First constraints on Helium ${}^{+}{\rm He}^{3}$ evolution in $z=3-4$ using the 8.67GHz hyperfine transition

The reionization of neutral hydrogen in the first billion years of the Universe (HI$\rightarrow$HII) is a major phase transition in the intergalactic medium (IGM), with 75 percent of the IGM composed of hydrogen gas. This key period is being studied extensively through a number of observational tracers because it traces the formation of the first stars and galaxies (likely responsible for the reionization; Furlanetto et al., 2006). One major observational tracer is the hyperfine transition of neutral hydrogen due to the energy-level splitting from the coupling of the spin states of the proton and electron, with a rest frequency of 1420 MHz (21 cm). The brightness temperature of this line encodes key information about the thermal and radiative state of the IGM, thereby indirectly probing the nature of the first stars and galaxies (Furlanetto et al., 2006; Koopmans et al., 2015). The ionisation energy of ground state hydrogen is 13.6eV, an energy available to be ionised by photons emitted in the ultraviolet part of the spectrum. The redshifted 21 cm transition is being pursued by many international experiments (Barry et al., 2019; Garsden et al., 2021; HERA Collaboration et al., 2023; Mertens et al., 2020; Gehlot et al., 2019; Trott et al., 2020).

Hydrogen combined at $z\approx 1100$ when the Universe had expanded and cooled sufficiently to bind the electron to the proton. At higher redshifts, $z\approx 6000$, Helium recombined (HeIII $\rightarrow$ HeII), when its inner electron, with a binding energy of 54.4eV, recombined (Switzer & Hirata, 2008). Helium-4 comprises almost 24 percent, by number, of the IGM after recombination, but Helium-3, which has a non-zero magnetic dipole moment that can produce hyperfine splitting, has a substantially smaller abundance (1 part in 10⁵, Kneller & Steigman, 2004). The first electron of neutral helium has a similar binding energy as hydrogen and is expected to reionize at similar redshifts to hydrogen ($z>6$), however the reionization of singly- to double-ionised helium is expected to occur much later, when AGN can provide sufficient high energy photons to unbind the 54.4eV second electron. This HeII to HeIII process therefore is the second major reionization period of the Universe, liberating further electrons into the IGM. Like hydrogen, the hydrogenic single-electron ${}^{+}{\rm He}^{3}$ ion has a hyperfine splitting of energy states, emitting a 8.67 GHz photon (3.5 cm, rest).

There is indirect evidence for Helium reionization being complete by $z\sim 3$, including optical depth to HeII (Worseck et al., 2011, 2016), increased IGM temperature (Lidz et al., 2010; Makan et al., 2021), and hardness of background radiation from metal ionization potentials (Turner et al., 2016; Morrison et al., 2019). Fast Radio Bursts (FRBs) also have the potential to probe this era because the spectral dispersion of their signals is linearly proportional to the line-of-sight electron component of the IGM (Caleb et al., 2019).

Worseck et al. (2011, 2016) have studied the spectra of $z>3.5$ AGN for evidence of Gunn-Peterson absorption of helium Ly-$\alpha$ Forest of the redshifted 304 Angstrom line, reporting that the IGM was highly-ionized by $z=3.4$ due to large transmission regions, and high variance between sightlines. Like the hydrogen Ly-$\alpha$ Forest, this probe provides detailed information along skewers through the IGM, but is less sensitive to the large-scale signal evolution. Similarly, the large optical depth to the Ly-$\alpha$ line (and the saturation of the line at low neutral fraction) makes this probe sensitive primarily to the end of reionization. McQuinn & Switzer (2010) considered the HeI Ly-$\alpha$ forest, with rest wavelength of 584 Angstrom, as a tracer of the reionization of HeII. Unlike the HeII forest, which saturates easily and has a shorter wavelength, this tracer is weakly absorbed, providing the potential for a quantitative study of singly-ionised helium.

Radio observation of the reionization of helium is via the radio hyperfine line, line-of-sight absorption to background AGN (Ly-$\alpha$ Forest - 304 Angstrom line), and indirectly in the IGM electron density (e.g., through observations of the dispersion measure - redshift relation with Fast Radio Bursts and other high-redshift transients). Optical tracers can probe Helium-4 because they rely on electron transitions. To-date, there has been no detection of the Helium-3 hyperfine transition, or attempts to undertake this experiment. Observationally, its small optical depth relative to hydrogen (due primarily to its very small primordial abundance) is balanced somewhat by the lower system temperature and reduced radio foreground at higher frequencies. A number of studies have predicted theoretically (McQuinn & Switzer, 2009; Bagla & Loeb, 2009), or simulated (Khullar et al., 2020), the helium hyperfine signal in $z=3-4$, predicting temperature fluctuations spanning 0.1–50$\mu$K on different scales. Khullar et al. (2020) considered the temperature fluctuations of HeII around QSOs in simulations at higher redshifts, commensurate with hydrogen reionization.

