VoIgt profile Parameter Estimation Routine (VIPER): H I photoionization rate at z<0.5

We have developed a parallel code called "VoIgt profile Parameter Estimation Routine (VIPER)" for automatically fitting the H I Ly-$\alpha$ forest seen in the spectra of QSOs. We obtained the H I column density distribution function (CDDF) and line width ($b$) parameter distribution for $z < 0.45$ using spectra of 82 QSOs obtained using Cosmic Origins Spectrograph and VIPER. Consistency of these with the existing measurements in the literature validate our code. By comparing this CDDF with those obtained from hydrodynamical simulation, we constrain the H I photoionization rate ($\Gamma_{\rm HI}$) at $z < 0.45$ in four redshift bins. The VIPER, together with the Code for Ionization and Temperature Evolution (CITE) we have developed for GADGET-2, allows us to explore parameter space and perform $\chi^2$ minimization to obtain $\Gamma_{\rm HI}$. We notice that the $b$ parameters from the simulations are smaller than what are derived from the observations. We show the observed $b$ parameter distribution and $b$ vs $\log {\rm N_{HI}}$ scatter can be reproduced in simulation by introducing sub-grid scale turbulence. However, it has very little influence on the derived $\Gamma_{\rm HI}$. The $\Gamma_{\rm HI}(z)$ obtained here, $(3.9 \pm 0.1) \times 10^{-14} \; (1+z)^{4.98 \pm 0.11} \;{\rm s^{-1}}$, is in good agreement with those derived by us using flux based statistics in the previous paper. These are consistent with the hydrogen ionizing ultra-violet (UV) background being dominated mainly by QSOs without needing any contribution from the non-standard sources of the UV photons.