Rogue waves from parametric resonance in pulsating white dwarfs

Conference presentation, 20 min. July 2018: TASC4/KASC11: TESS Asteroseismic Consortium, Aarhus, Denmark.

Transcript

1. http://jjherm.es
   J.J. Hermes
   Hubble Fellow
   University of North Carolina
   at Chapel Hill
   Rogue waves from parametric
   resonance in pulsating white dwarfs
   

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2. Rogue waves from parametric
   resonance in pulsating white dwarfs
   Key takeaway: outbursts are not rare in coolest pulsating WDs
   - only requirement seems to be high mode density for coupling
   - expression of energy transfer via nonlinear mode coupling
   

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3. A Visual Guide to Outbursts in Pulsating White Dwarfs
   Quiescent pulsations
   (All outburstersdominant >800 s)
   PG 1149+057: Hermes et al. 2015b
   recurrence time:
   chaotic; days to weeks
   duration:
   2-20 hr
   excess energy:
   1033-34 erg
   15% flux increase:
   700 K Teff
   increase
   

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4. (3-day sliding window)
   A Visual Guide to Outbursts in Pulsating White Dwarfs
   PG 1149+057: Hermes et al. 2015b
   pulsations are affected
   by the outbursts
   

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5. A Visual Guide to Outbursts in Pulsating White Dwarfs
   Keaton Bell 2017 (PhD thesis)
   outbursts seen in at least 13 DAVs
   (this is not a rare phenomenon!)
   none of the outbursts in pulsating
   WDs are periodic; appear chaotic
   each color is a
   different DAV
   

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6. He
   P.I. zone
   (30-20 kK)
   H
   P.I. zone
   (13-10 kK)
   DBV
   aka V477 Her
   DAV
   aka ZZ Ceti
   a step back: pulsating white dwarfs in the HR diagram
   

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7. 1000 s 200 s
   500 s 125 s
   white dwarfs: g-modes, not all
   modes are observed excited
   model: 11,245 K, 0.632 M¤
   ,
   10-4.12 MH
   /MWD
   (Romero et al. 2012)
   l=1
   l=2
   n=5
   n=10
   n>20
   n>35
   

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8. n
   l=1
   l=2
   l=1
   l=2
   

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9. n
   l=1
   l=2
   l=1
   l=2
   

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10. Spectroscopy Yields Effective Temperatures and Masses
    SDSS
    4.2m SOAR Telescope our
    workhorse
    we have obtained and analyzed SOAR
    spectra of 62 of the first 65 DAVs observed
    by K2 so far: first 27 at k2wd.org
    WDs Evolve (Cool) à
    Blue: Observed by Kepler
    Open: Ground-based
    fits via
    Pier-Emmanuel
    Tremblay
    

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11. Outbursting DAVs are Among the Coolest DAVs
    Blue: Observed by Kepler
    Red: Outbursting DAV
    Open: Ground-based
    more than 50% of DAVs from 11,200-10,600 K
    show outbursts in ~70 days of K2 monitoring
    

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12. Outbursting DAVs are Among the Coolest DAVs
    Blue: Observed by Kepler
    Red: Outbursting DAV
    Open: Ground-based
    GD 1212
    friendly bet: Josh Fuchs (formerly UNC)
    thought GD 1212 should pulsate based
    on his fits to SOAR spectra of DAVs
    

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13. GD 1212, Hermes et al. 2014a
    data from the 9-day K2 engineering test run
    V=13.3 mag
    

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14. GD 1212: The Brightest Outbursting White Dwarf
    Quiescent pulsations
    (1135.2 s, 856.9 s, …)
    In Outburst
    (864.1 s, 846.4 s, …)
    GD 1212: Hermes et al. 2018, in prep.
    >60 days between outbursts!
    K2 Campaign 12
    

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15. GD 1212: The Brightest Outbursting White Dwarf
    Quiescent pulsations
    (1135.2 s, 856.9 s, …)
    In Outburst
    (864.1 s, 846.4 s, …)
    GD 1212: Hermes et al. 2018, in prep.
    >60 days between outbursts!
    K2 Campaign 12
    

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16. GD 1212: K2 Campaign 12
    GD 1212: The Brightest Outbursting White Dwarf
    GD 1212: Hermes et al. 2018, in prep.
    

