Towards $21$-cm intensity mapping at $z=2.28$ with uGMRT using the tapered gridded estimator III: Foreground removal

Neutral hydrogen (HI) $21$-cm intensity mapping (IM) is a promising probe of the large-scale structures in the Universe. However, a few orders of magnitude brighter foregrounds obscure the IM signal. Here we use the Tapered Gridded Estimator (TGE) to estimate the multi-frequency angular power spectrum (MAPS) $C_{\mathrm{\ell }}(\mathrm{\Delta }\nu )$ from a $24.4\mathrm{M}\mathrm{H}\mathrm{z}$ bandwidth uGMRT Band $3$ data at $432.8\mathrm{M}\mathrm{H}\mathrm{z}$. In $C_{\mathrm{\ell }}(\mathrm{\Delta }\nu )$ foregrounds remain correlated across the entire $\mathrm{\Delta }\nu$ range, whereas the $21$-cm signal is localized within $\mathrm{\Delta }\nu \le [\mathrm{\Delta }\nu ]$ (typically $0.5-1\mathrm{M}\mathrm{H}\mathrm{z}$). Assuming the range $\mathrm{\Delta }\nu >[\mathrm{\Delta }\nu ]$ to have minimal $21$-cm signal, we use $C_{\mathrm{\ell }}(\mathrm{\Delta }\nu )$ in this range to model the foregrounds. This foreground model is extrapolated to $\mathrm{\Delta }\nu \le [\mathrm{\Delta }\nu ]$, and subtracted from the measured $C_{\mathrm{\ell }}(\mathrm{\Delta }\nu )$. The residual $[C_{\mathrm{\ell }}(\mathrm{\Delta }\nu ){]}_{\mathrm{r}\mathrm{e}\mathrm{s}}$ in the range $\mathrm{\Delta }\nu \le [\mathrm{\Delta }\nu ]$ is used to constrain the $21$-cm signal, compensating for the signal loss from foreground subtraction. $[C_{\mathrm{\ell }}(\mathrm{\Delta }\nu ){]}_{\mathrm{r}\mathrm{e}\mathrm{s}}$ is found to be noise-dominated without any trace of foregrounds. Using $[C_{\mathrm{\ell }}(\mathrm{\Delta }\nu ){]}_{\mathrm{r}\mathrm{e}\mathrm{s}}$ we constrain the $21$-cm brightness temperature fluctuations ${\mathrm{\Delta }}^2(k)$, and obtain the $2\sigma$ upper limit ${\mathrm{\Delta }}_{\mathrm{U}\mathrm{L}}^2(k)\le (18.07{)}^2\mathrm{m}{\mathrm{K}}^2$ at $k=0.247{\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}$. We further obtain the $2\sigma$ upper limit $[{\mathrm{\Omega }}_{\mathrm{H}\mathrm{I}}{b}_{\mathrm{H}\mathrm{I}}{]}_{\mathrm{U}\mathrm{L}}\le 0.022$ where ${\mathrm{\Omega }}_{\mathrm{H}\mathrm{I}}$ and $b_{\mathrm{H}\mathrm{I}}$ are the comoving HI density and bias parameters respectively. Although the upper limit is nearly $10$ times larger than the expected $21$-cm signal, it is $3$ times tighter over previous works using foreground avoidance on the same data.