Bulk viscosity from neutron decays to dark baryons in neutron star matter

TL;DR

The work assesses how a dark-sector neutron decay channel $n\rightarrow \chi+\phi$ impacts transport in neutron star mergers by constructing an $npe\chi$ equation of state with repulsive dark-baryon self-interactions to maintain $2M_\odot$ stars. It derives a two-channel bulk-viscosity framework, computes both the standard Urca rates and the in-medium neutron-dark-decay rates using the Nuclear Width Approximation (NWA), and analyzes the resulting bulk viscosity across merger-relevant temperatures. The main finding is that, for anomaly-consistent parameters, the in-medium dark decay is slow and the bulk viscosity is affected only modestly ( factor $\lesssim 2$–$3$). However, if the dark decay is faster within current bounds, bulk viscosity can be strongly enhanced at temperatures of tens of MeV, potentially damping merger oscillations on ms–tens of ms timescales and offering a potential observational signature of dark-sector transport in mergers.

Abstract

The possibility of neutron decay into dark particles has been proposed as a way to resolve a growing discrepancy between two different measurements of the neutron lifetime. The most popular formulation is a dark sector consisting of a dark baryon $χ$ and a dark scalar $φ$, where a neutron in vacuum decays about 1% of the time via the channel $n\rightarrow χ+φ$. In this work, we consider the effect of this additional neutron decay channel on transport in neutrons star mergers. We find that the neutron dark decay rate in medium is quite slow, and thus the dark baryons modify the dense matter equation of state in a way that decreases the Urca bulk viscosity by, at most, a factor of 2-3. However, if the neutron dark decay was to occur more rapidly, then the bulk viscosity at merger temperatures of tens of MeV would be strongly enhanced, potentially rapidly damping oscillations in merger environments and therefore providing a signature of slowly equilibrating matter in the merger.

Figures (11)

• Figure 1: The value of $g_{\phi}$ that resolves the neutron decay anomaly, as a function of the mass of the $\chi$, with $m_{\phi}=0$. The fiducial value chosen in this paper is represented by the black dot.
• Figure 2: Mass-radius curve of $npe\chi$-matter neutron stars with various values of $\chi$ self-repulsion strength $G'$. The pure $npe$ case, with no dark baryons, is shown in black. The $npe$ EoS can be achieved by taking the limit $G'\rightarrow\infty$.
• Figure 3: Particle fractions in beta equilibrium for self-repulsion strengths of $G'=44\text{ fm}^2$ (the minimum value allowed by the existence of $2M_{\odot}$ stars, left panel) and $G' = 1\text{ fm}^2$ (right panel). The particle fractions are calculated at zero temperature. The baryon density $n_B$ includes the dark baryon content (c.f. Eq.\ref{['eq:nB_definition']}).
• Figure 4: Bulk viscosity of $npe\chi$ matter with frozen $\chi$ content (i.e., $\lambda_2=0$). The density oscillation frequency is 1 kHz and the matter is at $n_B=1n_0$. Different color curves correspond to different choices of the dark baryon self-repulsion strength. The matter here is calculated in finite-temperature beta equilibrium (Eqs. \ref{['eq:truebeq_1']} and \ref{['eq:truebeq_2']}).
• Figure 5: Peak value (across all temperatures) of the Urca bulk viscosity $\zeta_1$, as a function of the baryon density. The left panel shows a variety of dark baryon self-repulsion strengths $G'$, while the right panel shows different values of the dark baryon mass $m_{\chi}$. The calculations in these plots are done at zero temperature.