HI Intensity Mapping cross-correlation with thermal SZ fluctuations: forecasted cosmological parameters estimation for FAST and Planck

This paper forecasts that cross-correlating thermal Sunyaev-Zel'dovich fluctuations from the Planck satellite with 21 cm intensity mapping data from the FAST telescope will significantly constrain the cosmic neutral hydrogen density, hydrostatic mass bias, and universal pressure profile parameters, thereby probing the distribution of neutral hydrogen within low-redshift galaxy clusters.

The Gist

Here is an explanation of the paper, translated into everyday language with some creative analogies.

The Big Picture: Connecting the Invisible Dots

Imagine the universe as a giant, three-dimensional city. In this city, there are two main types of "citizens" that astronomers want to study:

1. Galaxy Clusters: These are the massive skyscrapers of the universe, huge groups of galaxies held together by gravity. They are filled with super-hot gas that glows in X-rays and distorts light.
2. Neutral Hydrogen (HI): This is the "fog" or "dust" of the universe. It's the raw material (hydrogen gas) that makes up stars and galaxies. It's everywhere, but it's invisible to the naked eye.

The problem is that while we can see the "skyscrapers" (clusters) quite well, the "fog" (hydrogen) is hard to map because it's faint and gets lost in the static of the universe (like trying to hear a whisper in a crowded stadium).

The Goal of this Paper:
The authors are asking: What if we could listen to the "fog" and the "skyscrapers" at the same time and see how they talk to each other?

They are proposing a new way to map the universe by cross-referencing two different telescopes:

• FAST (The Giant Ear): A massive radio telescope in China that listens for the faint "hum" of neutral hydrogen.
• Planck (The Heat Sensor): A satellite that maps the "heat signature" left behind by galaxy clusters (called the Thermal Sunyaev-Zel'dovich effect).

The Analogy: The "Ghost" and the "Shadow"

Think of the universe like a dark room.

• The Galaxy Clusters are like heavy furniture. You can't see them in the dark, but if you shine a flashlight (Planck) at them, they cast a distinct shadow on the wall. This shadow is the "Thermal SZ" signal.
• The Neutral Hydrogen is like a faint, glowing ghost (the HI signal) that is floating around the furniture. It's very hard to see the ghost on its own.

The Paper's Idea:
Instead of trying to find the ghost by looking for it alone, the authors suggest looking for where the ghost and the shadow overlap. If the ghost is always hanging out near the furniture, then the "ghost signal" and the "shadow signal" should line up perfectly.

By combining the data from FAST (looking for the ghost) and Planck (looking for the shadow), they can prove where the hydrogen is hiding, even if it's too faint to see on its own.

The "Fisher Matrix" (The Crystal Ball)

The paper doesn't actually have the final data yet; it's a forecast. The authors used a mathematical tool called a "Fisher Matrix" (think of it as a high-tech crystal ball or a simulation).

They asked: "If we point the FAST telescope at the sky for one year and combine that data with the Planck satellite's maps, how much better will our understanding of the universe become?"

The Key Findings (What the Crystal Ball Showed)

1. Measuring the "Fog" Density:
   They found that this method could measure the total amount of hydrogen in the universe with incredible precision. It's like being able to weigh the fog in a room with a scale so sensitive it could detect a single grain of dust. They predict they can pin down the density of hydrogen to a tiny fraction of a percent.

2. The "One-Halo" Zone:
   They discovered that this cross-correlation is especially good at looking inside the "skyscrapers" (galaxy clusters). It helps them understand how much hydrogen gas is trapped inside these massive clusters, which is something other telescopes struggle to see.

3. Pressure Cookers:
   Galaxy clusters are like pressure cookers filled with hot gas. The authors showed that this method could help them understand the "pressure profile"—basically, how the heat and pressure are distributed inside these cosmic pressure cookers. This tells us how these clusters formed and evolved over billions of years.

Why This Matters

• Solving the "Missing" Mystery: We know how much hydrogen should be there based on the Big Bang, but it's hard to find it all. This method helps find the "missing" hydrogen hidden in the dark.
• Better Maps: It creates a much clearer map of the "Cosmic Web"—the giant network of gas and galaxies that makes up our universe.
• Future Proofing: This paper is a blueprint. It tells astronomers, "If you combine FAST and Planck data, you will get amazing results." It encourages scientists to keep working on these cross-correlation techniques.

