Molecular gas in QSO host galaxies at z > 5

We present observations with the IRAM Plateau de Bure Interferometer of three QSOs at z > 5 aimed at detecting molecular gas in their host galaxies as traced by CO transitions. CO (5-4) is detected in SDSS J033829.31+ 002156.3 at z = 5.0267, placing it amongst the most distant sources detected in CO. The CO emission is unresolved with a beam size of similar to 1 '', implying that the molecular gas is contained within a compact region, less than similar to 3 kpc in radius. We infer an upper limit on the dynamical mass of the CO emitting region of similar to 3 x 10(10) M-circle dot/sin(i)(2). The comparison with the Black Hole mass inferred from near-IR data suggests that the BH-to-bulge mass ratio in this galaxy is significantly higher than in local galaxies. From the CO luminosity we infer a mass reservoir of molecular gas as high as M(H-2) = 2.2 x 10(10) M-circle dot, implying that the molecular gas accounts for a significant fraction of the dynamical mass. When compared to the star formation rate derived from the far-IR luminosity, we infer a very short gas exhaustion timescale (similar to 10(7) years), comparable to the dynamical timescale. CO is not detected in the other two QSOs (SDSS J083643.85+ 005453.3 and SDSS J163033.90+ 401209.6) and upper limits are given for their molecular gas content. When combined with CO observations of other type 1 AGNs, spanning a wide redshift range (0 < z < 6.4), we find that the host galaxy CO luminosity (hence molecular gas content) and the AGN optical luminosity (hence BH accretion rate) are correlated, but the relation is not linear: L-CO' proportional to [lambda L-lambda (4400 angstrom)](0.72). Moreover, at high redshifts (and especially at z > 5) the CO luminosity appears to saturate. We discuss the implications of these findings in terms of black hole-galaxy co-evolution.