A carbon-oxygen white dwarf ( ) in a wide binary has a dynamical mass of from its…

PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Stellar death and compact objects · Stellar death and compact objects

Stars from the Inside, Ch White dwarfs: the relativistic polytrope, the Chandrasekhar mass and a cooling clock

Problem

A carbon-oxygen white dwarf (

\mu_e = 2

) in a wide binary has a dynamical mass of

1.00\,M_\odot

from its orbit and a gravitational redshift, measured against its companion's spectrum, of

v_{\rm gr} = 80\,\mathrm{km\,s^{-1}}

. Use

v_{\rm gr} = 0.636\,\mathrm{km\,s^{-1}}\,(M/M_\odot)(R/R_\odot)^{-1}

with

R_\odot = 6.957\times10^{5}\,\mathrm{km}

, and

M_{\rm Ch} = 1.46\,M_\odot

. ((a)) Find the radius the redshift implies. ((b)) Predict the radius of a

1.00\,M_\odot

white dwarf from the non-relativistic relation

R_{\rm nr} \approx 1.05\times10^4\,\mathrm{km}\,(M/0.6\,M_\odot)^{-1/3}(\mu_e/2)^{-5/3}

and from the full relation

R \approx R_{\rm nr}[1-(M/M_{\rm Ch})^{4/3}]^{1/2}

, and the redshift each radius predicts. ((c)) What mass would the non-relativistic relation need in order to give the radius found in (a)? Say what this means for treating this star's electrons as slow.

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