Estimating the effective lifetime of the $z\sim6$ quasar population from the composite proximity zone profile

TL;DR

This study estimates the effective lifetime of high-redshift quasars using composite proximity zone profiles, employing a Bayesian method to analyze spectra from 15 quasars at z~6, revealing a lifetime that challenges existing SMBH growth models.

Contribution

Introduces a Bayesian approach to infer quasar lifetime from composite spectra, providing a new estimate that questions current SMBH growth theories.

Findings

Estimated quasar lifetime as log10(tQ/yr)=5.7 with uncertainties.

Results are consistent with previous studies but challenge SMBH growth models.

Developed a robust method to account for spectral uncertainties.

Abstract

The lifetime of quasars can be estimated by means of their proximity zone sizes, which are regions of enhanced flux bluewards of the Lyman-$\alpha$ emission line observed in the rest-frame UV spectra of high-redshift quasars, because the intergalactic gas has a finite response time to the quasars' radiation. We estimate the effective lifetime of the high-redshift quasar population from the composite transmitted flux profile within the proximity zone region of a sample of $15$ quasars at $5.8\leq z\leq 6.6$ with precise systemic redshifts, and similar luminosities, i.e. $-27.6\leq M_{1450}\leq-26.4$, and thus a similar instantaneous ionizing power. We develop a Bayesian method to infer the effective lifetime from the composite spectrum, including robust estimates of various sources of uncertainty on the spectrum. We estimate an effective lifetime of the quasar population as a whole of $\log_{10}(t_{Q}/{yr}) = 5.7^{+0.5 (+0.8)}_{-0.3 (-0.5)}$ given by the median and $68$th ($95$th) percentile of the posterior probability distribution. While our result is consistent with previous quasar lifetime studies, it poses significant challenges on the current model for the growth of supermassive black holes (SMBHs) located in the center of the quasars' host galaxies, which requires that quasar lifetimes are more than an order of magnitude longer.