Maximum likelihood estimation of local stellar kinematics

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Maximum likelihood estimation of local stellar kinematics. / Aghajani, T.; Lindegren, Lennart.

I: Astronomy & Astrophysics, Vol. 551, A9, 2013.

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskrift

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TY - JOUR

T1 - Maximum likelihood estimation of local stellar kinematics

AU - Aghajani, T.

AU - Lindegren, Lennart

PY - 2013

Y1 - 2013

N2 - Context. Kinematical data such as the mean velocities and velocity dispersions of stellar samples are useful tools to study galactic structure and evolution. However, observational data are often incomplete (e. g., lacking the radial component of the motion) and may have significant observational errors. For example, the majority of faint stars observed with Gaia will not have their radial velocities measured. Aims. Our aim is to formulate and test a new maximum likelihood approach to estimating the kinematical parameters for a local stellar sample when only the transverse velocities are known (from parallaxes and proper motions). Methods. Numerical simulations using synthetically generated data as well as real data (based on the Geneva-Copenhagen survey) are used to investigate the statistical properties (bias, precision) of the method, and to compare its performance with the much simpler "projection method" described by Dehnen & Binney (1998, MNRAS, 298, 387). Results. The maximum likelihood method gives more correct estimates of the dispersion when observational errors are important, and guarantees a positive-definite dispersion matrix, which is not always obtained with the projection method. Possible extensions and improvements of the method are discussed.

AB - Context. Kinematical data such as the mean velocities and velocity dispersions of stellar samples are useful tools to study galactic structure and evolution. However, observational data are often incomplete (e. g., lacking the radial component of the motion) and may have significant observational errors. For example, the majority of faint stars observed with Gaia will not have their radial velocities measured. Aims. Our aim is to formulate and test a new maximum likelihood approach to estimating the kinematical parameters for a local stellar sample when only the transverse velocities are known (from parallaxes and proper motions). Methods. Numerical simulations using synthetically generated data as well as real data (based on the Geneva-Copenhagen survey) are used to investigate the statistical properties (bias, precision) of the method, and to compare its performance with the much simpler "projection method" described by Dehnen & Binney (1998, MNRAS, 298, 387). Results. The maximum likelihood method gives more correct estimates of the dispersion when observational errors are important, and guarantees a positive-definite dispersion matrix, which is not always obtained with the projection method. Possible extensions and improvements of the method are discussed.

KW - methods: numerical

KW - methods: analytical

KW - astrometry

U2 - 10.1051/0004-6361/201220430

DO - 10.1051/0004-6361/201220430

M3 - Article

VL - 551

JO - Astronomy & Astrophysics

JF - Astronomy & Astrophysics

SN - 1432-0746

M1 - A9

ER -