The high-z quasar Hubble Diagram

Two recent discoveries have made it possible for us to begin using high-z quasars as standard candles to construct a Hubble Diagram (HD) at z > 6. These are (1) the recognition from reverberation mapping that a relationship exists between the optical/UV luminosity and the distance of line-emitting gas from the central ionizing source. Thus, together with a measurement of the velocity of the line-emitting gas, e.g., via the width of BLR lines, such as Mg II, a single observation can therefore in principle provide a determination of the black hole's mass; and (2) the identification of quasar ULAS J1120+0641 at z = 7.085, which has significantly extended the redshift range of these sources, providing essential leverage when fitting theoretical luminosity distances to the data. In this paper, we use the observed fluxes and Mg II line-widths of these sources to show that one may reasonably test the predicted high-z distance versus redshift relationship, and we assemble a sample of 20 currently available high-z quasars for this exercise. We find a good match between theory and observations, suggesting that a more complete, high-quality survey may indeed eventually produce an HD to complement the highly-detailed study already underway (e.g., with Type Ia SNe, GRBs, and cosmic chronometers) at lower redshifts. With the modest sample we have here, we show that the Rh = ct Universe and ΛCDM both fit the data quite well, though the smaller number of free parameters in the former produces a more favorable outcome when we calculate likelihoods using the Akaike, Kullback, and Bayes Information Criteria. These three statistical tools result in similar probabilities, indicating that the Rh = ct Universe is more likely than ΛCDM to be correct, by a ratio of about 85% to 15%.