A cool phase of the interstellar medium has been observed in many giant elliptical galaxies , but its origin remains unclear .
We propose that uneven heating from Type Ia supernovae ( SNe Ia ) , together with radiative cooling , can lead to the formation of the cool phase .
The basic idea is that since SNe Ia explode randomly , gas parcels which are not directly heated by SN shocks will cool , forming multiphase gas .
We run a series of idealized high-resolution numerical simulations , and find that cool gas develops even when the overall SNe heating rate H exceeds the cooling rate C by a factor as large as 1.4 .
We also find that the time for multiphase gas development depends on the gas temperature .
When the medium has a temperature T = 3 \times 10 ^ { 6 } K , the cool phase forms within one cooling time t _ { c, 0 } ; however , the cool phase formation is delayed to a few times t _ { c, 0 } for higher temperatures .
The main reason for the delay is turbulent mixing .
Cool gas formed this way would naturally have a metallicity lower than that of the hot medium .
For constant H / C , there is more turbulent mixing for higher temperature gas .
We note that this mechanism of producing cool gas can not be captured in cosmological simulations , which usually fail to resolve individual SN remnants .