Parker Solar Wind

What you are seeing: the isothermal solar-wind solution: $u(r)$ passes through the sonic point at the critical radius $r_c = GM/(2 c_s^2)$ . Hotter coronae have smaller $r_c$ and faster asymptotic winds.

Figure 1. Parker solar wind profile.

T (10⁶ K)1.40

WHAT TO TRY

Raise the coronal temperature: the wind accelerates harder and the sonic point moves inward, since a hotter corona cannot be held by gravity and must blow off as a supersonic wind.
The unique transonic solution threads the critical point, subsonic near the Sun and supersonic far out, the only branch finite at both ends, Parker predicted in 1958.
Read u at 1 AU climbing past 400 km/s: the steady wind that shapes comet tails, drives aurorae, and carves the heliosphere out of the interstellar medium.