Scalar emission from neutron star-black hole binaries in scalar-tensor theories with kinetic screening

We explore scalar radiation from neutron star-black hole binaries in scalar-tensor theories with kinetic screening ($K$-essence). Using $3+1$ numerical relativity simulations in the decoupling limit, we investigate scalar dipole and quadrupole radiation for different values of the strong coupling constant $\mathrm{\ensuremath{\Lambda}}$. Our results show that kinetic screening effectively suppresses the scalar dipole radiation as $\mathrm{\ensuremath{\Lambda}}$ decreases. This is validated by comparing to analytic predictions for the screening of dipole scalar emission, with which our numerical results show good agreement. However, our numerical simulations show that the suppression of scalar quadrupole radiation is less efficient, even when the screening radius exceeds the wavelength of the emitted radiation. In fact, the dependence of the scalar quadrupole amplitude on $\mathrm{\ensuremath{\Lambda}}$ flattens out for the smallest $\mathrm{\ensuremath{\Lambda}}$ that we can simulate, and the quadrupole amplitude is suppressed only by a factor $\ensuremath{\lesssim}3$ relative to the Fierz-Jordan-Brans-Dicke case. Overall, our study shows that scalar quadrupole radiation from mixed binaries may be used to place constraints on $K$-essence theories with next-generation gravitational-wave detectors.