Application of Vector Spherical Harmonics and Kernel Regression to the Computations of OMM Parameters
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Other documents of the author: Marco Castillo, Francisco José; Martínez, M. J.; López Ortí, José Antonio
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Title
Application of Vector Spherical Harmonics and Kernel Regression to the Computations of OMM ParametersDate
2015-04Publisher
The American Astronomical SocietyISSN
0004-6256Bibliographic citation
MARCO, F. J.; MARTÍNEZ, M. J.; LÓPEZ, J. A. Application of Vector Spherical Harmonics and Kernel Regression to the Computations of OMM Parameters. The Astronomical Journal, 2015, vol. 149, no 4, p. 129.Type
info:eu-repo/semantics/articlePublisher version
http://iopscience.iop.org/article/10.1088/0004-6256/149/4/129/metaVersion
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Abstract
The high quality of Hipparcos data in position, proper motion, and parallax has allowed for studies about stellar
kinematics with the aim of achieving a better physical understanding of our galaxy, based on accurate ... [+]
The high quality of Hipparcos data in position, proper motion, and parallax has allowed for studies about stellar
kinematics with the aim of achieving a better physical understanding of our galaxy, based on accurate calculus of
the Ogorodnikov–Milne model (OMM) parameters. The use of discrete least squares is the most common
adjustment method, but it may lead to errors mainly because of the inhomogeneous spatial distribution of the data.
We present an example of the instability of this method using the case of a function given by a linear combination
of Legendre polynomials. These polynomials are basic in the use of vector spherical harmonics, which have been
used to compute the OMM parameters by several authors, such as Makarov & Murphy, Mignard & Klioner, and
Vityazev & Tsvetkov. To overcome the former problem, we propose the use of a mixed method (see Marco et al.)
that includes the extension of the functions of residuals to any point on the celestial sphere. The goal is to be able to
work with continuous variables in the calculation of the coefficients of the vector spherical harmonic developments
with stability and efficiency. We apply this mixed procedure to the study of the kinematics of the stars in our
Galaxy, employing the Hipparcos velocity field data to obtain the OMM parameters. Previously, we tested the
method by perturbing the Vectorial Spherical Harmonics model as well as the velocity vector field. [-]
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