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Rolling in their Graves: White Dwarf Rotation and the Endpoints of Angular Momentum Evolution

jjhermes
October 19, 2017

Rolling in their Graves: White Dwarf Rotation and the Endpoints of Angular Momentum Evolution

Colloquium, 45 min. October 2017: The Ohio State University, Columbus, OH.

jjhermes

October 19, 2017
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  1. http://jjherm.es
    J.J. Hermes
    Hubble Fellow
    University of North Carolina
    at Chapel Hill
    Rolling in their Graves: White Dwarf
    Rotation and the Endpoints of Angular
    Momentum Evolution

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  2. Rolling in their Graves: White Dwarf
    Rotation and the Endpoints of Angular
    Momentum Evolution
    U. North Carolina: Chris Clemens, Bart Dunlap, Erik Dennihy, Josh Fuchs, Stephen Fanale
    U. Warwick: Boris Gaensicke, Roberto Raddi, N. P. Gentile Fusillo, P.-E. Tremblay, Paul Chote
    U. Texas: Keaton J. Bell, Mike Montgomery, Don Winget, Zach Vanderbosch
    + Steve Kawaler, Judi Provencal, Agnes Bischoff-Kim, S.O. Kepler, Alejandra Romero

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  3. Solar Dynamics Observatory

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  4. BiSON; Thompson et al. 2003
    25 d
    30 d
    35 d
    tachocline
    surface
    core
    5 min 4 min
    6 min

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  5. J ∝
    MR2
    Prot
    M = 1.0 M¤
    R = 1.0 R¤
    Prot
    ~ 27 d
    Sun
    White dwarf
    M = 0.55 M¤
    R = 0.01 R¤
    Expect Prot
    ~min
    If the Sun perfectly conserved
    its angular momentum…

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  6. How fast to white dwarfs rotate?
    Are they differentially rotating?
    White dwarfs serve as empirical
    final boundary conditions
    on stellar evolution

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  7. g-modes—remarkably similar to the large-amplitude DAV pulsators (Winget et al. 19
    The observed pulsating white dwarf stars lie in three strips in the H-R diagram,
    in Figure 3. The pulsating pre-white dwarf PG 1159 stars, the DOVs, around 7
    170,000 K have the highest number of detected modes. The first class of pulsating
    5.5 5.0 4.5
    Planetary Nebula
    Main
    sequence
    DOV
    DBV
    DAV
    4.0 3.5 3.0
    log [T
    eff
    (K)]
    4
    2
    0
    –2
    –4
    log (L/L )
    Figure 3
    A 13-Gyr isochrone with z = 0.019 from Marigo et al. (2007), on which we have drawn the obs
    Annu. Rev. Astro. Astrophys. 2008.46:157-199. Downloaded fr
    by University of Texas - Austin on 01/28/09. For
    Winget & Kepler 2008
    H
    He
    C/O
    Pulsating white dwarfs are only found in
    narrow instability strips set by temperature

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  8. Mike Montgomery
    White dwarfs pulsate:
    periodic brightness changes,
    caused by surface
    temperature variations
    Nonradial g-modes with
    periods of 100-1400 s
    Spherical star:
    spherical harmonics!
    hotter
    cooler

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  9. m = +1
    m = -1
    m = 0
    1000 s 200 s
    500 s 125 s
    316.8 s
    345.3 s
    n = Number of radial nodes
    l = Number of vertical nodes
    m = Number of horizontal + vertical nodes
    n
    l = 1
    n = 5
    l = 1
    n = 6
    Prot
    = 0.9
    ± 0.2 day
    Data from a “typical” pulsating
    white dwarf

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  10. Giammichele et al. 2015
    The view from one
    telescope on the ground
    18.9 hr over 5 nights on
    3.6-m CFHT on Mauna Kea:
    1.57-d rotation in the star
    Ross 548
    V = 14.2 mag
    Actual signal

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  11. E. L. Robinson
    Nather et al. 1990
    Gaps in data cause
    cycle-count confusion
    (aliasing)

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  12. PG1159-035, V=14.9 mag -- poster child for WET
    (March 1989, 9 sites, 15 observers, 90.8% duty cycle over 12.0 days)
    Winget et al. 1991
    l = 1 l = 2

