Travis Metcalfe NCAR

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Computational Seismology using Genetic Algorithms
Travis Metcalfe (NCAR)
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Motivation

• Why study other stars when we have a much better
  view of the Sun?
• New opportunities to probe the fundamental
  physics of models
• Understanding stellar evolution in a broader
  context from ages

Bedding Kjeldsen (2003)
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Asteroseismology

• Only the lowest degree modes are detectable in
  distant stars (l lt 3)
• These modes probe deepest into the interior,
  several dozen excited
• Such data will allow low-resolution inversions of
  the inner 30 of radius

Gough Kosovichev (1993)
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Observing techniques
Velocity variation (ground)
Bouchy et al. (2004)
Light variation (space)
Aerts et al. (2006)
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Example a Cen AB

• Nearest stellar system, masses slightly above and
  below solar mass
• The range of excited frequencies scales with
  acoustic cutoff frequency
• Amplitudes and mode lifetimes generally agree
  with expectations

Butler et al. (2004)
a Cen A
Frohlich et al. (1997)
Sun
Kjeldsen et al. (2005)
a Cen B
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Kepler mission

• NASA mission currently scheduled for launch in
  November 2008
• 95-cm Schmidt corrector, 42 CCDs for planetary
  transits and seismology
• Single field for 4-6 years, 100,000 stars 30
  minute sampling, 512 at 1 minute

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Forward Modeling

• Traditional approach uses classical
  observations to define an error box
• Stellar evolution models are adjusted by hand to
  pass through the box
• Seismic observations provide complementary
  constraints on the models

DiMauro et al. (2003)
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Optimization
Charbonneau (1995)
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Genetic algorithms

• Generate N random trial sets of parameter values.
• Evaluate the model for each trial and calculate
  the variance.
• Assign a fitness to each trial, inversely
  proportional to the variance.
• Select a new population from the old one,
  weighted by the fitness.
• Encode-Breed-Mutate-Decode
• Loop to step 2 until the solution converges.

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Evolutionary operators
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Evolution as optimization
Evolution is cleverer than you are. Francis
Crick
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MPIKAIA package

• General purpose F77 model-fitting optimization
  subroutine
• Slight modification of the serial version of
  PIKAIA with additional MPI code
• Distributed with Makefile and submission script
  for supercomputers

http//mpikaia.asteroseismology.org/
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Local analysis SVD

• We use each GA result as a first guess for the
  local analysis
• SVD probes information content of the classical
  and seismic observables
• Levenberg-Marquardt method for optimization and
  covariance matrix

Creevey et al. (2007)
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Hare Hound GA

• First 128 models match the input frequencies to
  about 1-2 microHz
• Initial convergence driven by the crossover
  operator (first 30 generations)
• Subsequent improvement from a random favorable
  mutation operation

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Hare Hound SVD

• GA found the closest match possible, given the
  search resolution
• SVD improved estimate of M and X, with other
  parameters comparable
• Both within the typical uncertainties of the
  classical observables

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Summary

• Asteroseismology can calibrate the physics of
  solar / stellar models, much as helioseismology
  improved the standard solar model
• Space missions such as CoRoT and Kepler will soon
  unleash a flood of stellar pulsation data with
  unprecedented quality
• The genetic algorithm method can and should be
  applied to different areas of seismology, for
  many forward modeling problems