Efficiently Cooled Stellar Wind Bubbles in Turbulent Clouds I. Fractal
  Theory and Application to Star-Forming Clouds
  Winds from massive stars have velocities of 1000 km/s or more, and produce
hot, high pressure gas when they shock. We develop a theory for the evolution
of bubbles driven by the collective winds from star clusters early in their
lifetimes, which involves interaction with the turbulent, dense interstellar
medium of the surrounding natal molecular cloud. A key feature is the fractal
nature of the hot bubble's surface. The large area of this interface with
surrounding denser gas strongly enhances energy losses from the hot interior,
enabled by turbulent mixing and subsequent cooling at temperatures T =
10^4-10^5 K where radiation is maximally efficient. Due to the extreme cooling,
the bubble radius scales differently (R ~ t^1/2) from the classical Weaver77
solution, and has expansion velocity and momentum lower by factors of 10-10^2
at given R, with pressure lower by factors of 10^2 - 10^3. Our theory explains
the weak X-ray emission and low shell expansion velocities of observed sources.
We discuss further implications of our theory for observations of the hot
bubbles and cooled expanding shells created by stellar winds, and for
predictions of feedback-regulated star formation in a range of environments. In
a companion paper, we validate our theory with a suite of hydrodynamic
simulations.
