Exploring One-point Statistics in HERA Phase I Data: Effects of Foregrounds and Systematics on Measuring One-Point Statistics

TL;DR

The paper systematically investigates how instrumental effects, foreground removal, and systematics shape measurements of one-point statistics in 21 cm images from HERA Phase I. By forward-modeling 21 cm signals, foregrounds, and noise within the Direct Optimal Mapping framework, it shows that the PSF and wedge-filtering dramatically suppress $m_2$ and $m_3$, challenging non-Gaussian analyses. A likelihood approach using Phase I data disfavors the cold reionization scenario for $m_2$ in Band 2, but overall, $m_3$ signals remain hard to detect due to instrumental losses. Forecasts for the full HERA core indicate potential detections under ideal foreground removal, though real-world wedge-filtering and noise continue to limit sensitivity, highlighting the critical role of accurate instrument modeling for leveraging one-point statistics in EoR studies.

Abstract

Measuring one-point statistics in redshifted 21 cm intensity maps offers an opportunity to explore non-Gaussian features of the early universe. We assess the impact of instrumental effects on measurements made with the Hydrogen Epoch of Reionization Array (HERA) by forward modeling observational and simulation data. Using HERA Phase I observations over 94 nights, we examine the second (m2, variance) and third (m3) moments of images. We employ the DAYENU-filtering method for foreground removal and reduce simulated foreground residuals to 10% of the 21 cm signal residuals. In noiseless cosmological simulations, the amplitudes of one-point statistics measurements are significantly reduced by the instrument response and further reduced by wedge-filtering. Analyses with wedge-filtered observational data, along with expected noise simulations, show that systematics alter the probability distribution of the map pixels. Likelihood analysis based on the observational data shows m2 measurements disfavor the cold reionization model characterized by inefficient X-ray heating, in line with other power spectra measurements. Small signals in m3 due to the instrument response of the Phase I observation and wedge-filtering make it challenging to use these non-Gaussian statistics to explore model parameters. Forecasts with the full HERA array predict high signal-to-noise ratios for m2, m3, and S3 assuming no foregrounds, but wedge-filtering drastically reduces these ratios. This work demonstrates conclusively that a comprehensive understanding of instrumental effects on m2 and m3 is essential for their use as a cosmological probe, given their dependence on the underlying model.

Figures (18)

• Figure 1: PSF of HERA Phase I at 161.5MHz (left) and a Gaussian fit (right). We forward-model simulated maps using the PSF to capture pixel correlations. This PSF is integrated over 1 hr. FWHM of the Gaussian fit: 1.11$^\circ$ (major) and 0.75$^\circ$ (minor).
• Figure 2: HERA stripe, displaying foreground emission, ranging from 1.5 to 14.5 hours centered at -30.7$^\circ$ in declination. The map is created from observational data by connecting sky patches which are made at every hour of LST with the size of 15$\times$10 square degrees. Emissions at around 3 hr are grating lobes of Fornax A, which is one of the brightest foreground radio sources.
• Figure 3: Evolutionary history of $m_2$ (equivalent to $S_2$), $m_3$, $S_3$, and mean ionization fraction measured from raw simulations for the four distinct 21 cm models. Each line indicates the fiducial (Fid), cold reionization (CR), large halos (LH), and extended reionization (ER) models. Band 1 and Band 2 are highlighted in orange and blue shaded regions.
• Figure 4: Probability distribution of the fiducial (top row) and cold reionization (bottom row) models at specific redshifts for raw simulations (i.e., no instrumental effect). The dashed and solid vertical lines indicate the mean and median, respectively. At $z = 12.5$, both models exhibit asymmetric distributions due to heating, leading to a negative $m_3$. As reionization advances, a prominent pileup at the zero bin becomes noticeable. In the fiducial model, efficient heating by star-forming galaxies raises the temperature of the IGM, resulting in a tail towards positive values and thus a positive $m_3$ (top right panel). In the cold reionization model, the distribution at $z = 10.0$ centered around T$_B \sim -250$ mK exhibits negative tails. However, $m_3$ transitions to positive values due to the ionized IGM at the zero bin (bottom center panel). As reionization progresses further, $m_3$ becomes negative again as a large fraction of the IGM is ionized, leaving behind some negative IGM regions (bottom right panel).
• Figure 5: $m_2$ (top), $m_3$ (middle), and $S_3$ (bottom) for the fiducial model as a function of frequency given Phase I mock observations. $m_2$ (top), $m_3$ (middle), and $S_3$ (bottom) for the fiducial model are shown as functions of frequency, based on Phase I mock observations. The dotted line represents measurements from raw simulations without instrumental effects. The blue solid line and shaded region show the mean and sample variance after applying the PSF, assuming no foregrounds. The red dashed line and shaded region show results after applying both the PSF and wedge-filtering. The PSF significantly reduces the amplitudes of $m_2$ and $m_3$, with wedge-filtering further suppressing $m_3$, making detection of non-Gaussian features more difficult. For $m_3$, a linear scale is used between $-10^{-6}$ and $10^{-6}$; outside this range, the scale is logarithmic. For $S_3$, the linear range spans $-10^{-1}$ to $10^{-1}$, with logarithmic scaling beyond.