The spectrum of cosmic ultraviolet background radiation at He ii ionizing energies ( E \geq 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 \geq 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 \geq 1 Ryd , f _ { E } \propto E ^ { \alpha } , where the existing observations constrain the power-law index \alpha only up to \sim 2.3 Ryd .
Here , we constrain \alpha for E \geq 4 Ryd using recently measured He ii Lyman- \alpha effective optical depths ( \tau _ { \alpha } ^ { He II } ) , 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 _ { \alpha } ^ { He II } 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 _ { \alpha } ^ { He II } 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 \sim 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 _ { \alpha } ^ { He II } measurements .