Self‐similar Champagne Flows in HiiRegions

(Abridged) We consider the expansion of an initially self-gravitating,static, singular, isothermal cloud core. For t>0, the gas is ionized and heatedto a higher uniform temperature by the formation of a luminous, but massless,star in its center. The approximation that the mass and gravity of the centralstar is negligible for the subsequent motion of the HII region holds fordistances much greater than about 100 AU and for the massive cloud cores thatgive rise to high-mass stars. If the initial ionization and heating isapproximated to occur instantaneously at t=0, then the subsequent flow (for r>> 100 AU) caused by the resulting imbalance between self-gravity and thermalpressure is self-similar. Because of the steep density profile, pressuregradients produce a shock front that travels into the cloud, accelerating thegas to supersonic velocities in what has been called the ``champagne phase.''We then study the self-similar solutions of the expansion of HII regionsembedded in molecular clouds characterized by more general power-law densitydistributions with exponent 3/2 < n < 3. In these cases, the shock velocity isan increasing function of the exponent n, and diverges as n tends to 3. We showthat this happens because the model includes an origin, where the pressuredriving the shock diverges because the enclosed heated mass is infinite. Ourresults imply that the continued photoevaporation of massive reservoirs ofneutral gas (e.g., surrounding disks and/or globules) nearby to the embeddedionizing source is required in order to maintain over a significant timescalethe emission measure observed in champagne flows.Comment: 29 pages, 5 figures. The Astrophysical Journal, in pres