Monopolar and quadrupolar gravitational radiation from magnetically deformed neutron stars in modified gravity

Some modified theories of gravity are known to predict monopolar, in addition to the usual quadrupolar and beyond, gravitational radiation in the form of `breathing' modes. For the same reason that octupole and higher-multipole terms often contribute negligibly to the overall wave strain, monopole terms tend to dominate. We investigate both monopolar and quadrupolar continuous gravitational radiation from neutron stars deformed through internal magnetic stresses. We adopt the Parameterised-Post-Newtonian formalism to write down equations describing the leading-order stellar properties in a theory-independent way, and derive some exact solutions for stars with mixed poloidal-toroidal magnetic fields. We then turn to the specific case of scalar-tensor theories to demonstrate how observational upper limits on the gravitational-wave luminosity of certain neutron stars may be used to place constraints on modified gravity parameters, most notably the Eddington parameter $\gamma$. For conservative, purely poloidal models with characteristic field strength given by the spindown minimum, upper limits for the Vela pulsar yield $1-\gamma \lesssim 4.2 \times 10^{-3}$. For models containing a strong toroidal field housing $\sim 99\%$ of the internal magnetic energy, we obtain the bound $1- \gamma \lesssim 8.0 \times 10^{-7}$. This latter bound is an order of magnitude tighter than those obtained from current Solar system experiments, though applies to the strong-field regime.