Stars in Motion A Yale symposium in honor of Bill Van Altena September 2008 Stars in Motion A Yale symposium in honor of Bill Van Altena September 2008.

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Presentation transcript:

Stars in Motion A Yale symposium in honor of Bill Van Altena September 2008 Stars in Motion A Yale symposium in honor of Bill Van Altena September 2008 A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena New Haven, September 2008

Antonio Uribe B. Observatorio Astronómico Nacional Universidad Nacional de Colombia M67 most probable members and age estimation using BASTI isochrones A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 Observatorio Astronómico Nacional

Ruth Barrera Observatorio Astronómico Nacional Eduardo Brieva Observatorio Astronómico Nacional Mario Armando Higuera Observatorio Astronómico Nacional M67 most probable members and age estimation using BASTI isochrones Collaborators A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008

Laura Moreno Observatorio Astronómico Nacional Jean Paul Picon Observatorio Astronómico Nacional M67 most probable members and age estimation using BASTI isochrones Students A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008

M67 most probable members and age estimation using BASTI isochrones Table of contents A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 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

M67 most probable members and age estimation using BASTI isochrones Introduction A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 Open Clusters in galactic astronomy Data analysis in astrostatistics Data Bases Membership in open clusters Distance Moduli Galactic extinction Age of galactic clusters

M67 most probable members and age estimation using BASTI isochrones Introduction A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 Position α 2000 = 8h 50m 26.1s δ 2000 = 11 ο 48´ 46´´ Distance 870 pc Open Cluster M67

M67 most probable members and age estimation using BASTI isochrones Introduction A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 Age 4 Gyrs. Chemical composition. Solar type stars. The importance of M67

M67 most probable members and age estimation using BASTI isochrones Introduction A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 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

M67 most probable members and age estimation using BASTI isochrones The model and the likelihood function A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 PM vector point spread diagram Arcsec/cent

M67 most probable members and age estimation using BASTI isochrones The model and the likelihood function A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 PM bivariate normal components for the field and cluster stars Mark H. Slovak

M67 most probable members and age estimation using BASTI isochrones The model and the likelihood function A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 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.

M67 most probable members and age estimation using BASTI isochrones The model and the likelihood function A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008

M67 most probable members and age estimation using BASTI isochrones Parameters estimates of the mixture model A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 The EMMIX software

M67 most probable members and age estimation using BASTI isochrones Parameters estimates of the mixture model A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 Parameters estimation by EM

M67 most probable members and age estimation using BASTI isochrones Parameters estimates of the mixture model A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 The membership probabilities are found through a Bayesian rule =

M67 most probable members and age estimation using BASTI isochrones Parameters estimates of the mixture model A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 M67 most probable members...

M67 most probable members and age estimation using BASTI isochrones The age of M67 A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 Learning from Allan Sandage, Lori M. and Don VandenBerg

M67 most probable members and age estimation using BASTI isochrones The age of M67 A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 Main Hipparcos catalog cloud and isocrhones from Don VandenBerg Victoria Regina models

M67 most probable members and age estimation using BASTI isochrones The age of M67 A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 Main Hipparcos catalog cloud and isocrhones from Don VandenBerg Victoria Regina models

M67 most probable members and age estimation using BASTI isochrones The age of M67 A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 Isochrone by Pietrinferni-Cassisi-Salaris- Castelli 2006 Standard Model Scaled solar model & transformation (Castelli 1999)

M67 most probable members and age estimation using BASTI isochrones The age of M67 A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 M67 Color Magnitud Diagram and Age

M67 most probable members and age estimation using BASTI isochrones M67 solar type stars A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 M67 Stellar spectra by Allen L. et al.

M67 most probable members and age estimation using BASTI isochrones M67 solar type stars A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 M67 Stellar spectra by Allen L. et al....

M67 most probable members and age estimation using BASTI isochrones Results A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 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

M67 most probable members and age estimation using BASTI isochrones Results A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 Membership results Membership probability > Membership probability > G2V solar type stars Correct allocation rate 0.937

M67 most probable members and age estimation using BASTI isochrones References A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 Main references

M67 most probable members and age estimation using BASTI isochrones A. Uribe, R. Barrera, A. Higuera, E. Brieva A Yale symposium in honor of Bill Van Altena September 2008 Thanks to all of you Mainly to the organizers of the Yale symposium Stars in Motion in honor of Bill Van Altena