2006 Supplement 1: WORKSHOP ON MULTIFREQUENCY BEHAVIOUR OF HIGH ENERGY COSMIC SOURCES: Frascati, 2005 / Grimm

Statistical Properties of the Combined Emission of a Discrete Source Population: Astrophysical Implications

Hans-Jakob Grimm, Marat Gilfanov, Rashid Sunyaev

Abstract


We study the statistical properties of the combined emission of a population of discrete sources. In particular, we consider the dependence of their total luminosity (Ltot = ∑kLk) and fractional rmstot variability on the number of sources n or on the normalization of the luminosity function. We show that due to small number statistics a regime exists, in which Ltot grows non-linearly with n. This is in apparent contradiction with the seemingly obvious prediction langLtotrang = ∫LdN/dLdL ~ n. In this non-linear regime, the rmstot decreases with n significantly more slowly than expected from the rms ~ 1/n1/2 averaging law. Only in the limit of n >> 1 do these quantities behave as intuitively expected, Ltot ~ n and rmstot ~ 1/n1/2. Using the total X-ray luminosity of a galaxy due to its X-ray binary population as an example, we show that the LX–SFR and LX–M* relations predicted from the respective ``universal'' luminosity functions of high and low mass X-ray binaries are in a good agreement with observations.


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DOI: https://doi.org/10.1088/1009-9271/6/S1/26

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