Detecting Cosmic Reionization Using the Bispectrum Phase

Detecting neutral hydrogen (H i) via the 21 cm line emission from the intergalactic medium at $z\gtrsim 6$ has been identified as one of the most promising probes of the epoch of cosmic reionization—a major phase transition of the Universe. However, these studies face severe challenges imposed by the bright foreground emission from cosmic objects. Current techniques require precise instrumental calibration to separate the weak H i line signal from the foreground continuum emission. We propose to mitigate this calibration requirement by using measurements of the interferometric bispectrum phase. The bispectrum phase is unaffected by antenna-based direction-independent calibration errors and hence for a compact array it depends on the sky brightness distribution only (subject to the usual thermal-like noise). We show that the bispectrum phase of the foreground synchrotron continuum has a characteristically smooth spectrum relative to the cosmological line signal. The two can be separated effectively by exploiting this spectral difference using Fourier techniques, while eliminating the need for precise antenna-based calibration of phases introduced by the instrument, and the ionosphere, inherent in existing approaches. Using fiducial models for continuum foregrounds, and for the cosmological H i signal, we show the latter should be detectable in bispectrum phase spectra, with reasonable significance at $|k_{\parallel }|\gtrsim 0.5h{\mathrm{Mpc}}^{-1}$, using existing instruments. Our approach will also benefit other H i intensity mapping experiments that face similar challenges, such as those measuring baryon acoustic oscillations (BAO).

Figure 1

Spatial coherence amplitude spectra on antenna pairs forming a 14.6 m equilateral triad are shown in red, blue, and cyan. Solid and dotted lines show amplitudes from synchrotron foregrounds and a fiducial EOR model, respectively. The gray curve shows the typical noise obtained with 1 min integration. Typically, the foregrounds are $\gtrsim {10}^4$ times brighter than the EOR signal. The orange bands denote the frequency subbands centered on 125, 150, and 175 MHz each of 10 MHz effective bandwidth.

Figure 2

Bispectrum phase spectra of individual components in the sky model—single point source (black) with ${\varphi }_{\nabla }=0$, compact sources (cyan), diffuse foregrounds (blue), diffuse and compact components combined (red), and the EOR H i fluctuations (gray)—for a 14.6 m equilateral triad. The H i component is highly fluctuating relative to the foregrounds. The phase wrap discontinuities at ${\varphi }_{\nabla }=\pm \pi$ are not of a physical origin. The orange subbands are same as in Fig. 1.

Figure 3

Delay power spectra of bispectrum phases in subbands centered at 125 (left), 150 (middle), and 175 MHz (right) that include contributions from foregrounds, EOR signal, and noise. The corresponding redshifts are listed in each panel. The 14.6 m equilateral triad used is highlighted on a HERA-19 layout on the top left. The green curves show only the foreground contribution (${\varphi }_{\nabla }^m={\varphi }_{\nabla }^F$). The anisotropic foreground model employed [17] results in the asymmetry around $k_{\parallel }=0h^{-1}\mathrm{Mpc}$. The red curves show the effect of including noise fluctuations (${\varphi }_{\nabla }^m={\varphi }_{\nabla }^F+\delta {\varphi }_{\nabla }^N$), after averaging $N_m\sim {10}^6$ measurements. The gray curves apply when fluctuations from the EOR H i signal are included, ${\varphi }_{\nabla }^m={\varphi }_{\nabla }^F+\delta {\varphi }_{\nabla }^{\mathrm{H}\mathrm{I}}+\delta {\varphi }_{\nabla }^N$. The black curves are identical to the gray ones except the EOR H i signal is 10 times brighter. The dot and vertical markers denote positive and negative values, respectively. The latter results from the removal of noise bias by using cross-power spectra [Eq. (3)]. The EOR H i contribution is significantly detected at $|k_{\parallel }|\gtrsim 0.5h{\mathrm{Mpc}}^{-1}$ at $z\approx 8.5$ and $z\approx 7.1$. At $z\approx 10.4$, the EOR contribution is inseparable from foregrounds because the EOR signal is weaker (see power spectrum of faint galaxies model at $k=0.5{\mathrm{Mpc}}^{-1}$ in Fig. 2 of [49]) while the foregrounds are brighter. The detection significance depends on the strength of EOR H i signal relative to the foregrounds. A tenfold increase in EOR intensity shows a $\sim 100$-fold increase in $P_{\nabla }(k_{\parallel })$ at $|k_{\parallel }|\gtrsim 0.5h{\mathrm{Mpc}}^{-1}$ at $z\approx 8.5$ and $z\approx 7.1$, indicating its sensitive dependence on ${\rho }_{pq}^{\mathrm{H}\mathrm{I}}$. This detection measures the line-to-continuum ratio, from which the EOR H i brightness temperature fluctuations, $⟨[\delta T_{\mathit{b}}^{\mathrm{H}\mathrm{I}}(z){]}^2⟩$, can be inferred using a reliable foreground model.