ABSTRACT We present a new approach to measure the power-law temperature density relationship $T=T_0 (\rho/ \bar{\rho })^{\gamma -1}$ and UV background photoionization rate $\Gamma _{{{{\rm H\, {\small I}}}}{}}$ of intergalactic medium (IGM) based on Voigt profile decomposition Ly α forest into set discrete absorption lines with Doppler parameter b neutral hydrogen column $N_{\rm I}}$. Previous ...

<p style='text-indent:20px;'>In this paper we study the Riemann-Liouville fractional integral of order <inline-formula><tex-math id="M1">\begin{document}$ \alpha>0 $\end{document}</tex-math></inline-formula> as a linear operator from id="M2">\begin{document}$ L^p(I,X) into itself, when id="M3">\begin{document}$ 1\leq p\leq \infty $\end{document}</te...

The thermal state of the intergalactic medium (IGM) contains vital information about epoch reionization, one most transformative yet poorly understood periods in young universe. This is encoded small-scale structure Lyman-$\alpha$ (Ly$\alpha$) absorption quasar spectra. 1D flux power spectrum measures average along sightlines. At high redshifts, where opacity large, averaging mixes signal-to-no...