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Predicted number counts and clustering of Hi galaxies from future radio surveys

This paper utilizes three distinct galaxy simulation models (S $^3$ -SAX, GAEA, and IllustrisTNG) to predict the number counts and clustering properties of HI galaxies observable by future SKA-MID radio surveys, thereby forecasting the survey's cosmological performance and quantifying uncertainties arising from modeling and sample variance.

Original authors: Ainulnabilah Nasirudin, Philip Bull, Isabelle Ye

Published 2026-04-30

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CC BY 4.0

Original authors: Ainulnabilah Nasirudin, Philip Bull, Isabelle Ye

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, invisible web made of dark matter. Galaxies are like the glowing cities that form along the threads of this web. For a long time, astronomers have been trying to map these cities to understand how the web itself is shaped and how it's expanding.

This paper is about preparing for a massive new project: using giant radio telescopes (specifically the future SKA-MID) to take a census of galaxies that are filled with neutral hydrogen (a gas called HI). Think of neutral hydrogen as the "fuel" inside these galaxies. When this fuel emits a specific radio signal (the 21cm line), it acts like a lighthouse, allowing astronomers to pinpoint exactly where the galaxy is and how fast it's moving away from us.

Here is the story of what the authors did, explained simply:

1. The Problem: We Don't Know the "Menu"

Before you can order a meal, you need to know what's on the menu. Before building a massive survey with the SKA-MID telescope, scientists need to know:

How many HI galaxies will we actually see?
How are they clustered together? (Do they hang out in big groups or live alone?)

The problem is that we haven't seen enough of these galaxies yet to know the answers. So, the authors turned to computer simulations. They used three different "virtual universes" to predict what the telescope would see.

2. The Three Virtual Chefs

The authors compared three different computer models, which act like three different chefs trying to predict the same recipe:

S3-SAX: A model based on old-school math rules (semi-analytic) built on a dark matter simulation.
GAEA: A newer, updated version of those math rules, tweaked using data from fluid simulations.
IllustrisTNG: A super-complex simulation that actually models the physics of gas, stars, and black holes moving around (hydrodynamical).

The Surprise: The three chefs didn't agree on the menu.

At low distances (nearby galaxies), their predictions were off by a factor of 2 or 3.
At high distances (faraway galaxies), the disagreement was huge—sometimes by a factor of 10 or more!
It's like one chef predicting you'll find 100 apples in a forest, while another predicts 1,000.

3. The Cosmological Forecast: How Good Will Our Map Be?

The authors asked: "If we use these different predictions to plan our telescope survey, how accurate will our map of the universe be?"

They ran a "test drive" using the Fisher Matrix (a statistical tool that predicts how much error we might have).

The Result: For nearby galaxies (low redshift), it didn't matter much which simulation they used; the telescope would still get a decent map (within 10% error).
The Catch: For distant galaxies (high redshift), the choice of simulation mattered a lot. If you picked the "wrong" simulation, your error bars could balloon to be 11 times larger.
The Verdict: The SKA-MID telescope will be a great tool, but at high distances, the uncertainty in our theoretical models (the "menu") is the biggest limiting factor, not the telescope itself. To get really precise maps of the distant universe, we might need an even bigger telescope (like a hypothetical "SKA2").

4. The "Sample Variance" Experiment

To understand how much "luck" plays a role in these surveys, the authors took a high-resolution slice of the IllustrisTNG simulation (a snapshot of the universe at a specific time) and chopped it into nine different 20° x 20° patches.

Imagine looking at a forest through nine different windows. Even though it's the same forest, the view through each window is slightly different.

They counted the galaxies in each window and measured how clumpy they were.
Finding: The "clumpiness" (called the angular correlation function) varied quite a bit from window to window. This is called sample variance.
Why it matters: If you only survey a small patch of sky, your results might be skewed just because you got lucky (or unlucky) with where you looked. The authors found that while the overall "clumpiness" was consistent on average, the specific details of how galaxies group together (the "1-halo" term, or galaxies in the same cluster) changed significantly depending on how faint the galaxies were.

5. The "Halo Occupation" Puzzle

Finally, they tried to fit a model called Halo Occupation Distribution (HOD) to their data. Think of HOD as a rulebook that says: "For a dark matter cloud of this specific size, how many galaxies should live inside it?"

