Constraints on QSO emissivity using H I and He II Lyman alpha forest

The spectrum of cosmic ultraviolet background radiation at He II ionizing energies (E > 4 Ryd) is important to study the He II reionization, thermal history of the intergalactic medium (IGM) and metal lines observed in QSO absorption spectra. It is determined by the emissivity of QSOs at E > 4 Ryd obtained from their observed luminosity functions and the mean spectral energy distribution (SED). The SED is approximated as a power-law at energies E > 1 Ryd, $f_E \propto E^{\alpha}$, where the existing observations constrain the power-law index $\alpha$ only up to ~2.3 Ryd. Here, we constrain $\alpha$ for E > 4 Ryd using recently measured He II Lyman-alpha effective optical depths ($\tau_{HeII}$), H I photoionization rates and updated H I distribution in the IGM. We find that -1.6 > $\alpha$ > -2 is required to reproduce the $\tau_{HeII}$ measurements when we use QSO emissivity obtained from their luminosity function using optical surveys. We also find that the models where QSOs can alone reionize H I can not reproduce the $\tau_{HeII}$ measurements. These models need modifications, such as a break in mean QSO SED at energies greater than 4 Ryd. Even after such modifications the predicted He II reionization history, showing that the He II is highly ionized even at z~5, is significantly different from the standard models. Therefore, the thermal history of the IGM will be crucial to distinguish these models. We also provide the He II photoionization rates obtained from binned $\tau_{HeII}$ measurements.