The White Dwarf Age of NGC 2477

Elizabeth JefferySpace 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 WorkshopTübingen, Germany

August 17, 2010

A Bayesian Approach to Measuring Cluster Ages

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

Ages of Stellar PopulationsThe 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

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%

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! …

• 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 AgesWhite Dwarf Techniques

Simulated Cluster, 3 Gyr

0.5 Mo

0.8 Mo

Mv

Current Agreement

von Hippel 2005

NGC 3960 NGC 2660 NGC 2360

NGC 188*

* see Poster 72 by Williams, Jeffery, & For

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

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

Data – The ObservationsField of View Comparison – NGC 2477 (WFPC2)

Data – Deep Color-Magnitude Diagrams

NGC 2477NGC 2360 NGC 2660

NGC 3960 NGC 188

Things to Note:

(1) Data go deep

(2) Cluster Main Sequence

(3) Many field stars / background galaxies

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

Data – Deep Color-Magnitude Diagrams

NGC 2477

Fitting White Dwarf IsochronesNGC 2477

0.5 Gyr

1.5 Gyr

1.0 Gyr

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

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, Y2, 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

Data – Deep Color-Magnitude Diagrams

NGC 2477

Applying MCMC NGC 2477 Posterior Distributions

DSED (Dotter et al. 2008)

Y2 (Yi et al. 2001)

Girardi et al. (2000)

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)

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

Further Power of the TechniqueComparing complete distributions

NGC 2360

MS Fit

WD Fit

A Calibration of the AgesWhere we are now

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

Improving Error BarsNGC 2420

von Hippel & Gilmore 2000

2 +/- 0.2 Gyr

Applying MCMC NGC 2420

Applying MCMC The Example of NGC 2420

Applying MCMC The Example of NGC 2420

1.83 +/- 0.12 Gyr

Applying MCMC The Example of NGC 2420 – MSTO

What does the best fit demonstrate?

DSED vs. Y2 isochronesAge (Gyr) 1.53 +/- 0.06 2.09 +/- 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 +/- 0.06 2.09 +/- 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.

Ages from the Bright Cluster WDs Rationale of the Idea

A Test Case for the Bright White Dwarf IdeaThe Hyades White Dwarfs

DeGennaro S. von Hippel, T., Jefferys, W.H., Stein, N., van Dyk, D., & Jeffery, E., 2008, in prep

Data – Color-Magnitude Diagrams

NGC 2360 NGC 2477 NGC 2660

NGC 3960 NGC 2420 NGC 188

Data – Deep Color-Magnitude Diagrams

Things to Note:

(1) Data go deep

(2) Cluster Main Sequence

(3) Many field stars / background galaxies

NGC 2477

Data – Deep Color-Magnitude Diagrams

Things to Note:

(1) Data go deep

(2) Cluster Main Sequence

(3) Many field stars / background galaxies

NGC 2660

Data – Deep Color-Magnitude Diagrams

Things to Note:

(1) Data go deep

(2) Cluster Main Sequence

(3) Many field stars / background galaxies

NGC 188

Fitting White Dwarf Isochrones

NGC 2477NGC 2360 NGC 2660

NGC 3960 NGC 188