Eccentricity samples: Implications on the potential and the velocity distribution
Planar and vertical epicycle frequencies and local angular velocity are related to the derivatives up to the second order of the local potential and can be used to test the shape of the potential from stellar disc samples. These samples show a more complex velocity distribution than halo st...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Astronomical Observatory, Department of Astronomy, Belgrade
2017-01-01
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| Series: | Serbian Astronomical Journal |
| Subjects: | |
| Online Access: | http://www.doiserbia.nb.rs/img/doi/1450-698X/2017/1450-698X1700004C.pdf |
| Summary: | Planar and vertical epicycle frequencies and local angular velocity are
related to the derivatives up to the second order of the local potential and
can be used to test the shape of the potential from stellar disc samples.
These samples show a more complex velocity distribution than halo stars and
should provide a more realistic test. We assume an axisymmetric potential
allowing a mixture of independent ellipsoidal velocity distributions, of
separable or Staeckel form in cylindrical or spherical coordinates. We prove
that values of local constants are not consistent with a potential separable
in addition in cylindrical coordinates and with a spherically symmetric
potential. The simplest potential that fits the local constants is used to
show that the harmonical and non-harmonical terms of the potential are
equally important. The same analysis is used to estimate the local
constants. Two families of nested subsamples selected for decreasing planar
and vertical eccentricities are used to borne out the relation between the
mean squared planar and vertical eccentricities and the velocity dispersions
of the subsamples. According to the first-order epicycle model, the radial
and vertical velocity components provide accurate information on the planar
and vertical epicycle frequencies. However, it is impossible to account for
the asymmetric drift which introduces a systematic bias in estimation of the
third constant. Under a more general model, when the asymmetric drift is
taken into account, the rotation velocity dispersions together with their
asymmetric drift provide the correct fit for the local angular velocity. The
consistency of the results shows that this new method based on the
distribution of eccentricities is worth using for kinematic stellar samples. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. No 176011: Dynamics and Kinematics of Celestial Bodies and Systems] |
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| ISSN: | 1450-698X 1820-9289 |