The Epoch of Reionization 21 cm Bispectrum at $z=8.2$ from MWA data II: Smooth Component Filtering

Abstract

The 21 cm bispectrum (BS) offers a powerful probe of the Epoch of Reionization (EoR), but its observational access is severely hindered by dominant astrophysical foregrounds. Considering Murchison Widefield Array (MWA) observations at $154.2~\mathrm{MHz}$ ($z=8.2$), we mitigate the foregrounds with Smooth Component Filtering (SCF) and estimate the 21 cm BS. We validate the pipeline using a simulated 21 cm signal and show that the input BS is recovered for modes $k_{\parallel} \ge [k_\parallel]_f=0.135~{\rm Mpc}^{-1}$. Applied to actual data, the SCF produces substantial foreground suppression, reducing the amplitude of the cylindrical BS $B(k_{1\perp},k_{2\perp},k_{3\perp},k_{1\parallel},k_{2\parallel})$ by $3-4$ orders of magnitude. The artifacts due to the missing frequency channels in the data are also suppressed. The resulting EoR window is significantly cleaner at small $k_{\perp}$. We adopt the region $(k_{1 \perp},k_{2 \perp},k_{3 \perp})\leq 0.026~{\rm Mpc}^{-1}$ and $(k_{1\parallel},k_{2\parallel},k_{3\parallel})>0.135~{\rm Mpc}^{-1}$ to evaluate the 3D spherical BS and constrain the EoR signal. By combining estimates over all triangle shapes, we place the lower and upper limits on the mean cube brightness temperature fluctuations $Δ^3$. The estimates are consistent with statistical fluctuations from system noise. The most stringent lower limit $Δ^3_{\rm LL}=-(1.25\times 10^4)^3~{\rm mK}^3$ and upper limit $Δ^3_{\rm UL}=(1.22\times 10^4)^3~{\rm mK}^3$ are obtained at $k_1=0.281~{\rm Mpc}^{-1}$. Additional observing time will reduce the noise level and enable substantially tighter constraints on the EoR signal.

Figures (6)

