At large distances, the proper motions of the halo stars are either unreliable or generally unavailable, which hinders a direct measurement of their velocity dispersions. However, our off-centric location in the Galaxy means that the galactocentric radial (r) and heliocentric radial (s) directions are not the same. This difference is more significant in the inner halo, at a distance of r ≲ a couple of times of R0, where R0 is the distance of the Sun from the Galactic Centre. Hence, in the inner halo the observed line-of-sight velocities of the stars can be expressed in terms of all three orthogonal galactocentric velocities (vr, vθ, vϕ), or in other words the line-of-sight velocities have some contribution from the tangential galactocentric velocities. Provided we have a model that well represents the distribution of the halo stars, we can fit a model marginalized over the unknown tangential motions to the available four-dimensional data (position vector and a line-of-sight velocity), and thus estimate the velocity moments of the system. In the absence of proper motion, the approach of estimating moments of the velocities has been extensively used to predict the kinematics of the MW halo. For example, Sirko et al. (2004), Kafle et al. (2012), Kafle et al. (2013), Kafle et al. (2014) and King et al. (2015) fit an ellipsoidal distribution of velocities and similarly, Deason, Belokurov & Evans (2011a) apply an alternative power-law model to derive the halo kinematics. Using the marginalisation scheme, Kafle et al. (2012, 2013) studied halo Blue Horizontal Branch stars (BHBs), Kafle et al. (2014) studied both BHBs and K-Giant stars (KGs), while King et al. (2015) analysed a mixed bag of BHB and F-type stars to cumulatively construct the velocity dispersion and anisotropy of the outer halo. Interestingly, Kafle et al. (2012) found that the velocity anisotropy parameter of the Galactic halo is non-monotonic and has a prominent dip at a galactocentric radius of r ≃ 18 kpc. In their studies, King et al. (2015) find that the value of β at 15 ≲ R/kpc ≲ 25 is more tangentially biased, which they attribute to the difference in the spatial resolutions of the data sets and adopt a marginalization technique. A varying level of undulations in the anisotropy parameter has also been observed in simulated haloes (Rashkov et al. 2013; Loebman et al. 2017). There are a number of proposed scenarios that could explain such a feature, e.g. a transition from inner to outer halo or a local shell-like structure at the given radius. Moreover, it can also be due to the unrelaxed stars dispersed from the kinematically coherent satellite galaxies that are aligned with kinematically coherent planar structures; assuming that such planar structures have strong rotation as suggested by Ibata et al. (2013), Pawlowski, McGaugh & Jerjen (2015), Libeskind et al. (2015) and Ibata et al. (2015), etc. Recently, Loebman et al. (2017) suggest that a major merger as early as redshift z ∼ 1 can also result in a tangential dip in the value of β over a wide range of radii. While Bird & Flynn (2015) suggest that such a feature in the velocity anisotropy run of the halo is a transitory phase, Loebman et al. (2017) conclude that such dips are long-lived in the in situ stellar halo. In any case, there is currently no consensus view as to what causes such velocity anisotropy changes. Finally, in the outer halo there have been recent attempts to utilize multi-epoch Hubble Space Telescope data to estimate the halo velocity dispersion. In particular, recently Cunningham et al. (2016) used the Galactic foreground stars along the M31 galaxy and found that the halo is isotropic at r/kpc ∼ 25. In Fig. 10, we summarize the recent (this paper inclusive) measurements of the halo velocity anisotropy.
Citation: Kafle et al. (2013)
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