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17. 13/65 (20% of) DAVs with Kepler Data Show Outbursts
    Blue: Observed by Kepler
    Red: Outbursting DAV
    Open: Ground-based
    we expect all non-magnetic white dwarfs to pulsate at the appropriate
    temperature, and it appears most (all?) outburst at some point, too
    outbursts are likely a new phase of stellar evolution uncovered by Kepler/K2
    

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18. 150 s
    1000 s
    white dwarfs cool:
    longer-period
    (higher-radial-order)
    pulsations driven
    and
    mode density
    rapidly increases
    

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19. Coming Soon: NASA/TESS will observe all bright WDs every 2 min
    815 WDs in Cycle 1 accepted for 2-min
    monitoring
    ~70 I < 16 mag white dwarfs per sector
    

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20. Should Other Pulsating Stars Show Outbursts?
    DBVs (He-atmosphere WDs) have very similar structures to
    DAVs, and thus similar mode densities
    so far 7 DBVs observed by Kepler: none show outbursts
    (but so far none with dominant periods >1000 s)
    See poster by Zach Vanderbosch
    

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21. 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)
    Mode Coupling via Parametric Resonance
    à Driving exceeds damping
    Radiative damping ß
    outbursts are likely “limit cycles arising from sufficiently
    resonant 3-mode couplings between overstable parent
    modes and pairs of radiatively damped daughter modes”
    Jing Luan & Goldreich 2018
    

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22. à Driving
    Radiative damping ß
    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)
    Mode Coupling via Parametric Resonance
    ωp
    = 897.7 µHz
    (l=1, m=0, n=24)
    

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23. 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
    = 435.9 µHz
    (l=2, m=0, n=88)
    l=1
    l=2
    ωd2
    = 461.9 µHz
    (l=1, m=0, n=48)
    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)
    Mode Coupling via Parametric Resonance
    ωd1
    + ωd2
    = ωp
    + δω
    Limit cycle if: δω < γd
    (typical 1/γd
    < 1 day)
    

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24. ωp
    = 897.7 µHz
    (l=1, m=0, n=24)
    ωd1
    = 435.9 µHz
    (l=2, m=0, n=88)
    l=1
    l=2
    ωd2
    = 461.9 µHz
    (l=1, m=0, n=48)
    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)
    Mode Coupling via Parametric Resonance
    Wu & Goldreich 2001
    ωd1
    + ωd2
    = ωp
    + δω
    Limit cycle if: δω < γd
    (typical 1/γd
    < 1 day)
    

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25. Key Takeaways: Outbursts in the Coolest Pulsating WDs
    Blue: Observed by Kepler
    Red: Outbursting DAV
    Open: Ground-based
    - outbursts are not rare in coolest pulsating WDs
    - this is a common (universal?) phase of stellar evolution!
    - only requirement seems to be high mode density for coupling
    - nonlinear resonances expressed as outbursts are very likely responsible
    for the cessation of pulsations at the red edge of the DAV instability strip
    

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26. View Slide

27. Should Other Pulsating Stars Show Outbursts?
    the well-studied DBV GD 358
    showed pulsation changes and
    got ~20-30% brighter during
    2006 WET run for just one day
    nicknamed the ‘sforzando’ or
    often the ‘whoopsie’ GD 358:
    Montgomery et al. 2010
    

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28. WET, and KASC4 Boulder (7/2011 so SIX YEARS AGO!)
    He
    P.I. zone
    (30-20 kK)
    H
    P.I. zone
    (13-10 kK)
    Fontaine & Brassard 2008
    N2
    Ll
    2
    DAV Propagation Diagram
    Core Surface
    p-modes
    σ2 > Ll
    2, N2
    convection
    zone
    log σ2 (s-2)
    g-modes
    σ2 < Ll
    2, N2
    

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29. oDAV1
    10860 K
    0.70 M¤
    oDAV2
    11060 K
    0.64 M¤
    oDAV3
    10570 K
    0.56 M¤
    oDAV4
    11190 K
    0.62 M¤
    oDAV5
    10850 K
    0.53 M¤
    3rd & 4th: Bell et al. 2016, ApJ, arXiv: 1607.01392
    

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30. (3-day sliding window)
    As seen in other bright oDAV, outbursts affect pulsations!
    oDAV4, Kp
    = 16.7 mag
    

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31. 1000 s 500 s 360 s
    1400 s
    oDAV1
    10860 K
    0.70 M¤
    oDAV2
    11060 K
    0.64 M¤
    oDAV3
    10570 K
    0.56 M¤
    oDAV4
    11190 K
    0.62 M¤
    oDAV5
    10850 K
    0.53 M¤
    800 s
    3rd & 4th: Bell et al. 2016, ApJ, arXiv: 1607.01392
    

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