• Figure 1: Validating the SCF. The top panels show the cylindrical BS $B(k_{1\perp},k_{2\perp},k_{3\perp},k_{1\parallel},k_{2\parallel})$ plotted as a function of $(k_{1\perp},k_{1\parallel})$ for the cases before (left) and after (right) applying the SCF. Here we consider the equilateral triangles, $k_{1\perp}\simeq k_{2\perp}\simeq k_{3\perp}$, and set $k_{1\parallel}=k_{2\parallel}=-k_{3\parallel}/2$. The horizontal red dashed line marks the scale $[k_{\parallel}]_f=0.135\ \mathrm{Mpc}^{-1}$; the signal in the $k_{1\parallel}$ modes below this line is effectively suppressed by the filter. The middle panel shows the 3D spherical BS $\bar{B}$ as a function of $k_1$, obtained by combining estimates for all triangle shapes. The orange markers indicate the values measured from the simulations after the SCF, while the green solid line shows the analytical prediction for the BS $\bar{B}_{\rm Ana}$ of the simulated signal. The error bars on the estimates are obtained from $100$ independent realizations of the simulations. The bottom panel shows the fractional deviation, $\delta=(\bar{B}-\bar{B}_{\rm Ana})/\bar{B}_{\rm Ana}$. The brown-dashed line corresponds to the zero level, while the two black-dotted lines represent $\delta=\pm0.1$. The shaded region shows expected $2\sigma$ statistical fluctuations.
• Figure 2: MABS $B_A(\ell_1,\ell_2,\ell_3,\Delta\nu_1,\Delta\nu_2)$ before SCF (left column) and after SCF (right column) for the equilateral configuration $\ell_1=\ell_2=\ell_3=210$. Top panels: $B_A$ plotted as a function of $(\Delta\nu_1,\Delta\nu_2)$. Bottom panels: one-dimensional slices of the corresponding top-row heatmaps, showing $B_A$ as a function of $\Delta\nu_1$ at fixed $\Delta\nu_2=0$.
• Figure 3: The 3D cylindrical BS $B(k_{1 \perp},k_{2 \perp},k_{3 \perp},k_{1\parallel},k_{2\parallel})$ before SCF (left column) and after SCF (right column) for the equilateral configuration $k_{1\perp} =k_{2\perp}=k_{3\perp}= 0.023~{\rm Mpc}^{-1}$. This is computed via a 2D Fourier transform (Eq. \ref{['eq:3dbs_mabs']}) of the MABS shown in Figure \ref{['fig:mabs']}. Top panels: the BS plotted as a function of $(k_{1\parallel},k_{2\parallel})$. Bottom panels: one-dimensional slices of the corresponding top-row heatmaps, showing the BS as a function of $k_{1\parallel}$ with $k_{2\parallel}=k_{1\parallel}$ and $k_{3\parallel}=-2k_{1\parallel}$. The green dashed lines in the bottom-right panel mark the scales $\pm[k_{\parallel}]_f$; SCF filters out the signal from the $k_{\parallel}$ modes inside this band (see the top panels of Figure \ref{['fig:validation']}).
• Figure 4: The magnitude of the 3D cylindrical BS $\left|B(k_{1\perp},k_{2\perp},k_{3\perp},k_{1\parallel},k_{2\parallel})\right|$, with $k_{1\parallel}=k_{2\parallel}$. The left column shows the BS as a function of $(k_{1\perp},k_{1\parallel})$ before SCF, while the middle column shows the same quantity after SCF. The top row considers equilateral configuration with $k_{1\perp}\approx k_{2\perp}\approx k_{3\perp}$ and the bottom row considers the squeezed configurations with $k_{1\perp}\approx k_{2\perp}$, $k_{3\perp}\to 0$. The dashed line in the left panels show the predicted foreground wedge boundary $[k_{1\parallel}]_H = [r/(r'\Delta\nu_c)]k_{1\perp}$, whereas the dotted line in the bottom left panel shows $[k_{3\parallel}]_H$ corresponding to the minimum value of $k_{3\perp}$$(=0.005 \, {\rm Mpc}^{-1})$. The white dashed box in the middle panels demarcates the region $k_{1 \perp}\leq 0.026~{\rm Mpc}^{-1}$ and $k_{1\parallel}>0.135~{\rm Mpc}^{-1}$, highlighting the modes we have used to evaluate the spherical BS and constrain the EoR 21 cm signal. While only two representative triangle configurations are presented here for illustration, the subsequent analysis and resulting constraints on the EoR 21 cm signal employ the full set of possible triangle configurations. The right panels show 1D sections of the heatmaps, and plot the BS as a function of $k_{1\parallel}$ at fixed $k_{1\perp} \approx 0.019~\mathrm{Mpc}^{-1}$. The green and blue lines, respectively, show results before and after SCF.
• Figure 5: The top panels show the histogram of variable $X_3$ for a set of near-linear triangles $(\mu=0.95)$, with varying $t$. The $X_3$ statistics quantify how much the BS estimates exceed r.m.s. of noise ${\delta{B}_N}$. The $\mu_{X_3}$ and $\sigma_{X_3}$ denote the mean and standard deviation of the $X_3$ distribution, respectively. The green solid curve represents the best-fit Gaussian. The bottom panels show mean cube brightness temperature fluctuations $\Delta^3$. The black markers with $2\sigma$ error bars show the measurements obtained in the present work (after SCF). The green shaded band indicates the constrained range for the EoR signal, with its lower and upper boundaries marking the derived lower and upper limits. The red squares show the upper limit from Gill_2025_mwa1 (before SCF), computed for triangles whose three sides lie outside the foreground wedge (scenario A3 in Fig. 6 of Gill_2025_mwa1). The blue triangles also display the results before SCF, but consider the same mode selection used to obtain the black markers.