Hadron bubble evolution into the quark sea.

Abstract

A solution is presented for the evolution of hadron bubbles which nucleate in the quark sea if there is a first-order quark-hadron phase transition at a temperature ${T}_{c}$ on the order of 100 MeV. We make three assumptions: (1) the dominant mechanism for transport of latent heat is radiative, e.g., neutrinos; (2) the distance between nucleation sites is greater than the neutrino mean free path; and (3) the effects of hydrodynamic flow can be neglected. Bubbles nucleate with a characteristic radius $\frac{1 \mathrm{fm}}{\ensuremath{\Delta}}$, where $\ensuremath{\Delta}$ is a dimensionless parameter for the undercooling (we take $\ensuremath{\Delta}\ensuremath{\ge}{10}^{\ensuremath{-}4}$, so that the expansion of the Universe can be neglected). We argue that bubbles grow stably and remain spherical until the radius becomes as large as the neutrino mean free path, $l\ensuremath{\simeq}10$ cm. The growth then becomes diffusion limited and the bubbles become unstable to formation of dendrites, or finger-like structures, because latent heat can diffuse away more easily from long fingers than from spheres. We study the nonlinear evolution of structure with a geometrical model and argue that the hadron bubbles ultimately look like stringy seaweed. The percolation of seaweed-shaped bubbles can leave behind regions of quark phase that are quite small. In fact, one might expect the typical scale to be ${L}_{Q}=l\ensuremath{\simeq}10$ cm. Protons can easily diffuse out of such small regions (and neutrons back in). Thus, these instabilities can lead to important modifications of inhomogeneous nucleosynthesis, which requires ${L}_{Q}\ensuremath{\gtrsim}1$ m.