Radiation heats gas sufficiently to drive an escaping thermal outflow. It can remove material from protoplanetary disks, planetary atmospheres and irradiated clouds. In a heated Keplerian disk, the photoevaporative gravitational radius compares the sound speed with the orbital speed. The mass-loss rate depends on the heating, density and wind geometry rather than radiation pressure alone.
When a protoplanetary disk's inward viscous supply approaches its wind-loss rate, photoevaporation can prevent replenishment of the inner disk. That region drains on a viscous timescale, leaving a gap or hole. A negative density in a formal steady state calculation signals the breakdown of that approximation, not a physical continuation. An exposed outer edge can subsequently disperse rapidly.
For a sink outside , mass conservation gives in steady state. Remote feeding gives inside , and outside, where . The inward flux decreases towards the star because mass is diverted into the wind. A finite feeding radius or outer truncation supplies an additional boundary condition.
With constant kinematic viscosity and zero inner viscous torque in an accretion disk, . For the steady photoevaporating-disk mass flux, the density is inside and the displayed logarithmic profile outside. At equal feeding and wind rates the inner density vanishes, and the outer normalized profile rises from zero with zero slope and tends to one. Its near-edge expansion is .
The thermal binding scale defined by equating heated gas sound speed to circular Keplerian orbit speed. It is . The circular-orbit binding energy is per unit mass, while the gas specific enthalpy is of order . A heated disk surface at radii comparable to or larger than can therefore drive photoevaporation. The actual launching radius can differ by a factor of order unity; is not the ballistic escape speed.
