Feedback from Multiple Supernova Explosions inside a Wind-Blown Bubble

We study the evolution of multiple supernova (SN) explosions inside a pre-exiting cavity blown by winds from massive progenitor stars. Hydrodynamic simulations in one-dimensional spherical geometry, including radiative cooling and thermal conduction, are carried out to follow first the development of the wind-blown bubble during the main sequence and then the evolution of the SN-driven bubble. We find the size and mass of the SN-driven bubble shell depend on the structure of the pre-existing wind bubble as well as the SN explosion energy E_{SN} (= N_{SN} 10^{51} ergs). The hot cavity inside the bubble is 2-3 times bigger in volume and hotter than that of a bubble created by SNe exploded in a uniform interstellar medium (ISM). For an association with 10 massive stars in the average ISM, the SN-driven shell has an outer radius of R_{ss} ~ (85 pc) N_{SN}^{0.1} and a mass of M_{ss} ~ (10^{4.8} Msun) N_{SN}^{0.3}at 10^6 years after the explosion. By that time most of the explosion energy is lost via radiative cooling, while ~10% remains as kinetic energy and ~10% as thermal energy. We also calculate the total integrated spectrum of diffuse radiation emitted by the shock-heated gas of the SN bubble. For the models with 0.1 solar metalicity, the radiative energy loss is smaller and the fraction of non-ionizing photons is larger, compared to those with solar metalicity. We conclude the photoionization/heating by diffuse radiation is the most dominant form of feedback from SN explosions into the surrounding medium.