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For refcode 1991ApJ...382....1G:
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1991ApJ...382....1G SYSTEMATIC BIAS IN CLUSTER GALAXY DATA, AFFECTING GALAXY DISTANCES AND EVOLUTIONARY HISTORY DONALD H. GUDEHUS Department of Astronomy, University of Michigan, Ann Arbor, MI 48109; and Department of Physics, Oklahoma State University, Stillwater, OK 740781 Received 1990 August 13; accepted 1991 May 14 ABSTRACT Plots of galaxian surface brightness parameter versus log radius parameter have, for the past 15 years, been used to estimate cluster relative distances. The appeal of this approach is twofold: the scatter about the mean line is reasonably small and the relative distance is easily interpreted as a horizontal shift of one cluster mean line relative to another. However, the small scatter is deceiving; it results from the ratio of cosmic fluctuations in surface brightness parameter to cosmic fluctuations in log radius parameter, i.e., S, being approximately equal to the slope of the intrinsic mean line of the brightest galaxies, i.e., 2.5. Furthermore, actual fitted slopes and zero points will depend on the range of galaxy magnitudes used to construct each plot. A systematic error thus arises which makes cluster samples lacking large luminous galaxies appear to be farther away than they really are. This bias can be substantial and is illustrated with actual and simulated data. The data are mostly derived from CCD observations of 343 cluster galaxies which have been processed to remove the effects of overlapping images and blurring from seeing. A plot of log r against total magnitude for these data exhibits a change of slope at M_v_' = -23.04 and a'= 931 pc or R_e_' = 10.20 kpc(H_0_ = 50 km s^-1^ Mpc ^-1^,q_0_ = 0.5).While the systematic bias would occur even without this slope change, the magnitude of the bias is enhanced by it. Reanalyses of the data of Schombert and of Dressler et al. also exhibit the change of slope at about the same magnitude. Although introduction of a third parameter such as velocity dispersion tightens up the log r-M relation, the systematic error in the S-log r relation still persists at ~69% of its former value. A systematic bias in the log {sigma}_v_ -log D_n_ method also exists. While not as strong as the previous bias, clusters with an excess of luminous galaxies appear to be farther than they really are. The bias is caused by a nonlinearity in the log {sigma}_v_ -log D_n_ relation, and the presence of correlated fluctuations between these two quantities. In order to estimate relative galaxian distances in an unbiased way, aside from the Malmquist effect, making optimal use of the available photometric, structural, and dynamical information, a new distance estimator, the reduced galaxian radius parameter, r_g_, is introduced. With this estimator, relative distances good to +/- 31% for individual galaxies can be obtained. If the Coma cluster has no peculiar velocity, then the peculiar velocity of the Virgo cluster, as determined from r_g_, is 392 km s^-1^, yielding a Virgocentric motion of only - 47 km s^-1^ (infall). The relative distance modulus between Virgo and Coma is 4.07. The large correlation of cosmic fluctuations in the S-log r plot can completely dominate the slope of the faintest galaxies, i.e., - 1, and make them appear to follow the same relation as the brightest galaxies. Since the bright galaxy slope is the same as the slope expected from merging, it can thus erroneously appear that fainter cluster galaxies, are merger products. While high mass galaxies, i.e., those with M_v_ < - 23.04, follow the relations L is proportional to r and {sigma}_v_ ~constant, and thus appear to have formed from mergers, low- mass galaxies, which follow the relations L is proportional to r^2.4^ and L is proportional to {sigma}^3.1^_v_, formed by a different process, most likely dissipation. Three-parameter data are used to determine the dependence of M/L on L. There is little if any, change of this ratio from the least luminous to the most luminous cluster galaxies. This, together with an estimated M/L of 14, suggests that dark matter in clusters of galaxies does not concentrate near individual galaxies. Because surface brightness parameter is a function of absolute magnitude, an improved surface brightness test for luminosity evolution is suggested. By employing only cluster galaxies which lie near the peak, S', the test will be insensitive to a cluster's relative proportion of faint and luminous galaxies, and therefore dynamical evolution, as well as to deceleration parameter. Subject headings: cosmology - galaxies: clustering - galaxies: distances galaxies: evolution -galaxies: photometry - galaxies: redshifts
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