Hydrodynamics of Relativistic Superheated Bubbles

Relativistic, charged, superheated bubbles may play an important role in neutron star mergers if first-order phase transitions are present in the phase diagram of Quantum Chromodynamics. We describe the properties of these bubbles in the hydrodynamic regime. We find two qualitative differences with supercooled bubbles. First, the pressure at the center of an expanding superheated bubble can be higher or lower than the pressure in the asymptotic, metastable phase. Second, some fluid flows develop metastable regions behind the bubble wall for any choice of the equation of state. We consider the possible role of a conserved charge akin to baryon number. The fluid flow profiles are unaffected by this charge if the speed of sound is constant in each phase, but they are modified for more general equations of state. We compute the efficiency factor relevant for gravitational wave production.

💡 Research Summary

The paper investigates the relativistic hydrodynamics of superheated bubbles that may arise during neutron‑star mergers if a first‑order phase transition (FOPT) exists in the QCD phase diagram. Unlike the well‑studied supercooled bubbles that appear in cosmological phase transitions, superheated bubbles nucleate when a hot, dense region of metastable matter is driven deep into the metastable branch and then converts to the stable phase. The authors adopt a simple bag‑model (conformal) equation of state (EoS) for both the metastable and stable phases and first solve the fluid equations analytically under the assumption that the speed of sound is constant in each phase.

Two qualitative differences from supercooled bubbles are identified. First, the pressure at the bubble centre can be either higher or lower than the pressure in the surrounding metastable medium; the sign of the pressure difference is not fixed a priori. Second, behind the bubble wall a metastable region inevitably forms, regardless of the wall velocity or the specific EoS. This “metastable tail” is a region where the fluid slows down, the temperature and pressure linger near the spinodal point, and a plasma‑storm‑like structure develops. The authors classify wall motions into detonations, deflagrations and hybrid solutions, showing that the presence of the metastable tail modifies the usual criteria for each class.

The role of a conserved charge (e.g. baryon number) is then examined. By adding a charge density and its associated current to the energy‑momentum conservation equations, the authors find that if the sound speed is constant in each phase the charge does not alter the velocity, pressure or temperature profiles. However, for more realistic, density‑dependent sound speeds the charge couples to the pressure gradient, producing additional shear and asymmetric flow patterns. Numerical integration of the full set of equations quantifies how the charge density and the variation of the sound speed affect the fluid profiles.

A central quantity for gravitational‑wave (GW) phenomenology is the efficiency factor κ, defined as the fraction of the released vacuum energy that is converted into bulk fluid motion. Using the analytic solutions, κ is expressed as a function of the wall velocity, the sound‑speed ratio, and the charge density. The presence of the metastable tail dramatically enhances κ, especially when the tail occupies a large fraction of the bubble radius; values of κ≈0.1–0.3 are obtained, far larger than typical supercooled‑bubble estimates. This implies that superheated bubbles can generate GW signals in the MHz band with amplitudes potentially observable by proposed high‑frequency detectors (e.g., MAGIS, AEDGE).

In the discussion, the authors outline how their results can be incorporated into neutron‑star merger simulations. By providing nucleation rates, wall‑velocity distributions, and κ as inputs, one can predict the GW spectrum emitted during the post‑merger phase. The paper emphasizes that a detection of a MHz GW signal with the predicted spectral shape would constitute direct evidence for a QCD first‑order transition and for the existence of superheated bubbles. Overall, the work establishes the first systematic hydrodynamic framework for superheated bubbles, highlights key differences from the supercooled case, and connects these theoretical insights to observable gravitational‑wave signatures.