Mach-number convention in shock unbinding estimates (${\mathcal{M}}_{\mathrm{ad}}^2\gtrsim (16/5)W/E_{\mathrm{th}},{\mathcal{M}}_T^2\gtrsim (16/3)W/E_{\mathrm{th}}$)

For a strong monatomic shock, the planar shock compression of a finite slab gives bulk speed $3V_s/4$ and kinetic energy $E_{\mathrm{bulk}}=9M_c{V}_s^2/32$. The initial internal energy is $E_{\mathrm{th}}=3M_{c}p/(2\rho )$. A bulk-ballistic escape estimate $E_{\mathrm{bulk}}\gtrsim W$ uses positive binding-energy magnitude $W$, not negative gravitational potential energy. With adiabatic sound speed $c_{\mathrm{ad}}^2=5p/(3\rho )$ it yields the first displayed coefficient. Using the isothermal sound speed $c_T^2=p/\rho$ instead yields $16/3\simeq 5.3$. The definitions obey ${\mathcal{M}}_T^2=(5/3){\mathcal{M}}_{\mathrm{ad}}^2$. 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.