HI intensity mapping data traces the large-scale structure matter distribution using the integrated emission of neutral hydrogen gas (HI). The cross-correlation of the intensity maps with optical galaxy surveys can mitigate foreground and systematic effects, but has been shown to significantly depend on galaxy evolution parameters of the HI and the optical sample. Previously, we have shown that the shot noise of the cross-correlation scales with the HI content of the optical samples, such that the shot noise estimation infers the average HI masses of these samples. In this article, we present an adaptive framework for the cross-correlation of HI intensity maps with galaxy samples using our implementation of the halo model formalism (Murray et al 2018, in prep) which utilises the halo occupation distribution of galaxies to predict their power spectra. We compare two HI population models, tracing the spatial halo and the galaxy distribution respectively, and present their auto- and cross-power spectra with an associated galaxy sample. We find that the choice of the HI model and the distribution of the HI within the galaxy sample have minor significance for the shape of the auto- and cross-correlations, but highly impact the measured shot noise amplitude of the estimators, a finding we confirm with simulations. We demonstrate parameter estimation of the HI halo occupation models and advocate this framework for the interpretation of future experimental data, with the prospect of determining the HI masses of optical galaxy samples via the cross-correlation shot noise.
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