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.
