Revisiting the Galaxy Shape and Spin Alignments with the Large-Scale Tidal Field: An Effective Practical Model

An effective practical model with two characteristic parameters is presented to describe both of the tidally induced shape and spin alignments of the galactic halos with the large-scale tidal fields. We test this model against the numerical results obtained from the Small MultiDark Planck simulation on the galactic mass scale of $0.5\le M/(10^{11}\,h^{-1}\,M_{\odot})\le 50$ at redshift $z=0$. Determining empirically the parameters from the numerical data, we demonstrate how successfully our model describes simultaneously and consistently the amplitudes and behaviors of the probability density functions of three coordinates of the shape and spin vectors in the principal frame of the large scale tidal field. Dividing the samples of the galactic halos into multiple subsamples in four different mass ranges and four different types of the cosmic web, and also varying the smoothing scale of the tidal field from $5\,h^{-1}$Mpc to $10,\ 20,\ 30\,h^{-1}$Mpc, we perform repeatedly the numerical tests with each subsample at each scale. Our model is found to match well the numerical results for all of the cases of the mass range, smoothing scale and web type and to properly capture the scale and web dependence of the spin flip phenomenon.