The Bottom Line

This paper is a proposal to use two different "eyes" (one radio, one microwave) to look at the universe at the same time. By matching the "heat shadows" of galaxy clusters with the "faint hum" of hydrogen gas, astronomers hope to finally get a clear picture of where the universe's building blocks are hiding, how they are arranged, and how they have changed over time. It's like finally putting on 3D glasses to see the universe in high definition.

Technical Summary

Here is a detailed technical summary of the paper "HI Intensity Mapping cross-correlation with thermal SZ fluctuations: forecasted cosmological parameters estimation for FAST and Planck."

1. Problem Statement

The study addresses the challenge of precisely measuring the cosmic density of neutral hydrogen ($\Omega_{HI}$) and understanding the distribution of gas within galaxy clusters at low redshift ($z < 0.35$).

• Limitations of Current Methods: While HI intensity mapping (IM) is a powerful tool for tracing Large Scale Structure (LSS), individual galaxy detections at $z > 0.1$ are difficult due to the faintness of the 21 cm line. Furthermore, HI auto-correlation measurements are heavily contaminated by foregrounds (Galactic synchrotron and free-free emission), particularly on large scales.
• The Opportunity: The thermal Sunyaev-Zel'dovich (tSZ) effect, caused by inverse Compton scattering of CMB photons by hot electrons in galaxy clusters, provides a robust tracer of the LSS and cluster gas properties.
• The Goal: The authors aim to forecast the scientific potential of cross-correlating HI intensity mapping data from the Five-hundred-meter Aperture Spherical Telescope (FAST) with tSZ fluctuations from the Planck satellite. This cross-correlation is expected to be more robust against foregrounds than HI auto-correlation and can probe the connection between neutral hydrogen in galaxies and the hot intracluster medium (ICM).

2. Methodology

The authors employ a halo model framework to predict the cross-correlation signal and use Fisher matrix analysis to forecast parameter constraints.

A. Theoretical Framework (Halo Model)

• HI Distribution: They model neutral hydrogen as residing within dark matter halos. The HI mass function $M_{HI}(M, z)$ is defined based on halo mass, with a minimum mass cutoff ($v_{circ} \approx 30$ km/s) and a suppression scale at high masses ($v_{circ} \approx 200$ km/s). The spatial distribution of HI within a halo is modeled using an exponential density profile $\rho_{HI}(r) \propto \exp(-r/r_s)$.
• tSZ Distribution: The tSZ signal is modeled via the Compton-$y$ parameter, derived from the electron pressure profile. They adopt the Universal Pressure Profile (UPP) (Nagai et al. 2007) parametrized by parameters $\{P_0, c_{500}, \alpha, \beta, \gamma\}$ and include a hydrostatic mass bias parameter ($1-b_H$).
• Power Spectra: The angular cross-power spectrum ($C_\ell^{HI-y}$) is calculated as the sum of:
  • One-halo term: Dominates on small scales ($\ell \gtrsim 70$), representing HI and tSZ within the same halo.
  • Two-halo term: Dominates on large scales, representing the correlation between distinct halos tracing the underlying matter distribution.

B. Survey Parameters

• FAST: Assumed to operate in L-band (1050–1420 MHz) covering $0 < z < 0.35$. Due to Radio Frequency Interference (RFI) from GNSS, the usable frequency bands are split into 1050–1150 MHz and 1300–1420 MHz. The survey covers$\sim 20,000$deg$^2$ with a 1-year integration time.
• Planck: Provides the tSZ map (Compton-$y$) with a resolution of $N_{side}=512$.
• Noise & Foregrounds: The analysis assumes the measurement is limited by instrumental noise rather than foregrounds. They restrict the multipole range to $\ell \in [10, 1000]$ to avoid foreground contamination at low $\ell$ and resolution limits at high $\ell$.

