Lyman-$α$ forest 1D flux power spectrum constraints on QSO-assisted reionization models

Abstract: Recent JWST observations have revealed a large population of faint Quasi-Stellar Objects (QSOs) at redshifts 4 < z < 6, including a highly reddened sub-population of Little Red Dots. We exploit the sensitivity of the Lyman-$α$ forest 1D flux power spectrum to thermal fluctuations in the Intergalactic Medium (IGM) to place statistical constraints on the spectral properties of the QSOs. By post-processing simulated Lyman-$α$ forest spectra from the Sherwood-Relics suite of Lyman-$α$ forest simulations with added HeII reionization by QSOs, in conjunction with published precision measurements of the Lyman-$α$ forest 1D flux power spectrum between 4.2 < z < 5.0, we find that the addition of temperature boosts of the IGM within the HeIII regions improves agreement with the measured power spectra. While the contribution of the Little Red Dot population to HeII reionization is consistent with both a mild temperature boost of $ΔT_b=1\times10<sup>4$ K for soft spectra QSOs and $ΔT_b=2\times10<sup>4$ K for hard spectra QSOs, a contribution from the larger population of faint QSOs found by JWST having $M_{\rm UV} &gt; -21.6$ is excluded at the 2$σ$ level if their spectra are sufficiently hard to boost the IGM temperature in HeIII regions by $ΔT_b=2\times10<sup>4$ K or greater.