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Using a spectral analysis of bright Chandra X-ray sources located in 27nearby galaxies and maps of star-formation rate (SFR) and ISM surface densitiesfor these galaxies, we constructed the intrinsic X-ray luminosity function(XLF) of luminous high-mass X-ray binaries (HMXBs), taking into accountabsorption effects and the diversity of HMXB spectra. The XLF per unit SFR canbe described by a power law dN/d log L=2.0(L/10^39 erg/s)^(-0.6)(M_Sun/yr)^(-1) from L=10^38 to 10^40.5 erg/s, where L is the unabsorbedluminosity at 0.25-8 keV. The intrinsic number of luminous HMXBs per unit SFRis a factor of ~2.3 larger than the observed number reported before. Theintrinsic XLF is composed of hard, soft and supersoft sources (defined here asthose with the 0.25-2 keV to 0.25-8 keV flux ratio of <0.6, 0.6-0.95 and >0.95,respectively) in ~2:1:1 proportion. We also constructed the intrinsic HMXB XLFin the soft X-ray band (0.25-2 keV). Here, the numbers of hard, soft andsupersoft sources prove to be nearly equal. The cumulative present-day 0.25-2keV emissivity of HMXBs with luminosities between 10^38 and 10^40.5 erg/s is ~510^39 erg/s (M_Sun/yr)^(-1), which may be relevant for studying the X-raypreheating of the early Universe.

Bright end of the luminosity function of high-mass X-ray binaries: contributions of hard, soft and supersoft sources