C. Statistical Forecast

• A Fisher Matrix formalism is used to estimate the uncertainty ($\sigma$) on cosmological and astrophysical parameters.
• The analysis combines information from:
  1. HI auto-correlation ($C_\ell^{HI-HI}$)
  2. tSZ auto-correlation ($C_\ell^{y-y}$)
  3. HI-tSZ cross-correlation ($C_\ell^{HI-y}$)

3. Key Contributions

1. First Forecast of FAST-Planck Cross-Correlation: This is the first study to forecast the specific cross-correlation signal between FAST's HI intensity mapping and Planck's tSZ data.
2. Probe of Low-Redshift HI in Halos: The study demonstrates that the cross-correlation in the "one-halo regime" can probe the abundance and profile of neutral hydrogen within galaxy group and cluster halos, a regime difficult to access with traditional targeted observations.
3. Foreground Robustness: The paper highlights that cross-correlation with tSZ (which is not affected by 21 cm foregrounds) offers a cleaner path to constrain $\Omega_{HI}$ compared to auto-correlation, which suffers from foreground removal losses on large scales.
4. Parameter Degeneracy Analysis: The authors analyze the correlations between the HI concentration parameter ($c_{HI,0}$) and the cosmic density ($\Omega_{HI}$), as well as the interplay between tSZ pressure profile parameters and the hydrostatic mass bias.

4. Key Results

The Fisher forecast yields the following constraints (assuming a flat $\Lambda$CDM cosmology fixed to Planck 2018 values):

• Cosmic Neutral Hydrogen Density ($\Omega_{HI}$):
  • The cross-correlation allows for a highly precise constraint: $\sigma(\Omega_{HI}) = 1.0 \times 10^{-6}$.
  • This is significantly tighter than previous estimates. The inclusion of HI auto-correlation improves precision by >40% compared to using cross-correlation alone.
• Halo Mass Sensitivity:
  • The average halo mass contributing to the HI-$y$ cross-power spectrum in the one-halo regime is $\sim 1.5 \times 10^{14} M_\odot$.
  • This indicates the signal is dominated by massive galaxy groups and clusters.
• Astrophysical Parameters:
  • **Hydrostatic Mass Bias ($1-b_H$):** Constrained with$\sigma \approx 0.16$.
  • Universal Pressure Profile (UPP): The study forecasts constraints on the UPP parameters ($P_0, c_{500}, \alpha, \beta$) with standard deviations of roughly $\sigma(P_0) \approx 0.22$, $\sigma(c_{500}) \approx 0.48$, etc.
  • HI Concentration ($c_{HI,0}$): Constrained with $\sigma \approx 3.7$.
• Correlations:
  • An anti-correlation is found between the HI concentration parameter ($c_{HI,0}$) and the cosmic density ($\Omega_{HI}$).
  • The hydrostatic mass bias ($b_H$) is positively correlated with the pressure normalization ($P_0$), likely due to gravitational collapse physics.

5. Significance

• Cosmological Precision: The forecasted precision on $\Omega_{HI}$ ($10^{-6}$) suggests that FAST and Planck data can provide one of the most stringent measurements of the neutral hydrogen budget in the local universe, crucial for understanding baryon evolution and star formation history.
• Astrophysical Insight: The ability to constrain the UPP and hydrostatic mass bias using HI-tSZ cross-correlation offers a new, independent method to study the thermodynamics of galaxy clusters and the accuracy of mass estimates derived from X-ray or SZ observations.
• Future Synergy: The paper lays the groundwork for future "6x2-point" analyses (combining auto- and cross-correlations of HI, tSZ, and galaxies) which could break parameter degeneracies and further enhance the precision of cosmological measurements.
• Validation of IM: It reinforces the viability of HI intensity mapping as a primary cosmological probe, even in the presence of challenging foregrounds, by leveraging cross-correlation techniques with complementary tracers like the tSZ effect.

In conclusion, the paper establishes that the synergy between the high-sensitivity FAST telescope and the all-sky Planck tSZ map offers a powerful, foreground-robust method to map the large-scale distribution of neutral hydrogen and the hot gas in galaxy clusters, leading to unprecedented constraints on cosmological and astrophysical parameters at low redshift.