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We develop a new model within which the radius-dependent transition of thesubhalo inner spins with respect to the cosmic web and the variation of thetransition threshold radius ($r_{\rm th}$) with subhalo mass ($M_{\rm vir}$),smoothing scale ($r_{f}$), and redshift ($z$) can be coherently explained. Thekey tenet of this model is that the competition between the pressure effect ofthe inner mass and the compression effect of the local tidal field determineswhich principal direction of the tidal field the inner spins are aligned with.If the former predominates, then only the tidal torques turn on, resulting inthe alignments of the inner spins with the intermediate principal axes of thetidal field. Otherwise, the subhalo spins acquire a tendency to be aligned withthe shortest axes of the subhalo shapes, which is in the major principaldirections of the tidal field. Quantifying the two effects in terms of thedensities, we make a purely analytical prediction for $r_{\rm th}(M_{\rm vir},z, r_{f})$. Testing this model against the numerical results from ahigh-resolution dark matter only N-body simulation in the redshift range of$0\le z\le 3$ on the galactic mass scale of $11.8\le \log[M_{\rmvir}/(h^{-1}M_{\odot})]\le 12.6$ for two different cases of $r_{f}/(h^{-1}{\rmMpc})=0.5$ and $1$, we find excellent agreements of the model predictions withthe numerical results. It is also shown that this model naturally predicts thealignments between the inner spins of the present subhalos with the principalaxes of the high-$z$ tidal field at the progenitors' locations.

The Density Parity Model for the Evolution of the Subhalo Inner Spin Alignments with the Cosmic Web