X-ray ionization of the intergalactic medium by quasars

We investigate the impact of quasars on the ionization of the surrounding intergalactic medium (IGM) with the radiative transfer code $\mathtt{\text{CRASH4}}$, now accounting for X-rays and secondary electrons. After comparing with analytic solutions, we post-process a cosmic volume ($\approx 1.5\times {10}^4$ Mpc${}^3{h}^{-3}$) containing a ULAS J1120+0641-like quasar (QSO) hosted by a $5 \times 10^{11} {\rm M}_\odot h^{-1}$ dark matter (DM) halo. We find that: (i) the average HII region ($R\sim 3.2$~pMpc in a lifetime $t_f={10}^7$~yrs) is mainly set by UV flux, in agreement with semi-analytic scaling relations; (ii) a largely neutral ($x_{\text{HII}}<0.001$), warm ($T\sim {10}^3$~K) tail extends up to few Mpc beyond the ionization front, as a result of the X-ray flux; (iii) LyC-opaque inhomogeneities induce a line of sight (LOS) scatter in $R$ as high as few physical Mpc, consistent with the DLA scenario proposed to explain the anomalous size of the ULAS J1120+0641 ionized region. On the other hand, with an ionization rate ${\dot{N}}_{\gamma ,0}\sim {10}^{57}$~s${}^{-1}$, the assumed DLA clustering and gas opacity, only one LOS shows an HII region compatible with the observed one. We deduce that either the ionization rate of the QSO is at least one order of magnitude lower or the ULAS J1120+0641 bright phase is shorter than ${10}^7$~yrs.