Mukremin Kilic, Warren Brown, D. E. Winget, Carlos Allende Prieto, Alex Gianninas, Anjum S. Mukadam, Antonio Cabrera-Lavers, Scott J. Kenyon, John W. Kuehne, K. I. Winget, E. L. Robinson, Paul A. Mason, Samuel T. Harrold!

multitude of astrophysical phenomena, most importantly SNe Ia scenarios • We have discovered a 12.75-min detached, eclipsing WD+WD binary, J0651 – This system will come into contact in ~1 Myr – We see evidence that its orbit is shrinking rapidly, consistent with (albeit a bit faster than) expectations of gravitational wave emission – This is the best known verification binary for grav. wave direct detection – We can also explore the role of tides on binary mergers, which depend on the WD interiors; our new pulsating He-core WDs will probe these interiors D. Berry, GSFC!

! • The Galaxy is not old enough to produce isolated ELM WDs! • Binary interaction drives mass loss, preventing core He ignition! – “Low-Mass White Dwarfs Need Friends” (Marsh et al. 1995)! – > 90% binary fraction for ELM WDs! • Many are companions to pulsars (especially MSPs)! – J1012+5307 (van Kerkwijk, Bergeron & Kulkarni 1996), J1911−5958A (Bassa et al. 2006), J0437−4715 (Durant et al. 2012), etc.! • Several found recently with eclipsing WD companions! – NLTT 11748 (Steinfadt et al. 2010), CSS 41177 (Parsons et al. 2011), GALEX J1717+6757 (Vennes et al. 2011)! David A. Aguilar, CfA!

yield targets, 6.5m MMT & 1.5m FLWO yield spectra! – 15 < g0 < 20 mag! – ~70% complete through DR4! • 40+ ELM WDs, 24 of which will merge within tHubble ! • So far 3 systems have orbital periods under an hour:! – 39.8-min (J1630, Kilic et al. 2011 MNRAS 418 L157)! – 39.1-min (J0106, Kilic et al. 2011 MNRAS 413 L101)! – 12.75-min (J0651, Brown et al. 2011 ApJ 737 L23)! • These are strong gravitational wave sources! Brown et al. 2012, ApJ 744 142 Kilic et al. 2012, ApJ 751 141 Hermes et al. 2012, ApJ, 749, 42!

from the ELM Survey: 12.75-min! • Discovered 2 Mar 2011 on the 6.5 m MMT! • Back-to-back spectra over 6 min showed >1200 km s-1 RV shift! • Wealth of photometric information:! – Primary (~15%) and secondary (~4%) eclipses! – Ellipsoidal variations from tides on the primary (~5%)! – Relativistic beaming (~0.5%)! Brown et al. 2011, ApJL 737 L23 Figure 2. Best-ﬁt WD model atmosphere (dotted line) compared to broadband photometry (dots). The ultraviolet, optical, and near-infrared m our spectroscopic ﬁt for a 0.25 M WD. Figure 3. Radial velocity observations phased to the 765 s orbital period. The best-ﬁt orbit (dotted line) has a 1314.6 km s−1 velocity amplitude speed of light. 3 The Astrophysical Journal Letters, 737:L23 (6pp), 2011 August 10 Figure 4. J0651 light curve. The upper panel plots the observed photometry vs. orbital phase, while the lower panel compares the binned data

May 2012, we obtained an additional 197.4 hr of observations:! – Spectroscopy:! • 79 x 90 s spectra on the MMT 6.5 m! – Photometry:! • 196.8 hr from Argos on the McDonald 2.1 m! • 3.0 hr from Agile on the APO 3.5 m! • 6.8 hr from GMOS-N on the Gemini-North 8.1 m! • 2.5 hr from OSIRIS on the GTC 10.4 m! Hermes et al. 2012, ApJL 757 L21

Velocity semi-amplitude:! – K = 616.9 ± 5.0 km s−1" – Must include 2.3% K correction factor (each 90 s spectra ~12% of orbit)! – This is smaller than our original determination, K = 657 ± 14 km s−1! • Fits to 79 phased, summed spectra with S/N ~ 78 per resolution element:! – 16,530 ± 200 K, log g = 6.76 ± 0.04 (models of Tremblay & Bergeron 2009)! – M1 à 0.25 M¤ (Panei et al. 2007)! Hermes et al. 2012, ApJL 757 L21

limb- and gravity darkening coefﬁcients we get from light curve ﬁts:! – R1 = 0.0371 ± 0.0012 R¤ ! ! !R2 = 0.0142 ± 0.0010 R¤ "" – Inc. = 84.4 ± 2.3 deg! ! !M2 = 0.50 ± 0.04 M¤ " " "M1 = 0.26 ± 0.04 M¤ " Our 8.1 m Gemini-N and 10.4 m GTC data, folded at orbital period (top) and binned (below) with our best model ! Fits using JKTEBOP (Southworth et al. 2004)!

