Modeling Foreground Spatial Variations in 21 cm Gaussian Process Component Separation

Abstract The 21 cm line from neutral hydrogen captures rich cosmological information. However, the 21 cm signals are highly contaminated by foreground emission, making accurate component separation vital for cosmological analyses. Gaussian processes (GPs) have been utilized for component separation in 21 cm data analyses, exploiting the distinct spectral behavior of the cosmological and foreground signals, which are modeled through the GP covariance kernel. Previous approaches have employed a global GP kernel along all lines of sight (LoS). In this work, we study Bayesian approaches that allow for spatial variations in foreground kernel parameters, testing them against simulated H i intensity mapping observations, which measures the total H i intensity in large voxels. We consider a no-pooling (NP) model, treating each LoS independently by fitting for separate covariance kernels, and a hierarchical Gaussian process (HGP) model, allowing for variation in kernel parameters between different LoS, regularized through a global hyperprior. We find that including spatial variations in the GP kernel parameters results in a significant improvement in cosmological signal recovery, achieving up to a 30% reduction in the standard deviation of the residual distribution. Allowing for spatial variations also improves the recovery of the H i power spectra and wavelet scattering transform coefficients. While the NP model achieves superior recovery as measured by the residual distribution, it is computationally demanding, faces convergence challenges, and is prone to overfitting. The HGP model strikes a balance between accuracy and robustness. Further improvements to the HGP model will require more physically-motivated modeling of foreground spatial variations. Our code can be found in the following repository: https://github.com/dkn16/H21F .