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Title: The alignment of the second velocity moment tensor in galaxies
Authors: Evans, N. W.
Sanders, J. L.
Williams, A. A.
An, J.
Lynden-Bell, D.
Dehnen, W.
First Published: 22-Jan-2016
Publisher: Oxford University Press (OUP), Royal Astronomical Society
Citation: Monthly Notices of the Royal Astronomical Society, 2016, 456 (4), pp. 4506-4523 (18)
Abstract: We show that provided the principal axes of the second velocity moment tensor of a stellar population are generally unequal and are oriented perpendicular to a set of orthogonal surfaces at each point, then those surfaces must be confocal quadric surfaces and the potential must be separable or Stäckel. This is true under the mild assumption that the even part of the distribution function (DF) is invariant under time reversal vi → −vi of each velocity component. In particular, if the second velocity moment tensor is everywhere exactly aligned in spherical polar coordinates, then the potential must be of separable or Stäckel form (excepting degenerate cases where two or more of the semiaxes of ellipsoid are everywhere the same). The theorem also has restrictive consequences for alignment in cylindrical polar coordinates, which is used in the popular Jeans Anisotropic Models (JAM) of Cappellari. We analyse data on the radial velocities and proper motions of a sample of ∼7300 stars in the stellar halo of the Milky Way. We provide the distributions of the tilt angles or misalignments from both the spherical polar coordinate systems. We show that in this sample the misalignment is always small (usually within 3°) for Galactocentric radii between ∼6 and ∼11 kpc. The velocity anisotropy is very radially biased (β ≈ 0.7), and almost invariant across the volume in our study. Finally, we construct a triaxial stellar halo in a triaxial NFW dark matter halo using a made-to-measure method. Despite the triaxiality of the potential, the velocity ellipsoid of the stellar halo is nearly spherically aligned within ∼6° for large regions of space, particularly outside the scale radius of the stellar halo. We conclude that the second velocity moment ellipsoid can be close to spherically aligned for a much wider class of potentials than the strong constraints that arise from exact alignment might suggest.
DOI Link: 10.1093/mnras/stv2729
ISSN: 0035-8711
eISSN: 1365-2966
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: © 2016 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society Archived with reference to SHERPA/RoMEO and publisher website.
Appears in Collections:Published Articles, Dept. of Physics and Astronomy

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