Annu. Rev. Astron. Astrophys. 1997. 35: 389-443
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2. BASIC METHODOLOGIES

The primary observational material consists of a number of measurements for every galaxy in a survey that can be regarded as statistically complete. Completeness means that the results of one survey can be compared with those of other observers and with the predictions of contemporary models that take account of the various selection criteria. Raw measurements for each galaxy in a given survey typically include isophotal or pseudototal magnitudes, aperture colors, spectroscopic redshifts, and line strengths (such as [O II] 3727-Å emission line fluxes or equivalent widths); dynamical line widths; and, from HST, images, sizes, and shapes. Derived pseudophysical parameters for each galaxy include its luminosity in some rest-frame bandpass, the star-formation rate as inferred from emission line characteristics or ultraviolet (UV) continuum flux, and some form of classification. Simple considerations (Struck-Marcell & Tinsley 1978) suggest that galaxies of similar Hubble types have had similar star-formation histories, providing the strong incentive to classify faint samples. This has been done variously via a morphological type from the HST image (Glazebrook et al 1995b, Driver et al 1995a, b), by examination of the color or spectral energy distribution (SED) (Lilly et al 1995), or via cross-correlation of detailed spectral features against local spectroscopic data (Heyl et al 1997, Kennicutt 1992). Assuming completeness, population statistics can then be derived, such as the galaxy luminosity function and the volume-averaged star-formation rate, both as a function of redshift and galaxy type. These data can be used with other indicators, such as probes of the gas content, to infer the global history of star formation and metal production (Songaila et al 1990, Fall et al 1996, Madau et al 1996).

Before discussing how observers transform their raw measurements into population statistics, an important point of principle needs to be discussed. In the above methodology, the population statistics are used only to present an empirical description of galaxy evolution; no extensive modeling is usually involved, although occasionally extrapolations are made into territories where no data exist. Recent examples of the empirical approach include redshift survey articles by Lilly et al (1996), Ellis et al (1996a), Cowie et al (1996). An alternative approach, which we call the ab initio approach, starts from a cosmogonic theory. A particular initial power spectrum of density fluctuations is adopted and gas-consumption time scales and morphological types are assigned to assemblies of dark and baryonic matter, which grow hierarchically. Star-formation histories for model galaxies are then used to predict observables directly in the context of particular surveys. The ab initio approach has its origins in the evolutionary predictions made by Tinsley (1980), Bruzual (1983), Guiderdoni & Rocca-Volmerange (1987), Yoshii & Takahara (1988) on the basis of simple assumptions that did not rely on particular cosmogonic models. However, more elaborate calculations are now possible in the physical context of hierarchical dark matter cosmologies, such as in recent articles by Kauffmann et al (1994), Cole et al (1994a), Baugh et al (1996).

Both the empirical and ab initio approaches have their place in observational cosmology. The empirical approach attempts to encapsulate the data in the simplest way and has the advantage of presenting results in a way that is not tied to any particular cosmogonic theory. However, it is not always clear how uncertainties in the raw data plane transform to those in the derived physical plane. The complexity of various selection effects is increasingly used in many areas of astronomy as an argument for the ab initio approach (cf simulations of the Lyman alpha forest discussed by Miralda-Escude et al 1996). Numerical simulations are now sufficiently sophisticated that remarkably realistic predictions can be made that take into account complexities such as merging, starbursts, feedback, and ionization effects that affect model galaxies according to their physical situation rather than their observable quantities. In such cases, intuitive approaches are not possible. Ultimately the ab initio approach may become the preferred way to interpret data, but this will only occur when such models have strong predictive capabilities. The difficulty of relying entirely on the ab initio approach is that, at most, the current methodology reveals models that are only consistent with the observational datasets; one might argue this is the minimum required of any model! In no sense does agreement of a complex model with data imply that that particular model is correct.

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