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Historically, the Schechter luminosity function was inspired by the Press–Schechter model. [ 8 ] However, the connection between the two is not straight forward. If one assumes that every dark matter halo hosts one galaxy, then the Press-Schechter model yields a slope α ∼ − 3.5 {\displaystyle \alpha \sim -3.5} for galaxies instead of the ...
The Press–Schechter formalism predicts that the number of objects with mass between and + is: = (+) ¯ (+) / (() (+) /). where is the index of the power spectrum of the fluctuations in the early universe (), ¯ is the mean (baryonic and dark) matter density of the universe at the time the fluctuation from which the object was formed had gravitationally collapsed, and is a cut-off mass ...
Paul L. Schechter (born May 30, 1948) is an American astronomer and observational cosmologist. He is the William A. M. Burden Professor of Astrophysics, Emeritus, at MIT . Schechter received his bachelor's degree from Cornell in 1968, and his Ph.D. degree from Caltech in 1975.
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Martin Schechter (1930, Philadelphia – June 7, 2021) was an American mathematician whose work concerned mathematical analysis (specially partial differential equations and functional analysis and their applications to mathematical physics). He was a professor at the University of California, Irvine. [1] [2]
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The dashed red line is an example luminosity function when the Malmquist bias is not corrected for. The more numerous low luminosity objects are underrepresented because of the apparent magnitude limit of the survey. The solid blue line is the properly corrected luminosity function using the volume-weighted correction method.