A Hubble Diagram for Quasars

Abstract: We present a new method to test the cosmological model, based on the non-linear relation between ultraviolet and X-ray luminosity of quasars. We built a data set of ~1,138 quasars by merging several literature samples with X-ray measurements at 2 keV and SDSS photometry, which was used to estimate the extinction-corrected 2500 Angstrom flux. We obtained three main results: (1) we checked the relation between X-ray and UV luminosities in small redshift bins up to z~6, confirming that it holds at all redshifts with the same slope; (2) we built a Hubble diagram for quasars up to z~6, which is well matched to that of supernovae in the common z=0-1.4 interval, and extends the test of the cosmological model up to z~6; (3) we showed that this relation is a powerful tool to estimate cosmological parameters. Assuming a LambdaCDM model, we obtain Omega_M=0.22+0.08-0.10 and Omega_Lambda=0.92+0.18-0.30 (Omega_M=0.28+-0.04 and Omega_\Lambda=0.73+-0.08 from a joint quasar-SNe fit). However, much more precise measurements will be achieved in the future. A few thousands SDSS quasars already have serendipitous X-ray observations with Chandra or XMM-Newton, and at least 100,000 quasars with UV and X-ray data will be available from the eROSITA all-sky survey in a few years. Euclid, LSST, and Athena surveys will further increase the sample size to at least several hundred thousands. Our simulations show that these samples will provide tight constraints on the cosmological parameters, and will allow to test possible deviations from the standard model with higher precisions than available today.