Modeling the Nonlinear Power Spectrum in Low-redshift HI Intensity Mapping

We present a simulation-based framework to forecast the HI power spectrum on non-linear scales ($k\gtrsim 1\ {\rm Mpc^{-1}}$), as measured by interferometer arrays like MeerKAT in the low-redshift ($z\leq 1.0$) universe. Building on a galaxy-based HI mock catalog, we meticulously consider various factors, including the emission line profiles of HI discs and some observational settings, and explore their impacts on the HI power spectrum. While it is relatively insensitive to the profile shape of HI emission line at these scales, we identify a strong correlation with the profile width, that is, the Full Width at Half Maxima (FWHM, also known as $W_{\rm 50}$ in observations) in this work. By modeling the width function of $W_{50}$ as a function of $v_{\rm max}$, we assign each HI source a emission line profile and find that the resulting HI power spectrum is comparatively close to results from particles in the IllustrisTNG hydrodynamical simulation. After implementing $k$-space cuts matching the MeerKAT data, our prediction replicates the trend of the measurements obtained by MeerKAT at $z\approx 0.44$, though with a significantly lower amplitude. Utilizing a Monte Carlo Markov Chain sampling method, we constrain the parameter $A_{W_{\rm 50}}$ in the $W_{\rm 50}$ models and $\Omega_{\rm HI}$ with the MeerKAT measurements and find that a strong degeneracy exists between these two parameters.