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

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.

jjhermes

October 30, 2012
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  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!

    View Slide

  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!

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  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!

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  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!

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  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

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  6. J0651: A 12.75-Minute WD+WD Binary
    Earth
    Moon

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  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  

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  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  

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  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)!

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  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)!

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  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!

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  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"

    View Slide

  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:!

    View Slide

  14. January 2012: A Comparison of Methods

    View Slide

  15. J0651: An (O-C) by Eye

    View Slide

  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!

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  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…!

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  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.

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  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  

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  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  

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  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  

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  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?!

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  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!
    propagacore! surface!

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  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!

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  25. View Slide

  26. New RV Fit to Discovery Data

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  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

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