Bondi sonic point ( $r_{s}$ )

The isothermal Bondi sonic point is

r_{s} = GM / (2 c_{s}^{2})

, where the regular transonic solution has

u = c_{s}

.

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- Critical point of the isothermal Bondi equation Bondi sonic point

Critical point of the isothermal Bondi equation

At the critical point, both the coefficient of

d u / d r

and the remaining right-hand side of the Isothermal Bondi equation vanish, allowing a finite derivative through the sonic transition.

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