Detection of intergalactic ${}^{+}{\rm He}^{3}$ requires a contrast between the resonant signal temperature and the CMB temperature. McQuinn & Switzer (2009) argues that both weak Wouthysen-Field coupling and small collisional coupling in the IGM would make the temperature contrast small and the signal very difficult to measure. Instead, they consider three avenues for using ${}^{+}{\rm He}^{3}$ to understand the evolution of the Universe. Firstly, because absorption of continuum light to a background source by HeII is proportional to the source flux density (and not the CMB), identifying and performing spectral absorption measurements on $z>3.5$ QSOs would be possible. Secondly, at higher redshift, when HeI is transitioning to HeII, first producing the 8.67GHz hyperfine signal, absorption would probe HeI-HeII reionization. Finally, HeII that is self-shielded in halos with sufficient density for collisional coupling to produce an emission signal, could be used to trace the biased signal evolution (similar to post-reionization hydrogen).

In this paper, we aim to place constraints on the spherically-averaged (three-dimensional) power spectrum of brightness temperature fluctuations of singly-ionised Helium-3 over $z=2.9-4.2$. This work acts as a demonstration of how to undertake this experiment with real telescope data. In Section 2 we introduce the methods, including theoretical predictions and observations; in Section 2.3 the power spectrum methodology is introduced; in Section 3 the results are presented, before being discussed in Section 4.

The 2D and 1D power spectra were inspected for each subset of 10 hours of observations, for each sub-band described in Table 3. Most subsets displayed reasonable results, where the power were consistent with thermal noise across most wavemodes. One subset showed clear systematic contamination and was removed from the final coherent average. The remaining subsets were coherently averaged to $\simeq$190 hours of data, except for the $z=4.14$ subband, where only 120 hours of data showed good behaviour.

The eight individual subbands showed different systematic behaviour. Three that spanned the full band displayed the cleanest data, with most modes consistent with thermal noise. These subbands are italicised in Table , and correspond to power at $z=2.91,3.39,4.14$. These were processed to the final power spectra. Figure 1 displays a 2D power spectrum at $z=3.39$ in units of mK² h^-3 Mpc³. The DC ($k_{\parallel}=0$) mode has been omitted. The data show positive and negative modes, consistent with thermal noise when cross power spectra are considered. The positive modes at high $k_{\bot}$, low $k_{\parallel}$ show residual foreground power that has not been removed by the linear fitting to the visibilities.

The three subbands of data are then spherically-averaged to 1D, for each polarization, and square-rooted to produce the spectrum of temperature fluctuations shown in Figure 2.

In each, the blue shaded region denotes the 2$\sigma$ thermal noise with noise-dominated regions showing shading to the bottom of the plot. The red points and blue line denote the measured power, while the green line denotes the estimated 2$\sigma$ noise level. Many modes are consistent with thermal noise. The best measured temperature is at $z=2.91$ with $\Delta{(k)}$ = 489$\mu$K, and a 2$\sigma$ upper limit of 557$\mu$K. Table 2 displays the measured and upper limit temperature fluctuations for the three subbands and their angular scale. For all redshifts, the YY power spectrum yielded cleaner results, and are reported here. The XX polarisation results are only marginally poorer, and this likely points to localised RFI that affects one polarisation more than the other.

In each case, the angular mode corresponds to the shortest baseline available to the ATCA (30.6 m), which is typically occupied by a single baseline, and therefore has poor sensitivity. For comparison, Figure 3 shows the expected temperature fluctuation of the shielded model from Equation 3, for $z=2.9,4.1$ and assuming that 10% of gas is collisionally-coupled. The broad level is $\sim 0.01-0.1\mu$K, which is 3–4 orders of magnitude below the measurements, demonstrating the difficulty of the experiment.

This work is an attempt to place upper limits on the power spectrum of temperature fluctuations for Helium-3, and provides an approach to how to undertake such an experiment. Despite not having the sensitivity to theoretically detect the signal, our data exhibit two important characteristics that currently impede interferometric 21 cm experiments pursuing hydrogen reionization: (1) A single clean and simple foreground source that can be removed effectively, due to the wide instantaneous bandwidth; (2) sufficiently-low residual RFI that the data are mostly noise-limited at 200 hours.

