Evolution of multiple supernova remnants

Heating of the interstellar medium (ISM) by multiple supernova (SN) explosions is at the heart of producing galaxy-scale outflows in starburst galaxies. Standard models of outflows assume a high efficiency of SNe in heating the gas to X-ray emitting temperatures and filling the central region of starburst with hot gas, in order to launch vigorous outflows. We use hydrodynamical simulations to study the efficiency of multiple SNe in heating the ISM and filling the volume with gas of high temperatures. We argue that it is important for SN remnants to have a large filling factor and a large heating efficiency. For this, they have to be clustered in space and time, and keep exploding until the hot gas percolates through the whole region, in order to compensate for the radiative loss. In the case of a limited number of SNe, we find that although the filling factor can be large, the heating efficiency declines after reaching a large value. In the case of a continuous series of SNe, the hot gas (T >= 3 x 10(6) K) can percolate through the whole region after the total volume filling factor reaches a threshold of similar to 0.3. The efficiency of heating the gas to X-ray temperatures can be >= 0.1 after this percolation epoch, which occurs after a period of approximate to 10 Myr for a typical starburst SN rate density of v(SN) approximate to 10(-9) pc(-3) yr(-1) and gas density of n approximate to 10 cm(-3) in starburst nuclei regions. This matches the recent observations of a time delay of similar order between the onset of star formation and galactic outflows. The efficiency to heat gas up to X-ray temperatures (>= 10(6.5) K) roughly scales as v(SN)(0.2)n(-0.6). For a typical SN rate density and gas density in starburst nuclei, the heating efficiency is similar to 0.15, also consistent with previous interpretations from X-ray observations. We discuss the implications of our results with regard to observational diagnostics of ionic ratios and emission measures in starburst nuclei regions.