The 21cm-galaxy cross-correlation: Realistic forecast for 21cm signal detection and reionisation constraints

This paper presents a realistic forecast demonstrating that detecting the 21cm-galaxy cross-correlation and distinguishing reionisation scenarios requires wide-area, medium-to-deep slitless spectroscopic surveys that effectively sample large-scale modes, with optimal performance achieved at redshifts greater than 7.

The Gist

Imagine the early universe as a giant, dark room filled with a thick, invisible fog. This fog is made of neutral hydrogen gas. For hundreds of millions of years, this room was pitch black. Then, the first stars and galaxies flickered on, acting like tiny flashlights. Their light began to burn holes in the fog, turning it into clear, ionized air. This process is called Reionization.

The big mystery astronomers face today is: Who burned the holes? Was it a few massive, bright "super-stars" (like a few powerful floodlights), or was it a vast army of tiny, faint stars (like millions of weak nightlights)?

This paper is a "forecast" or a "blueprint" for how we can solve this mystery using two different tools working together:

1. The Radio Telescope (SKA): A giant ear listening to the "hum" of the hydrogen fog (the 21cm signal).
2. The Galaxy Survey: A camera taking pictures of the early galaxies (specifically those glowing with Lyman-alpha light).

The Problem: The "Static" on the Radio

The problem is that the radio signal from the early universe is incredibly faint. It's like trying to hear a whisper in a stadium full of people screaming. The "screaming" comes from our own galaxy and other bright radio sources in the sky. These are called foregrounds.

Usually, when you try to listen to the whisper, the static drowns it out. However, the authors realized that the static (foregrounds) doesn't care about the galaxies. The galaxies and the static are unrelated. So, if you look at the radio signal only where the galaxies are, and ignore the rest, you might be able to cancel out the static and hear the whisper. This is called Cross-Correlation.

The Experiment: Designing the Perfect Survey

The authors built a computer simulation to ask: "What kind of camera and radio telescope setup do we need to actually hear this whisper and figure out who burned the holes in the fog?"

They tested different "recipes" for the survey:

• How wide should the camera look? (Field of View: Looking at a tiny patch of sky vs. a huge panorama).
• How deep should the camera see? (Limiting Luminosity: Can it see only bright galaxies, or can it spot the faint, tiny ones too?).
• How sharp is the focus? (Redshift Uncertainty: Do we know exactly where in space the galaxy is, or is it a bit blurry?).

The Findings: What Works?

Here is what they discovered, translated into everyday terms:

1. Bigger is Better (The Panorama Effect)
If you want to hear the whisper, looking at a huge area of the sky is the most important thing. It's like trying to find a pattern in a crowd; if you only look at one person, you might miss the pattern. If you look at the whole stadium, the pattern becomes clear.

• Analogy: A wide-angle lens is more powerful than a deep zoom lens for this specific job.

2. The "Static" Matters Most
The success of the experiment depends entirely on how well we can clean up the radio static.

• The "Moderate" Scenario: If we can only clean up the loudest static (leaving a "wedge" of noise near the horizon), we need a huge, deep, and very precise camera. We need to see faint galaxies over a massive area. This is hard to do with current technology.
• The "Optimistic" Scenario: If we develop better software to clean up almost all the static (even the tricky parts), we can get away with smaller, simpler, and cheaper cameras. We could even use "photometric" surveys (which are like taking a slightly blurry photo but covering a huge area) instead of expensive, high-precision spectroscopic surveys.

3. The "Sweet Spot" for Time
The authors found that looking at the universe when it was 7 to 8 billion years after the Big Bang (redshift 7-8) is the sweet spot.

• Why? At this time, the fog is half-burned. The pattern of the "holes" is most distinct. If we look too early, the fog is too thick and the galaxies are too rare. If we look too late, the fog is gone, and the pattern disappears.

4. The "Ghost" Pattern
The signal they are looking for has a specific shape: it starts negative (anti-correlated) and then flips.

• Analogy: Imagine the galaxies are islands in a sea of fog. The radio signal is the water level. If the islands are big and powerful, they clear a huge area of fog around them. If they are weak, they only clear a tiny circle. The shape of the "clearing" tells us if the islands are "Super-Islands" or "Tiny-Islands."

