To derive the proper relative numbers

To derive the proper relative numbers - characteristic...

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To derive the proper relative numbers, one must correct for the different volumes within which each object would appear in the catalog. This apparent distribution declines fainter than absolute blue magnitude -21.5, while the space density continues to increase greatly to fainter absolute magnitudes. An important analytic approximation to the overall galaxy luminosity function is the Schechter (1976, ApJ 203, 297) form Φ (L) dL = φ * (L/L * ) α e -(L/L * ) (dL/L * ) where φ * (L/L * ) is the normalizing factor, set by the number of galaxies per Mpc 3 , L * is a characteristic luminosity, and α is an asymptotic slope to be fit; a value around -5/4 usually agrees with the data. The plot (from Schechter's paper, reproduced by permission of the AAS) shows the fit to the mean of galaxy counts in 13 clusters. L * appears to be constant among various clusters, and maybe even for non-cluster galaxies, at a given cosmic epoch, so that one may read references to "an L * galaxy". This is sometimes taken as a
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Unformatted text preview: characteristic scale for galaxy formation. The brightest cD galaxies may require some additional process; they may violate the LF shape in that there should be virtually no galaxies so luminous in the observable Universe if the Schechter function held absolutely. Different kinds of galaxies have different LF shapes and normlizations; this explains why Hubble thought of the LF as approximately Gaussian, from studies of (giant) spirals, while Zwicky counted everything, dissented vigorously and as usual correctly, and found a divergence at faint magnitudes. Zwicky distinguished dwarf, pygmy, and gnome galaxies (see his idiosyncratic book Morphological Astronomy ). The LF must converge somewhere to avoid Olbers' paradox. The LF is simple only for dwarfs; the various types are distributed in Virgo as follows, from Fig. 1 of Binggeli, Sandage, and Tammann 1988 (Ann. Rev. 26, 509 - an excellent reference for the whole topic, figure reproduced from the ADS)....
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