1. The White Dwarf Age of NGC 2477 Elizabeth Jeffery Space Telescope Science Institute Collaborators: Ted von Hippel, Steven DeGennaro, David van Dyk, Nathan Steinn, W.H. Jefferys, D.E. Winget, Kurtis Williams White Dwarf European Workshop Tübingen, Germany August 17, 2010 A Bayesian Approach to Measuring Cluster Ages

2. Talk Outline Stellar Ages : Main Sequence and White Dwarf Ages  Calibration using open clusters Clusters for study Hubble Space Telescope data  WD ages New Bayesian technique  analysis of clusters

3. Ages of Stellar Populations The Question of When Fundamental property in astronomy Two main ways: Main Sequence Isochrones vs. the White Dwarf Luminosity Function Winget, et al. 1987 vs. Alcaino et al. 1998

4. Comparing Ages in Open Star Clusters Why do both? Calibrate MSTO and WD ages Why not use white dwarfs in halo globular clusters? More difficult to observe (3 to date) Gradually increase calibration; thoroughly understand physics WDs provide independent check of MS models, and vice versa increase understanding of both MS models have uncertainties up to 20% between models. WD models have uncertainties up to 5% – 20%

5. Observing Cluster White Dwarfs Cluster white dwarfs are FAINT, requiring large or space-based telescopes (Hubble) This is expensive This is time consuming … but it’s possible! …

6. Relationship between a WD’s luminosity and cooling time (i.e., age) Location of the terminus of the cluster WD sequence is determined by the age Open Clusters Ages White Dwarf Techniques Simulated Cluster, 3 Gyr 0.5 Mo 0.8 Mo MvMv

7. Current Agreement von Hippel 2005 NGC 3960NGC 2660NGC 2360 NGC 188* * see Poster 72 by Williams, Jeffery, & For

8. Talk Outline Stellar Ages : Main Sequence and White Dwarf Ages  Calibration using open clusters Clusters for study Hubble Space Telescope data  WD ages New Bayesian technique  analysis of clusters

9. Data – The Observations HST, ACS and WFPC2: Deep observations of the white dwarfs CTIO 1m/Y4kCam CCD : Observations of cluster turn off, giants, and upper main sequence

10. Data – The Observations Field of View Comparison – NGC 2477 (WFPC2)

11. Data – Deep Color-Magnitude Diagrams NGC 2477NGC 2360NGC 2660 NGC 3960NGC 188 Things to Note: (1)Data go deep (2)Cluster Main Sequence (3)Many field stars / background galaxies

12. Data – Deep Color-Magnitude Diagrams CMD Features: (1)Cluster Main Sequence NGC 2477 1 2 4 3 CMD Features: (1)Cluster Main Sequence (2)Background population (3)Background galaxies (4)White Dwarfs CMD Features: (1)Cluster Main Sequence (2)Background population (3)Background galaxies (4)White Dwarfs CMD Features: (1)Cluster Main Sequence (2)Background population (3)Background galaxies (4)White Dwarfs

13. Data – Deep Color-Magnitude Diagrams NGC 2477

14. Fitting White Dwarf Isochrones NGC 2477 0.5 Gyr 1.5 Gyr 1.0 Gyr

15. Talk Outline Stellar Ages : Main Sequence and White Dwarf Ages  Calibration using open clusters Clusters for study Hubble Space Telescope data  WD ages New Bayesian technique  analysis of clusters

16. New Machinery Using Bayesian Statistics Bayesian Statistics – Bayes Theorem: Posterior α Likelihood * Prior Use Markov Chain Monte Carlo (MCMC) technique to numerically sample posterior probability distributions Simultaneously fit age, distance, reddening, and metallicity by modeling photometry. Run with different models: DSED, Y 2, Girardi von Hippel, T., et al. 2006, ApJ, 645, 1436 Jeffery, E. et al. 2007, ApJ, 658, 391 DeGennaro S. et al. 2009, ApJ, 696, 12

17. Data – Deep Color-Magnitude Diagrams NGC 2477

18. Applying MCMC NGC 2477 Posterior Distributions DSED (Dotter et al. 2008) Y 2 (Yi et al. 2001) Girardi et al. (2000)

19. Applying MCMC NGC 2477 DSED (Dotter et al. 2008) Y2 (Yi et al. 2001) Girardi et al. (2000) WD Age (Gyr) : 1.035 ± 0.054 ± 0.087 Weighted Average (“Answer”) Error among models (“external”) Error within models (“internal”) MSTO Age = 1.0 Gyr (Kassis et al. 1997)

20. Applying MCMC NGC 2477 DSED (Dotter et al. 2008) Y2 (Yi et al. 2001) Girardi et al. (2000) WD Age (Gyr) : 1.035 ± 0.054 ± 0.087

21. Further Power of the Technique Comparing complete distributions NGC 2360 MS Fit WD Fit

22. A Calibration of the Ages Where we are now

23. Concluding Remarks Open clusters provide ideal environment for calibration of MS ages and WD ages, testing theory against theory Analysis of six clusters New Bayesian Algorithm High precision fits allows us to pin down problems in the models Compare distributions – not just single numbers Incorporate different combinations of model ingredients, pushing the models to their limits Good agreement found for clusters included here

25. Improving Error Bars NGC 2420 von Hippel & Gilmore 2000 2 +/- 0.2 Gyr

26. Applying MCMC NGC 2420

27. Applying MCMC The Example of NGC 2420

28. 1.83 +/- 0.12 Gyr

29. Applying MCMC The Example of NGC 2420 – MSTO

30. What does the best fit demonstrate? DSED vs. Y 2 isochrones Age (Gyr)1.53 +/- 0.062.09 +/- 0.10 [Fe/H]+0.187 +/- 0.03-0.109 +/- 0.03 Which is right?  Compare age with the White Dwarfs White dwarf age is 1.83 +/- 0.12 Gyr. Age (Gyr)1.53 +/- 0.062.09 +/- 0.10 [Fe/H]+0.187 +/- 0.03-0.109 +/- 0.03 Discrepancy in age is likely caused by inadequate incorporation of metallicity in the models.

31. Ages from the Bright Cluster WDs Rationale of the Idea

32. A Test Case for the Bright White Dwarf Idea The Hyades White Dwarfs DeGennaro S. von Hippel, T., Jefferys, W.H., Stein, N., van Dyk, D., & Jeffery, E., 2008, in prep

33. Data – Color-Magnitude Diagrams NGC 2360NGC 2477NGC 2660 NGC 3960NGC 2420 NGC 188

34. Data – Deep Color-Magnitude Diagrams Things to Note: (1)Data go deep (2)Cluster Main Sequence (3)Many field stars / background galaxies NGC 2477

35. Data – Deep Color-Magnitude Diagrams Things to Note: (1)Data go deep (2)Cluster Main Sequence (3)Many field stars / background galaxies NGC 2660

36. Data – Deep Color-Magnitude Diagrams Things to Note: (1)Data go deep (2)Cluster Main Sequence (3)Many field stars / background galaxies NGC 188

37. Fitting White Dwarf Isochrones NGC 2477NGC 2360NGC 2660 NGC 3960 NGC 188