Tidal deformabilities and neutron star mergers

Finite size effects in a neutron star merger are manifested, at leading order, through the tidal deformabilities of the stars. If strong first-order phase transitions do not exist within neutron stars, both neutron stars are described by the same equation of state, and their tidal deformabilities are highly correlated through their masses even if the equation of state is unknown. If, however, a strong phase transition exists between the central densities of the two stars, so that the more massive star has a phase transition and the least massive star does not, this correlation will be weakened. In all cases, a minimum deformability for each neutron star mass is imposed by causality, and a less conservative limit is imposed by the unitary gas constraint, both of which we compute. In order to make the best use of gravitational wave data from mergers, it is important to include the correlations relating the deformabilities and the masses as well as lower limits to the deformabilities as a function of mass. Focusing on the case without strong phase transitions, and for mergers where the chirp mass M <= 1.4 M-circle dot, which is the case for all observed double neutron star systems where a total mass has been accurately measured, we show that the ratio of the dimensionless tidal deformabilities satisfy Lambda(1)/Lambda(2) similar to q(6), where q=M-2/M-1 is the binary mass ratio; A and M are the dimensionless deformability and mass of each star, respectively. Moreover, they are bounded by q(n-) >= Lambda(1)/Lambda(2) >= q(n0++qn1+), where n_ < n(0+ )+ qn(1+); the parameters depend only on M, which is accurately determined from the gravitational-wave signal. We also provide analytic expressions for the wider bounds that exist in the case of a strong phase transition. We argue that bounded ranges for Lambda(1)/Lambda(2) tuned to M, together with lower bounds to Lambda(M), will be more useful in gravitational waveform modeling than other suggested approaches.