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  13. Original Kepler Mission (4 years):
    Just 20 white dwarfs observed,
    6 pulsating WDs (just two >3 months)
    K2 through Campaign 13:
    >1200 white dwarf candidates observed
    53 more pulsating WDs
    now >55 pulsating WDs with space data!
    K2 has given us hundreds of
    candidate pulsating white
    dwarfs to observe

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  14. PG1159-035, V=14.9 mag -- poster child for WET
    (March 1989, 9 sites, 90.8% duty cycle over 12.0 days)
    SDSSJ0106+0145, g=16.2 mag -- typical K2 light curve
    (K2 Campaign 8, 96.0% duty cycle over 78.7 days)
    Winget et al. 1991 Hermes et al. 2017d: k2wd.org
    l = 1 l = 2
    l = 2
    l = 2
    l = 1
    l = 1

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  15. K2 is helping us answer big
    questions about white dwarfs:
    • How thick are the outer
    H/He layers?
    • What’s the carbon/oxygen
    ratio in the core?
    • How can the pulsations
    help us understand
    convection?
    A ‘typical’ white dwarf
    electron degenerate
    C/O core
    (r = 8500 km)
    non-degenerate
    He layer
    (260 km) non-degenerate
    H layer
    (30 km)
    [thermal reservoir]
    [insulating blanket]

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  16. Mode Identification -> Rotation Falls Readily from K2 Data
    Hermes et al. 2017d
    k2wd.org

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  17. 1 10 100
    White Dwarf Rotation Period (hr)
    0
    2
    4
    6
    8
    10
    N
    Kepler & K2
    Kawaler (2015)
    Most isolated white
    dwarfs rotate between
    0.5-2.2 days
    Hermes et al. 2017d: k2wd.org
    None of the stars are
    currently in binaries:
    Representative of
    single-star evolution
    Mode Identification -> Rotation Falls Readily from K2 Data
    0.5 d 1 d 2 d 4 d

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  18. 5.5 5.0 4.5
    Planetary Nebula
    Main
    sequence
    DOV
    DBV
    DAV
    4.0 3.5 3.0
    log [T
    eff
    (K)]
    4
    2
    0
    –2
    –4
    log (L/L )
    Sun (1.0 M¤
    )
    vrot
    ~ 2 km/s
    (solid body)
    Main Sequence
    (Core H burning)
    ~Solid body rotation
    A stars (2.5 M¤
    )
    vrot
    ~ 200 km/s
    (solid body, Kurtz+ 2015)
    The Rotational
    Evolution of
    1-3 M¤
    stars Red Giants
    (Shell H burning)
    Differential rotation
    1.0-2.0 M¤
    RGB
    vrot
    ~ 2 km/s @ surface
    vrot
    ~ 20 km/s @ core
    e.g., Mosser+ 2012

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  19. Red giants pulsations
    propagate in both the
    core and envelope

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  20. Mosser et al. 2012
    Pulsations of red giants probe deeply – below 0.01 Rstar
    The cores of first-ascent red giants are rotating ~10 times faster
    than surface
    But the cores are
    slowing down
    as they contract!

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  21. There is a missing angular momentum transport process that couples
    contracting red giant cores to their surface – i.e., missing physics
    Cantiello et al. 2014
    observed (Mosser+ 2012)
    plus Taylor-Spruit (magnetic
    torques from dynamo-driven
    fields in radiative regions)
    with hydrodynamic rotational
    instabilities (Heger+ 2000)
    R-2
    Internal gravity waves also insufficient (Fuller+ 2014)

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  22. 5.5 5.0 4.5
    Planetary Nebula
    Main
    sequence
    DOV
    DBV
    DAV
    4.0 3.5 3.0
    log [T
    eff
    (K)]
    4
    2
    0
    –2
    –4
    log (L/L )
    Sun (1.0 M¤
    )
    vrot
    ~ 2 km/s
    (solid body)
    Main Sequence
    (Core H burning)
    ~Solid body rotation
    A stars (2.5 M¤
    )
    vrot
    ~ 200 km/s
    (solid body, Kurtz+ 2015)
    The Rotational
    Evolution of
    1-3 M¤
    stars Red Giants
    (Shell H burning)
    Differential rotation
    1.0-2.0 M¤
    RGB
    vrot
    ~ 2 km/s @ surface
    vrot
    ~ 20 km/s @ core
    e.g., Mosser+ 2012
    Red Clump
    (Core He burning)
    Less differential rotation
    2.2-2.9 M¤
    clump stars
    e.g., Deheuvels+ 2015

