EuroWD2010, Tubingen August 16-20, 2010

Bayesian Analysis of Bayesian Analysis of Stellar EvolutionStellar Evolution

Team Members:Steve DeGennaro (UT)Elizabeth Jeffery (STScI)Bill Jefferys (UT, UVM)Nathan Stein (Harvard)David van Dyk (UC, Irvine)PI: Ted von Hippel (Siena, UT)

from Hugh Harris:“160 WDs with new or improved USNO parallaxes that will be in our next paper (Dahn et al AJ 2011, almost completed)”

Bayesian Approach

• Write Bayes equation for this problem, cannot analytically integrate it

• Simulate star clusters, binaries, single white dwarfs using isochrones, IFMR, WD cooling and atmosphere models, then recover input parameters using MCMC

• Markov chain Monte Carlo constructs a draw from the posterior distributions that are used to infer the quantities of interest (stellar masses, ages)

dist

[Fe/H]

dust

0.9

0.5

? ?

MWD crystal

MWD cooling

precursor ages

star A

star BA+B

Das Ende

Bayesian Inference

posterior distribution α likelihood * priororp(model|data) = p(data|model) * p(model) / p(data)

with Θ = model or model parameters

p(data) = ∫ p(data| Θ) p(Θ) d Θ

→ Markov Chain Monte Carlo

Theory: Ingredients

1. IMF (e.g., Miller & Scalo 1979)

2. pre-WD evolution (e.g., Girardi et al. 2000)

3. Initial-Final Mass Relation (e.g., Weidemann 2000)

4. WD cooling time scales (e.g., Wood 1992)

5. WD atmosphere colors (e.g., Bergeron et al. 1995)

6. binaries, non-DA/DA ratio, Mwd,up

7. other variants on the above

Sarajedini et al. 1999

NGC 188

0.30.8

1.0

An Example