We study the X-ray emission of a representative sample of 27 local luminous infrared galaxies (LIRGs). The median IR luminosity of our sample is log L_IR/L_sun = 11.2, thus the low-luminosity end of the LIRG class is well represented. We used new XMM-Newton data as well as Chandra and XMM-Newton archive data. The soft X-ray (0.5-2 keV) emission of most of the galaxies (>80%), including LIRGs hosting a Seyfert 2 nucleus, is dominated by star-formation related processes. These LIRGs follow the star-formation rate (SFR) versus soft X-ray luminosity correlation observed in local starbursts. We find that ~15% of the non-Seyfert LIRGs (3 out of 20) have an excess hard X-ray emission relative to that expected from star-formation that might indicate the presence of an obscured AGN. The rest of the non-Seyfert LIRGs follow the SFR versus hard X-ray (2-10 keV) luminosity correlation of local starbursts. The non-detection of the 6.4 keV Fe K alpha emission line in the non-Seyfert LIRGs allows us to put an upper limit to the bolometric luminosity of an obscured AGN, L_bol <1043 erg s-1 . That is, in these galaxies, if they hosted a low luminosity AGN, its contribution to total luminosity would be less than 10%. Finally we estimate that the AGN contribution to the total luminosity for our sample of local LIRGs is between 7% and 10%.

Accepted for Publication in A&A, 22 pages, 9 figures