Boosting H <scp>i</scp>-Galaxy Cross-Clustering Signal through Higher-Order Cross-Correlations

Abstract After reionization, neutral hydrogen (${\rm H\, \small {I}}$) traces the large-scale structure (LSS) of the Universe, enabling ${\rm H\, \small {I}}$ intensity mapping (IM) to capture the LSS in 3D and constrain key cosmological parameters. We present a new framework utilizing higher-order cross-correlations to study ${\rm H\, \small {I}}$ clustering around galaxies, tested using real-space data from the IllustrisTNG300 simulation. This approach computes the joint distributions of k-nearest neighbor (kNN) optical galaxies and the ${\rm H\, \small {I}}$ brightness temperature field smoothed at relevant scales (the kNN-field framework), providing sensitivity to all higher-order cross-correlations, unlike two-point statistics. To simulate ${\rm H\, \small {I}}$ data from actual surveys, we add random thermal noise and apply a simple foreground cleaning model, filtering out Fourier modes of the brightness temperature field with k∥ &amp;lt; kmin, ∥. Under current levels of thermal noise and foreground cleaning, typical of a Canadian Hydrogen Intensity Mapping Experiment (CHIME)-like survey, the ${\rm H\, \small {I}}$-galaxy cross-correlation signal in our simulations, using the kNN-field framework, is detectable at &amp;gt;30σ across r = [3, 12] h−1 Mpc. In contrast, the detectability of the standard two-point correlation function (2PCF) over the same scales depends strongly on the foreground filter: a sharp k∥ filter can spuriously boost detection to 8σ due to position-space ringing, whereas a less sharp filter yields no detection. Nonetheless, we conclude that kNN-field cross-correlations are robustly detectable across a broad range of foreground filtering and thermal noise conditions, suggesting their potential for enhanced constraining power over 2PCFs.