= Mach-number convention in shock unbinding estimates
{c}
{title2=$\mathcal M_{\rm ad}^2\gtrsim(16/5)W/E_{\rm th},\quad \mathcal M_T^2\gtrsim(16/3)W/E_{\rm th}$}
For a strong monatomic shock, the <planar shock compression of a finite slab> gives bulk speed $3V_s/4$ and kinetic energy $E_{\rm bulk}=9M_cV_s^2/32$. The initial <internal energy> is $E_{\rm th}=3M_cp/(2\rho)$. A bulk-ballistic escape estimate $E_{\rm bulk}\gtrsim W$ uses positive binding-energy magnitude $W$, not negative gravitational potential energy. With <adiabatic sound speed> $c_{\rm ad}^2=5p/(3\rho)$ it yields the first displayed coefficient. Using the <isothermal sound speed> $c_T^2=p/\rho$ instead yields $16/3\simeq5.3$. The definitions obey $\mathcal M_T^2=(5/3)\mathcal M_{\rm ad}^2$. Heating, subsequent expansion and energy loss can alter the physical escape threshold, so the coefficient is not independent of the energy budget and Mach convention.
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