Beyond power spectrum to unveil systematics on HI intensity maps

Technical Summary: Beyond Power Spectrum to Unveil Systematics on Hi Intensity Maps

Problem Statement
Neutral hydrogen (Hi) intensity mapping is a primary technique for probing large-scale structure, particularly at intermediate redshifts ($z < 1$) where nonlinear gravitational evolution renders the matter distribution strongly non-Gaussian. Traditionally, cosmological information from these surveys is extracted using the angular power spectrum ($C_\ell$), a two-point statistic that effectively captures Gaussian features but discards higher-order correlations. At redshifts such as $z \approx 0.425$ (the target of MeerKLASS L-band observations), the Hi signal is dominated by nonlinear structures (filaments, clusters, voids) that $C_\ell$ cannot fully characterize. Furthermore, observational systematics—including telescope beam smoothing, partial sky coverage (masking), instrumental noise, and foreground residuals (Galactic synchrotron, extragalactic point sources)—can bias standard analyses. The paper addresses the need for summary statistics that can capture non-Gaussian information and remain robust against these systematics to improve cosmological parameter inference.

Methodology
The authors employ a simulation-based inference (SBI) framework using the JaxILI library to perform likelihood-free Bayesian inference.

• Simulations: They generated 10,000 full-sky Hi brightness temperature maps at $z = 0.425$ using the GLASS and CAMB frameworks. These maps model lognormal matter fields weighted by redshift-dependent Hi bias and mean brightness temperature.
• Observational Effects: The simulations incorporate realistic observational conditions:
  • Beam: Convolution with Gaussian beams (1.34° for single-dish MeerKLASS-like and 0.5° for future interferometric configurations).
  • Masking: Application of binary masks representing sky fractions ($f_{sky}$) of 0.60, 0.19, and 0.014.
  • Noise: Addition of uncorrelated Gaussian thermal noise based on system temperature and integration time.
  • Systematics: Controlled toy models for multiplicative and additive stripe patterns (scanning artifacts), Galactic synchrotron residuals, extragalactic point source residuals, and X-shaped scanning patterns.
• Summary Statistics: Two statistics were extracted and compared:
  1. Angular Power Spectrum ($C_\ell$): Computed from spherical harmonic coefficients, excluding low multipoles ($\ell < 10$) to mitigate systematics.
  2. Starlet $\ell_1$-norm: A multi-scale, higher-order statistic based on the isotropic undecimated wavelet transform (starlet). The map is decomposed into wavelet coefficients across multiple scales ($J=5$ and $J=8$), normalized, and binned in signal-to-noise space. The $\ell_1$-norm of these coefficients quantifies the sparsity and strength of non-Gaussian features.
• Inference: A conditional neural density estimator (masked autoregressive flow) was trained on the simulation pairs (parameters $\theta = \{\Omega_c, h, A_s\}$, summary statistics $x$) to approximate the posterior $p(\theta|x)$.

Key Contributions

1. Extension of Starlet $\ell_1$-norm: The paper adapts the starlet $\ell_1$-norm, previously successful in weak lensing, to Hi intensity mapping, demonstrating its efficacy in capturing non-Gaussian information in the 21 cm brightness temperature field.
2. Systematic Robustness Analysis: The study provides a comprehensive assessment of how both $C_\ell$ and the starlet $\ell_1$-norm perform under various systematic effects (beam, masking, noise, stripes, and foreground residuals).
3. Diagnostic Capability: The authors demonstrate that the starlet $\ell_1$-norm can distinguish between different types of foreground residuals (Galactic synchrotron vs. extragalactic point sources) and detect the presence of residual contamination, acting as a diagnostic tool.
4. Efficiency: The work highlights the computational and environmental advantages of SBI with compact summary statistics (the starlet $\ell_1$-norm uses significantly fewer data points than the full $C_\ell$ vector) over traditional MCMC methods.

Results

• Cosmological Constraints: The starlet $\ell_1$-norm consistently outperforms the angular power spectrum in constraining cosmological parameters ($\Omega_c$, $h$, $A_s$).
  • In a noiseless, full-sky scenario, the starlet $\ell_1$-norm improves the Figure of Merit (FoM) by a factor of 1.59 over $C_\ell$.
  • In realistic scenarios with a 0.5° beam and instrumental noise, increasing the number of starlet scales from 5 to 8 yields a 2.81× improvement in FoM relative to $C_\ell$.
• Robustness to Systematics:
  • Beam & Masking: While beam smoothing degrades $C_\ell$ significantly by suppressing small-scale power, the starlet $\ell_1$-norm remains robust, retaining sensitivity to structural contrast across scales. It also maintains performance under strong masking ($f_{sky}=0.014$) where $C_\ell$ suffers from mode coupling.
  • Stripes & Scanning: The starlet $\ell_1$-norm is largely insensitive to multiplicative and additive stripe patterns and X-shaped scanning artifacts, whereas $C_\ell$ exhibits strong biases and artificial tightening of posteriors.
  • Foreground Residuals: The starlet $\ell_1$-norm shows greater sensitivity to residual contamination than $C_\ell$. While this introduces a mild bias at high contamination levels, it allows the statistic to differentiate between synchrotron and point source residuals, a task $C_\ell$ fails to perform.
• Parameter Degeneracies: The starlet approach lifts degeneracies between parameters (particularly $h$, which is weakly constrained by $C_\ell$) by utilizing non-Gaussian information.

Significance
The paper concludes that multi-scale, higher-order statistics like the starlet $\ell_1$-norm are essential complements to traditional two-point analyses for Hi intensity mapping. By capturing non-Gaussian features missed by the power spectrum, the starlet $\ell_1$-norm significantly enhances cosmological inference, particularly in the nonlinear regime ($z < 1$). Its demonstrated robustness against complex observational systematics and its ability to serve as a diagnostic for foreground residuals make it a promising tool for current surveys like MeerKLASS and future large-volume surveys such as the SKA Observatory (SKAO). The work advocates for the adoption of simulation-based inference with such statistics to maximize the scientific return of upcoming Hi intensity mapping data.