A. Uribe, R. Barrera, A. Higuera, E. Brieva

Transcription

1 New Haven,

2 Stars in Motion A Yale symposium in honor of Bill Van Altena New Haven,

3 M67 most probable members and age estimation using BASTI isochrones Antonio Uribe B. Observatorio Astronómico Nacional Universidad Nacional de Colombia Observatorio Astronómico

4 Collaborators Ruth Barrera Observatorio Astronómico Nacional Mario Armando Higuera Observatorio Astronómico Nacional Eduardo Brieva Observatorio Astronómico Nacional

5 Students Laura Moreno Observatorio Astronómico Nacional Jean Paul Picon Observatorio Astronómico Nacional

6 Table of contents Table of contents 1. Introduction 2. The model and the likelihood function 3. Parameters estimates of the mixture model 4. The age of M67 5. M67 solar type stars 6. Results Age of M67 Membership in the sky region of M67 7. References

7 Introduction Open Clusters in galactic astronomy Data analysis in astrostatistics Data Bases Membership in open clusters Distance Moduli Galactic extinction Age of galactic clusters

8 Introduction Open Cluster M67 Position α2000= 8h 50m 26.1s δ2000= 11 ο Distance 870 pc

9 Introduction The importance of M67 Age 4 Gyrs. Chemical composition. Solar type stars.

10 Introduction Membership study Proper Motions from 1866 stars W. Sanders Photometry from Montgomery, Sanders, Girard Mixture Density Model Bivariate normal components Parameter estimation EM algorithm EMMIX software

11 The model and the likelihood function PM vector point spread diagram Arcsec/cent UX

12 The model and the likelihood function PM bivariate normal components for the field and cluster stars Mark H. Slovak 2 f(x j ; Θ) = α i f i (x j ; µ i, Σ i ), i=1

13 The model and the likelihood function The EM algorithm This has been the statistical approach to estimate the parameters of the mixture model. This goal is reached because the EM algorithm allows to find a point of the parameter space that maximizes the log-likelihood function through the E and the M steps.

14 The model and the likelihood function

15 Parameters estimates of the mixture model The EMMIX software

16 Parameters estimates of the mixture model Parameters estimation by EM

17 Parameters estimates of the mixture model The membership probabilities are found through a Bayesian rule =

18 Parameters estimates of the mixture model M67 most probable members......

19 The age of M67 Learning from Allan Sandage, Lori M. and Don VandenBerg

20 The age of M67 Main Hipparcos catalog cloud and isocrhones from Don VandenBerg Victoria Regina models

21 The age of M67 Main Hipparcos catalog cloud and isocrhones from Don VandenBerg Victoria Regina models

22 The age of M67 Isochrone by Pietrinferni-Cassisi-Salaris- Castelli 2006 Standard Model Scaled solar model & transformation (Castelli 1999)

23 The age of M67 M67 Color Magnitud Diagram and Age

24 M67 solar type stars M67 Stellar spectra by Allen L. et al.

25 M67 solar type stars M67 Stellar spectra by Allen L. et al....

26 Results The age of M67 CMD with 314 M67 most probable members Three Basti isochrones (3.75, 4 y 4.5) Gyr Isochrones are based on a scaled solar model with 2000 points [Fe/H] = 0.58, Z=0.0198, Y= Distance modulus = hipparchos stars from HMC

27 Results Membership results Membership probability > Membership probability > G2V solar type stars Correct allocation rate 0.937

28 References Main references

29 Thanks to all of you Mainly to the organizers of the Yale symposium Stars in Motion in honor of Bill Van Altena