The accuracy of the subtraction of B1934-638 is sufficient at the 200 hour level, but there are indications that both a first- and second-order polynomial fit leaves residuals that are not consistent with zero-mean noise in some parts of the band. The residual signal in a 1 MHz channel should not exceed 1 $\mu$Jy, according to McQuinn & Switzer (2009), requiring a dynamic range of 10⁷ for a 12 Jy source. If the source can be fitted by a low-order polynomial, then the full band can be used for foreground estimation and subtraction, providing sufficient SNR. E.g., across 650 channels and fitting for a single parameter, 200 hours with all 15 ATCA baselines yields a dynamic range of 2$\times$10⁶. Increasing the order of the polynomial fit increases the chances of signal loss, by introducing spectral structure that has a non-zero projection onto the spectral Helium-3 structure (i.e., complex spectral structure may be due to Helium-3, and not the foreground source), whereas a first-order polynomial over 650 MHz will not impact the underlying Helium-3 structure (any global Helium-3 signal evolution has already been removed by omitting the auto-correlations).

Residual RFI and spectral structure does affect a lot of the band; hence why only three out of the eight bands were used for the final analysis. Figure 4 displays YY power spectra for a poorly-performing subband of 96 channels near $z=3.6$. For these data, there is residual spectral structure across the subband visible in the gridded visibility spectra, leading to increased leakage from foregrounds modes.

It may be noted that the auto-correlation data may be used to study the global temperature evolution of the Helium-3 signal. With a single power-law continuum source as the only bright foreground in the field, a broad non-power law evolution of the spectrum may indicate the global reionization of Helium (similar to that undertaken with the EDGES experiment for hydrogen; Bowman et al., 2018). However, inspection of the auto-correlations from ATCA show high-amplitude oscillations, consistent with reflections off structures within the dishes. The systematics in these data were not deemed able to be modelled sufficiently to undertake this experiment. Similarly, one may perform a Helium-3 absorption study with the cross-correlation spectra, if B1934-638 were a background, high-redshift source (instead, it is $z=0.12$). McQuinn & Switzer (2009) predicted that absorption against a background continuum source provided the highest detectability, because the absorption flux density is dictated by the strength of the source and the optical depth. Given the lack of expected emission signal from the IGM, and the low signal expectation from the self-shielded gas in halos, the absorption study may be the best observational approach to tackle.

ATCA is well-suited to undertake this experiment, due to its wide CABB backend and small field-of-view, but is ultimately hampered by its few baselines and lack of sensitivity. Prospects for detection with other current and future telescopes is dependent on: (1) overall sensitivity; (2) field-of-view (too small and the results are sample variance-limited, and too large and the foregrounds become complicated); (3) low-RFI environment to retain spectral smoothness and afford bands without flagged channels; (4) short baselines to access large-scale structures; (5) a broad, instantaneous bandwidth to measure the full signal evolution and for accurate foreground removal. Few telescopes have all of these properties; in particular the wide-band backend system.

SKA-Mid is an obvious instrument for this experiment. Band 3, which is not proposed to be available initially⁴⁴4http://www.skao.int, spans 1400 MHz instantaneously across 1650–3050 MHz. Bands 1 and 2 would probe Helium at higher redshift. Using the SKA-Mid baseline distribution (Braun et al., 2019), there will be $\simeq$90 baselines with physical lengths shorter than 50 m. With this configuration, a 100-hour, 100 MHz bandwidth experiment should yield noise levels of 1$\mu$K at $k=0.14h$Mpc^-1, in the absence of RFI and other spectral systematics. The precursor MeerKAT array has $\simeq$10 baselines shorter than 50 m (minimum 29 m), and with an existing wideband S-band receiver, should reach 1$\simeq\mu$K noise level after 1000 hours. Other facilities with good $uv$-coverage have narrower fractional bandwidth at these frequencies, which will hinder their ability to perform accurate foreground subtraction without the potential for signal loss (e.g., VLA). Higher-redshift ⁺He³, as explored by Khullar et al. (2020), is accessible at lower frequencies, but there are few radio interferometers with feeds that access 800–1200 MHz. For gas around $z=5.1$ (1420 MHz), the signal will be confused with local neutral hydrogen, making its observation almost impossible.

We attempted a measurement of the spherically-averaged power spectrum of ⁺He³ (single-ionised Helium-3) using the 3.5 cm (8.67 GHz) hyperfine line, at $z=2.9-4.1$ using 190 hours of publicly-available data from the ATCA archive. After RFI flagging, identification of spectral bands with no missing data, and a simple foreground subtraction, power spectra were found to be noise-limited across many angular wavemodes. The upper limits on the power are not cosmologically-interesting, being 3–4 orders of magnitude larger in temperature than theoretical expectations, but is the first attempt to measure this signal. This work demonstrates the potential for this experiment to yield improved results, which would be cosmologically-relevant, with a telescope with higher sensitivity.