Statistical properties of the combined emission of a population of discrete sources: astrophysical implications

摘要: We study the statistical properties of combined emission a population discrete sources (e.g. X-ray galaxy due to its binaries population). Namely, we consider dependence their total luminosity L_tot=SUM(L_k) and fractional rms_tot variability on number N or, equivalently, normalization function. show that small statistics regime exists, in which L_tot grows non-linearly with N, an apparent contradiction seemingly obvious prediction =integral(dN/dL*L*dL) ~ N. In this non-linear regime, decreases significantly more slowly than expected from rms 1/sqrt(N) averaging law. For example, for power law function slope a=3/2, N^2 does not depend at all Only limit N>>1 do these quantities behave as intuitively expected, 1/sqrt(N). give exact solutions derive convenient analytical approximations rms_tot. Using binary Lx-SFR Lx-M* relations predicted respective ``universal'' functions high low mass are good agreement observations. Although caused by examples extends far SFR<4-5 Msun/yr log(M*/Msun)<10.0-10.5, respectively.