Treat the corona as isothermal

PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Stellar structure, energy generation and evolution · Astrophysical fluid dynamics and plasmas

Stars from the Inside, Ch The Sun as a test: calibration, sound, neutrinos and a magnetised atmosphere

Problem

Treat the corona as isothermal, fully ionised hydrogen (μ=0.5\mu = 0.5), with GM⊙=1.327×1020 m3 s−2GM_\odot = 1.327\times10^{20}\,\mathrm{m^3\,s^{-2}} and 1 AU=1.496×1011 m1\,\mathrm{AU} = 1.496\times10^{11}\,\mathrm{m}, and use the transonic relation of the Parker wind, (v/cs)2−ln⁡(v/cs)2=4ln⁡(r/rc)+4rc/r−3(v/c_s)^2 - \ln(v/c_s)^2 = 4\ln(r/r_c) + 4r_c/r - 3. ((a)) For T=1.0×106 KT = 1.0\times10^{6}\,\mathrm{K}, find csc_s, rcr_c and the wind speed at 1 AU1\,\mathrm{AU}. ((b)) Repeat for T=2.0×106 KT = 2.0\times10^{6}\,\mathrm{K}. ((c)) Does doubling the coronal temperature double the wind speed at Earth?

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