The X-ray luminosity function and number counts of spiral galaxies

We discuss the X-ray luminosity function and number counts of normal spiral galaxies. A detailed comparison is performed of the LFs compiled at infrared, radio and optical wavelengths and converted into XLFs using available relations in the literature with the XLF directly estimated in the 0.5-2 keV energy band from X-ray surveys. We find that the XLF from the local sample of IRAS galaxies provides a good representation of all available data samples; pure luminosity evolution of the form (1 + z)(eta), with eta <= 3, is favoured over pure density evolution. We also find that the local X-ray luminosity density is well defined, 3 x 10(37) +/- 30% erg s(-1) Mpc(-3). We discuss different estimates of the galaxies Log N-Log S, selected from the Chandra Deep Field surveys with different selection criteria, and find that these have similar slopes, but normalisations scattered within a factor similar to 2 ( which is not far from the Poissonian error on the number counts). We then compare the observed galaxies Log N-Log S with the counts predicted by the integration of our reference z = 0 XLF. From the analysis of number counts alone, it is not possible to discriminate between density and luminosity evolution; however, the evolution of galaxies must be stopped in both cases at a redshift z similar to 1-2. The contribution of galaxies to the cosmic X-ray background is found to be in the range 6%-12%. By means of a complementary analysis with cosmic star formation models, we also find that the observed X-ray number counts might be not compatible with very high star formation rates at z similar to 3 as suggested by sub-mm observations. Concerning the content of current and, possibly, future X-ray surveys, we determine the fraction of normal galaxies around the current flux limit. At similar to 3 x 10(-17) erg s(-1) cm(-2) in the 0.5-2.0 keV band, the normal galaxies in the Chandra Deep Field surveys are about the (30 +/- 12)% of the total number of objects. At fainter fluxes the fraction of galaxies will probably rise, and exceed the counts from AGN at fluxes <= 10(-17) erg s(-1) cm(-2).