Stars Crushed by Black Holes. II. A Physical Model of Adiabatic Compression and Shock Formation in Tidal Disruption Events

We develop a Newtonian model of deep tidal disruption event (TDE), for which the pericenter distance star, $r_{\rm p}$, is well within radius black hole, t}$, i.e., when $\beta \equiv r_{\rm t}/r_{\rm p} \gg 1$. find that shocks form \gtrsim 3$, but they are weak (with Mach numbers $\sim 1$) all $\beta$, and reach center star prior to time maximum adiabatic compression 10$. The density temperature reached during TDE follow much shallower relations with $\beta$ than previously predicted $\rho_{\rm max} \propto \beta^3$ $T_{\rm \beta^2$ scalings. Below \simeq 10$, this dependence occurs because pressure gradient dynamically significant before comparable ram freefalling gas, while above 10$ we prematurely halt yield scalings \beta^{1.62}$ \beta^{1.12}$. excellent agreement between our results high-resolution simulations. Our demonstrate that, in limit, experienced by completely independent mass hole. discuss context existing (affine) models, polytropic vs.~non-polytropic stars, general relativistic effects, become important nears direct capture radius, at \sim 12.5$ (2.7) solar-like disrupted $10^6M_{\odot}$ ($10^{7}M_{\odot}$) supermassive