🔭 astrophysics

One with HI: Modelling HI Intensity Mapping one-point statistics including systematics

This paper presents a theoretical model for the neutral hydrogen (HI) one-point probability density function that incorporates observational systematics like foregrounds and telescope beams, demonstrating that this statistic can extract non-Gaussian information to break degeneracies between bias and clustering amplitude and thereby improve cosmological parameter constraints.

Original authors: Bernhard Vos-Gines, Cora Uhlemann

Published 2026-07-08

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Bernhard Vos-Gines, Cora Uhlemann

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 ocean. Most of this ocean is made of "dark matter," which we can't see directly. However, floating within this dark ocean is a gas called Neutral Hydrogen (HI). Think of HI as the "sea foam" or "bubbles" that trace where the dark matter is thickest.

A massive new radio telescope project called the Square Kilometre Array (SKAO) wants to map this sea foam across the entire history of the universe. Their goal is to understand how the universe is built and how it has changed over time.

This paper is about a new, smarter way to read the map that this telescope will create. Here is the breakdown in simple terms:

1. The Problem: A Noisy, Blurry Photo

The scientists want to take a picture of the universe's hydrogen gas. But taking this picture is like trying to photograph a stormy sea from a shaky boat while wearing foggy glasses. There are three main problems:

The Foggy Glasses (Telescope Beam): The telescope isn't perfect. It blurs the image, smoothing out the tiny details, especially when looking at distant parts of the universe.
The Static (Foregrounds): Our own galaxy is like a giant radio station broadcasting loud static. This static is millions of times brighter than the faint signal from the hydrogen gas. Scientists have to use math to "turn down the volume" on the static, but this process accidentally cuts off some of the deepest, most distant parts of the signal.
The Hiss (Thermal Noise): The telescope itself gets warm and creates a gentle "hiss" of noise, like a radio tuned between stations.

2. The Old Way: Counting the Waves (Power Spectrum)

For a long time, scientists have analyzed these maps by looking at the Power Spectrum. Imagine you are at the beach listening to the waves. The Power Spectrum is like counting how many big waves there are versus small waves. It tells you the "average" behavior of the ocean. It's a very useful tool, but it only tells you about the average height of the waves, not the weird, lumpy, or chaotic shapes they might take.

3. The New Way: The Shape of the Foam (One-Point PDF)

This paper introduces a new tool called the One-Point Probability Density Function (PDF).

The Analogy: Instead of just counting wave heights, imagine you take a bucket of water from the ocean and look at the shape of the foam inside it. Is it mostly flat? Is it spiky? Is it lumpy?
The PDF measures the distribution of these shapes. It captures the "lumpiness" or non-Gaussian information—the weird, irregular patterns that the old "wave counting" method misses.

4. The Challenge: Modeling the Blur

The authors built a new mathematical model to predict what this "foam shape" (PDF) should look like after the telescope blurs it and the static is removed.

They used a technique called Large Deviation Statistics (think of it as a sophisticated way to predict how likely extreme events are, like a massive wave forming).
They combined this with a model of how hydrogen gas clumps around dark matter (like foam sticking to rocks).
Crucially, they built the "blur" and "static removal" directly into their math. They didn't just ignore the telescope's flaws; they modeled exactly how those flaws would change the shape of the foam.

5. The Result: Breaking the Knot

When the scientists tested their model against super-computer simulations of the universe, they found:

It Works: Their model accurately predicted the "foam shapes" even with the telescope's blur and static included.
It Helps: By combining the "wave counting" (Power Spectrum) with the "foam shape" (PDF), they could untangle a confusing knot in the data.
- The Knot: The old method couldn't tell the difference between "how much stuff is there" (clustering amplitude) and "how strongly the gas sticks to the dark matter" (bias). It was like trying to guess how heavy a box is without knowing if the box itself is made of lead or styrofoam.
- The Solution: The new PDF method provided extra clues that allowed them to separate these two factors. This means they can measure the universe's properties (like how much matter exists and how fast it's clumping) much more precisely.

Summary

This paper is a recipe for reading the universe's map more clearly. The authors showed that even with a blurry telescope and loud static, if you look at the shape of the hydrogen gas distribution (not just its average size) and use their new math to account for the telescope's flaws, you can unlock secrets about the universe that were previously hidden. It's like realizing that while the foggy glasses blur the view, the pattern of the blur actually tells you even more about the storm than a clear view would have.

Technical Summary: One with HI: Modelling HI Intensity Mapping One-Point Statistics Including Systematics

Problem Statement
Neutral hydrogen (HI) intensity mapping (IM) offers a unique window into the post-reionization Universe ( $z \leq 6$ ) and will be a primary science driver for upcoming surveys like the Square Kilometre Array Observatory (SKAO). While the power spectrum ( $P(k)$ ) has been the standard tool for extracting cosmological information, it captures only Gaussian information. Beyond two-point statistics, such as the one-point probability density function (PDF), promise to extract additional non-Gaussian information. However, modeling these statistics accurately is challenging due to observational systematics inherent to radio surveys, specifically telescope beam effects, foreground removal, and thermal noise. These systematics dampen specific modes and smooth the signal, potentially obscuring the non-Gaussian signatures required to break degeneracies between cosmological parameters (e.g., $\Omega_M$ and $\sigma_8$ ) and bias parameters ( $b_1$ ).

