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

The 21-cm forest signal is a promising probe of the Epoch of Reionization complementary to other 21-cm line observables and Ly\(\alpha\) forest signal. Prospects of detecting it have significantly improved in the last decade thanks to the discovery of more than 30 radio-loud quasars at these redshifts, upgrades to telescope facilities, and the notion that neutral hydrogen islands persist down to \(z\lesssim 5.5\). We forward-model the 21-cm forest signal using semi-numerical simulations and incorporate various instrumental features to explore the potential of detecting the 21-cm forest at \(z=6\), both directly and statistically, with the currently available (uGMRT) and forthcoming (SKA1-low) observatories. We show that it is possible to detect the 1D power spectrum of the 21-cm forest spectrum, especially at large scales of \(k\lesssim8.5\,\rm MHz^{-1}\) with the \(500\,\rm hr\) of the uGMRT time and \(k\lesssim32.4\,\rm MHz^{-1}\) with the SKA1-low over \(50\,\rm hr\) if the intergalactic medium (IGM) is \(25\%\) neutral and these neutral hydrogen regions have a spin temperature of \(\lesssim30\,\rm K\). On the other hand, we infer that a null-detection of the signal with such observations of 10 radio-loud sources at \(z\approx6\) can be translated into constraints on the thermal and ionization state of the IGM which are tighter than the currently available measurements. Moreover, a null-detection of the 1D 21-cm forest power spectrum with only \(50\,\rm hr\) of the uGMRT observations of 10 radio-loud sources can already be competitive with the Ly\(\alpha\) forest and 21-cm tomographic observations in disfavouring models of significantly neutral and cold IGM at \(z=6\).