we ﬁt only for the mid-eclipse times! • We compare observed (O) mid-eclipse times to calculated (C) times that assume a ﬁxed period to make an (O-C) diagram:! rom McDonald Observatory, which yields (−8.2±3.2)×10 −12 s s −1 . arameters from our analysis in Section 3 and ﬁt each ubset of observations only for the mid-eclipse time near- st the mean time of the observations. Following Kepler et al. (1991), if the orbital period is hanging slowly with time, we can expand the observed mid-time of the Eth eclipse, tE , in a Taylor series around E0 to arrive at the classic (O − C) equation O − C = ∆T0 + ∆P0 E + 1 2P0 ˙ PE2 + ... where T0 is the mid-time of the ﬁrst eclipse, ∆T0 is the ncertainty in this mid-point, P0 is the orbital period at he ﬁrst eclipse and ∆P0 is the uncertainty in this period. Any secular change in the period, dP/dt, will cause a arabolic curvature in an (O − C) diagram. Currently, he acceleration in the period change, d(dP/dt)/dt, is egligible, and we will limit our discussion to a second- rder polynomial ﬁt. To construct an (O − C) diagram, we must ﬁrst de- ermine T0 and P0 . A preliminary estimate comes from simple Fourier transform of our whole data set, which we use to create an initial (O − C) diagram. We then it- ratively adjust T0 and P0 by the zeroth- and ﬁrst-order erms from our best-ﬁt parabola until the adjustments re smaller than the error in these terms; these errors re- ult from the covariance matrix. Our recomputed, ﬁnal O−C) diagram uses this new ephemeris and period and P0 = 765.206543(55) s"

mid-eclipse times, we can follow the phase of the ellipsoidal variations by ﬁtting a series of sine curves at the orbital period and its harmonics to calculate a model-independent (O-C) diagram at the half-orbital period:!

gravitational waves: !(-8.2 ± 1.7) x 10-12 s s-1" – Uncertainty dominated by estimates of M1 , M2! • Observed from mid-eclipse times: ! !(-9.8 ± 2.8) x 10-12 s s-1! – Including Sep/Oct 2012 (O-C) points:! ! !(-11.4 ± 1.7) x 10-12 s s-1! – Using only Argos data for timing consistency: !(-11.2 ± 1.9) x 10-12 s s-1! • Our observations conﬁrm this system is a proliﬁc emitter of gravitational waves & establish this is an excellent optical clock! – J0651 has provided the cleanest optical detection of gravitational radiation! • After the 5.4-min AM CVn system HM Cnc, J0651 is the second- strongest gravitational wave source known: eLISA would detect this with S/N > 4 within a week and S/N > 100 within a year! – We have already constrained the orbital frequency to better than 10-7 mHz: forb = 1.30683671(9) mHz ! • This system is also an excellent laboratory for testing tidal effects on merging binaries…!

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.

the last year we have discovered the ﬁrst 3 pulsating ELM WDs! • Asteroseismology of these hydrogen-atmosphere WDs offers a unique opportunity to probe the interior of He-core WDs! • With enough modes to match the models, we can constrain their overall mass, hydrogen layer mass, surface temperature, core composition, convection zones, and test whether they are tidally synchronized! Hermes et al. 2012, ApJL 750 L28 Hermes et al. 2012, submi.ed

et al. TABLE 4 Properties of the Three Known Pulsating ELM WDs Property Value Property Value SDSS J184037.78+642312.3 Teﬀ 9390 ± 140 K log g 6.49 ± 0.06 Mass ∼0.17 M⊙ Porb 4.5912 ± 0.001 hr Periods 2094 − 4890 s Max Amp. > 5.1% SDSS J111215.82+111745.0 Teﬀ 9590 ± 140 K log g 6.36 ± 0.06 Mass ∼0.17 M⊙ Porb 4.1395 ± 0.0002 hr Periods 107.6 − 2855 s Max Amp. > 0.7% SDSS J151826.68+065813.2 Teﬀ 9900 ± 140 K log g 6.80 ± 0.05 Mass ∼0.23 M⊙ Porb 14.624 ± 0.001 hr Periods 1335 − 3848 s Max Amp. > 3.5% al. 1983; Starrﬁeld et al. 1983; Hansen et al. 1985). How- ever, despite exhaustive searches (e.g. Robinson 1984; • All three new pulsating ELM WDs have high-amplitude, multiperiodic brightness variations! – These are temperature variations on the surface of the WD, driven to observability by a hydrogen partial ionization zone! Hermes et al. 2012, ApJL 750 L28 Hermes et al. 2012, submi.ed

