Self-similar evolution of wind-blown bubbles with mass-loading by conductive evaporation

We present similarity solutions for adiabatic bubbles that are blown by win ds having time dependent mechanical luminosities and that are each mass-loa ded at a rate per unit volume proportional to T(5/2)r(lambda), where T is t he temperature, r is the distance from the bubble center, and X is a consta nt. In the limit of little mass loading a similarity solution found by Dyso n (1973) for expansion into a smooth ambient medium is recovered. For solut ions that give the mass of swept-up ambient gas to be less than tile sums o f the! masses of tile wind and the evaporated material, lambda greater than or similar to 4. The Mach number in a shocked mass-loaded wind shows a rad ical dependence that varies qualitatively from solution to solution. In som e cases it is everywhere less than unity in the frame of the clumps being e vaporated, while in others it is everywhere greater than unity. In some sol utions the mass-loaded shocked wind undergoes one or two sonic transitions in the clump frame. Maximum possible values of the ratio of evaporated mass to stellar wind mass are found as a consequence of the evaporation rates d ependence on temperature and the lowering of the temperature by mass-loadin g, Mass-loading tends to reduce tile emissivity in the interior of the bubb le relative to its limb, whilst simultaneously increasing the central tempe rature relative to the limb temperature.