A mass-velocity anisotropy relation in galactic stellar disks
  The ellipsoid of stellar random motions is a fundamental ingredient of galaxy
dynamics. Yet it has long been difficult to constrain this component in disks
others than the Milky Way. This article presents the modeling of the
azimuthal-to-radial axis ratio of the velocity ellipsoid of galactic disks from
stellar dispersion maps using integral field spectroscopy data of the CALIFA
survey. The measured azimuthal anisotropy is shown to be not strongly dependent
on the assumed vertical-to-radial dispersion ratio of the ellipsoid. The
anisotropy distribution shows a large diversity in the orbital structure of
disk galaxies from tangential to radial stellar orbits. Globally, the orbits
are isotropic in inner disk regions and become more radial as a function of
radius, although this picture tends to depend on galaxy morphology and
luminosity. The Milky Way orbital anisotropy profile measured from the Second
Gaia Data Release is consistent with those of CALIFA galaxies. A new
correlation is evidenced, linking the absolute magnitude or stellar mass of the
disks to the azimuthal anisotropy. More luminous disks have more radial orbits
and less luminous disks have isotropic and somewhat tangential orbits. This
correlation is consistent with the picture in galaxy evolution in which orbits
become more radial as the mass grows and is redistributed as a function of
time. With the help of circular velocity curves, it is also shown that the
epicycle theory fails to reproduce the diversity of the azimuthal anisotropy of
stellar random motions, as it predicts only nearly radial orbits in the
presence of flat curves. The origin of this conflict is yet to be identified.
It also questions the validity of the vertical-to-radial axis ratio of the
velocity ellipsoid derived by many studies in the framework of the epicyclic
approximation.