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  23. Isolated core He-burning giants
    (2-3 M¤
    ) have cores rotating slightly
    faster than their envelopes
    Deheuvels et al. 2015
    10 100
    Secondary Clump Rotation Period (d)
    0
    1
    2
    3
    4
    5
    6
    7
    8
    N
    Deheuvels et al. 2015
    Tayar et al., in prep.
    Jamie Tayar et al. 2017, in prep.
    Red clump core rotation rates
    range from ~30-180 days
    towards core
    towards surface
    slower
    faster

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  24. 1
    WD R
    0.4
    0.5
    0.6
    0.7
    0.8
    0.9
    WD Mass (M⊙
    )
    1 10 100
    White Dwarf Rotation Period (hr)
    0
    2
    4
    6
    8
    10
    N
    Kepler & K2
    Kawaler (2015)
    WD cavity
    ~0.005-0.013 R¤
    10 100
    Secondary Clump Rotation Period (d)
    0
    1
    2
    3
    4
    5
    6
    7
    8
    N
    Deheuvels et al. 2015
    Tayar et al., in prep.
    Clump RGB cavity
    ~0.02-0.10 R¤
    White dwarfs rotate within a factor of two
    of expected conserving internal rotation of
    core He-burning giants
    Prot
    : 30-180 d
    Prot
    : 0.2-5 d

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  25. 1 10 100
    White Dwarf Rotation Period (hr)
    0
    2
    4
    6
    8
    10
    N
    Kepler & K2
    Kawaler (2015)
    Most isolated white
    dwarfs rotate between
    0.5-2.2 days
    Hermes et al. 2017d: k2wd.org
    Hard upper limit of 4.5 d
    (sensitive up to 40 d Prot
    )
    Mode Identification -> Rotation Falls Readily from K2 Data
    0.5 d 1 d 2 d 4 d

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  26. Kp
    = 18.9 mag
    The most rapidly rotating pulsating WD is massive
    SDSS
    Hermes et al. 2017c
    500 s 200 s 118 s
    Nyquist
    ambiguity
    EPIC 211914185

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  27. The most rapidly rotating pulsating WD is massive
    500 s 200 s 118 s
    Hermes et al. 2017c
    Ground-based time-series photometry
    breaks Nyquist ambiguity
    EPIC 211914185

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  28. The most rapidly rotating pulsating WD is massive
    500 s 200 s 118 s
    Prot
    : 1.13 ± 0.02 hr
    Hermes et al. 2017c
    Ground-based time-series photometry
    breaks Nyquist ambiguity
    EPIC 211914185

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  29. The most rapidly rotating pulsating WD is massive
    SDSS
    Hermes et al. 2017c
    SOAR spectroscopy
    yields
    WD mass
    Teff
    : 13,590± 340 K
    log(g) = 8.434 ± 0.052
    MWD
    : 0.87 ± 0.03 M¤
    Using cluster-calibrated
    initial-to-final mass relation:
    MProg.
    : 4.0 ± 0.5 M¤
    The fastest-rotating
    pulsating white dwarf is
    also the most massive

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  30. 1 10 100
    WD Rotation Period (hr)
    0.4
    0.5
    0.6
    0.7
    0.8
    0.9
    WD Mass (M⊙
    )
    1.0
    1.5
    2.0
    2.5
    3.0
    3.5
    4.0
    ZAMS Progenitor Mass (M⊙
    )
    1 10 100
    White Dwarf Rotation Period (hr)
    0
    2
    4
    6
    8
    10
    N
    Kepler & K2
    Kawaler (2015)
    1 d 2 d 4 d
    We Can Finally Probe WD Rotation as a Function of Mass
    Hermes et al. 2017d: k2wd.org
    SOAR spectroscopy
    gets us WD masses

