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Using Asteroseismology to Solve the Mysteries of Planet Inflation

skgrunblatt
July 03, 2017
27

Using Asteroseismology to Solve the Mysteries of Planet Inflation

Inflated planets have been known for over 20 years, yet their origin remains mysterious. However, using new techniques to characterize the seismic signal of stars to give precise masses and radii, we can distinguish between different mechanisms for planet inflation.

skgrunblatt

July 03, 2017
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  1. USING ASTEROSEISMOLOGY TO SOLVE THE MYSTERIES OF PLANET INFLATION SAMUEL

    GRUNBLATT1, DANIEL HUBER1, ERIC GAIDOS1, ERIC LOPEZ2 1. UNIVERSITY OF HAWAII 2. NASA GODDARD SPACE FLIGHT CENTER Image credit: C. Carreau / ESA
  2. Part 1: A Search for Re-Inflation Part 2: Asteroseismology Part

    3: Gaussian Process Lightcurve Fitting Part 4: Are They Re-Inflated Planets?
  3. Part 1: A Search for Re-Inflation Part 2: Asteroseismology Part

    3: Gaussian Process Lightcurve Fitting Part 4: Are They Re-Inflated Planets?
  4. Charbonneau et al. (2000) “The derived value of Rp =

    1.27 +/- 0.02 RJup is in excellent agreement with the early predictions of Guillot et al. (1996), who calculated the radius for a strongly irradiated radiative/convective extrasolar planet for a variety of masses.”
  5. Lopez & Fortney (2016) maximum expected radius highly inflated not

    inflated Inflated Hot Jupiters are ubiquitous.
  6. The Mechanism of Planet Inflation e.g., Bodenheimer+ (2001), Showman &

    Guillot (2002),
 Batygin & Stevenson (2010), Ginzburg & Sari (2016) Class I: planet interior inflated directly by increased stellar irradiation Class II: cooling delayed after planet formation e.g., Burrows+ (2000), Chabrier & Baraffe (2007), Leconte & Chabrier (2012), Wu & Lithwick (2013)
  7. How to distinguish between Classes I and II? Class I:

    re-inflation Class II: no re-inflation
  8. A SEARCH FOR GIANTS ORBITING GIANTS WITH K2 ➤ 10,000

    targets in C1-10 ➤ K2 limit for asteroseismology: 283 μHz (~3.5 Rsun) ➤ Transit detection limit: ~10 Rsun ➤ Temperature limits: 4500—5500 K 
 (to avoid horizontal branch stars) Huber et al. (2016)
  9. Part 1: A Search for Re-Inflation Part 2: Asteroseismology Part

    3: Gaussian Process Lightcurve Fitting Part 4: Are They Re-Inflated Planets?
  10. Two Asteroseismic Hosts Grunblatt et al. (submitted) Rs = 3.85

    +/- 0.13 R⊙ Ms = 1.08 +/- 0.08 M⊙ Rs = 4.20 +/- 0.14 R⊙ Ms = 1.16 +/- 0.12 M⊙
  11. Part 1: A Search for Re-Inflation Part 2: Asteroseismology Part

    3: Gaussian Process Lightcurve Fitting Part 4: Are They Re-Inflated Planets?
  12. What is Gaussian process estimation? Gaussian process (GP) estimation is

    a nonparametric estimation of 1-D data described by a kernel function and its hyperparameters. Source: Rasmussen and Williams (2005)
  13. What is a Gaussian process estimator? A Gaussian process (GP)

    estimator is a nonparametric estimator of 1-D data described by a kernel function and its hyperparameters. ⌃ij = k ( ti, tj) = h2 exp  ⇣ti tj ⌘2 Simplest kernel function: Squared exponential (SE) Source: Rasmussen and Williams (2005)
  14. What is a Gaussian process estimator? A Gaussian process (GP)

    estimator is a nonparametric estimator of time-series data described by a kernel function and its hyperparameters. ⌃ij = k ( ti, tj) = h2 exp  ⇣ti tj ⌘2 Simplest kernel function: Squared exponential (SE) Source: Rasmussen and Williams (2005)
  15. What is a Gaussian process estimator? A Gaussian process (GP)

    estimator is a nonparametric estimator of time-series data described by a kernel function and its hyperparameters. ⌃ij = k ( ti, tj) = h2 exp  ⇣ti tj ⌘2 Simplest kernel function: Squared exponential (SE) covariance matrix Source: Rasmussen and Williams (2005)
  16. What is a Gaussian process estimator? A Gaussian process (GP)

    estimator is a nonparametric estimator of time-series data described by a kernel function and its hyperparameters. ⌃ij = k ( ti, tj) = h2 exp  ⇣ti tj ⌘2 Simplest kernel function: Squared exponential (SE) covariance matrix now with off-diagonal terms! Source: Rasmussen and Williams (2005)
  17. • Simplest kernel: squared exponential. Described by: • where (h,

