3.4
Quark-hadron phase transition
Update
The standard picture of cosmology assumes that a phase
transition (associated with chiral symmetry breaking following
the electroweak transition) occurred at approximately
after the Big Bang to convert a plasma of free quarks and gluons
into hadrons. Although this transition can be of significant
cosmological importance, it is not known with certainty whether
it is of first order or higher, and what the astrophysical
consequences might be on the subsequent state of the Universe.
For example, the transition may play a potentially observable
role in the generation of primordial magnetic fields. The QCD
transition may also give rise to important baryon number
inhomogeneities which can affect the distribution of light
element abundances from primordial Big Bang nucleosynthesis. The
distribution of baryons may be influenced hydrodynamically by the
competing effects of phase mixing and phase separation, which
arise from any inherent instability of the interface surfaces
separating regions of different phase. Unstable modes, if they
exist, will distort phase boundaries and induce mixing and
diffusive homogenization through hydrodynamic turbulence
[102
, 112, 95, 4, 137]
.
In an effort to support and expand theoretical
studies, a number of one-dimensional numerical simulations have
been carried out to explore the behavior of growing hadron
bubbles and decaying quark droplets in simplified and isolated
geometries. For example, Rezolla et al.
[138]
considered a first order phase transition and the nucleation of
hadronic bubbles in a supercooled quark-gluon plasma, solving the
relativistic Lagrangian equations for disconnected and
evaporating quark regions during the final stages of the phase
transition. They investigated numerically a single isolated quark
drop with an initial radius large enough so that surface effects
can be neglected. The droplet evolves as a self-similar solution
until it evaporates to a sufficiently small radius that surface
effects break the similarity solution and increase the
evaporation rate. Their simulations indicate that, in neglecting
long-range energy and momentum transfer (by electromagnetically
interacting particles) and assuming that baryon number is
transported with the hydrodynamical flux, the baryon number
concentration is similar to what is predicted by chemical
equilibrium calculations.
Kurki-Suonio and Laine
[108]
studied the growth of bubbles and the decay of droplets using a
one-dimensional spherically symmetric code that accounts for a
phenomenological model of the microscopic entropy generated at
the phase transition surface. Incorporating the small scale
effects of finite wall width and surface tension, but neglecting
entropy and baryon flow through the droplet wall, they simulate
the process by which nucleating bubbles grow and evolve to a
similarity solution. They also compute the evaporation of quark
droplets as they deviate from similarity solutions at late times
due to surface tension and wall effects.
Update
Ignatius et al.
[96]
carried out parameter studies of bubble growth for both the QCD
and electroweak transitions in planar symmetry, demonstrating
that hadron bubbles reach a stationary similarity state after a
short time when bubbles grow at constant velocity. They
investigated the stationary state using numerical and analytic
methods, accounting also for preheating caused by shock
fronts.
Update
Fragile and Anninos
[76]
performed two-dimensional simulations of first order QCD
transitions to explore the nature of interface boundaries beyond
linear stability analysis, and determine if they are stable when
the full nonlinearities of the relativistic scalar field and
hydrodynamic system of equations are accounted for. They used
results from linear perturbation theory to define initial
fluctuations on either side of the phase fronts and evolved the
data numerically in time for both deflagration and detonation
configurations. No evidence of mixing instabilities or
hydrodynamic turbulence was found in any of the cases they
considered, despite the fact that they investigated the parameter
space predicted to be potentially unstable according to linear
analysis. They also investigated whether phase mixing can occur
through a turbulence-type mechanism triggered by shock proximity
or disruption of phase fronts. They considered three basic cases
(see image sequences in Figures
5,
6, and
7
below): interactions between planar and spherical deflagration
bubbles, collisions between planar and spherical detonation
bubbles, and a third case simulating the interaction between both
deflagration and detonation systems initially at two different
thermal states. Their results are consistent with the standard
picture of cosmological phase transitions in which hadron bubbles
expand as spherical condensation fronts, undergoing regular
(non-turbulent) coalescence, and eventually leading to collapsing
spherical quark droplets in a medium of hadrons. This is
generally true even in the detonation cases which are complicated
by greater entropy heating from shock interactions contributing
to the irregular destruction of hadrons and the creation of quark
nuggets.
However, Fragile and Anninos also note a
deflagration ‘instability’ or acceleration mechanism evident in
their third case for which they assume an initial thermal
discontinuity in space separating different regions of nucleating
hadron bubbles. The passage of a rarefaction wave (generated at
the thermal discontinuity) through a slowly propagating
deflagration can significantly accelerate the condensation
process, suggesting that the dominant modes of condensation in an
early Universe which super-cools at different rates within
causally connected domains may be through supersonic detonations
or fast moving (nearly sonic) deflagrations. A similar
speculation was made by Kamionkowski and Freese
[102]
who suggested that deflagrations become unstable to
perturbations and are converted to detonations by turbulent
surface distortion effects. However, in the simulations,
deflagrations are accelerated not from turbulent mixing and
surface distortion, but from enhanced super-cooling by
rarefaction waves. In multi-dimensions, the acceleration
mechanism can be exaggerated further by upwind phase mergers due
to transverse flow, surface distortion, and mode dissipation
effects, a combination that may result in supersonic front
propagation speeds, even if the nucleation process began as a
slowly propagating deflagration.