**A Hubble diagram for Quasars**

Edwin Hubble's 1929 paper is well known for showing that the recessional velocity of a galaxy increases with its distance from the Earth, implying that the Universe is expanding. This has marked a turning pointin understanding the Universe, and it has been one of the most important discoveries of the 20^{th} century. Since Hubble's original paper, many versions of the so-called "Hubble Diagram" have been made, and it was soon after recognized that exploding stars in other galaxies (i.e. "supernovae") could have been used as distance indicators.

An optimal "standard candle" for cosmological studies is defined by two fundamental properties: it has a standard (or *standard-izable*) instrinsic luminosity (therefore one can infer its distance from earth from its observed luminosity), and it is easy to observe in a wide redshift range. Type Ia supernovae have a fairly narrow distribution in intrinsic brightness, but they can be seen only up to redshift 1.4. Quasars are the best class of astrophysical sources concerning the latter property, but completely lack the former: their observed emission spans several orders of magnitude in luminosity. As a consequence, quasars, at a first glance, are far from being useful tools to set the cosmic distance scale as a function of redshift.

However, even weak correlations between spectral features and luminosity, albeit with large dispersion and observational biases, can in principle be useful for cosmological measurements, provided that the quasar sample is large enough. A non-linear relation between X-ray and UV luminosities in quasars has been discovered with the first X-ray surveys in the early 80's and it has been confirmed with various samples of a few hundred quasars observed with the main X-ray observatories over a redshift range from 0 to 6.5 and about five decades in UV luminosity. The potential use of such relation as a cosmological probe is obvious: assuming no redshift evolution of the relation, the observed X-ray flux is a function of the observed UV flux, the redshift, and the parameters of the adopted cosmological model. The relation can be then fitted to a set of UV and X-ray observations of quasars in order to estimate the cosmological parameters.

Figure 1: Hubble Diagram for the quasar sample (small grey points) and supernovae (cyan points) from the Union 2.1 sample (Suzuki et al 2012). The large red points are quasar averages in small redshift bins. The inner box shows a zoom of the z=0-1.5 range, in order to better visualize the match between the SNe and the quasar samples. The continuous line is obtained from a joint fit to the two samples assuming a standard ΛCDM cosmological model. |

In this framework, Guido Risaliti and Elisabeta Lusso (INAF-Arcetri Observatory) have recently published in the Astropysical Journal the first Hubble Diagram for quasars suitable for cosmological measurements. Thanks to the increase by about an order of magnitude of the number of quasars with observed UV and X-ray emission (provided by recent optical and X-ray surveys), it has been possible to significantly constrain the cosmological parameters, and to test the cosmological model over the whole redshift range out to redshift 6.5, when the Universe was only 0.8 billion years old. The resulting Hubble Diagram for quasars is shown in Figure 1. The resulting cosmological parameters with the present data, assuming a ΛCDM model, are Ω_{M}=0.22^{+0.10}_{-0.08} and Ω_{Λ}=0.92^{+0.18}_{-0.30} (Ω_{M}=0.28±0.04 and Ω_{Λ}=0.73±0.08 from a joint quasar-supernovae fit). The outcome for the determination of the cosmological parameters is shown in Figure 2.

Figure 2: 68% and 95% confidence level contours for ΩM and ΩΛ, assuming a standard ΛCDM model, as derived from the Hubble diagram of quasars (blue), from the Supernovae Union 2.1 sample (empty black contours) and from a joint fit (orange-red). |

These findings, presented in the article "A Hubble Diagram with Quasars" to be published in the Astrophysical Journal, open a new branch of observational cosmology. Future larger quasar samples will provide tight constraints on the cosmological parameters, and will allow to test possible deviations from the standard model with higher precision than available today.

Edited by Anna Gallazzi and Elisabeta Lusso, 28/09/2015