Degeneracy in the Inference of Phase Transitions in the Neutron Star Equation of State from Gravitational Wave Data

Gravitational wave (GW) detections of binary neutron star inspirals will be crucial for constraining the dense matter equation of state (EOS). We demonstrate a new degeneracy in the mapping from tidal deformability data to the EOS, which occurs for models with strong phase transitions. We find that there exists a new family of EOS with phase transitions that set in at different densities and that predict neutron star radii that differ by up to $\sim 500\mathrm{m}$ but that produce nearly identical tidal deformabilities for all neutron star masses. Next-generation GW detectors and advances in nuclear theory may be needed to resolve this degeneracy.

Figure 1

Top row (in purple): Bayesian inference of the EOS for mock data, generated assuming Gaussian errors in tidal deformability, $\mathrm{\Lambda }$, for LIGO at the sensitivity of its fifth observing run ($\mathrm{A}+$), for a series of GW170817-like events (${\sigma }_{\mathrm{\Lambda }}=46$). From left to right, we show the most likely tidal deformability curves, mass-radius curves, and EOSs inferred in our Bayesian inference. To highlight the degeneracy of the solutions, we randomly sample curves from the 68% confidence interval and color them according to their posteriors, relative to the most likely solution. Bottom row (in blue): an identical inference, but with Gaussian errors in $\mathrm{\Lambda }$ for the proposed XG detector Cosmic Explorer (${\sigma }_{\mathrm{\Lambda }}=8$).

Figure 2

Example pairs of EOS models that undergo a first-order phase transition at significantly different densities (40% fractional difference) and yet produce nearly identical tidal deformability curves. From left to right, we show the EOS models, their corresponding mass-radius relations, and their corresponding tidal deformability curves. Each pair of EOS models was constructed assuming perfect knowledge of the crust EOS to ${\rho }_{\mathrm{sat}}$ (top row, in green), $1.2{\rho }_{\mathrm{sat}}$ (middle row, in blue), or $1.5{\rho }_{\mathrm{sat}}$ (bottom row, in red).

Figure 3

Absolute differences in the tidal deformability $\mathrm{\Lambda }$ between each pair of doppelgängers shown in Fig. 2. As the crust EOS is assumed to higher densities, the tidal deformability curves become more distinct, with the largest differences emerging at low masses. The vertical shaded bands indicate the expected 68%-measurement uncertainty in $\mathrm{\Lambda }$ for a population of neutron star mergers observed over one year with the sensitivity of LIGO at design sensitivity (aLIGO), the anticipated sensitivity of LIGO during its fifth observing run ($\mathrm{A}+$), and the proposed XG detector Cosmic Explorer (CE) [15].