Dynamical tidal response of neutron stars as a probe of dense-matter properties

Abstract

Dynamical tidal deformations play a crucial role in the gravitational waves emitted by binary neutron star systems during their late inspiral. In this work, we systematically explore how relativistic (dynamical and dissipative) tidal deformations depend on the internal structure of a neutron star using two analytic classes of equations of state. The first class is a nucleonic model that is parameterized by nuclear physics observables, such as the symmetry energy coefficients and saturation properties. The second class is a toy model of quark matter, the MIT bag model. To model tidal dissipation, we self-consistently include contributions from weak-interaction-driven bulk-viscous effects while considering both the nucleonic and the quark-matter equations of state. The dissipative tide is sensitive to frequency and temperature, but its magnitude, as predicted by weak-interaction-driven bulk-viscous effects, is too small (within the equation-of-state models studied here) to be detectable by current or future observations. However, we find that the (conservative) dynamical tidal response function depends strongly on the slope of the symmetry energy and on higher-order coefficients of the symmetry energy; this implies that gravitational-wave observations could be used to probe higher-order coefficients of the symmetry energy through their effect on the (conservative) dynamical tide.

Figures (9)

• Figure 1: Cartoon of the tidal response of neutron stars in a binary system (not to scale). Qualitatively, the conservative response creates the tidal bulge and the dissipative response causes the tidal bulge to lag behind the gravitational field sourced by its companion. Both the conservative and the dissipative responses are enhanced as the orbital frequency $f$ increases due to gravitational wave emission.
• Figure 2: Frequency-dependent bulk viscosity versus temperature, at $\omega = 2\pi\times1$ kHz, for various $L_{\mathrm{sym}}$ (green), $K_{\mathrm{sym}}$ (red), and $B$ (purple), at $n_B=3.5n_{\mathrm{sat}}$ (solid) and $n_B=5n_{\mathrm{sat}}$ (dashed). Lighter colored curves indicate lower values of the parameter of interest. In some temperature ranges, two curves (the green and red traces) are indistinguishable and lie on top of each other; the resulting overplotting appears as a light brown trace and does not correspond to an additional parameter choice. For $npe$ matter, increasing either $L_{\mathrm{sym}}$ or $K_{\mathrm{sym}}$---and density---systematically increases the bulk viscosity across most temperatures. In contrast, for quark matter, the bulk viscosity is mostly insensitive to the changes in the bag constant and densities, aside from a modest change for the largest value of $B$ and at $5n_{\mathrm{sat}}$, but its peak occurs at a markedly different temperature than the peak for $npe$ matter.
• Figure 3: Variation of the mass--radius curves with respect to different components of $\theta_{\mathrm{NPE}}$, while the remaining parameters are fixed to their fiducial values in Eq. \ref{['eq:theta-canonical']}. In each panel, lighter colored curves indicate lower values of the parameter of interest. The $M$--$R$ constraints from NICER Miller:2019cacRiley:2019ydaMiller:2021qhaRiley:2021pdl (red--orange contours labeled with J0740 and J0030) and LIGO LIGOScientific:2017vwqLIGOScientific:2018hzeLIGOScientific:2018cki (blue--green contours labeled GW170817) are also shown for comparison. The top, left panel explores the dependence of the $M$--$R$ curve with respect to the symmetry energy $S_{\mathrm{sym}}$ (black dash-dotted band) and the temperature $T$ (red band). Observe that the $M$--$R$ curve is almost insensitive to these parameters. The variation of the mass-radius curves with respect to the incompressibility $K_0$, the slope $L_{\mathrm{sym}}$ and the curvature $K_{\mathrm{sym}}$ of the symmetry energy are presented in the top right, bottom left and bottom right panel, respectively. For the range considered in Eq. \ref{['eq:parameter-range-NPE']}, we see that the mass-radius curve varies significantly with respect to $K_{\mathrm{sym}}$ (bottom right) across all central densities, while the variation with respect to $L_{\mathrm{sym}}$ (bottom left) is more significant at lower central densities.
• Figure 4: Variation of the $M$--$R$ curves with $L_{\mathrm{sym}}$ and $K_{\mathrm{sym}}$ for parameter values consistent with PREX-II experiment. Lighter colored curves indicate lower values of the parameter of interest. Observe that the large value of $L_{\rm sym}$ in the PREX-II measurement pushes the curves to larger radii as compared to Fig. \ref{['fig:MR_curves_npe']}. The general trends of the M--R curves with $K_{\rm sym}$ and $L_{\rm sym}$, however, remain.
• Figure 5: Variation of the $M$--$R$ curve of the quark EoS model with respect to the bag constant. Lighter colored curves indicate lower values of the bag constant. Observe that increasing the bag constant decreases the stiffness of the EoS, leading to a smaller mass and radius at a given number density.