They tested this rulebook against their nine different windows.
Result: The rulebook worked surprisingly well. Even though the number of galaxies changed with the sensitivity of the telescope, the underlying rules about how galaxies live in dark matter clouds remained fairly stable.
They provided a set of "best guess" numbers for these rules, which other scientists can use to plan future surveys.

Summary

This paper is a "dress rehearsal" for the future of radio astronomy. The authors warn us that while our computer models are getting better, they still disagree significantly on how many galaxies exist and how they are arranged, especially in the distant universe.

Good news: For nearby surveys, the SKA-MID telescope will work great regardless of which model we trust.
Caution: For distant surveys, our lack of agreement between models is a bigger problem than the telescope's sensitivity.
Takeaway: We need to keep refining our computer simulations and be prepared for "sample variance" (the luck of the draw) when looking at smaller patches of the sky.

In short: We have a powerful new camera coming, but we still need to figure out exactly what the scene looks like before we press the shutter.

1. Problem Statement

The detection of the 21cm emission line from neutral hydrogen (Hi) in galaxies offers a powerful method for spectroscopic redshift determination and mapping the large-scale structure of the Universe. Upcoming radio arrays, particularly the Square Kilometre Array Mid-frequency array (SKA-MID), are expected to catalogue hundreds of thousands to millions of Hi galaxies. However, accurate cosmological forecasts for these surveys are hindered by significant theoretical uncertainties regarding:

Number Counts: The expected number density of Hi galaxies as a function of redshift and flux sensitivity is poorly constrained, especially at faint flux levels ( $\mu$ Jy) and higher redshifts ( $z > 0.5$ ).
Clustering Properties: The bias of Hi galaxies relative to the underlying dark matter distribution is uncertain.
Model Dependence: Different simulation approaches (Semi-Analytic Models vs. Hydrodynamical simulations) yield divergent predictions, making it difficult to quantify the theoretical error budget for future cosmological constraints.

2. Methodology

The authors employed a multi-faceted approach combining three distinct galaxy simulations with observational forecasting techniques:

A. Simulation Comparison
The study utilized three different simulated galaxy catalogues to predict Hi galaxy properties:

S3-SAX: A semi-analytic model (SAM) based on the Millennium dark matter-only simulation.
GAEA: An updated SAM partially calibrated using hydrodynamical simulations.
IllustrisTNG: A full magnetohydrodynamical simulation (specifically TNG100 and TNG300 boxes).

B. Survey Specifications

Instrument: SKA-MID (Band 1: 350–1050 MHz; Band 2: 950–1760 MHz).
Configurations: Two array configurations were modeled: AA* (144 dishes) and AA4 (197 dishes).
Survey Parameters: A total of 10,000 hours over a 5,000 deg $^2$ area.
Selection Cuts: Galaxies were selected based on a 5 $\sigma$ flux density threshold ( $S_{rms}$ ) and a minimum line width ( $W_\theta$ ) to exclude face-on galaxies lacking the characteristic double-horned profile.

C. Cosmological Forecasts (Fisher Matrix)
Using the number density ($dN/dz$) and bias ( $b(z)$ ) derived from S3-SAX and GAEA, the authors performed Fisher matrix forecasts to predict constraints on cosmological parameters:

Expansion rate $H(z)$ and angular diameter distance $D_A(z)$ .
Linear growth rate $f\sigma_8(z)$ and bias $b\sigma_8(z)$ .
The analysis assumed a Planck 2018 flat $\Lambda$ CDM fiducial model.

D. Clustering and Sample Variance Analysis

Data Source: A high-resolution snapshot ( $z \approx 0$ ) from the IllustrisTNG300 simulation.
Mock Catalogs: The simulation box was divided into nine sub-volumes ( $20^\circ \times 20^\circ$ each) to simulate independent sky realizations.
Statistical Analysis:
- Calculated the Angular Correlation Function (ACF), $w(\theta)$ , for flux thresholds of 100, 250, and 500 $\mu$ Jy.
- Applied the Landy-Szalay estimator to measure $w(\theta)$ .
- Used Jackknife resampling to estimate the covariance matrix.
- Performed Bayesian MCMC inference to fit a Halo Occupation Distribution (HOD) model to the ACF, constraining parameters: $\log M_{min}$ , $\log M_1$ , $f_c$ (central fraction), and $\beta_g$ .

