)(1 + z). For q0 = 0, the top panel shows residuals and best fit trend applying k-correction and luminosity distance effects only; no luminosity evolution is seen. The middle and bottom panels show the residuals when evolution is modeled for single burst populations formed at zF = 2 and 5, respectively. High z galaxies are less luminous than expected, presumably because they are still accreting material. Quantitatively, the effect amounts to a factor of 2-4 less stellar mass depending on the assumed q0 (c.f. [van Dokkum et al 1999]).

In the late 1970's therefore, the motivation for studying faint galaxies became one of understanding their history rather than using them as tracers of the cosmic expansion (see inset panel in Figure 1). This is not to say that uncertainties in the cosmological model do not affect the conclusions drawn. The connection between cosmology and source evolutions remains strong in three respects:

1. We use our knowledge of stellar evolution to predict the past appearance of stellar populations in galaxies observed at high redshift. However, stellar evolution is baselined in physical time (the conventional unit is the Gyr: 10⁹ yr), whereas we observe distant sources in redshift units. The mapping of time and redshift depends on the world model. Broadly speaking there is less time for the necessary changes to occur in a high _M universe and consequently evolutionary trends are much stronger in such models.

2. Many evolutionary tests depend on the numbers of sources, the most familiar being the number-magnitude count which is remarkably sensitive to small changes in source luminosity. However, the relativistic volume element dV(z) depends sensitively on curvature being much larger in open and accelerating Universes than in the Einstein-de Sitter case.

3. Predictions for the mass assembly history of a galaxy in hierarchical models depend also on the cosmological model in a fairly complex manner since these models jointly satisfy constraints concerned with the normalisation of the mass power spectrum via the present abundance of clusters (e.g. [Baugh et al 1998]). Figure 3 illustrates one aspect of this dependence ([Kauffmann & Charlot 1998]); structure grows more rapidly in a dense Universe so the decline with redshift in the abundance of massive spheroidal galaxies, which are thought in this picture to forms via mergers of smaller systems, is much more marked in high density models than in open or accelerating Universes.

Figure 3. The abundance of massive (>1011 M) systems as a function of redshift in two hierarchical models ([Kauffmann & Charlot 1998]) showing the strong decline in a high density (CDM) model c.f. that in a low density accelerating model (CDM).

Fortunately, we are making excellent progress in constraining the cosmological parameters from independent methods, the most prominent of which include the angular fluctuation spectrum in the microwave background ([de Bernardis et al 2000, Balbi et al 2000]), the Hubble diagram of distant Type Ia supernovae ([Garnavich et al 1998, Perlmutter et al 1999]), the abundance of rich clusters at various epochs ([Bahcall & Fan 1998]) and the redshift-space distortion in large redshift surveys such as 2dF ([Peacock et al 2000]).

Given it matters, how then should we respond to the widely-accepted concordance in the determination of H₀, _M, from various probes (Ostriker & Steinhardt 1995, Bahcall 1999)? The claimed convergence on the value of Hubble's constant ([Mould et al 2000]) is not so important for the discussion below since most evolutionary tests are primarily concerned with relative comparisons at various look-back times where H₀ cancels. The most bewildering aspect of the concordance picture is the resurrection of a non-zero , the evidence for which comes primarily from the Hubble diagram for Type Ia supernovae.

As a member of the Supernova Cosmology Project ([Perlmutter et al 1999]) I obviously take the supernova results seriously! However, this does not prevent me from being surprised as to the implications of a non-zero . The most astonishing fact is how readily the community has apparently accepted the resurrection of - a term for which there is no satisfactory physical explanation (c.f [Wang et al 2000]). To one poorly-understand component of the cosmic energy density (non-baryonic dark matter), we seem to have added another (vacuum energy). It seems a remarkable coincidence that all three significant constituents (_B, _DM, ) are comparable in magnitude to within a factor of 10, and hardly a step forward that only one is physically understood!

The lesson I think we should draw from the cosmic concordance is similar to the comment I made in Section 1 when we discussed some theorists' triumphant reconciliation of their theories with faint galaxy data (a point we will debate in detail in Section 3). In both cases, the hypothesis certainly reproduces a wide range of observations but note it takes, as input, parameters for which there is not yet a clear physical model. One should not, therefore, regard a concordant picture as anything other than one of many possible working hypotheses. In the case of the cosmological models, we need to invest effort into understanding the physical nature of dark matter and vacuum energy. In the case of galaxy evolution our goal should be to test the basic ingredients of hierarchical galaxy formation.