We model SNRs at a variety of heights above the disk with a detailed numerical simulation that includes non-equilibrium ionization and recombination and follows the remnants ’ evolution until their hot bubbles have cooled .
We analytically calculate the bubbles ’ buoyant acceleration and frictional drag .
From the simulation results , combined with the rates for isolated supernova explosions above a height of 130 pc , we estimate the time and space average O ^ { +5 } , N ^ { +4 } , and C ^ { +3 } column densities and emission intensities , 1 / 4 keV soft X-ray surface brightness , area coverage , and volume occupation due to the population of isolated SNRs above the Galaxy ’ s HI layer .
Irrespective of assumed supernova explosion energy , ambient nonthermal pressure , or frictional drag coefficient used in the calculations , the predicted O ^ { +5 } column density as a function of height matches the observed distribution between 130 pc and 2000 pc .
The O VI resonance line emission ( 1032 , 1038 \lambda \lambda ) contributes significantly to the average observed intensity .
Assuming our modest supernova explosion rate , the population of isolated extraplanar SNRs can explain 80 \% of the observed 1 / 4 keV surface brightness attributed to the extraplanar gas beyond the H I layer in the southern hemisphere .
Within the range of uncertainty in the SN rate , such SNRs can explain all of this observed emission ( 400 counts s ^ { -1 } arcmin ^ { -2 } ) .
Thus , extraplanar SNRs could be the most important sources of hot gas between the Local Bubble and z \sim 2000 pc in the relatively quiescent southern hemisphere .
These results stand whether the remnants are assumed to be buoyant or not .
The population of old extraplanar SNRs should cover most , but not all of the high latitude sky , thus explaining the mottled appearance of the soft X-ray maps ( outside of superbubbles ) .
Bright young extraplanar SNRs should cover less than 1 \% of the high latitude sky .
Perhaps the \ell = 247 ^ { o } ,b = -64 ^ { o } crescent in the 1 / 4 keV X-ray maps could be such a remnant .