Orbital Decay from Gravitational Wave Radiation in a 12.75-min WD+WD Binary

70d4f7eb14525537a3fd6c15a33a8ac1?s=47 jjhermes
October 30, 2012

Orbital Decay from Gravitational Wave Radiation in a 12.75-min WD+WD Binary

Seminar, 45 min. October 2012: Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA.

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jjhermes

October 30, 2012
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  1. 1.

    JJ Hermes! 2012 October 2930! SSP Seminar, Harvard-Smithsonian CfA! !

    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!
  2. 2.

    Motivation and Outline •  Merging binaries shed insight into a

    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!
  3. 3.

    Primer: Extremely Low-Mass (ELM) WDs •  MWD ≤ 0.25 M¤

    ! •  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!
  4. 4.

    The ELM Survey: 24+ Merger Systems •  SDSS color cuts

    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!
  5. 5.

    SDSS J065133.338+284423.37 (J0651) •  So far the most compact system

    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
  6. 7.

    J0651: A 12.75-Minute WD+WD Binary •  From April 2011 to

    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  
  7. 8.

    J0651: New Spectroscopy •  Better coverage has refined the Radial

    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  
  8. 9.

    J0651: New Photometry & Light Curve Fits •  Fixing the

    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)!
  9. 10.

    J0651: Gemini g - and r -band Photometry •  Fits

    to g-band and
 r-band data show
 the secondary
 contributes:! •  3.7 ± 0.2% of
 light in g-band! •  4.6 ± 0.6% of
 light in r-band! •  Primary (Panei et al. ʻ07):! –  Mg = 8.9 ± 0.1 mag! –  Mr = 9.2 ± 0.1 mag! •  Secondary:! –  Mg = 12.5 ± 0.2 mag! –  Mr = 12.5 ± 0.2 mag! –  T2 = 8700 ± 500 K, 700 Myr
 " " "(P. Bergeron WD cooling tracks)!
  10. 11.

    0.01 x R¤! 0.26 M¤ WD! 0.26 M¤ primary:! Model:!

    0.0337 R¤! (Panei et al. 2007)! Eclipses:! 0.0371 ±! 0.0011 R¤! 3.2% oblate! ! ! ! 0.50 M¤ secʼd:! Eclipses:! 0.0142 ±! 0.0010 R¤ ! 0.50 M¤ WD!
  11. 12.

    J0651: Evolution of Mid-Eclipse Times •  Fixing all LC parameters,

    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"
  12. 13.

    J0651: Evolution of Ellipsoidal Variations •  Instead of using the

    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:!
  13. 16.

    We Continue to Monitor J0651 •  We obtained another 9

    hr in Sept. 2012 and 11 hr in Oct. 2012: Our observations are still consistent with GR to the 1-σ level! 1 Jan 2012! 1 July 2012! 1 July 2011!
  14. 17.

    Expected Rate of Orbital Period Change •  GR prediction from

    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…!
  15. 18.

    Expected Rate of Orbital Period Change •  Tidal torques should

    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.
  16. 19.

    Discovery of g -mode Pulsations in ELM WDs •  In

    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  
  17. 20.

    A New Class of He-core DAVs (ZZ Ceti Stars) mes

    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  
  18. 21.

    J1840: The First Pulsating ELM WD •  Non-adiabatic pulsation models

    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  
  19. 22.

    An Extended DAV Instability Strip •  We are beginning to

    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?!
  20. 23.

    An Extended DAV Instability Strip •  Weʼve now re-motivated the

    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!
  21. 24.

    Summary: The Relativistic WD+WD J0651 •  We have detected rapid

    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!
  22. 25.
  23. 27.

    Table of System Parameters Gravity Darkening, Primary ! ! β1

    = 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