Using a spectral analysis of bright Chandra X-ray sources located in 27 nearby galaxies and maps of star-formation rate ( SFR ) and ISM surface densities for these galaxies , we constructed the intrinsic X-ray luminosity function ( XLF ) of luminous high-mass X-ray binaries ( HMXBs ) , taking into account absorption effects and the diversity of HMXB spectra .
The XLF per unit SFR can be described by a power law dN / d \log L _ { X,unabs } \approx 2.0 ( L _ { X,unabs } / 10 ^ { 39 } { erg~ { } s } ^ { % -1 } ) ^ { -0.6 } ( M _ { \odot } yr ^ { -1 } ) ^ { -1 } from L _ { X,unabs } = 10 ^ { 38 } to 10 ^ { 40.5 } erg s ^ { -1 } , where L _ { X,unabs } is the unabsorbed luminosity at 0.25–8 keV .
The intrinsic number of luminous HMXBs per unit SFR is a factor of \sim 2.3 larger than the observed number reported before .
The intrinsic XLF is composed of hard , soft and supersoft sources ( defined here as those 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 \sim 2:1:1 proportion .
We also constructed the intrinsic HMXB XLF in the soft X-ray band ( 0.25–2 keV ) .
Here , the numbers of hard , soft and supersoft sources prove to be nearly equal .
The cumulative present-day 0.25–2 keV emissivity of HMXBs with luminosities between 10 ^ { 38 } and 10 ^ { 40.5 } erg s ^ { -1 } is \sim 5 \times 10 ^ { 39 } erg s ^ { -1 } ( M _ { \odot } yr ^ { -1 } ) ^ { -1 } , which may be relevant for studying the X-ray preheating of the early Universe .