Methodology
The authors develop a theoretical framework to model the HI intensity PDF in spherical cells, incorporating observational systematics and validating it against high-resolution simulations.

Simulation Data: The study utilizes the UNIT suite of cosmological simulations (dark-matter-only N-body) with a volume of $1 \, h^{-3}\text{Gpc}^3$ . Galaxy properties and cold gas masses are assigned to halos using the Semi-Analytic Galaxy Evolution (SAGE) model. HI masses are derived from cold gas masses and mapped to intensity maps using a Nearest Grid Point (NGP) scheme in cubic voxels ( $1 \, \text{Mpc}/h$ ).
Modeling Systematics:
- Foreground Removal: Modeled as an exponential suppression of large radial modes ( $k_\parallel$ ) to emulate the removal of smooth galactic synchrotron emission.
- Telescope Beam: Modeled as a Gaussian convolution in the transverse plane, suppressing small angular scales.
- Thermal Noise: Added as a Gaussian random field with variance derived from instrument specifications (SKA1-MID).
- These effects are applied in Fourier space to the HI intensity field.
Theoretical Framework:
- Matter PDF: Modeled using Large Deviation Theory (LDT) and the Spherical Collapse (SC) approximation to predict the non-linear matter density PDF.
- HI Bias and Stochasticity: The conditional distribution of HI given dark matter density, $P(\delta_{HI}|\delta_m)$ , is modeled using a quadratic Eulerian bias expansion and a non-Poissonian stochasticity parameterization. The authors utilize the CosMomentum code to compute the tracer PDF by convolving the matter PDF with this conditional distribution.
- Power Spectrum: Modeled using hmcode-2020 for the non-linear matter power spectrum, combined with a linear bias model, shot noise, and the systematic kernels (beam and foreground) applied as a modulation function $S_{eff}(k)$ .
Validation and Forecasting: The theoretical models are validated against the simulation-based statistics using a jackknife resampling technique to estimate covariances. A Fisher information matrix analysis is performed to forecast constraints on cosmological parameters ( $\Omega_M, \sigma_8$ ) and the linear bias ( $b_1$ ) for an SKA1-MID survey configuration.

Key Contributions

Systematics-Integrated PDF Model: The paper presents a theoretical model for the HI one-point PDF that explicitly incorporates the effects of telescope beams, foreground removal, and thermal noise. This is achieved by modifying the rate function in the LDT framework to include systematic kernels and adjusting the conditional bias/stochasticity parameters.
Bias and Stochasticity Characterization: The authors quantify the scale-dependent bias and stochasticity of HI tracers in the presence of systematics, demonstrating that a quadratic bias model and a second-order expansion for stochasticity provide a good fit to the simulation data, though higher-order terms may be needed at smaller scales.
Degeneracy Breaking: The work demonstrates how combining the HI PDF with the power spectrum can break the degeneracy between the linear bias ( $b_1$ ) and the amplitude of fluctuations ( $\sigma_8$ ), a limitation inherent to two-point statistics alone.

Results

Model Accuracy: The theoretical PDF predictions agree with simulation-based measurements within percent-level accuracy (typically $<4\%$ deviation at the smallest smoothing scale $R=15.5 \, \text{Mpc}/h$ ) when using simulated conditional moments. When using parametric bias models, discrepancies are slightly larger but remain within acceptable bounds for Fisher forecasts.
Impact of Systematics: The telescope beam is identified as the dominant systematic, significantly reducing the variance of the PDF. Foreground removal slightly modifies the shape, while thermal noise is largely suppressed by spherical smoothing.
Cosmological Constraints:
- $\Omega_M - \sigma_8$ Plane: Combining the power spectrum with the PDF at a large smoothing scale ( $R=31.0 \, \text{Mpc}/h$ ) reduces the degeneracy between $\Omega_M$ and $\sigma_8$ significantly, tightening uncertainties by approximately 64% for $\Omega_M$ and 49% for $\sigma_8$ compared to the power spectrum alone. This is attributed to the misalignment of the degeneracy directions between the two statistics.
- $\sigma_8 - b_1$ Degeneracy: For breaking the degeneracy between $\sigma_8$ and the bias $b_1$ , the PDF at a smaller smoothing scale ( $R=15.5 \, \text{Mpc}/h$ ) proves most effective. This is because the reduced skewness of the PDF is more sensitive to the bias parameter on smaller, more non-Gaussian scales.
Parameter Bias: The authors find that the bias in recovered parameters due to differences between the theoretical model and simulations is generally below $1\sigma$ for the simulated volume. However, they note that for the much larger volumes expected from SKA, these biases could become significant if not corrected (e.g., via Edgeworth corrections to the skewness).

Significance
The paper establishes that the HI intensity one-point PDF, even when degraded by realistic observational systematics, retains sufficient non-Gaussian information to complement the power spectrum. By providing a validated theoretical model that accounts for these systematics, the work enables the extraction of tighter cosmological constraints and the breaking of critical parameter degeneracies (specifically $b_1$ vs. $\sigma_8$ ) in future SKAO surveys. The authors emphasize that while their current model is robust for the simulated volumes, future work will require refined modeling of skewness rescaling and larger simulation volumes to fully exploit the capabilities of SKA data.