Genetic Algorithms in Computational Seismology for Stellar Evolution Models

1. Computational Seismology using Genetic Algorithms Travis Metcalfe (NCAR)

2. 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)

3. Asteroseismology • 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)

4. Observing techniques Velocity variation (ground) Bouchy et al. (2004) Light variation (space) Aerts et al. (2006)

5. Example: a Cen A+B Butler et al. (2004) a Cen A • 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 Frohlich et al. (1997) Sun Kjeldsen et al. (2005) a Cen B

6. 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

7. 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)

8. Optimization Charbonneau (1995)

9. 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.

10. Evolutionary operators

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

12. 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/

13. 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)

14. 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

15. 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

16. 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