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  31. WDs from 1-3 M¤
    progenitors
    rotate at 0.5-2.2 d
    (WD Prot
    : 35 ± 28 hr)
    Link emerging between higher
    WD mass and faster rotation
    Hard upper limit at 4.5 d
    (sensitive up to 40 d Prot
    )
    1 10 100
    0
    1
    2
    3
    4
    N
    1.7 2.0 M ZAMS
    WD Prot = 1.48 ± 0.94 d
    1 10 100
    0
    1
    2
    3
    4
    N
    2.0 2.5 M ZAMS
    WD Prot = 1.35 ± 0.74 d
    1 10 100
    0
    1
    2
    3
    4
    N
    2.5 3.0 M ZAMS
    WD Prot = 1.32 ± 1.04 d
    1 10 100
    White Dwarf Rotation Period (hr)
    0
    1
    2
    3
    4
    N
    3.5 4.0 M ZAMS
    WD Prot = 0.17 ± 0.15 d
    We Can Finally Probe WD Rotation as a Function of Mass
    Hermes et al. 2017d: k2wd.org

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  32. Used to Be, Getting Data Required
    Going to the Telescope

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  33. *PG 1159 star = hot pre-white-dwarf (aka DOV)

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  34. Vauclair et al. 2002
    Maidanak Observatory,
    Uzbekistan
    2-week coordinated, global (14-site)
    Whole Earth Telescope run in 1994

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  35. THE MAIN LOG
    Observations at Maidanak observatory in Uzbekistan. Aug 1994
    Observers: E. Meistas, and local assistant Alexey V. Chernyshev

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  36. Jul 27th
    Uzbeks introduced new rules for the visas ... spent long
    8 night hours in the old stinking Russian bus, which,
    using longest possible route and stopping more than ten
    times for the repairs, after which passengers were
    supposed to push the bus to start the engine, brought us
    to Shakhrisabz.
    Jul 28th
    Old military jeep, which exhaust went more inside
    than via its pipes, after 5 hours brought us to
    Maidanak [Observatory]. ... Some windows of our
    living house were broken, no clean sheets ... no
    butter, meat, sugar. Running water system was not
    working anymore, not to mention hot water.
    THE MAIN LOG
    Observations at Maidanak observatory in Uzbekistan. Aug 1994
    Observers: E. Meistas, and local assistant Alexey V. Chernyshev

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  37. Jul 29th
    I checked telescope; tracking and positioning were
    working, but telescope mirrors needed cleaning...
    Jul 30th
    Managed to repair distiller and to get 3 L of water late
    in the evening only. Decided to wash mirrors next day.
    Still lots of yellow Afghanistan dust in the sky.
    Jul 31st
    Washed mirrors, cleaned telescope inner surfaces from
    thick dust layer. Started the full scale system test.
    THE MAIN LOG
    Observations at Maidanak observatory in Uzbekistan. Aug 1994
    Observers: E. Meistas, and local assistant Alexey V. Chernyshev

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  38. Aug 1st
    All day no clouds, but wind increasing to the
    evening. Worked all night.
    Aug 3rd
    All day clear sky with some clouds. Quite strong wind in
    day time but diminished before the night.
    THE MAIN LOG
    Observations at Maidanak observatory in Uzbekistan. Aug 1994
    Observers: E. Meistas, and local assistant Alexey V. Chernyshev

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  39. Aug 5th
    It was first night there on the mountain without me. I was
    at that time in Kitab Hospital severely injured by the
    Tashkent Astrophysical Institute Director son Iskander
    Yuldashbaev, apparently mentally ill young man of about 21.
    THE MAIN LOG
    Observations at Maidanak observatory in Uzbekistan. Aug 1994
    Observers: E. Meistas, and local assistant Alexey V. Chernyshev

