The ZZ Ceti instability strip contains hydrogen-atmosphere (DA) white dwarfs in which…

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

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

Problem

The ZZ Ceti instability strip contains hydrogen-atmosphere (DA) white dwarfs in which hydrogen partial ionisation opens a thin convection zone just below the surface, and that zone drives non-radial g-mode pulsations by convective driving. Empirically this occurs for effective temperatures

10\,800\,\mathrm{K} \lesssim T_{\rm eff} \lesssim 12\,300\,\mathrm{K}

\log g = 8.0

. Two DA white dwarfs, A and B, both with

\log g = 8.0

, have

T_{\rm eff,A} = 13\,800\,\mathrm{K}

and

T_{\rm eff,B} = 11\,600\,\mathrm{K}

. ((a)) Predict which of the two, if either, is expected to show ZZ Ceti pulsations at the temperature given. ((b)) A white dwarf's effective temperature falls steadily as it radiates away its thermal energy (Mestel cooling). Using this fact and the location of the hydrogen partial-ionisation zone, explain what is expected to happen to the pulsational state of the star that is not currently pulsating, later in its cooling history.

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