Astronomy and Astrophysics – Astrophysics
Scientific paper
Jul 1983
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983a%26a...123..238o&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 123, no. 2, July 1983, p. 238-248.
Astronomy and Astrophysics
Astrophysics
18
Ellipsoids, Main Sequence Stars, Monte Carlo Method, Radial Velocity, Stellar Motions, Kinematics, Maximum Likelihood Estimates, Stellar Evolution, Stellar Spectrophotometry
Scientific paper
Possible gradients of the velocity ellipsoid for nearby stars in the galactic plane are studied using basic kinematical material derived from compilations and catalogs. A numerical method is used for main sequence stars to show approximately possible variations of the velocity ellipsoid according to distance, galactic longitude, and stellar age. These values are considered as initial solutions for a more efficient method which applies the maximum likelihood method to solve both the proper motions and radial velocity relations. The method is used to calculate the velocity of the centroid, the dispersions of the residual velocities, the deviations of the vertex, and their gradients. Two systems of equations are obtained, the first linear for the centroid with simple solutions, the second nonlinear for the dispersions, the vertex deviations, and their gradients. The latter system is resolved by the Monte Carlo method with a random selection of solutions progressively refined using the covariance matrix. Results are presented for subgroups of stars as a function of age.
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