Gravitational waveforms and radiation powers of the triple system PSR J0337+1715 in modified theories of gravity

In this paper, we study the gravitational waveforms, polarizations and radiation powers of the first relativistic triple systems PSR J0337 + 1715, observed in 2014, by using the post-Newtonian approximations to their lowest order. Although they cannot be observed either by the current or the next generation of the detectors, they do provide useful information to test different theories of gravity. In particular, we carry out the studies in three different theories, General Relativity (GR), Einstein-aether theory (ae-theory), and Brans-Dicke (BD) gravity. The tensor modes h(+) and h(x) exist in all three theories and have almost equal amplitudes. Their frequencies are all peaked at two locations, f(1)(+,x) = 0.068658 mu Hz and f(2)(+,x) = 14.212 mu Hz, which are about twice the outer and inner orbital frequencies of the triple system, as predicted in GR. In ae-theory, all of the six polarization modes are different from zero, but the breathing (h(b)) and longitudinal (h(L)) modes are not independent and also peaked at two frequencies. A somehow surprising result is that, for h(b) and h(L), the peaked frequencies are not twice the outer and inner orbital frequencies, as for the h(+) and h(x) modes, but, instead, they are almost equal to them, f(1)(b,L) = 0.045772 mu Hz and f(2)(b,L) = 7.0947 mu Hz. A similar phenomenon is also observed in BD gravity, in which only the three modes h(+), h(x), and h(b) exist, where f(1)(b) and f(2)(b) are almost equal to outer and inner orbital frequencies. We also study the radiation powers, and find that the quadrupole emission in each of the three theories has almost the same amplitude, but the dipole emission can be as big as the quadrupole emission in ae-theory. This provides a very promising window to obtain severe constraints on ae-theory by the multiband gravitational wave astronomy.