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

We investigate the conditions under which $\Delta(1232)$ 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 $0.15 \lesssim x_{\sigma\Delta} - x_{\omega\Delta} \lesssim 0.2$ and $x_{\sigma\Delta} \gtrsim 1.3$, the onset of $\Delta^-$ resonances produces a van der Waals-like instability driven by a self-amplifying feedback in the scalar meson sector, in which the $\Delta^-$ 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 $\Delta$-free outer core from a $\Delta$-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 $\Lambda_{1.4} \approx 190$-$480$, compatible with NICER observations and GW170817. We compute, for the first time for a $\Delta$-induced interface, the $\ell = 2$ composition $g$-mode eigenfrequencies, obtaining $\nu_g \sim 400$-$1100$ Hz with gravitational-wave damping times $\tau_g \sim 10^3$-$10^9$ 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.