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  40. Aug 5th
    It was first night there on the mountain without me. I was
    at that time in Kitab Hospital severely injured by the
    Tashkent Astrophysical Institute Director son Iskander
    Yuldashbaev, apparently mentally ill young man of about 21.
    He did some cleaning ... suddenly saying no words grabbed my
    hair with his left hand and hit my throat with a broken
    knife from our kitchen. I ran in horror, but he managed to
    hit me twice into my back. I ran to the Russian house for
    the help all in the blood. It was no phone connection with
    outside world and two of them had to run all the way to
    Maidanak to soldiers, and in three hours at last I was
    delivered to Kitab hospital in rather weak condition.
    THE MAIN LOG
    Observations at Maidanak observatory in Uzbekistan. Aug 1994
    Observers: E. Meistas, and local assistant Alexey V. Chernyshev

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  41. THE MAIN LOG
    Observations at Maidanak observatory in Uzbekistan. Aug 1994
    Observers: E. Meistas, and local assistant Alexey V. Chernyshev
    Aug 5th
    It was first night there on the mountain without me. I was
    at that time in Kitab Hospital severely injured by the
    Tashkent Astrophysical Institute Director son Iskander
    Yuldashbaev, apparently mentally ill young man of about 21.
    He did some cleaning ... suddenly saying no words grabbed my
    hair with his left hand and hit my throat with a broken
    knife from our kitchen. I ran in horror, but he managed to
    hit me twice into my back. I ran to the Russian house for
    the help all in the blood. It was no phone connection with
    outside world and two of them had to run all the way to
    Maidanak to soldiers, and in three hours at last I was
    delivered to Kitab hospital in rather weak condition.
    ... He is in a custody now and cannot say the reason either,
    says he did not like the way I looked at him. But he was
    smart enough to steal before that event good sum of my money
    ... Until helicopter arrived I explained the basics of the
    work with the quilt program to Alexey -- my assistant.
    Luckily I trained him on almost everything...

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  42. Aug 10th
    Alexey arrived from the Maidanak in the afternoon.
    Everything seems OK.
    Aug 11th Aug 12th
    I lived in the Russian hotel in Kitab ... working with
    data: writing logs, marking bad points. Tomorrow night
    Uzbeks promised to bring me to the Samarkand airport.
    My throat is swollen, still hurts and ugly.
    END OF CAMPAIGN HERE IN THE UZBEKISTAN
    ------------------------------------------------------------------------
    THE MAIN LOG
    Observations at Maidanak observatory in Uzbekistan. Aug 1994
    Observers: E. Meistas, and local assistant Alexey V. Chernyshev
    Aug 8th
    I ... practically defected from Kitab hospital, where
    black bugs were running on the walls at night even in
    the patient's beds, over the face too. Throat is badly
    swollen and hurts.

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  43. Today We Are Spoiled with
    Telescopes in Space

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  44. PG 0112+104: Hermes et al. 2017a
    l=1 modes l=2 modes
    The Most Evolved Test of Radial Differential Rotation
    PG 0112+104 is a ~31,000 K
    pulsating He-atmosphere WD
    (DBV)

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  45. The Most Evolved Test of Radial Differential Rotation
    l=1
    l=2
    PG 0112+104: Hermes et al. 2017a
    Splittings of l=1 and l=2 modes
    both indicate rotation period of
    10.1±0.9 hr in PG 0112+104
    Each pulsation mode is trapped to
    different depths in such a stratified
    star

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  46. We also see a surface spot
    Surface: 10.17404 hr
    Towards core: 10.18±0.27 hr
    The Most Evolved Test of Radial Differential Rotation
    Using l=1 and l=2 modes we
    measure a rotation period of
    Prot
    = 10.18 ± 0.27 hr
    l=1
    l=2
    PG 0112+104: Hermes et al. 2017a
    Giammichele et al. 2017, in prep.