conﬁrm the periods seen in J1840 are unstable and thus probably g-modes! • These are likely high radial-order (deep) modes! – The 4698 s dominant mode has 43 < k < 46! – Typical C/O-core DAVs: 1 < k < 10 ! Hermes et al. 2012, ApJL 750 L28 Corsico et al. 2012, arXiv: 1209.5108

establish an empirical instability strip for the He-core, pulsating ELM WDs! • These are not tidally induced pulsations; the driving is most likely similar to the C/O-core DAVs (ZZ Ceti stars)! • Are these new ELM WDs an extension of the “pure” C/O instability strip?!

theorists to pulsate He-core WDs! – Córsico et al. in Argentina and Fontaine et al. in Montreal are independently working on this problem their own evolutionary models! – In Austin we are actively working with MESA to model He-core WDs! propaga<on diagrams from Córsico et al. 2012, arXiv: 1209.5107 core! surface!

orbital decay in a 12.75-minute WD+WD binary, conﬁrming the system emits gravitation waves! – Observed rate of orbital decay: !(–11.4 ± 1.7) x 10-12 s s-1! – Expected rate from solely GR: !(–8.2 ± 1.7) x 10-12 s s-1! • Follow-up observations have constrained the system parameters:! – M1 = 0.26 ± 0.04 M¤ ! ! !M2 = 0.50 ± 0.04 M¤ ! – R1 = 0.0371 ± 0.0012 R¤ ! !R2 = 0.0142 ± 0.0010 R¤ ! – T1 = 16,530 ± 200 K ! ! !T2 = 8700 ± 500 K! • We will continue monitoring this system: The mid-eclipse time have already shifted by ~15 s as compared to April 2011! – Further observations will explore the difference between pure gravitational wave losses and tides, as the stars are spun-up to remain synchronized! – This tidal efﬁciency is sensitive to the internal ELM WD composition! • Our newfound pulsating ELM WDs will allow us to explore g-mode pulsations in He-core WDs! – We can perform asteroseismology to explore their interior structure!

= 0.36! Gravity Darkening, Secondary ! ! β2 = 0.36! The Astrophysical Journal Letters, 757:L21 (6pp), 2012 October 1 Table 1 System Parameters Parameter Value (Method used to derive parameter) Orbital period (phot.) 765.206543(55) s K1 (corrected for smearing) (spec.) 616.9 ± 5.0 km s−1 γvel (spec.) −7.7 ± 4.5 km s−1 Primary Teff (spec.) 16530 ± 200 K Primary log g (spec.) 6.76 ± 0.04 Primary Mass (M1) (phot.) 0.26 ± 0.04 M Primary Radius (R1) (phot.) 0.0371 ± 0.0012 R Inclination (i) (phot.) 84.4 ± 2.3 deg Mass ratio (q) (phot., spec.) 1.92 ± 0.46 Secondary mass (M2) (spec.) 0.50 ± 0.04 M Secondary Teff (phot.) 8700 ± 500 K Secondary radius (R2) (phot.) 0.0142 ± 0.0010 R Limb darkening, primary, g band c1 = −0.106, c2 = 0.730 Limb darkening, secondary, g band c1 = −0.128, c2 = 0.898 Limb darkening, primary, r band c1 = −0.076, c2 = 0.562 Limb darkening, secondary, r band c1 = −0.099, c2 = 0.735 smearing should be at its minimum). For these spectra at quadrature, we ﬁnd that Teff is 500 K lower and log g is 0.07 dex higher. These differences reﬂect our systematic error, this best-ﬁt m R2 = 0.0142 (Wood 1995), primary radiu surface gravity but consistent using the Pane Finally, we luminosity an and gravity-da and compone secondary con 4.6% ± 0.6% Adopting M for the 0.26 M thus has Mg cooling mode the secondary 700 Myr (Holb Tremblay et a 4. DET We demons by constructin