3. Key Contributions

Quantification of Theoretical Uncertainty: The paper provides a rigorous comparison of Hi predictions across three major simulation frameworks, highlighting where they agree and where they diverge significantly.
SKA-MID Performance Forecast: It offers updated forecasts for the cosmological capabilities of SKA-MID configurations (AA* and AA4), explicitly linking survey performance to the choice of simulation model.
Sample Variance Characterization: By analyzing nine sub-volumes of a large hydrodynamical simulation, the study quantifies the impact of sample variance on low-redshift clustering measurements, a critical factor for wide-area but shallow surveys.
HOD Parameter Constraints: It derives robust HOD parameters for low-redshift Hi galaxies and demonstrates their stability (or lack thereof) across different flux density thresholds.

4. Key Results

A. Number Counts and Bias Discrepancies

Low Redshift ( $z < 0.5$ ): Simulations agree within a factor of a few. However, at higher flux thresholds ( $S_{rms} > 50 \mu$ Jy), TNG100 predicts the highest number densities, while S3-SAX predicts the lowest.
High Redshift ( $z > 0.5$ ): Discrepancies become severe. At $z \sim 1$ , number densities can differ by orders of magnitude between simulations.
Bias: The bias values show a wide range, particularly at high redshifts and high flux thresholds, with differences reaching a factor of 6. TNG100 consistently shows lower bias ( $\sim 0.8$ ) at $z < 0.4$ compared to S3-SAX and GAEA, likely due to its smaller simulation volume.

B. Cosmological Forecasts

Precision: The AA4 configuration using GAEA predictions yields constraints on $H(z)$ and $D_A(z)$ better than 10% for $z < 0.5$ , improving to 2–3% at $z \approx 0.4$ .
Degradation: At $z > 0.5$ (Band 1), constraints degrade significantly depending on the simulation used. For example, the AA* S3-SAX prediction shows uncertainties up to 11 times larger than the best-case scenario at $z \sim 0.9$ .
Comparison to Optical: Even with optimistic assumptions, SKA-MID constraints are currently inferior to optical surveys like DESI due to lower number densities and sample variance at low redshift.

C. Clustering and HOD Analysis

Sample Variance: The angular correlation function $w(\theta)$ shows significant scatter between the nine sub-volumes, particularly at large angular separations ( $\theta \ge 0.5^\circ$ ), where variations can reach two orders of magnitude.
Flux Threshold Dependence:
- The 2-halo term (large-scale clustering) is largely insensitive to flux density thresholds, except at very large angles.
- The 1-halo term (small-scale clustering) shows a factor of 5 difference between flux thresholds at $\theta \sim 0.2^\circ$ .
HOD Parameters: The inferred bias ( $b_{gal}$ ) decreases slightly ( $\Delta b \approx -0.05$ ) as the flux threshold increases by an order of magnitude. The parameter $\log M_1$ (mass hosting one satellite) increases with flux threshold, while $\log M_{min}$ and $f_c$ decrease.
Consistency: The HOD-derived bias agrees with simulation predictions within $\sim 20\%$ .

5. Significance and Conclusion

This paper establishes that while low-redshift cosmological forecasts for SKA-MID are relatively robust to the choice of simulation (limited primarily by sample variance), high-redshift forecasts are highly sensitive to theoretical modeling uncertainties.

Theoretical Uncertainty: The large spread in predicted number counts and bias at $z > 0.5$ implies that current simulations cannot yet provide precise error budgets for high-redshift Hi surveys without observational calibration.
Survey Strategy: To achieve sub-percent cosmological constraints, future instruments (e.g., "SKA2") will need significantly higher sensitivity ( $\lesssim 10 \mu$ Jy) to access higher redshifts where sample variance is less dominant.
Practical Utility: The derived HOD parameters and the identification of flux-threshold insensitivity in the 2-halo term provide a solid foundation for modeling low-redshift Hi clustering in the interim, before large-scale observational data becomes available.

The authors conclude that while simulations are essential for planning, they must be assigned significant theoretical uncertainty margins until new Hi survey data allows for model refinement.