Scalar emission from binary neutron stars in scalar-tensor theories with kinetic screening

Abstract

We investigate the scalar emission from binary neutron stars in shift-symmetric scalar-tensor theories with kinetic screening ($K$-essence), using 3+1 numerical simulations in the decoupling limit. To construct static binary initial data in the regime where the screening radius $r_{\ast }$ greatly exceeds the orbital separation, we introduce a hyperbolization of the static field equations that bypasses the Keldysh-type breakdown affecting direct time evolutions. For equal-mass binaries, where the scalar emission is dominated by the $\ell =m=2$ mode, kinetic screening acts non-monotonically on the scalar radiation, suppressing or enhancing the quadrupolar amplitude depending on the relative size of $r_{\ast }$ and ${\lambda }_{22}$ (with ${\lambda }_{22}$ the wavelength): for ${\lambda }_{22}\ll r_{\ast }$ it is suppressed relative to the Fierz-Jordan-Brans-Dicke (FJBD) case, while for ${\lambda }_{22}\gtrsim r_{\ast }$ it is amplified above FJBD. For unequal-mass binaries a scalar dipole re-emerges, growing linearly with the mass asymmetry, while the quadrupolar screening remains close to the equal-mass case down to mass ratios $\sim 0.6$. The non-monotonic behavior of kinetic screening that we uncover has potential implications for gravitational-wave-based tests of gravity. The relativistic double pulsar, in particular, requires $r_{\ast }\gg 10^9$~km to efficiently suppress the scalar quadrupole; for cosmologically-motivated $\Lambda$, $r_{\ast }\sim 10^{11}$~km (for a solar-mass source), giving only moderate suppression.