The Conclusion: What Do We Need?

To solve the mystery of the early universe, we need:

1. A Giant Radio Eye: The Square Kilometre Array (SKA) is the telescope needed to hear the signal.
2. A Wide-Angle Camera: We need to map a very large area of the sky, not just a tiny patch.
3. Better Noise Cleaning: We need to get really good at removing the radio static. If we can do this perfectly, we can use simpler galaxy surveys. If not, we need the most powerful, expensive galaxy surveys possible.

The Bottom Line:
This paper tells us that we can solve the mystery of how the universe woke up from its dark age, but only if we build the right combination of telescopes and get really good at cleaning up the radio noise. It's like trying to find a specific voice in a noisy room: you need a big enough room to hear the echo, and you need to be very good at ignoring the background chatter.

Technical Summary

1. Problem Statement

The Epoch of Reionisation (EoR) was driven by the first galaxies ionizing the intergalactic medium (IGM). While the James Webb Space Telescope (JWST) provides data on early galaxies, it cannot directly measure the ionizing radiation from the faintest galaxies due to the partially neutral IGM. The 21cm signal from neutral hydrogen offers a complementary probe, but its detection is severely hindered by bright, spectrally smooth foregrounds (the "foreground wedge") that leak into the signal space.

The Core Challenge:

• Detection: Isolating the cosmological 21cm signal from foregrounds is difficult.
• Morphology vs. Global State: While the global ionization fraction ($\langle \chi_{HII} \rangle$) can be estimated, distinguishing how reionization occurred (e.g., driven by many faint galaxies vs. a few bright galaxies) requires measuring the ionization morphology.
• Survey Design Tension: 21cm observations benefit from large survey volumes (to reduce cosmic variance), while galaxy surveys (specifically Lyman-$\alpha$ Emitters, LAEs) benefit from deep, narrow fields to minimize shot noise and redshift uncertainty. There is a lack of systematic forecasts on how to balance these competing requirements to detect the 21cm–LAE cross-correlation and distinguish between different reionization scenarios.

2. Methodology

The authors developed a pipeline to forecast the Signal-to-Noise Ratio (S/N) of the 21cm–LAE cross-power spectrum ($P_{21,gal}$) by combining theoretical simulations with realistic observational error modeling.

• Simulations: They utilized the Astraeus framework, specifically two models from Hutter et al. (2023b):
  • mhdec: Reionization driven by faint, low-mass galaxies.
  • mhinc: Reionization driven by bright, massive galaxies.
  • These models self-consistently simulate galaxy evolution and the resulting ionization morphology.
• Signal Calculation:
  • Computed the 21cm differential brightness temperature ($\delta T_b$) and galaxy overdensity ($\delta_{gal}$).
  • Derived the cross-power spectrum $P_{21,gal}(k)$ for various redshifts ($z=7, 8$) and minimum Lyman-$\alpha$ luminosities ($L_{min}^\alpha$).
• Uncertainty Modeling:
  • Calculated total variance ($\sigma^2_{21,gal}$) combining cosmic variance, thermal noise (SKA-Low1), shot noise (galaxy density), and redshift damping.
  • Foreground Wedge: Modeled two scenarios:
    • Moderate: Excludes modes below the horizon plus a 0.1 $h$ Mpc$^{-1}$ buffer.
    • Optimistic: Recovers all modes down to the beam limit.
  • Survey Parameters: Varied Field of View (FoV), limiting luminosity ($L_{min}^\alpha$), and redshift uncertainty ($\sigma_z$) for spectroscopic, grism, and photometric-like surveys.
• Discrimination Metric: Defined a specific S/N metric, $(S/N)_{EoR}$, using a $\chi^2$ analysis to quantify the ability to distinguish between the mhdec and mhinc scenarios.

3. Key Contributions

• Systematic Parameter Space Exploration: Unlike previous studies that varied single parameters, this work systematically maps the interplay between FoV, galaxy depth ($L_{min}^\alpha$), redshift precision ($\sigma_z$), and foreground assumptions.
• Morphology Constraints: Demonstrates that the large-scale negative peak of the cross-power spectrum encodes the average neutral gas density and ionization morphology, distinct from the global ionization fraction.
• Realistic Foreground Forecasts: Provides concrete requirements for future surveys (e.g., PFS, Roman, WST) under both conservative (moderate) and optimistic foreground cleaning scenarios.
• Redshift Evolution Insight: Highlights that distinguishing scenarios is actually easier at higher redshifts ($z > 7$) where global ionization fractions differ more significantly, despite lower galaxy number densities.

