A census of the high-z quasar lifetime distribution

Lifetime measurements of luminous quasars (QSOs), when tied to BH mass estimates, will shed unique light on the physical mechanisms responsible for fueling SMBH growth in the high-z universe. An exceptional probe of these lifetimes is the size of the proximity zones of such QSOs, in combination with the Lyman-alpha damping wing signature imprinted on their spectra by the foreground neutral intergalactic medium (IGM). In the coming years, EUCLID will detect a number of high-z QSOs never seen before, whose exquisite spectra collected by JWST will call for powerful statistical methods to conduct an unprecedented census of their lifetime distribution. We developed a state-of-the-art Bayesian inference pipeline that allows us to disentangle the IGM absorption imprint from a QSO's unknown intrinsic spectrum and infer its lifetime to 0.2-1.0 dex, as well as the HI column density in front of it to 0.2-0.9 dex, also constraining the global timing of reionization. We account for covariances across the full spectral range caused by IGM transmission fluctuations, QSO continuum reconstruction, and spectral noise. We present a first census of the lifetime distribution of 41 QSOs between z=5.75 and 7.6, based on current ground-based as well as the first JWST/NIRSpec spectra. By analyzing realistic mock observational spectra resembling the distribution of EUCLID QSOs, we provide a forecast of the observational constraints extending out to z=10 that will be achievable in the coming years.