Constraining warm dark matter power spectrum using the cross-correlation of HI 21 cm signal and the Lyman-$\alpha$ forest

Abstract

We have considered the prospects for measuring the cross Warm Dark Matter (WDM) power spectrum of the redshifted HI 21-cm signal and the Lyman-$\alpha$ forest and thereby constraining WDM mass using observations with upcoming radio-interferometers - the Ooty Wide Field Array (OWFA) and SKA1-mid, and a spectroscopic survey of the quasars. We have considered a quasar survey with a mean observed quasar number density of ${\bar{\mathrm{n}}}_{\mathrm{Q}}=48$ deg${}^{-2}$ over a collecting area of 14455 deg${}^2$, and a mean spectroscopic SNR = 5. Our analysis with OWFA shows that it is possible to measure the WDM power spectrum in several $k$-bins at $k<0.4$ Mpc${}^{-1}$ with $\mathrm{SNR}>5$ using an observation of 200 hours each in 100 different fields-of-view for $m_{\mathrm{WDM}}=0.25$ keV. Considering the possibility of the joint measurement of the parameters, the warm dark matter density parameter ${\Omega }_{\mathrm{WDM}}$, and the dark energy density parameter ${\Omega }_{\Lambda 0}$, we find that the relative error on the $1-\sigma$ measurement of the parameter ${\Omega }_{\mathrm{WDM}}$ is $\sim 0.8$ for a fiducial $m_{\mathrm{WDM}}=0.25$ keV. We further find that it is possible to have a measurement of the suppression of power from the Cold Dark Matter (CDM) power spectrum at a confidence level of $\sim 7.2-\sigma$ and $\sim 2.7-\sigma$ in two different $k$-bins over the $k$-range $0.1\le k\le 3.13$ Mpc${}^{-1}$ for $m_{\mathrm{WDM}}=0.15$ keV. Considering the analysis with SKA1-mid, we find that for a fiducial $m_{\mathrm{WDM}}=0.25$ keV, the suppression in the cross power spectrum can be measured at $\sim 10-\sigma$ around $k\sim 0.2{\mathrm{Mpc}}^{-1}$ for a total observing time of $20000$ hrs distributed uniformly over $50$ independent pointings where the available $k$-range is binned as $\Delta k=k/5$.

to be submitted at JCAP