Probing quasar lifetimes with proximate 21-centimetre absorption in the diffuse intergalactic medium at redshifts z≥6

Enhanced ionizing radiation in close proximity to redshift \(z\gtrsim6\) quasars creates short windows of intergalactic Ly\(\alpha\) transmission blueward of the quasar Ly\(\alpha\) emission lines. The majority of these Ly\(\alpha\) near-zones are consistent with quasars that have optically/UV bright lifetimes of \(t_{\rm Q}\sim10^5−10^7\,\rm yr\). However, lifetimes as short as \(t_{\rm Q}\lesssim10^4\,\rm yr\) appear to be required by the smallest Ly\(\alpha\) near-zones. These short lifetimes present an apparent challenge for the growth of \(\sim10^9M_{\odot}\) black holes at \(z\gtrsim6\). Accretion over longer time-scales is only possible if black holes grow primarily in an obscured phase, or if the quasars are variable on time-scales comparable to the equilibriation time for ionized hydrogen. Distinguishing between very young quasars and older quasars that have experienced episodic accretion with Ly\(\alpha\) absorption alone is challenging, however. We therefore predict the signature of proximate 21-cm absorption around \(z\gtrsim6\) radio-loud quasars. For modest pre-heating of intergalactic hydrogen by the X-ray background, where the spin temperature \(T_{\rm S}\lesssim10^2\,\rm K\) prior to any quasar heating, we find proximate 21-cm absorption should be observable in the spectra of radio-loud quasars. The extent of the proximate 21-cm absorption is sensitive to the integrated lifetime of the quasar. Evidence for proximate 21-cm absorption from the diffuse intergalactic medium within \(2−3\,\rm pMpc\) of a (radio-loud) quasar would be consistent with a short quasar lifetime, \(t_{\rm Q}\lesssim10^5\,\rm yr\), and would provide a complementary constraint on models for high-redshift black hole growth.