Quasars as standard candles

V. Accounting for the dispersion in the L_X–L_UV relation down to ≤ 0.06 dex

¹ Dipartimento di Fisica e Astronomia, Università di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino, Firenze, Italy
e-mail: matilde.signorini@unifi.it
² INAF – Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, 50125 Firenze, Italy
³ University of California-Los Angeles, Department of Physics and Astronomy, PAB, 430 Portola Plaza, Box 951547, Los Angeles, CA 90095-1547, USA
⁴ Scuola Superiore Meridionale, Largo S. Marcellino 10, 80138 Napoli, Italy
⁵ Istituto Nazionale di Fisica Nucleare (INFN), Sez. di Napoli, Complesso Univ. Monte S. Angelo, Via Cinthia 9, 80126 Napoli, Italy
⁶ Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA

Received: 13 December 2023
Accepted: 22 March 2024

Abstract

A characteristic feature of quasars is the observed non-linear relationship between their monochromatic luminosities at rest-frame 2500 Å and 2 keV. This relationship is evident across all redshifts and luminosities and, due to its non-linearity, can be implemented to estimate quasar distances and construct a Hubble Diagram for quasars. Historically, a significant challenge in the cosmological application of this relation has been its high observed dispersion. Recent studies have demonstrated that this dispersion can be reduced by excluding biased objects from the sample. Nevertheless, the dispersion remains considerable (δ ∼ 0.20 dex), especially when compared to the Phillips relation for supernovae Ia. Given the absence of a comprehensive physical model for the relation, it remains unclear how much of the remaining dispersion is tied to the physical mechanism behind the relation itself and how much can be attributed to other factors, not addressed by the sample selection and by the choice of X-ray and UV indicators. Potential contributing factors include (i) the scatter produced by using X-ray photometric results instead of spectroscopic ones, (ii) the intrinsic variability of quasars, and (iii) the inclination of the accretion disc relative to our line of sight. In this study, we thoroughly examine these three factors and quantify their individual contributions to the observed dispersion. Based on our findings, we argue that the characteristic dispersion of the X-ray–UV luminosity relationship (which is attributable to the physical mechanism behind it) is likely below 0.06 dex. This result reinforces the validity of using quasars as standard candles and offers valuable insights for developing physical models of the X-ray/UV relation. Achieving such a low dispersion on large observed data sets is hardly feasible, due to the complexity of removing all the empirical contributions to the scatter. Nevertheless, we argue that high-redshift subsamples can show a significantly lower dispersion than the average subsample. This aspect is particularly significant for cosmological applications, indicating that targeted observations of select high-redshift objects can enhance the cosmological power of quasars in constraining the shape of the Hubble Diagram at high redshift.