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X-ray emission from star-forming galaxies - III. Calibration of the Lx-SFR relation up to redshift z$\simeq$1.3

We investigate the relation between total X-ray emission from star-forming galaxies and their star formation activity. Using nearby late-type galaxies and ULIRGs from Paper I and star-forming galaxies from Chandra Deep Fields, we construct a sample of 66 galaxies spanning the redshift range z~0-1.3 and the star-formation rate (SFR) range ~0.1-10^3 M_sun/yr. In agreement with previous results, we find that the Lx-SFR relation is consistent with a linear law both at z=0 and for the z=0.1-1.3 CDF galaxies, within the statistical accuracy of ~0.1 in the slope of the Lx-SFR relation. For the total sample, we find a linear scaling relation Lx/SFR~(4.0\pm 0.4)x10^{39}(erg/s)/(Msun/yr), with a scatter of ~0.4 dex. About ~2/3 of the 0.5-8 keV luminosity generated per unit SFR is expected to be due to HMXBs. We find no statistically significant trends in the mean Lx/SFR ratio with the redshift or star formation rate and constrain the amplitude of its variations by <0.1-0.2 dex. These properties make X-ray observations a powerful tool to measure the star formation rate in normal star-forming galaxies that dominate the source counts at faint fluxes.