Travis Metcalfe (NCAR)

Computational Seismology using Genetic Algorithms

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)

• Only the lowest degree modes are detectable in distant stars (l < 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)

Asteroseismology

Observing techniques

Light variation(space)

Velocity variation(ground)

Aerts et al. (2006)

Bouchy et al. (2004)

Example: Cen A+B

Kjeldsen et al. (2005)

Butler et al. (2004)

Frohlich et al. (1997)

Cen A

Cen B

Sun

• 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

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

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)

Optimization

Charbonneau (1995)

Genetic algorithms

1. Generate N random trial sets of parameter values.

2. Evaluate the model for each trial and calculate the variance.

3. Assign a “fitness” to each trial, inversely proportional to the variance.

4. Select a new population from the old one, weighted by the fitness.

5. Encode-Breed-Mutate-Decode

6. Loop to step 2 until the solution converges.

Evolutionary operators

Evolution as optimization

“Evolution is cleverer than you are.” – Francis Crick

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/

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)

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

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

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