The EoR 21-cm Bispectrum at $z=8.2$ from MWA data I: Foregrounds and preliminary upper limits

We attempt to measure the $z = 8.2$ Epoch of Reionization (EoR) 21-cm bispectrum (BS) using Murchison Widefield Array (MWA) $154.2~\mathrm{MHz}$ data. We find that $B(k_{1\perp}, k_{2\perp}, k_{3\perp}, k_{1\parallel}, k_{2\parallel})$ the 3D cylindrical BS exhibits a foreground wedge, similar to $P(k_{1\perp},k_{1\parallel})$ the 21-cm cylindrical power spectrum. However, the BS foreground wedge, which depends on $(k_{1\perp},k_{1\parallel})$, $(k_{2\perp},k_{2\parallel})$ and $(k_{3\perp},k_{3\parallel})$ the three sides of a triangle, is more complicated. Considering various foreground avoidance scenarios, we identify the region where all three sides are outside the foreground wedge as the EoR window for the 21-cm BS. However, the EoR window is contaminated by a periodic pattern of spikes that arises from the periodic pattern of missing frequency channels in the data. We evaluate the binned 3D spherical BS for triangles of all possible sizes and shapes, and present results for $\Delta^3$ the mean cube brightness temperature fluctuations. The best $2\sigma$ upper limits we obtain for the EoR 21-cm signal are $\Delta^3_{\rm UL} = (1.81\times 10^3)^3~\mathrm{mK}^3$ at $k_1 = 0.008~\mathrm{Mpc}^{-1}$ and $\Delta^3_{\rm UL} = (2.04\times 10^3)^3~\mathrm{mK}^3$ at $k_1 = 0.012~\mathrm{Mpc}^{-1}$ for equilateral and squeezed triangles, respectively. These are foreground-dominated, and are many orders of magnitude larger than the predicted EoR 21-cm signal $(\sim 10^3 ~\mathrm{mK}^3)$.