Impact of crust-core connection procedures on the tidal deformability of neutron stars

TL;DR

The paper investigates how nonunified crust-core equations of state, treated with three connection procedures (Direct connection, Crossover connection, Segmented method), affect neutron-star tidal deformability. By combining RMF core and inner-crust EOSs with an outer BPS crust and employing Newton polynomial interpolation for EOS extraction, the study quantifies the impact on tidal quantities via the TOV formalism and Love-number analysis, focusing on the canonical $1.4$ $M_\odot$ star. It shows that mass-radius is largely insensitive to the connection method, while the tidal deformability $\Lambda$ exhibits substantial scheme-dependent variations, with direct connection yielding the largest uncertainties and the segmented method offering the most stable results. The findings provide practical guidance for robust tidal-deformability inference from gravitational-wave observations when using nonunified EOSs.

Abstract

We study the impact of crust-core connection procedures on various neutron-star properties, especially on the tidal deformability. We consider three types of connection procedures to treat the discontinuity in a nonunified equation of state around the crust-core transition: (1) the direct connection procedure, (2) the crossover connection procedure, and (3) the segmented method. Our results indicate that the mass-radius relations of neutron stars are almost unaffected by the details of the connection procedure. However, the tidal deformabilities of neutron stars are sensitive to the crust-core connection procedures. The tidal deformability is closely related to gravitational-wave measurements. For a canonical 1.4$M_\odot$ neutron star, uncertainties in the tidal deformability $Λ_{1.4}$ from different connection procedures can exceed 20\%. We find that the direct connection procedure yields significantly larger uncertainties in the tidal deformability, while the segmented method and crossover connection procedure provide relatively stable results.

Figures (10)

• Figure 1: The neutron-star matter EOSs used in this work. The energy density $\varepsilon$ as a function of the pressure $P$ includes three segments: outer crust, inner crust, and core, shown by different colors. The BPS EOS is adopted for the outer crust, and its matching point to the inner crust is marked by the black filled square. The end of the inner crust is marked by the colored filled stars. The colored filled triangles divide each core EOS into two segments. The connection procedure affects only the dash-dotted segments below the triangles.
• Figure 2: Profiles for all nonunified EOSs constructed by the direct connection procedure. (a) shows the results for the combination of BigApple (core) + TM1e (crust). (b) is for IUFSU (core) + TM1 (crust). (c) is for TM1e (core) + TM1 (crust).
• Figure 3: Mass-radius relations predicted by the direct-connection EOSs shown in Fig. \ref{['eosdc']}. The insets show more details for canonical neutron stars with masses around 1.4$\,{M}_{\odot}$.
• Figure 4: (a,b,c-1) Love number $k_2$ and (a,b,c-2) tidal deformability $\Lambda$ as a function of the neutron-star mass $M$ predicted by the direct-connection EOSs shown in Fig. \ref{['eosdc']}. The insets show more details for canonical neutron stars with masses around 1.4$\,{M}_{\odot}$. (a,b,c-3) The $y(r)$ profiles as given in Eq. \ref{['eq:yr']} for a 1.4$\,{M}_{\odot}$ neutron star. The insets show the results in the direct connection region. The pressures corresponding to the vertical lines are consistent with those in Fig. \ref{['eosdc']}.
• Figure 5: Profiles of the crossover-connection EOSs. (a) shows the results for the combination of BigApple (core) + TM1e (crust). (b) is for IUFSU (core) + TM1 (crust). (c) is for TM1e (core) + TM1 (crust).