A model of a main-sequence star of radius ( ) gives its adiabatic sound speed at six radii

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

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

Problem

A model of a main-sequence star of radius R=1.5 R⊙R = 1.5\,R_\odot (R⊙=6.957×108 mR_\odot = 6.957\times10^{8}\,\mathrm{m}) gives its adiabatic sound speed at six radii. Data (r/Rr/R, csc_s in km s−1\mathrm{km\,s^{-1}}): 00, 450450; 0.20.2, 400400; 0.40.4, 310310; 0.60.6, 220220; 0.80.8, 130130; 0.90.9, 8080. ((a)) Estimate the sound-crossing time τ=∫dr/cs\tau = \int\mathrm{d}r/c_s from the centre to 0.9 R0.9\,R with the trapezoid rule. ((b)) Estimate the large frequency separation Δν\Delta\nu. ((c)) Will the star's measured Δν\Delta\nu be larger or smaller than this estimate, and why?

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