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  47. Surface Spots Are Common on >3 MG Magnetic WDs
    Hermes et al. 2017b

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  48. 1 10 100
    White Dwarf Rotation Period (hr)
    0
    2
    4
    6
    8
    10
    N
    K2 Asteroseismic
    Asteroseismic
    K2 Magnetic
    Magnetic
    10.0 d
    2.0 d
    0.5 d
    5 hr
    1 hr
    10 min
    The long stare of K2 is helping us find many new spotted,
    even low-magnetic-field white dwarfs

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  49. 100 101 102
    White Dwarf Rotation Period (hr)
    0.6
    0.8
    1.0
    1.2
    1.4
    WD Mass (M )
    1 10 100
    White Dwarf Rotation Period (hr)
    0
    2
    4
    6
    8
    10
    N
    K2 Asteroseismic
    Asteroseismic
    K2 Magnetic
    Magnetic
    1 hr 0.5 d 10 d
    2.5 M¤
    6.5 M¤
    4.5 M¤
    Progenitor:
    v sin i
    lower limits
    10 min
    This is the first bulk
    ensemble of white
    dwarf rotation
    rates, especially
    delineated by mass

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  50. 100 101 102
    White Dwarf Rotation Period (hr)
    0.6
    0.8
    1.0
    1.2
    1.4
    WD Mass (M )
    1 10 100
    White Dwarf Rotation Period (hr)
    0
    2
    4
    6
    8
    10
    N
    K2 Asteroseismic
    Asteroseismic
    K2 Magnetic
    Magnetic
    2.5 M¤
    6.5 M¤
    4.5 M¤
    Progenitor:
    The fastest rotating
    isolated white dwarf
    (727.5 s) is both
    massive and strongly
    magnetic (>200 MG)
    Very likely a merger
    byproduct
    Burleigh et al. 1999
    HST far UV
    1 hr 0.5 d 10 d
    10 min

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  51. 100 101 102
    White Dwarf Rotation Period (hr)
    0.6
    0.8
    1.0
    1.2
    1.4
    WD Mass (M )
    2.5 M¤
    6.5 M¤
    4.5 M¤
    Progenitor:
    Is the wider spread in
    magnetic WD
    rotation rates telling
    us something about
    their histories?
    Asteroseismic
    targets should be
    representative of
    single star
    evolution
    Gaia kinematics
    will illuminate
    merger histories
    1 hr 0.5 d 10 d
    10 min
    1 10 100
    White Dwarf Rotation Period (hr)
    0
    2
    4
    6
    8
    10
    N
    K2 Asteroseismic
    Asteroseismic
    K2 Magnetic
    Magnetic

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  52. 5.5 5.0 4.5
    Planetary Nebula
    Main
    sequence
    DOV
    DBV
    DAV
    4.0 3.5 3.0
    log [T
    eff
    (K)]
    4
    2
    0
    –2
    –4
    log (L/L )
    Sun (G type)
    vrot
    ~ 2 km/s
    Main Sequence
    (Core H burning)
    ~Solid body rotation
    A stars (2.5 M¤
    )
    vrot
    ~ 200 km/s
    (~solid body, Kurtz+ 2015)
    Red Giants
    (Shell H burning)
    Differential rotation
    1.0-2.0 M¤
    RGB
    vrot
    ~ 2 km/s @ surface
    vrot
    ~ 20 km/s @ core
    e.g., Mosser+ 2012
    100,000+ K,
    Young WDs
    Solid body
    vrot
    ~ 1 km/s
    Charpinet+ 2009
    30,000 K WDs
    ~Solid body
    vrot
    ~ 1 km/s
    Hermes+ 2017
    Most WDs, 0.6 M¤
    : vrot
    < 1 km/s
    But >0.9 M¤
    WD (from >4 M¤
    ZAMS): vrot
    ~ 15 km/s
    Red Clump
    (Core He burning)
    Less differential rotation
    2.2-2.9 M¤
    clump stars,
    Deheuvels+ 2015
    AGB
    (Shell He burning)
    Here be dragons!
    The Rotational
    Evolution of
    1-3 M¤
    stars

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  53. This outburst phenomenon never seen before in
    40+ years of pulsating white dwarf studies
    A surprising discovery with Kepler: Aperiodic Outbursts
    Quiescent pulsations
    (1151.9 s, 1160.8 s, …)
    In Outburst
    (999.9 s, 896.6 s, …)
    PG 1149+057: Hermes et al. 2015b

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  54. • White dwarf Teff
    = 11,060 K
    • é 14% mean flux = é 750 K
    • é >25% flux = é >1500 K
    Black line is
    30-min running mean
    Event 1
    Event 7
    Quiescence
    Pulsations Persist in Outburst, But Surface >700 K Hotter

