Annu. Rev. Astron. Astrophys. 1992. 30:
613-52 Copyright © 1992 by Annual Reviews. All rights reserved |
Counts of galaxies as a function of apparent magnitude, A(m), depend on the cosmological model, clustering characteristics, the luminosity function, and the mixture of galaxy types (meaning their intrinsic surface brightness profiles and their spectral energy distributions). The cosmological model enters via the volume element dV / dz and the luminosity distance dL at each redshift. If the evolution of the stellar population is specified in terms of look-back time, then the cosmological model enters in an additional way because it determines the conversion between look-back time and the measured redshift.
For a given apparent surface brightness, different physical radii are reached for galaxies at different redshifts. At high redshifts especially, the fraction of the light seen above the threshold may be very sensitive to observational details, such as the degree of image blur from seeing and other sources, depending on the shape of the intrinsic profile for each galaxy (Pritchet and Kline 1981). For this reason, it is of critical importance in a galaxy-count model to know the frequency distribution of galaxy intrinsic profile types. Since the visibility of distant galaxies depends on image profile and the spectral energy distribution, ideally a more general statistical distribution function than the luminosity function (M) should be used, say (M, color, surface brightness). Unfortunately, catalogues of nearby galaxies suitable for deriving do not yet exist. The alternative is to adopt different functions for (M) according to galaxy type.
3.2.1 SPECTRAL ENERGY DISTRIBUTIONS
Most galaxy count models use only five or six galaxy
types. This coarse grid of spectra can be traced back to
Wells's (1972)
large-aperture spectrophotometry of field
galaxies. This set of data allowed K-corrections and colors
as a function of redshift to be computed, for similar
galaxies, once the spectra were suitably extrapolated to
shorter and longer wavelengths (Wells's spectra covered only
the range 3500-5500). These spectra were
first used by
Brown and Tinsley
(1974) and
Pence (1976),
and later by
Coleman, Wu, and
Weedman (1980) and
Tinsley (1980).
Subsequent models have followed implicitly the same
procedure, for instance
King and Ellis (1985),
Guiderdoni and
Rocca-Volmerange (1990),
Yoshii and Peterson
(1991), and
Cole, Treyer, and Silk
(1992).
It is sobering to consider the foundations of this work.
Large-aperture spectrophotometry of luminous elliptical
galaxies had already been made by
Schild and Oke (1971),
and it was known that the galaxies contributing to faint counts
would be mainly spirals. Wells was able to observe only
seven spiral galaxies. These fell naturally into three
groups of similar spectra, which were then averaged. These
mean spectra could be characterized by the respective mean
colors, but have been more commonly labelled by nominal
morphological type ``Sdm-Im,'' ``Sbc,'' and ``Sab.'' A class
called ``Scd'' was invented by
Pence (1976)
by interpolation between ``Sdm-Im'' and ``Sbc'' and has been adopted by others
(e.g.
Coleman et al. 1980).
The bluest categories are of particular interest because
of the anticipation that such galaxies may appear in greater
proportions at high redshifts, since their K-corrections are
smaller.
Pence's (1976)
bluest class (``Im'') contains
NGC 1140 and NGC 145.
NGC 1140 is called Sb pec: in the
Revised Shapley Ames Catalog
(Sandage and Tammann
1981),
it appears on the Palomar Sky Survey to have high surface
brightness, and on the RSA system has MB = -20.4.
NGC 145 is
listed in the
Arp (1966)
atlas (No. 019) and is a
striking,
high-surface-brightness spiral; it has MB = -21.5. Neither
galaxy bears any resemblance to Magellanic irregulars.
Coleman, Wu, and
Weedman (1980)
chose not to use NGC 145 in
their mean spectra because it was not sufficiently blue for
their bluest class. In fact, in their list only NGC 4449 is
bluer in (B - V)T0, by only 0.01 mag.) The
next-bluest galaxy measured by Wells is NGC 1659, which has
MB = -22.1. Thus the galaxies in Wells's list, and the
galaxies observed in the ultraviolet by
Coleman, Wu, and
Weedman (1980),
are for the most part quite luminous systems. NGC 4449 at
MB = -18.8 is the least luminous galaxy in either of these
lists. Since there is a trend for lower-luminosity galaxies
to be bluer
(Huchra 1977),
the complete lack of low-luminosity galaxies in the library of galaxy
spectral energy distributions is an important limitation.
In summary, the models ultimately based on Wells's spectrophotometry
suffer from several shortcomings: the galaxies used to define the
classes are few and do not properly span the range of colors or
luminosities; the blue galaxies do not represent their designated
morphological types (and even if they did, the calculation of the numbers
of such galaxies per cubic megaparsec would be problematic);
it seems likely that there is a selection bias in the
spectrophotometric samples in favor of high-surface-brightness galaxies;
and it has not been demonstrated that
the galaxies are representative of either magnitude-limited
or volume-limited samples.