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

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