Towards $21$-cm intensity mapping at $z=2.28$ with uGMRT using the tapered gridded estimator II: Cross-polarization power spectrum

Abstract

Neutral hydrogen ($\mathrm{HI}$) $21$-cm intensity mapping (IM) offers an efficient technique for mapping the large-scale structures in the universe. We introduce the 'Cross' Tapered Gridded Estimator (Cross TGE), which cross-correlates two cross-polarizations (RR and LL) to estimate the multi-frequency angular power spectrum (MAPS) $C_{\ell }(\Delta \nu )$. We expect this to mitigate several effects like noise bias, calibration errors etc., which affect the 'Total' TGE which combines the two polarizations. Here we apply the Cross TGE on a $24.4\mathrm{MHz}$ bandwidth uGMRT Band $3$ data centred at $432.8\mathrm{MHz}$ aiming $\mathrm{HI}$ IM at $z=2.28$. The measured $C_{\ell }(\Delta \nu )$ is modelled to yield maximum likelihood estimates of the foregrounds and the spherical power spectrum $P(k)$ in several $k$ bins. Considering the mean squared brightness temperature fluctuations, we report a $2\sigma$ upper limit ${\Delta }_{UL}^2(k)\le (58.67{)}^2{\mathrm{mK}}^2$ at $k=0.804{\mathrm{Mpc}}^{-1}$ which is a factor of $5.2$ improvement on our previous estimate based on the Total TGE. Assuming that the $\mathrm{HI}$ traces the underlying matter distribution, we have modelled $C_{\ell }(\Delta \nu )$ to simultaneously estimate the foregrounds and $[{\Omega }_{\mathrm{HI}}{b}_{\mathrm{HI}}]$ where ${\Omega }_{\mathrm{HI}}$ and $b_{\mathrm{HI}}$ are the $\mathrm{HI}$ density and linear bias parameters respectively. We obtain a best fit value of $[{\Omega }_{\mathrm{HI}}{b}_{\mathrm{HI}}{]}^2=7.51\times 10^{-4}\pm 1.47\times 10^{-3}$ which is consistent with noise. Although the $2\sigma$ upper limit $[{\Omega }_{\mathrm{HI}}{b}_{\mathrm{HI}}{]}_{UL}\le 0.061$ is $\sim 50$ times larger than the expected value, this is a considerable improvement over earlier works at this redshift.

16 pages, 13 figures, accepted for publication in MNRAS

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• Towards $21$-cm intensity mapping at $z=2.28$ with uGMRT using the tapered gridded estimator -- IV. Wideband analysis
• Calibration requirement for Epoch of Reionization 21-cm signal observation -- III. Bias and variance in uGMRT ELAIS-N1 field power spectrum
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