Shocked gas inside a young supernova remnant has electron density and temperature

PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Radiation, radiative transfer and stellar atmospheres · Radiation, radiative transfer and stellar atmospheres

Stars from the Inside, Ch Hot and fast electrons: bremsstrahlung, Compton scattering and synchrotron emission

Problem

Shocked gas inside a young supernova remnant has electron density ne=1.0×1010 m−3n_e = 1.0\times10^{10}\,\mathrm{m^{-3}} and temperature T=1.0×107 KT = 1.0\times10^{7}\,\mathrm{K}. Treat the gas as fully ionised hydrogen (ni=nen_i = n_e) with thermal bremsstrahlung emissivity ϵff=1.7×10−40 ne2 T1/2 W m−3\epsilon_{\rm ff} = 1.7\times10^{-40}\,n_e^2\,T^{1/2}\ \mathrm{W\,m^{-3}} (SI units throughout) and thermal energy density u=3nekBTu = 3n_ek_BT. ((a)) Compute ϵff\epsilon_{\rm ff}. ((b)) Compute the bremsstrahlung cooling time tcool=u/ϵfft_{\rm cool} = u/\epsilon_{\rm ff}, in years. ((c)) The remnant is about 1000 yr1000\,\mathrm{yr} old. Say whether free-free cooling is important for this gas, contrasting with the intracluster case where the cooling time is far longer than the age of the universe.

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