Based on a homogeneous set of X-ray , infrared and ultraviolet observations from Chandra , Spitzer , GALEX and 2MASS archives , we study populations of high-mass X-ray binaries ( HMXBs ) in a sample of 29 nearby star-forming galaxies and their relation with the star formation rate ( SFR ) .
In agreement with previous results , we find that HMXBs are a good tracer of the recent star formation activity in the host galaxy and their collective luminosity and number scale with the SFR , in particular , L _ { \mathrm { X } } \approx 2.6 \cdot 10 ^ { 39 } \times \mathrm { SFR } .
However , the scaling relations still bear a rather large dispersion of rms \sim 0.4 dex , which we believe is of a physical origin .

We present the catalog of 1057 X-ray sources detected within the D 25 ellipse for galaxies of our sample and construct the average X-ray luminosity function ( XLF ) of HMXBs with substantially improved statistical accuracy and better control of systematic effects than achieved in previous studies .
The XLF follows a power law with slope of 1.6 in the \log ( L _ { \mathrm { X } } ) \sim 35 - 40 luminosity range with a moderately significant evidence for a break or cut-off at L _ { \mathrm { X } } \sim 10 ^ { 40 } \mathrm { erg } / \mathrm { s } .
As before , we did not find any features at the Eddington limit for a neutron star or a stellar mass black hole .

We discuss implications of our results for the theory of binary evolution .
In particular we estimate the fraction of compact objects that once upon their lifetime experienced an X-ray active phase powered by accretion from a high mass companion and obtain a rather large number , f _ { \mathrm { X } } \sim 0.2 \times \left ( 0.1 ~ { } { Myr } / \tau _ { \mathrm { X } } \right ) ( \tau _ { \mathrm { X } } is the life time of the X-ray active phase ) .
This is \sim 4 orders of magnitude more frequent than in LMXBs .
We also derive constrains on the mass distribution of the secondary star in HMXBs .