On the Universal X-ray Luminosity Function of Binary X-ray Sources in Galaxies

The empirically determined universal power-law shape of X-ray luminosity function of high mass X-ray binaries in galaxies is explained by fundamental mass-luminosity and mass-radius relations for massive stars. The unique possibilities offerred by modern X-ray space observatories Chandra and XMM-Newton make it possible to observe point-like X-ray sources in nearby galaxies which allows studies of formation and evolution of the population of close binary systems as a whole. Recently, Grimm, Gilfanov and Sunyaev (2002, 2003) reported that the differential luminosity function of point-like X-ray sources in nearby galaxies has a universal power-law shape dN dLx ∝ SFR× L x in the wide range of X-ray luminosities ∼ 10−10 erg/s, where SFR means the star formation rate in a specific galaxy, α = 1.61± 0.12. In this Letter we show that the empirically found power-law form of the X-ray luminosity function naturally appears during accretion of matter in close binary systems. In high-mass X-ray binaries, the compact star accretes matter from stellar wind from an early-type optical companion. Observations suggest (De Jager, 1980) that stellar wind mass loss rate from massive (> several M⊙) main sequence stars can be parametrized as Ṁw ∝ Lo v∞ (1) where L is the stellar luminosity, v∞ is the stellar wind velocity at the infinity. With a good accuracy the latter is proportional to the escape velocity near stellar photosphere v∞ ≈ 3vp. Formula (1) simply refelcts the radiation pressure driven wind.