High-Frequency Gravitational Waves from Phase Transitions in Nascent Neutron Stars

Abstract

Tentative evidence suggests that the cores of massive neutron stars consist of deconfined quark matter. We argue that the formation of such a quark matter core during a galactic supernova could be accompanied by the emission of gravitational waves in the MHz band. These signals constitute a new target for high-frequency gravitational wave detectors, demonstrating that such detectors may offer unique opportunities for testing quantum chromodynamics in an otherwise inaccessible regime.

Figures (7)

• Figure 1: Neutron star equations of state for both hadronic matter and quark matter. For the latter, we use a bag equation of state. In the $p$-vs.-$\mu_b$ plane (left panel), the crossing point between the hadron (coloured curves) and quark (black dashed curve) EoS defines the critical pressure. In the $p$-vs.-$n_b$ plane (right panel), the various phases can be clearly distinguished. The hadron and quark EoS are plotted separately in the inset.
• Figure 2: Mass--radius relations for the neutron star equations of state considered in this work (coloured curves), compared to constraints from NICER (light grey) Mauviard:2025dmdSalmi:2024aumVinciguerra:2023qxqChoudhury:2024xbkShirke:2025gfi, GW170817 (yellow) LIGOScientific:2018cki, and the theoretical limit from causality (dark grey) Demorest:2010bx. At large masses, the curves fan out to reflect the variation due to the choice of the exponent $\Gamma$ ($0.3 \leq \Gamma \leq 1.2$) in the polytrope describing the mixed phase.
• Figure 3: Peak characteristic strain as function of the stalling pressure for a neutron star 8kpc from Earth. The circle, square and diamond markers represent the first time the expected bubble number decreases to 10, 2, and 1. Part of the curves for the SRO(KDE0v1) and HS(IUF) EoS are emphasized to indicate where the conditions $x_q(t_s) > 0.03$ and $N_{\rm bubbles} > 2$ are both fulfilled, implying that the emission of GWs is most likely. $N_{\rm bubbles}$ is always $> 10$ for HS(IUF).
• Figure 4: Expected power spectral density (PSD), $\sqrt{S_h} = h_c / \sqrt{f}$, of GWs from a hadron-to-quark phase transition in a supernova at 8kpc (coloured curves) compared to the noise-equivalent strain power spectral density, $S_h^{\rm noise}$, of existing (orange) and proposed (gray) high-frequency GW detectors Aggarwal:2025noe. Solid lines indicate broadband detectors, dotted lines those which are only sensitive in a narrow (but tunable) frequency range. We show signal predictions for different EoS, in each case choosing $p_s$ such that $N_{\rm bubbles} = 2$. (For HS(IUF), $N_{\rm bubbles}$ is always $> 2$, so we choose the maximum $p_s$, yielding the maximum GW signal.) The bold curves for HS(IUF) and SRO(KDE0v1) indicate that $x_q(t_s) \gtrsim 0.03$ and $N_{\rm bubbles} \gg 2$ can be satisfied simultaneously, making GW emission likely. Curves are cut off at $f = 1/R_c$. The expected signals for EoS not appearing in the plot are below the plot range. The maximum amplitude of cosmological signals and a typical primordial black hole merger signal are shown in black. Figure created using HFGWPlotter muia_2025_15720342Aggarwal:2025noe.
• Figure 5: Snapshot from one of our lattice simulations of bubble dynamics, showing on the left a slice through the 3D grid (red regions are in the quark phase, grey regions in the hadron phase), and on the right the corresponding tesselation of the bubble walls, with black dot indicating vertices and red arrows the corresponding normal vector. To improve the readability of this illustration, we have chosen a more coarse-grained grid ($40 \times 40 \times 40$) than for our main simulation, and we have seeded 10 bubbles at random locations by hand rather than nucleating new bubbles in each time step.