Effective bias expansion for circumventing 21 cm foregrounds

Abstract

The 21 cm line of neutral hydrogen is a promising probe of the Epoch of Reionization (EoR) but suffers from contamination by spectrally smooth foregrounds, which obscure the large-scale signal along the line of sight. We explore the possibility of indirectly extracting the 21 cm signal in the presence of foregrounds by taking advantage of nonlinear couplings between large and small scales, both at the level of the density field and a biased tracer of that field. When combined with effective field theory techniques, bias expansions allow for a systematic treatment of nonlinear mode-couplings in the map between the underlying density field and the 21 cm field. We apply an effective bias expansion to density information generated with $\texttt{21cmFAST}$ using a variety of assumptions about which information can be recovered by different surveys and density estimation techniques. We find that the 21 cm signal produced by our effective bias expansion, combined with our least optimistic foreground assumptions, produces $\sim30\%$ cross-correlations with the true 21 cm field. Providing complementary density information from high-redshift galaxy surveys yields a cross-correlation of 50-70%. The techniques presented here may be combined with foreground mitigation strategies in order to improve the recovery of the large-scale 21 cm signal.

Figures (6)

• Figure 1: The steps involved in our procedure. Starting at the left, radio telescopes will measure high-$k$ 21 cm modes (step 1). Since the 21 cm signal is a biased matter tracer, one can infer the underlying matter density field information, which will also mostly be at high $k_\parallel$ values (step 2). We can then take advantage of nonlinear couplings to reconstruct the missing density modes (step 3) and then use the bias expansion to translate the density fluctuations back into 21 cm fluctuations (step 4).
• Figure 2: Terms in the bias expansion when applied to the $\delta_\mathrm{m, obs}$ with density modes missing in the foreground wedge. The first row shows the cross-correlation of each term with the true 21 cm signal, and the second row shows the ratio of the power spectrum of each term to the 21 cm power spectrum from 21cmFAST. Within the foreground region, the only term with a significant amplitude is the quadratic bias ($\delta^2$), which shows a $\sim30\%$ correlation with the 21 cm fluctuations and is the dominant contribution to the bias expansion.
• Figure 3: Same as Fig. \ref{['fig:terms_growth_EFTonly']}, but applying density reconstruction to obtain density modes within the foreground wedge before mapping to 21 cm with the bias expansion. Compared to Fig. \ref{['fig:terms_growth_EFTonly']}, including density reconstruction improves the recovery of both the phase information and amplitude of the linear terms, $\delta$ and $k^2 \delta$. Nonlinear terms such as $\delta^2$ and $\mathcal{G}_2$ have an enhanced amplitude compared to Fig. \ref{['fig:terms_growth_EFTonly']}. The sum of the terms, shown in the rightmost panel, has a similar cross-correlation to the true 21 cm signal as in Fig. \ref{['fig:terms_growth_EFTonly']}, since the nonlinear terms already exhibited a significant cross-correlation.
• Figure 4: Same as Fig. \ref{['fig:terms_growth_recon']}, but now assuming the flat (top panel) and isotropic (bottom panel) foreground shapes. Both cases show improved accuracy in the cross-correlation and power spectrum in foreground-contaminated regions as compared to the case with wedge-shaped foregrounds shown in Fig. \ref{['fig:terms_growth_recon']}.
• Figure 5: The 21 cm intensity field resulting from different assumptions about the density field substituted into Eq. \ref{['eqn:d21_renorm']} and smoothed over $k > 0.1$ cMpc$^{-1}$. In order to facilitate comparison between the different input density fields, we consistently use the bias coefficients fit using the full density field and normalize each panel arbitrarily.