We investigate the alignment of galaxy and halo orientations using the TNG300-1 hydrodynamical simulation. Our analysis reveals that the distribution of the 2D misalignment angle $\theta_{ \rm{ 2D}}$ can be well described by a truncated shifted exponential (TSE) distribution with only { \textit{ one}} free parameter across different redshifts and galaxy/halo properties. We demonstrate that the galaxy-ellipticity (GI) correlations of galaxies can be reproduced by perturbing halo orientations with the obtained $\theta_{ \rm{ 2D}}$ distribution, with only a small bias ($<3^{ \circ}$) possibly arising from unaccounted couplings between $\theta_{ \rm{ 2D}}$ and other factors. We find that both the 2D and 3D misalignment angles $\theta_{ \rm{ 2D}}$ and $\theta_{ \rm{ 3D}}$ decrease with ex situ stellar mass fraction $F_{ \rm{ acc}}$, halo mass $M_{ \rm{ vir}}$ and stellar mass $M_{ *}$, while increasing with disk-to-total stellar mass fraction $F_{ \rm{ disk}}$ and redshift. These dependences are in good agreement with our recent observational study based on the BOSS galaxy samples. Our results suggest that $F_{ \rm{ acc}}$ is a key factor in determining the galaxy-halo alignment. Grouping galaxies by $F_{ \rm{ acc}}$ nearly eliminates the dependence of $\theta_{ \rm{ 3D}}$ on $M_{ \rm{ vir}}$ for all three principle axes, and also reduces the redshift dependence. For $\theta_{ \rm{ 2D}}$, we find a more significant redshift dependence than for $\theta_{ \rm{ 3D}}$ even after controlling $F_{ \rm{ acc}}$, which may be attributed to the evolution of galaxy and halo shapes. Our findings present a valuable model for observational studies and enhance our understanding of galaxy-halo alignment.
Categories: astro-ph.GA