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The Galaxy Luminosity Function and the Redshift-Distance Controversy (A Review) (Cosmology/Clusters of Galaxies) E

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The Galaxy Luminosity Function and the Redshift-Distance Controversy (A Review) (Cosmology/Clusters of Galaxies) E Proc. Nati. Acad. Sci. USA Vol. 83, pp. 3056-3063, May 1986 Astronomy The galaxy luminosity function and the redshift-distance controversy (A Review) (cosmology/clusters of galaxies) E. E. SALPETER AND G. L. HOFFMAN, JR. Newman Laboratory of Nuclear Studies, Cornell University, Ithaca, NY 14853; and Lafayette College, Easton, PA 18042 Contributed by E. E. Salpeter, December 20, 1985 ABSTRACT The mean relation between distance and law" or "linear law," p = 1, remarkably early-partly redshift for galaxies is reviewed as an observational question. for a theoretical reason: A simple extrapolation of this The luminosity function for galaxies is an important ingredient expansion law (the same for all observers) leads back to and is given explicitly. We discuss various observational a unique "starting time" for the expansion. Different selection effects that are important for comparison ofthe linear subclasses of the "standard cosmological models" make and quadratic distance-redshift laws. Several lines of evidence different predictions for large redshifts but all reduce to are reviewed, including the distribution of galaxy luminosities the linear law, p = 1, for z << 1. On the other hand, Segal in various redshift ranges, the luminosities ofbrightest galaxies in 1972 proposed a different kind of cosmological model, in groups and clusters at various redshifts, and the Tully-Fish- one that predicts instead the quadratic law, p = 2 (again for er correlation between neutral hydrogen velocity widths and Z << 1). luminosity. All of these strongly favor the linear law over the Much of the literature on the controversy of p = 1 versus quadratic. p = 2 is interlaced with theoretical discussions, but one can consider the redshift-distance relation as an observational question. Segal and his collaborators have raised a number of Section 1. Introduction questions on observational procedures, many in this journal, as well as on theory and statistical analysis. The present In 1920 a "cosmological controversy" was sparked by a paper is meant as a review in a very limited sense: to famous debate between Curtis and Shapley: Are "spiral emphasize the direct observational nature of the question we nebulae" distant galaxies, like our own Milky Way galaxy, or shall not discuss or quote any theoretical papers (not even merely small nebulae inside our galaxy? In 1925 Hubble (1) Newton or Einstein) and avoid sophisticated statistical settled the debate by discovering and analyzing Cepheid tests-presenting observational data in "almost raw form," variable stars in a few such "spirals;" by calibrating against i.e., using only the most naive and transparent statistical Cepheids in our galaxy, he found the distances to these analysis. This omits much of the relevant literature on the spirals to be much larger than the diameter ofour galaxy (=30 controversy and it may seem surprising that we have any- kpc; 1 pc = 3.086 x 1016 m), so they are definitely external thing left to review. Fortunately, there has been such a galaxies. Nevertheless, these few galaxies were all closer remarkable "data explosion" in extragalactic observational than 1 Mpc (= 3.086 x 1024 cm) and all members of the astronomy over the last ten years or so, that the controversy so-called "Local Group" of galaxies (see Section 3). The can now be settled from "almost raw data" alone. The two Cepheid method (with certain refinements) is still the most most important individual developments are (i) the magni- direct way to measure distances, up to a few megaparsecs but tude-limited "CfA survey" of more than 2400 galaxies (3) not beyond. This range includes a handful of galaxy groups with optical redshifts for all and (ii) the development of the similar to our local group, typically containing two or three "Tully-Fisher method" (4) for measuring distances r to spiral galaxies like our galaxy and =20 or 30 smaller ones (some galaxies even when r is very large. Recent extensive work on other fairly direct optical methods extend this distance range the brightest galaxies in clusters is particularly suitable for slightly). the present discussion. In 1929 Hubble (2) published values for the radial velocities Statistical discussions have been given by a number of relative to the sun for various galaxies outside of the local authors but have not yet been applied to the recent obser- group and found that most of them are redshifted, indicating vational data. We give here (without critique) a few refer- that they are receding from us. The sun's orbital velocity in ences (which themselves quote earlier work). First, some our galaxy is =230 km's'l and the sun's total velocity relative early contributions by Segal and his