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  55. A surprising discovery with Kepler: Aperiodic Outbursts
    Keaton Bell et al. 2017
    None of the outbursts in pulsating
    WDs are periodic; appear chaotic
    Outburst recurrence times can be
    as short as a few hours and as long
    as 45 days

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  56. • Wu & Goldreich (2001) predicted nonlinear mode coupling could
    transfer energy into damped modes in the cool DAVs
    l=1
    l=2
    Adiabatic Model: 11,245 K, 0.632 M¤
    , 10-4.12 MH
    /MWD
    Observed: 11,060(170) K, 0.64(0.03) M¤
    (Romero et al. 2012)
    (Gianninas et al. 2011)
    Likely Cause: Mode Coupling via Parametric Resonance

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  57. • Wu & Goldreich (2001) predicted nonlinear mode coupling could
    transfer energy into damped modes in the cool DAVs
    l=1
    l=2
    Adiabatic Model: 11,245 K, 0.632 M¤
    , 10-4.12 MH
    /MWD
    Observed: 11,060(170) K, 0.64(0.03) M¤
    (Romero et al. 2012)
    (Gianninas et al. 2011)
    ωp
    = 897.7 µHz
    (l=1, m=0, n=24)
    Likely Cause: Mode Coupling via Parametric Resonance

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  58. • Wu & Goldreich (2001) predicted nonlinear mode coupling could
    transfer energy into damped modes in the cool DAVs
    ωp
    = 897.7 µHz
    (l=1, m=0, n=24)
    ωd1
    = 407.1 µHz
    (l=1, m=0, n=54)
    l=1
    l=2
    ωd2
    = 491.1 µHz
    (l=1, m=0, n=45)
    Adiabatic Model: 11,245 K, 0.632 M¤
    , 10-4.12 MH
    /MWD
    Observed: 11,060(170) K, 0.64(0.03) M¤
    (Romero et al. 2012)
    (Gianninas et al. 2011)
    Likely Cause: Mode Coupling via Parametric Resonance

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  59. (3-day sliding window)
    Of order 1033-1034 erg per outburst
    At least 1033 erg kinetic energy in a
    single pulsation mode
    Outbursts seen in 9 pulsating WDs so far (not rare)
    Possibly rapid energy transfer via
    parametric resonance
    PG 1149+057: Hermes et al. 2015b
    A surprising discovery with Kepler: Aperiodic Outbursts

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  60. 5.5 5.0 4.5
    Planetary Nebula
    Main
    sequence
    DOV
    DBV
    DAV
    4.0 3.5 3.0
    log [T
    eff
    (K)]
    4
    2
    0
    –2
    –4
    log (L/L )
    Sun (G type)
    vrot
    ~ 2 km/s
    Main Sequence
    (Core H burning)
    ~Solid body rotation
    A stars (2.5 M¤
    )
    vrot
    ~ 200 km/s
    (~solid body, Kurtz+ 2015)
    Red Giants
    (Shell H burning)
    Differential rotation
    1.0-2.0 M¤
    RGB
    vrot
    ~ 2 km/s @ surface
    vrot
    ~ 20 km/s @ core
    e.g., Mosser+ 2012
    100,000+ K,
    Young WDs
    Solid body
    vrot
    ~ 1 km/s
    Charpinet+ 2009
    30,000 K WDs
    ~Solid body
    vrot
    ~ 1 km/s
    Hermes+ 2017
    Most WDs, 0.6 M¤
    : vrot
    < 1 km/s
    But >0.9 M¤
    WD (from >4 M¤
    ZAMS): vrot
    ~ 15 km/s
    Red Clump
    (Core He burning)
    Less differential rotation
    2.2-2.9 M¤
    clump stars,
    Deheuvels+ 2015
    AGB
    (Shell He burning)
    Here be dragons!
    The Rotational
    Evolution of
    1-3 M¤
    stars

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  61. Outbursting
    DAVs

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  62. As Convection Zone Deepens, Longer Mode Periods Driven
    Open circles:
    Known DAV
    from ground
    WMP > 500 s
    WMP > 500 s

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