2014ApJ...790...82L

The pulsar triple system J0337+1715 is remarkably regular and highly hierarchical. Secular interactions transfer angular momentum between inner and outer orbits unless their apsidal lines are parallel or anti-parallel. These choices correspond to orthogonal eigenmodes p and are characterized by e_p, 1_/ep, 2_∼ a₁/a₂ and e_a, 1_/ea, 2_∼ (a₁/a₂)^–3/2(m₂/m₁). Mode p dominates the current state so e₁/e₂remains close to e_p, 1_/ep, 2_. A small contribution by Mode a causes e₁and e₂to oscillate with a period of ∼10³ yr which should be apparent in a few years. These will reveal the effects of general relativity, and possibly the distortion of the inner white dwarf (WD). Phinney proposes that the epicyclic energy of a WD-pulsar binary reaches equipartition with the kinetic energy of a single convective eddy when the WD's progenitor fills its Roche lobe. We extend Phinney's theory to apply to modes rather than individual orbits. Thus we predict that Mode p and Mode a achieved equipartition with eddies in the giant envelopes of the progenitors of the outer and inner WD, respectively. The most effective eddies are those with lifetimes closest to the orbit period. These were far more energetic in the progenitor of the outer WD. This explains why Mode p overwhelms Mode a, and also why the inner binary's orbit is far more eccentric than orbits of other WD-pulsar binaries with similar orbit periods. Mode a's small but finite amplitude places a lower bound of Q ∼ 10⁶ on the tidal quality parameter of the inner WD.