(a) A classical Cepheid variable has mass and radius . Using the pulsation constant…

PHYSICS · Subjective · Fermi University Physics · Astrophysics & Cosmology · Stellar structure, energy generation and evolution · Stellar structure, energy generation and evolution

Stars from the Inside, Ch Pulsating stars: the kappa mechanism, the Leavitt law and asteroseismology

Problem

(a) A classical Cepheid variable has mass

M = 6\,M_\odot

and radius

R = 60\,R_\odot

. Using the pulsation constant

Q = 0.040\,\mathrm{d}

calibrated from Delta Cephei, estimate its radial fundamental pulsation period. (b) A different, non-radially oscillating star has

\nu_{\max} = 50\,\mu\mathrm{Hz}

\Delta\nu = 5.0\,\mu\mathrm{Hz}

and

T_{\rm eff} = 4900\,\mathrm{K}

. Using the asteroseismic scaling relations calibrated to the Sun (

\Delta\nu_\odot = 135\,\mu\mathrm{Hz}

\nu_{\max,\odot} = 3090\,\mu\mathrm{Hz}

T_{{\rm eff},\odot} = 5777\,\mathrm{K}

), find its mass and radius.

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