increase the rate of orbital decay in J0651! – High-amplitude ellipsoidal variations show the primary nearly tidally locked! – Additional angular momentum is lost from the orbit to spin-up the WDs to remain synchronized, leading to of order 5% faster rate of orbital decay
(Piro 2011, Benaquista 2011)! • This spin-up depends on the tidal forcing efﬁciency of the WDs! • Can parameterize as
Q, tidal quality factor,
but that value is relatively
unconstrained! • We have another way
at exploring g-modes
in He-core WDs…! Fuller & Lai 2011, MNRAS 421 426 Piro 2011, ApJL 740 L53 Benaquista 2011, ApJL 740 L54 show numerical integrations of equa- , using the mass and radii appropriate dal Q parameters are set to be constant and Q2 = 2 × 107, so as to give heat- 765 s that are the same as the present ach star. The WDs are assumed to be ially at a large orbital period, but are kly spun up by tides until dσ/dt ≈ 0 is nt with the assumptions for my analytic integration ends when the Roche-lobe WD becomes equal to its radius, which 20 s (ignoring potential changes to R1 ing). The He WD is spinning signiﬁ- y than the orbital period because of its ertical dotted line denotes the current 1 at 800, 000 yr before merger. If the ain constant, the luminosity of the He a factor of ∼ 15 before tidal disruption. el of Figure 2, I calculate the rotational imary V1 = Ω1R1, as a function of or- en the values of Q are chosen to match osities, V1 ≈ 120 km s−1. Another case = 107 is also plotted, which represents hen the WDs are nearly tidally locked, 200 km s−1. Since the binary is eclips- e between these cases may be measur- iter-McLaughlin eﬀect (Groot 2011). consequence of the tidal interactions is period derivative deviates from what is ystem is purely driven by gravitational ing equation (7), gravitational waves 0−4M M M−1/3P−5/3 s yr−1, Fig. 1.— The binary evolution as a function of time, using Q1 = 7 × 1010 and Q2 = 2 × 107. Masses and radii are chosen to match J0651. The top panel shows the spin period of each star. The orbital period of the binary is nearly equal to the spin period of the C/O WD (dashed line) and thus is not plotted. The middle panel plots the tidal heating rate for each star, and the bottom panel shows the surface eﬀective temperatures. The vertical dotted line shows the current location of J0651.