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1977Apj. . .213. .327A the Astrophysical Journal, 213:327-344 .327A .213. The Astrophysical Journal, 213:327-344, 1977 April 15 . © 1977. The American Astronomical Society. All rights reserved. Printed in U.S.A. 1977ApJ. THE LUMINOSITY FUNCTION AND STRUCTURE OF THE COMA CLUSTER G. O. Abell Department of Astronomy, University of California, Los Angeles Received 1976 August 6 ABSTRACT The luminosity function of the galaxies in the Coma cluster is determined by a procedure of extrafocal photographic photometry. The logarithmic integrated luminosity function rises sharply with increasing magnitude through the interval mv = 11.6 to 14.5, and then slowly for greater magnitudes to the limit mv = 19.4. The data suggest a moderate increase in the slope of the function for magnitudes fainter than mv = 17.5. The cluster is found, in projection, to be ellipsoidal in shape, centered at (1950) a = 12h56IP9; 0 5 = +28 14'. To the limit mv = 18.3 the cluster is estimated to have 1525 member galaxies. The brighter galaxies in the inner part of the cluster have a distribution resembling that of the iso- thermal polytrope, but there is no marked segregation of bright and faint galaxies, as would be required for complete statistical equilibrium. The luminosity of the cluster is estimated at 2 x 1013 L©. The mass-to-light ratio (in solar units) is found probably not to exceed 122. Subject headings: galaxies : clusters of—galaxies: photometry I. INTRODUCTION II. OBSERVATIONS The first important discussion of the galaxian a) Photometric Procedure luminosity function was by Hubble (1926), who Galaxian magnitudes are obtained here by a investigated the absolute magnitudes of 134 late method of extrafocal photographic photometry spirals and 11 irregular galaxies (most of which are described by Abell and Mihalas (1966). In this pro- not in conspicuous clusters). He represented_their cedure several photographs are taken of the galaxy luminosity function by a Gaussian curve with Afpg = field, each photograph a different distance out of — 14.19 and a = 0.85 mag (for the Hubble constant, focus. In the extrafocal photographs the stars image as 1 1 if = 50 km s “ Mpc" , Hubble’s Mpg becomes —19.4). disks, while each galaxy images as a disk, correspond- Later, Zwicky (1942) summarized evidence for large ing to its bright central nucleus, surrounded by a numbers of galaxies of low luminosity, and suggested “fuzz” consisting of the overlapping extrafocal images that the luminosity function rises monotonically with of the other portions of the galaxy. The farther out of increasing magnitude. Still later, from an analysis of focus the photograph, the greater is the fraction of the the numbers of visible galaxies in clusters of various galaxy’s light that images on top of the image disk of angular sizes, Zwicky (1957) found the number the nucleus, and the more the extrafocal galaxian N(<m) of galaxies in a cluster with magnitudes image resembles that of a star. On each photograph brighter than m to rise as 10°-2m. the densities of the galaxian images are compared with In 1958 the writer began a program of photometry those of the images of stars whose magnitudes have of cluster galaxies to establish whether the Zwicky been measured photoelectrically. In this way a luminosity function is correct and general, and in sequence of successively brighter magnitudes is particular to find whether any feature in the cluster obtained for each galaxy corresponding to the sequence luminosity function permits the determination of of photographs successively farther out of focus. relative cluster distances. He found (Abell 1962) that From the run of magnitudes of each galaxy, its the Coma cluster luminosity function is qualitatively total magnitude is derived by comparing those similar to the Zwicky formula at faint magnitudes but measures to calculated magnitudes of hypothetical has a much steeper slope at the bright end. galaxies described by an assumed surface brightness He has found similar results for other clusters law. In other words, the magnitude assigned to a (Bautz and Abell 1973, Abell 1975), as have Oemler galaxy is that of a model galaxy with an assumed (1973, 1974), Krupp (1974), Gudehus (1971, 1973), surface-brightness distribution whose calculated magni- Massey (1975), and Austin and Peach (1974ö, 6; tudes at various extrafocal distances most nearly Austin, Godwin, and Peach 1975). In this paper are match the observed magnitudes for the real galaxy. given the details of the photometry of the Coma The magnitudes so derived can have rather large cluster, as well as a discussion of its structure and other statistical errors, both because of errors in matching properties. the image densities and because all galaxies cannot be © American Astronomical Society • Provided by the NASA Astrophysics Data System .327A .213. ABELL 328 . expected to obey exactly the same surface brightness one plate in focus and the other 0.3 mm out of focus. law. The uncertainties are greatest for faint galaxies In this larger field, galaxies can be identified on the that are visible only on photographs that are not too in-focus plate, and their magnitudes can be estimated 1977ApJ. far out of focus. However, the procedure automatically by comparing their extrafocal images with the 0.3 mm takes care of the aperture correction in a self-consistent extrafocal images of typical galaxies in the central manner, and is free from systematic errors that depend part of the cluster, whose magnitudes are determined on the intrinsic size and luminosity of a galaxy or its by the techniques described in the last section. Thus distance. Moreover, rich clusters contain galaxies that we have magnitude measures of galaxies in the central are all or nearly all of types E or SO, for which the 2?7 field of the cluster, and magnitude estimates over surface-brightness law assumed seems to be valid ; in the much larger 6?4 field. fact, the vast majority of galaxies so observed yield sequences of extrafocal magnitudes that match closely c) Photoelectric Standards the calculated ones for the model galaxies (see Abell A photoelectric sequence of 13 stars was set up just and Mihalas 1966). Thus this method of extrafocal north of the cluster center with the 2.5 m telescope on photographic photometry is especially well suited to Mount Wilson during observing runs in 1959 January the determination of magnitudes of large numbers of and February, 1960 March, and 1963 February. These galaxies for such purposes as finding luminosity stars are identified in Figure 1, and the magnitude, functions. color, and number of observations of each are given In the work described here all photographs were in Table 1. taken with the 1.2 m Palomar Schmidt telescope. On The mpg magnitudes from the blue (103a-O) plates the Schmidt plates in-focus images of galaxies fainter are not the same as B magnitudes. However, the B—V than about mv = 18.0 appear nearly stellar. Ex- colors were transformed to P—V colors with the perience has shown that if galaxies this faint are color equation, compared directly with standard stars by measuring them with an iris-diaphragm astrophotometer on P — V = 1.22(2?— V) — 0.37 , (1) in-focus plates, the magnitudes obtained for them agree with those found by the extrafocal technique. determined by the writer from B—V observations Astrophotometer measures can therefore be used to of 24 stars in Selected Area 68, for which P — V obtain magnitudes of galaxies near the plate limit, observations are published by Stebbins, Whitford, and whose images are not visible on plates taken far Johnson (1950). The P magnitudes were taken to be enough out of focus to utilize the extrafocal method, close enough to the mpg magnitudes. although with somewhat diminished confidence in the Interpolation with iris-diaphragm astrophotometer magnitude scale. measures of these and additional stars on the in-focus plates provided secondary standards. These secondary b) Photographic Material standards and the stars listed in Table 1 establish the photometric system for the photometry of Coma In the spring of 1957, two sets of photographs were cluster galaxies. taken of the Coma cluster, Number 1656 in the Abell (1958) catalog. Each photograph covers a 2?61 x 2?70 d) Precision of Galaxy Magnitudes field centered on the cluster, and is contained on one- quarter of a 36-cm-square Palomar Schmidt plate. If a measured galaxy has a surface brightness One set is on the 103a-D emulsion exposed through a distribution similar to that assumed for the model yellow Plexiglas filter, to yield magnitudes that are galaxies, its total magnitude (as defined in § Ha) can very nearly on the visual system (mv). The other is on the 103a-O emulsion without a filter (other than the plate-glass correcting lens of the telescope), and yields TABLE 1 magnitudes that are roughly on the old photographic Photoelectric Sequence in Cluster 1656 system (mpg). Each set contains six photographs, one in focus, and the others extrafocal by 0.3, 0.75, 1.50, Star V B—V n 3.0, and 5.0 mm. The focal ratio of the Schmidt telescope is f/2.44, so the largest extrafocal images are 1 9.38 +0.87 4 just over 2 mm in diameter, and the smallest 0.12 mm; 2 9.76 +0.57 1 3 11.08 +0.60 4 thus for the brightest galaxies, which can be seen even 4 12.28 +1.01 1 on the plates farthest out of focus, magnitudes are 5 12.54 +0.83 3 obtained at extrafocal distances ranging over more 6 13.87 +0.67 4 than a factor of 16. The faintest galaxies measured by 7 14.58 +0.87 1 to the extrafocal technique are visible only on the plates 8 14.74 +0.90 u> 0.3 and 0.75 mm out of focus; their magnitudes had 9 15.19 +0.88 10.
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