The Delta-isobar masquerade: intrahadronic phase transitions and their quark-mimicking signatures in neutron stars

Abstract

We investigate the conditions under which $Δ(1232)$ isobars trigger a first-order phase transition within purely hadronic neutron-star matter, using the SW4L relativistic mean-field parametrization. For scalar-vector coupling differences $0.15 \lesssim x_{σΔ} - x_{ωΔ} \lesssim 0.2$ and $x_{σΔ} \gtrsim 1.3$, the onset of $Δ^-$ resonances produces a van der Waals-like instability driven by a self-amplifying feedback in the scalar meson sector, in which the $Δ^-$ particle fraction acts as the order parameter of a Landau-type transition. A Maxwell construction yields a sharp density discontinuity at baryon densities $n_b \sim (1.3$-$2)\,n_0$, separating a $Δ$-free outer core from a $Δ$-rich inner core. The resulting neutron-star sequences satisfy all current multimessenger constraints: maximum masses $M_{\rm max} \approx 2.15$-$2.25\,M_\odot$, radii $R_{1.4} \approx 11$-$12$ km, and tidal deformabilities $Λ_{1.4} \approx 190$-$480$, compatible with NICER observations and GW170817. We compute, for the first time for a $Δ$-induced interface, the $\ell = 2$ composition $g$-mode eigenfrequencies, obtaining $ν_g \sim 400$-$1100$ Hz with gravitational-wave damping times $τ_g \sim 10^3$-$10^9$ s. These frequencies overlap quantitatively with those predicted for hadron-quark phase-transition interfaces, demonstrating that the mass-radius ``knee'', reduced tidal deformability, and $g$-mode spectrum conventionally regarded as signatures of quark deconfinement can be reproduced by a purely intrahadronic mechanism. This extends the masquerade problem from static observables to the domain of gravitational-wave asteroseismology, implying that a future detection of a discontinuity $g$-mode alone would not suffice to identify quark matter in neutron-star cores.

Figures (4)

• Figure 1: (a)–(d) Gibbs free energy per baryon $G$ as a function of the pressure $P$ for the four coupling sets of Table \ref{['tab:eos_params']}. The multivalued structure of $G(P)$ reflects the presence of two competing equilibrium branches (a $\Delta$–free and a $\Delta$–rich phase); the black dot marks the pressure $P_{\mathrm{tr}}$ at which their Gibbs free energies coincide, signaling a hadron–hadron FOPT. (e)–(h) Volume per baryon $v = n_b^{-1}$ as a function of $P$ for the same models. The characteristic "S-shaped" loops indicate the spinodal region where $dv/dP>0$ and homogeneous matter is mechanically unstable. The vertical solid line denotes the transition pressure $P_{\mathrm{tr}}$ selected by the Maxwell construction, at which the system jumps discontinuously from the low-density to the high-density branch.
• Figure 2: (a)–(d) Total pressure as a function of the baryon number density $n_b$ for the four parameter sets defined in Table \ref{['tab:eos_params']}. The horizontal plateaus correspond to the constant transition pressure $P_{\mathrm{tr}}$ obtained from the Maxwell construction; the endpoints of each plateau mark the baryon densities on the two sides of the discontinuity. The light-blue band indicates the region consistent with chiral effective field theory (cEFT) calculations at low densities based on Ref. Drischler:2021lma. (e)–(h) Corresponding particle fractions $Y_i = n_i/n_b$. The shaded vertical bands indicate the density gaps spanned by the pressure plateaus, i.e., the range of $n_b$ that is not realized in a homogeneous phase during the FOPT. The onset of the transition is associated with the rapid appearance of $\Delta^-$-isobars, which is accompanied by a sharp depletion of the electron and muon populations and a noticeable increase in the proton fraction, signaling a global reorganization of the Fermi seas across the transition. The black vertical line in each lower panel marks the central baryon density of the corresponding maximum-mass stellar configuration.
• Figure 3: Macroscopic structure of neutron stars for the selected EoS parametrizations. (a) Mass–radius relations compared with observational constraints from massive pulsars (shaded horizontal bands) and from NICER and GW170817 (colored confidence regions). The change in slope ("knee") of the curves reflects the onset of the $\Delta$-rich phase in the stellar core; the sharpness of this feature correlates with the strength of the FOPT. (b) Dimensionless tidal deformability $\Lambda$ as a function of stellar mass. The black diamond with error bars indicates the constraint on $\Lambda_{1.4}$ from the binary neutron star merger GW170817. All four EoS yield compact stars compatible with current multimessenger observations Abbott:2018gmo
• Figure 4: Properties of the composition $g$-mode associated with the hadron–hadron phase-transition interface. (a) Gravitational wave frequency, $\nu_g$, as a function of stellar mass. (b) Damping time due to gravitational-wave emission, $\tau_g$, as a function of the stellar mass.