A unified study of nuclear physics and dark matter constraints through gravitational-wave observations of binary neutron star mergers

Abstract

Understanding the properties of strongly interacting matter at extreme densities is a central problem in fundamental physics, but neutron star mergers provide a natural laboratory for probing this regime. However, the complexity of the merger process complicates the interpretation of the associated gravitational-wave and electromagnetic signals. This picture becomes even more complex in the potential scenario in which dark matter accumulates around and in neutron stars, altering their structure and the associated observables. In this work, we study synthetic gravitational-wave observations of binary neutron star mergers with next-generation detectors, investigating their potential to extract both nuclear physics and dark-matter constraints. We also examine how the potential presence of fermionic, non-interacting dark matter inside neutron stars affects the inference of nuclear empirical parameters. We find that combining observations can tighten constraints on nuclear empirical parameters. However, the inferred values remain sensitive to systematic modeling biases and intrinsic degeneracies among the parameters. Conversely, our analysis reveals that even in the presence of dark matter, it will be unlikely to find decisive evidence for dark matter when analyzing gravitational-wave signals. Consequently, systematic biases in nuclear empirical parameter inference potentially resulting from the presence of dark matter are expected to be negligible even for observations with next-generation gravitational-wave detectors.

Figures (5)

• Figure 1: Overview of the employed EOS sets illustrating the macroscopic NS properties. The left panel depicts the mass-radius relationship, while the right panel shows the tidal deformability-mass plane. The MM-SS EOS set is represented in blue, the MM EOS set in orange, and the Skyrme EOS set is shown in green. Injected EOSs within each set are shown using the same color scheme.
• Figure 2: Normalized prior distributions of NEPs for the different EOSs described in Sec. \ref{['Subsec:BMEOSsets']}. The selected EOS injections are shown as vertical dashed lines for each of the models and are motivated through findings in Koehn:2024set.
• Figure 3: Posterior distributions of selected NEPs obtained when injecting with MM-SS (left column), MM (middle column), and Skyrme (right column), while recovering each injection with MM-SS (blue), MM (orange), and Skyrme (green) EOS sets, respectively. The posterior distributions represent the combined posterior across the four simulated BNS events A–D as shaded regions and the prior is shown for each EOS as dotted lines. The injections of NEPs are color-coded, respectively, and are shown as dashed lines.
• Figure 4: Combined constraints on the neutron skin thicknesses $\Delta r$ and electric dipole polarizabilities $\alpha_{D}$ for ${}^{208}\rm Pb$ and ${{}^{48}\rm Ca}$ obtained from the joint analysis of simulated BNS events A–D. The combined posterior distributions (green) are compared with the corresponding priors (gray), while the injected values (red dashed lines) correspond to quantities consistently computed within the Skyrme EDF framework from the NEPs of the injected Skyrme EOS (cf. Fig. \ref{['fig:injEOS_basedon_Nucparams']}). The JSD, $D_{\rm JS}$, between the combined posterior and prior is reported in the upper right corner of each panel. Vertical shaded bands with $1\sigma$ ranges denote previous findings: CREX for $\Delta r({}^{48}\mathrm{Ca})$CREX:2022kgg and Birkhan et al. (2017) for $\alpha_{D}({}^{48}\mathrm{Ca})$Birkhan:2016qkr.
• Figure 5: Constraints on DM parameters for BNS event C. The upper (lower) panels show the parameter-estimation results obtained by sampling with the DMA MM and (Skyrme) EOS set, respectively. In each subpanel, the prior (gray shaded) is compared to posteriors recovered using the ET (blue) and ET+CE (black) detector configurations, with the JSD, $D_{\rm JS}$, quantifying the information gain of the posterior relative to the prior. Red dashed lines indicate the injected values of the DM fraction, particle mass, and EOS index. The DM particle mass is fixed to $m_{\chi} = 483$ MeV and the DM fraction for this simulated BNS event C is $f_{\chi} = 0.3$%.