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Quasiequilibrium sequences of binary neutron stars undergoing dynamical scalarization

We calculate quasiequilibrium sequences of equal-mass, irrotational binary neutron stars (BNSs) in a scalar-tensor (ST) theory of gravity that admits dynamical scalarization. We model neutron stars with realistic equations of state (notably through piecewise polytropic equations of state). Using these quasiequilibrium sequences we compute the binary's scalar charge and binding energy versus orbital angular frequency. We find that the absolute value of the binding energy is smaller than in general relativity (GR), differing at most by ~14% at high frequencies for the cases considered. We use the newly computed binding energy and the balance equation to estimate the number of gravitational-wave (GW) cycles during the adiabatic, quasicircular inspiral stage up to the end of the sequence, which is the last stable orbit or the mass-shedding point, depending on which comes first. We find that, depending on the ST parameters, the number of GW cycles can be substantially smaller than in GR. In particular, we obtain that when dynamical scalarization sets in around a GW frequency of ~130 Hz, the sole inclusion of the ST binding energy causes a reduction of GW cycles from ~120 Hz up to the end of the sequence (~1200 Hz) of ~11% with respect to the GR case. We estimate that when the ST energy flux is also included the reduction in GW cycles becomes of ~24%. Quite interestingly, dynamical scalarization can produce a difference in the number of GW cycles with respect to the GR point-particle case that is much larger than the effect due to tidal interactions, which is on the order of only a few GW cycles. These results further clarify and confirm recent studies that have evolved BNSs either in full numerical relativity or in post-Newtonian theory, and point out the importance of developing accurate ST-theory waveforms for systems composed of strongly self-gravitating objects, such as BNSs.