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Determining the equation of state of matter at nuclear density and hence thestructure of neutron stars has been a riddle for decades. We show how theimminent detection of gravitational waves from merging neutron star binariescan be used to solve this riddle. Using a large number of accuratenumerical-relativity simulations of binaries with nuclear equations of state,we find that the postmerger emission is characterized by two distinct androbust spectral features. While the high-frequency peak has already beenassociated with the oscillations of the hypermassive neutron star produced bythe merger and depends on the equation of state, a new correlation emergesbetween the low-frequency peak, related to the merger process, and the totalcompactness of the stars in the binary. More importantly, such a correlation isessentially universal, thus providing a powerful tool to set tight constraintson the equation of state. If the mass of the binary is known from the inspiralsignal, the combined use of the two frequency peaks sets four simultaneousconstraints to be satisfied. Ideally, even a single detection would besufficient to select one equation of state over the others. We test ourapproach with simulated data and verify it works well for all the equations ofstate considered.

Constraining the Equation of State of Neutron Stars from Binary Mergers