ROSAT X-ray sources in the field of the LMC. III.The log N -- log S of background AGN and the LMC gas

We use 50 (candidate) background X-ray sources (AGN) in the LMC field observed in ROSAT PSPC observations to derive the observed log N - log S relation. We correct for the varying PSPC exposure and the absorption due to the galactic and the LMC gas. We compare the observed log N - log S with a theoretical log N - log S of the soft extragalactic X-ray background (AGN and a cluster of galaxy contribution). We find that the observed log N - log S has a deficiency with respect to the theoretical log N - log S. Factors which can account for such a deficiency are: (1) incompleteness of the selected AGN and cluster of galaxies sample, (2) deviation of the log N - log S in the LMC field from the log N - log S derived from a large sample of AGN in several fields, (3) existence of gas additional to the HI represented in the Parkes HI map of the LMC field. We investigate the likely contribution of these effects and find that (1) a fraction of at most 30% of the background sources may not have been found in this analysis and may contribute to the observed deficiency. (2) We cannot exclude a deviation of the log N - log S in the field of the LMC from a theoretical log N - log S, especially the cluster of galaxy contribution may show variations across the sky. (3) If LMC gas (restricted to >10^21 cm^-2 columns) in addition to the HI represented in the Parkes map would be responsible for the deficiency, then a factor of >0.3 (at 90% confidence) of additional gas would be required. This would equal a molecular mass fraction of >21%, which would be larger than, but within the uncertainties consistent with a molecular mass fraction of ~30% derived from CO observations (for columns >10^21 cm^-2).