Pair-Instability Collapse and Explosion Are Decided at Densities Far Below the Density Bound

The most massive stars meet an instability with no counterpart at lower masses: their cores grow hot enough that photons convert to electron-positron pairs, pressure support softens, and the core contracts or disrupts depending on its mass. This paper places the central densities at which pair instability operates, 1e8 to 1e11 kg per cubic metre, against both relevant branches of the density bound and tabulates the standard outcomes by helium-core mass. At 1e9 kg per cubic metre the fractions attained are 3.48e-43 of the electron branch and 1.03e-49 of the neutron branch; at the top of the range the electron fraction is still only 3.48e-41. Pulsational instability, full disruption and direct collapse are therefore decided entirely by pair thermodynamics and nuclear burning, at densities that are low by the standards of compact-object physics. Simulated from stated assumptions, not measured.