Quasar lifetime measurements from extended Ly$\alpha$ nebulae at $z\sim 6$

The existence of billion-solar-mass black holes hosted in luminous quasars within the first gigayear of cosmic history poses a challenge to our understanding of supermassive black hole (SMBH) growth. The problem is further exacerbated by the very short quasar lifetimes of $t_{\rm Q}\lesssim 10^6$ years, as derived from the extent of their proximity zone (PZ) sizes observed in the quasars' rest-UV spectra. However, the quasar lifetime estimates based on the extents of the proximity zones may be underestimated, as time-variable obscuration effects might have limited the quasars' emission along our sightline in the past. In this work, we present independent quasar lifetime measurements for six quasars at $z \sim 6$ leveraging the extended nebular emission perpendicular to our line-of-sight. We use observations from the Very Large Telescope/Multi-Unit Spectroscopic Explorer (MUSE) to search for extended Ly$\alpha$ emission in the circumgalactic medium around quasars with small proximity zones and estimate their lifetimes as the light travel time between the SMBH and the outer edge of the nebula. We find agreement between the independent lifetime estimates. For one object we find a proximate absorption system prematurely truncating the extent of the quasar's proximity zone, which thus results in an expected discrepancy between the lifetime estimates. Our results provide further evidence that the quasars' current accretion episode has only recently begun, challenging our models of SMBH growth.