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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.
[email protected] Astronómico NacionalUniversidad 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. BrievaA 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. Introduction2. The model and the likelihood function3. Parameters estimates of the mixture model4. The age of M675. M67 solar type stars6. Results • Age of M67• Membership in the sky region of M677. 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 ModuliGalactic extinction Age of galactic clusters
M67 most probable members and age estimation using BASTI isochrones
Introduction
A. Uribe, R. Barrera, A. Higuera, E. BrievaA Yale symposium in honor of Bill Van Altena
September 2008
Position α2000= 8h 50m 26.1s δ2000= 11ο 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. SandersPhotometry from Montgomery, Sanders, GirardMixture Density Model Bivariate normal componentsParameter estimationEM algorithmEMMIX software
M67 most probable members and age estimation using BASTI isochrones
The model and the likelihood function
A. Uribe, R. Barrera, A. Higuera, E. BrievaA Yale symposium in honor of Bill Van Altena
September 2008
PM vector point spread diagram
Arcsec/cent
-4
-2
0
2
4
-4 -2 0 2 4
UX
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. BrievaA 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. BrievaA 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. BrievaA 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. BrievaA 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= 0.273 Distance modulus = 9.7 24082 hipparchos stars from HMC
M67 most probable members and age estimation using BASTI isochrones
Results
A. Uribe, R. Barrera, A. Higuera, E. BrievaA Yale symposium in honor of Bill Van Altena
September 2008
Membership results
1510 518 Membership probability > 0.5 314 Membership probability > 0.9 12 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