4. Key Results

A. Signal Characteristics

• The cross-power spectrum exhibits a large-scale negative peak (anti-correlation) because LAEs reside in ionized bubbles where the 21cm signal is suppressed.
• Morphology Dependence: In the mhdec scenario (faint galaxies), ionization fronts follow the cosmic web density more closely, resulting in a weaker large-scale anti-correlation compared to the mhinc scenario (bright galaxies).
• Scale Dependence: The position of the zero-crossing indicates the typical size of ionized regions.

B. Detection Requirements (S/N > 3)

• General Trends: S/N increases with larger FoV, fainter $L_{min}^\alpha$, and smaller $\sigma_z$. FoV is the dominant factor when redshift uncertainty is low.
• Moderate Foreground Wedge:
  • Photometric surveys are insufficient.
  • Requires medium-deep ($L_{min}^\alpha \gtrsim 10^{42.5}$ erg s$^{-1}$), wide-area ($FoV > 20$ deg$^2$) slitless spectroscopic or spectroscopic surveys.
• Optimistic Foreground Wedge:
  • Detection is possible with deep ($L_{min}^\alpha \gtrsim 10^{42.3}$), wide-area ($FoV \gtrsim 80$ deg$^2$) photometric-like surveys.
  • Alternatively, shallower ($L_{min}^\alpha \simeq 10^{42.8}$), small-area ($FoV \simeq 2-3$ deg$^2$) slitless spectroscopic surveys suffice.

C. Distinguishing Reionization Scenarios

• The Challenge: At $z=7$, the global ionization fractions of the two scenarios are similar; differences are purely morphological. This makes discrimination harder than at $z=8$.
• Moderate Wedge: Requires deep-wide spectroscopic surveys ($FoV \gtrsim 50-100$ deg$^2$, $L_{min}^\alpha \lesssim 10^{42}$) to achieve marginal discrimination ($S/N \sim 1-3$).
• Optimistic Wedge: Medium-area ($FoV \simeq 10$ deg$^2$), shallower ($L_{min}^\alpha \simeq 10^{42.8}$) slitless spectroscopic surveys can robustly distinguish scenarios ($S/N > 3$).
• Redshift Advantage: Moving to $z=8$ (or $z>7$) improves discrimination significantly because the global ionization fractions diverge, shifting the peak of the cross-power spectrum to larger scales where more modes are available.

D. Optimal Strategy

• Maximizing S/N for both detection and model discrimination requires sampling the large-scale peak of the cross-power spectrum.
• As reionization proceeds, this peak shifts to larger physical scales (smaller $k$).
• Therefore, surveys at $z > 7$ (more neutral IGM) are more promising for morphology constraints, provided galaxy number densities remain sufficient.

5. Significance and Implications

• Survey Design: The paper provides a "recipe" for upcoming instruments. It suggests that while large-area spectroscopic surveys (like PFS on Subaru or the proposed WST) are ideal, foreground cleaning technology is the critical bottleneck. If foregrounds can be cleaned aggressively (optimistic wedge), even smaller, shallower surveys could yield breakthroughs.
• Physics of Reionization: It establishes that 21cm–galaxy cross-correlations are not just a detection tool but a unique probe of ionization morphology, capable of answering whether reionization was driven by the "many faint" or "few bright" galaxies.
• Future Directions: The authors note that recovering modes within the foreground wedge is essential. They suggest that future work should explore non-Gaussian statistics (e.g., wavelet cross-correlations, bispectra) and machine learning techniques to further break degeneracies.

Conclusion:
The 21cm–LAE cross-correlation is a viable path to constraining reionization physics, but its success hinges on large survey volumes and advanced foreground subtraction. Under realistic (moderate) foreground assumptions, only deep, wide-area spectroscopic surveys can distinguish between competing reionization models. Under optimistic assumptions, the requirements relax significantly, making the goal achievable with near-future facilities.