Toward a Physical Understanding of Galaxy-Halo Alignment

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 ${\theta }_{2\mathrm{D}}$ can be well described by a truncated shifted exponential (TSE) distribution with only {$\mathit{\text{one}}$} 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 ${\theta }_{2\mathrm{D}}$ distribution, with only a small bias ($<3^{\circ }$) possibly arising from unaccounted couplings between ${\theta }_{2\mathrm{D}}$ and other factors. We find that both the 2D and 3D misalignment angles ${\theta }_{2\mathrm{D}}$ and ${\theta }_{3\mathrm{D}}$ decrease with ex situ stellar mass fraction $F_{\mathrm{a}\mathrm{c}\mathrm{c}}$, halo mass $M_{\mathrm{v}\mathrm{i}\mathrm{r}}$ and stellar mass $M_{\ast }$, while increasing with disk-to-total stellar mass fraction $F_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{k}}$ and redshift. These dependences are in good agreement with our recent observational study based on the BOSS galaxy samples. Our results suggest that $F_{\mathrm{a}\mathrm{c}\mathrm{c}}$ is a key factor in determining the galaxy-halo alignment. Grouping galaxies by $F_{\mathrm{a}\mathrm{c}\mathrm{c}}$ nearly eliminates the dependence of ${\theta }_{3\mathrm{D}}$ on $M_{\mathrm{v}\mathrm{i}\mathrm{r}}$ for all three principle axes, and also reduces the redshift dependence. For ${\theta }_{2\mathrm{D}}$, we find a more significant redshift dependence than for ${\theta }_{3\mathrm{D}}$ even after controlling $F_{\mathrm{a}\mathrm{c}\mathrm{c}}$, 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.