colleagues (5, 6); a to the centroid ofthe Local Group ofgalaxies is =300 km s'l. nonparametric procedure (7) was given in 1983 and a recent It is convenient to express all external velocities relative to paper (8) gives many references. Two pairs of papers (refs. 9 the Local Group centroid, with an uncertainty of =50 km s'1, and 10, 11 and 12) address controversies on statistical and we shall quote all observed redshifts with this correction. techniques. Here we concentrate on direct observational We define redshift z and "velocity" V in terms of the data, especially data leading to an explicit luminosity function observed wavelength Xobs in the simplest formulation, that we feel is essential for the reader to draw his or her own conclusions. We also have to deal with our slightly unusual z = V/c = (Xobs/Xrest)-1, [1] position-we live in the outskirts of a concentration of galaxies, the "Local Supercluster." appropriate for the low-redshift range (z < 0.1) to which we shall restrict ourselves. Section 2. Some definitions and procedures For galaxies outside of the Local Group, an empirical relation between redshift z and distance r of the form z a rP For the sake of readers who are not astronomers we compile (with p of order 1 or 2) was already apparent in Hubble's afew definitions and numerical values (13). We start with (the time. In spite of the small number of observations, most derived) absolute magnitude M, a logarithmic measure ofthe of the astronomical community accepted the "Hubble absolute luminosity L of an object, restrict ourselves to the 3056 Downloaded by guest on September 30, 2021 Astronomy: Salpeter and Hoffman Proc. Natl. Acad. Sci. USA 83 (1986) 3057 "UBV blue magnitude MB" and drop the subscript. In solar the "distance modulus" (m - M) and the distance r. Various units the absolute magnitude M and the apparent magnitude slight refinements of this method have been proposed (e.g., m (measuring the directly observed flux L/r2) read in refs. 21 and 22) and are summarized in a recent paper (23). The scatter in the Tully-Fisher relation is smallest for Sb and M = 5.48 - 2.5 loglo(L/L), Sc galaxies, but it still holds reasonably well for other types m = M + 25 + 5 of spirals. The method works fairly well out to z 0.04. loglo(r/l Mpc), For statistical work on galaxies without measured dis- where r is the distance to the object. We shall test the two tances, two magnitude-limited optical catalogs with galaxy rival for M from m and redshifts are particularly useful. One is the so-called RSA hypotheses deriving V, catalog (24) with a rough magnitude cutoffof 13.2, listing 1246 V galaxies (including southern galaxies); another, the CfA r (1 V \r (1 12 3 survey (3), with a magnitude limit of about 14.5, listing 2401 1 Mpc (Ho km s') oKo km s-) * [3] galaxies. Since different magnitude definitions have been used by different sources in the past there are some ambi- Unlike stars, galaxies do not have a sharply defined "outer guities in the cutoffs but not by more than a few tenths of a edge" and the assigned apparent magnitude m depends on the magnitude. Furthermore, the catalogs are not complete right angular area over which one sums the optical surface bright- up to the cutoff but have a (reasonably well determined) ness CL. For spiral galaxies, like our own, CTL decreases "completeness function." Excluding dwarf galaxies (which exponentially with distance from the center and there is little have a low central surface brightness) it is safe to consider ambiguity in the integral of aL. For our own galaxy the these catalogs complete to apparent magnitude m, about 12.2 exponential scalelength is =6 kpc and the absolute magnitude and 13.8, respectively. An important property ofthe catalogs is M -20.2 (see, e.g., ref. 14), with an uncertainty of order is their redshift completeness; i.e., every galaxy on each list ±1.0. For giant elliptical galaxies, on the other hand, the has a measured velocity. In particular, the catalogs could surface brightness decreases less sharply than exponential have missed only very few galaxies of large redshift but and, for intermediate values of angular distance 6 from the brighter than mc. The "data-explosion" in this field is center, the integrated flux increases approximately as (ln 6 + considerable-a catalog only seven years old (e.g., ref. 25) is constant). For the relatively small redshifts considered here already "old-fashioned." The slightly larger random magni- (z < 0.1) these "optical halos" need not be a problem in tude errors in the CfA catalog are not very troublesome, but principle: The central optical surface brightness crL(O) is the extension to larger redshifts is very important because of typically much brighter than that ofthe night sky (discounting the clustering to be discussed below. dwarf galaxies, which are of no interest here); the angular radius Osb where aL drops to some predetermined surface brightness is large enough (>10 arcsec) so it can in principle Section 3.
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