    λ) are the hyperparameters: parameters of the kernel. Kernel function basics Roberts et al. (2012) λ = 0.1 λ = 1 λ = 10 ⌃ij = k ( ti, tj) = h2 exp  ⇣ti tj ⌘2 h t
  18. • Given a set of input data,
 and a choice

    of covariance kernel… ⌃ij = k ( ti, tj) = h2 exp  ⇣ti tj ⌘2
  19. • …find the best-fit hyperparameters by maximizing the appropriate likelihood

    function: log[ L ( r )] = 1 2 rT⌃ 1r 1 2 log |⌃| N 2 log(2 ⇡ ) ⌃ij = k ( ti, tj) = h2 exp  ⇣ti tj ⌘2
  20. Gaussian Process Model Evaluate choice of mean function parameters and

    kernel hyperparameters with likelihood function. (for squared exponential case) log[ L ( r )] = 1 2 rT⌃ 1r 1 2 log |⌃| N 2 log(2 ⇡ ) r = v Ksin ⇣2⇡(t tc) P orb ⌘ ⌃ij = k ( ti, tj) = h2 exp  ⇣ti tj ⌘2
  21. Comparing different models: Used squared exponential and simple harmonic oscillator

    GP kernel functions to account for granulation noise no GP
  22. Used squared exponential and simple harmonic oscillator GP kernel functions

    to account for granulation noise SE GP Comparing different models:
  23. Used squared exponential and simple harmonic oscillator GP kernel functions

    to account for granulation noise SHO GP Comparing different models:
  24. Combined transit + GP models Used squared exponential and simple

    harmonic oscillator GP kernel functions to account for granulation noise Grunblatt et al. (submitted)
  25. Derived planet radii that agree for both GP models. Grunblatt

    et al. (submitted) Transit depths agree!
  26. SHO GP tells us about star, too Simple harmonic oscillator

    GP traces stellar granulation & oscillation signals: estimate of νmax from time-domain! SHO GP Grunblatt et al. (submitted)
  27. TWO NEW TRANSITING PLANETS AROUND ASTEROSEISMIC HOSTS Grunblatt et al.

    (submitted) Rs = 4.20 +/- 0.14 R⊙ Ms = 1.16 +/- 0.12 M⊙ Rp = 1.31 +/- 0.11 RJ Rs = 3.85 +/- 0.13 R⊙ Ms = 1.08 +/- 0.08 M⊙ Rp = 1.30 +/- 0.07 RJ
  28. Part 1: A Search for Re-Inflation Part 2: Asteroseismology Part

    3: Gaussian Process Lightcurve Fitting Part 4: Are They Re-Inflated Planets?
  29. Are they planets? Mp = 0.48 +/- 0.07 MJ Mp

    = 0.49 +/- 0.06 MJ Grunblatt et al. (submitted)
  30. Are they planets? Also yes. Mp = 0.48 +/- 0.07

    MJ Mp = 0.49 +/- 0.06 MJ Grunblatt et al. (submitted)
  31. Are they re-inflated planets? Grunblatt et al. (submitted) avg incident

    flux on main sequence: K2-97b: 
 170 +140 -60 F EPIC2287b: 190 +150 -80 F
  32. typical incident flux range for 1.3 RJ planets current incident

    flux: K2-97b: 
 900 +200 -150 F EPIC2287b: 850 +250 -140 F current incident fluxes Grunblatt et al. (submitted) Are they re-inflated planets?
  33. Data implies 0.023%+0.023% -0.012% heating efficiency Class II ] Class

    I Results consistent with re-inflation… Grunblatt et al. (submitted)
  34. Data implies 0.033%+0.037% -0.021% heating efficiency Class II ] Class

    I Results consistent with re-inflation… Grunblatt et al. (submitted)
  35. Need >2 RJ initial radius, cooling delayed 
 by 100x

    to explain current planet radii. Class II …and inconsistent with delayed cooling! ] Grunblatt et al. (submitted)
  36. Data implies 0.033%+0.037% -0.021% heating efficiency Class II ] Class

    I Results consistent with re-inflation… Grunblatt et al. (submitted) Kepler-422b: 1.15 Msun 0.43 MJ 7.89 days
  37. Data implies 0.033%+0.037% -0.021% heating efficiency Class II ] Class

    I Results consistent with re-inflation… Grunblatt et al. (submitted) Kepler-422b: 1.15 Msun 0.43 MJ 7.89 days
  38. Need >2 RJ initial radius, cooling delayed 
 by 100x

    to explain current planet radii. Class II …and inconsistent with delayed cooling! ] Grunblatt et al. (submitted) Kepler-422b: 1.15 Msun 0.43 MJ 7.89 days
  39. The first transiting planets found orbiting asteroseismic stars with K2:

    
 ~1.3 RJ, ~0.5 MJ, ~9 day period 
 (agree within <10%!) Suggests planet re-inflation during RGB phase
 (~0.03% heating efficiency) Summary Seeing Double with K2: Testing Re-Inflation With Two Remarkably Similar Planets Around Red Giant Stars Grunblatt et al. (submitted), arXiv:1706.05865
  40. Future Work: Red Giant Planet Occurrence ? ? ? ?

    ? ? Expected yield: ~5 planets. New candidates incoming! EPIC228754001.01 K2-97b
  41. Why are they so similar? 0.01 0.10 1.00 10.00 planet

    mass (Jupiters) 0.0 0.2 0.4 0.6 0.8 1.0 survey bias factor Short answer: survey bias * intrinsic planet occurrence