Constraining the Equation of State of Neutron Stars from Binary Mergers

Determining the equation of state of matter at nuclear density and hence the structure of neutron stars has been a riddle for decades. We show how the imminent detection of gravitational waves from merging neutron star binaries can be used to solve this riddle. Using a large number of accurate numerical-relativity simulations of binaries with nuclear equations of state, we find that the postmerger emission is characterized by two distinct and robust spectral features. While the high-frequency peak has already been associated with the oscillations of the hypermassive neutron star produced by the merger and depends on the equation of state, a new correlation emerges between the low-frequency peak, related to the merger process, and the total compactness of the stars in the binary. More importantly, such a correlation is essentially universal, thus providing a powerful tool to set tight constraints on the equation of state. If the mass of the binary is known from the inspiral signal, the combined use of the two frequency peaks sets four simultaneous constraints to be satisfied. Ideally, even a single detection would be sufficient to select one equation of state over the others. We test our approach with simulated data and verify it works well for all the equations of state considered.

Figure 1

Top panel: Evolution of $h_{+}$ for representative binaries with the APR4 and GNH3 EOSs (dark-red and blue lines, respectively) for sources at a polar distance of 50 Mpc. Bottom panel: Spectral density $2\tilde{h}(f)f^{1/2}$ windowed after the merger for the two EOSs and sensitivity curves of Advanced LIGO (green line) and ET (light-blue line); the dotted lines show the power in the inspiral, while the circles mark the contact frequency.

Figure 2

Left panel: Fitted values of the low-frequency peaks as a function of the stellar compactness for the six different EOSs considered; note the universal behavior exhibited also by unequal-mass binaries (filled squares). Shown as a solid black line is the cubic fit, while the gray band is the estimate of the total errors. Right panel: Fitted values of the high-frequency peaks as a function of the average rest-mass density; no universal behavior appears.

Figure 3

Examples of use of the spectral features to constrain the EOS. Once a detection is made, the relations $\overline{M}=\overline{M}(\overline{R},f_1)$ and $\overline{M}=\overline{M}(\overline{R},f_2;\mathrm{EOS})$ (colored solid lines) will cross at one point the curves of equilibrium configurations (colored dashed lines). Knowledge of the mass of the system (horizontal line) will provide a fourth constraint, removing possible degeneracies. The left and right panels refer to the ALF2 and APR4 EOSs, but all other EOSs behave in the same way.