Hydrodynamics of Relativistic Superheated Bubbles

TL;DR

This work studies the hydrodynamics of relativistic, charged, superheated bubbles that may arise from first-order QCD phase transitions in neutron star mergers. Using a self-similar, relativistic fluid framework with a conformal bag-model EoS (c_s^2=1/3 in both phases) and a conserved charge, the authors derive the wall/shock matching conditions and classify expanding solutions into deflagrations, detonations, and hybrids, including the possibility of metastable regions behind the wall. They show that the velocity profile can decouple from the conserved charge when c_s is constant, quantify the gravitational-wave energy efficiency κ, and establish bounds on allowed flows; they also explore the impact of a large jump in degrees of freedom, finding that only deflagrations persist in that limit. The analysis reveals two qualitative differences from supercooled bubbles: the interior pressure can be higher or lower than the exterior pressure, and metastable regions behind the wall can arise and decay, with implications for GW signatures in NS mergers. The results provide a framework for understanding superheated bubble dynamics and motivate extensions to more realistic QCD equations of state and their astrophysical consequences.

Abstract

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.

Figures (8)

• Figure 1: Two possible phase transitions in QCD, indicated by the solid red curves. $T$ and $\mu$ are the temperature and the baryon chemical potential, respectively. The dotted black curve on the left panel shows a possible evolution of a region of a NS merger as this region is heated and/or compressed. The points dubbed $A$, $A'$ and $C$ correspond to the states shown in Fig. \ref{['meta']}. See text and Ref. Casalderrey-Solana:2022rrn.
• Figure 2: Energy density as a function of the position along the black dotted curve in Fig. \ref{['FOPTquark']}. Both $T$ and $\mu$ increase from left to right. The black, dotted, vertical line indicates the location of the phase transition, determined by the condition that the states $A$ and $A'$ have the same free energy density. The green and blue curves indicate stable and metastable states, respectively. As some region of the NS merger is sufficiently heated and/or compressed, it enters the lower metastable branch. At the point $B$ bubbles of the preferred state $C$ on the upper stable branch are nucleated. The direction of this phase transition is the opposite of that in a supercooled phase transition, which would take place as indicated by the vertical, dotted, red arrow.
• Figure 3: Self-similar flows for superheated bubbles in the case $c_s^2=1/3$. The vertical dotted line lies at $\xi=c_s$, marking the beginning of detonations. The dashed blue curve corresponds to the locus $\nu(\xi,v)\xi=c_s^2$, where the shock must be located . The dotted-dashed red curve indicates the points where the boosted velocity $\nu(\xi,v)=c_s$ and $\partial_{\xi}v\rightarrow\infty$. Expanding bubbles in the shaded area are not allowed.
• Figure 4: Phase diagram for the choice $a_H=b_H=c_H=1$ and $a_L=b_L=c_L=1/2$. "$L$" and "$H$" refer to the low- and high-energy phases, respectively. All quantities are measured in units of the bag constant, $\epsilon$, which is the energy difference between the two phases at $T=\mu=0$.
• Figure 5: Fluid flows for superheated bubbles in the case of deflagrations (top), detonations (middle) and hybrids (bottom), with parameters $\xi_w=\{0.35,0.8,0.5\}$ and $\alpha_n=\{0.0614,0.143,0.0421\}$, respectively. The left panel shows the fluid velocity. The right panel shows the enthalpy (solid-black) and the charge density (dashed-black) normalized to their values at infinity. Grey regions correspond to the $H$-phase and white regions to the $L$-phase, with the boundary being the bubble wall. Vertical dotted lines indicate the speed of sound.