The anisotropy parameter β characterizes the extent to which orbits in stellar systems are predominantly radial or tangential, and is likely to constrain, for the stellar halo of the Milky Way, scenarios for its formation and evolution. We have measured the anisotropy β as a function of Galactocentric radius from 5 − 100 kpc for over 8600 metal poor ([Fe/H] < −1.3) halo K giants from the LAMOST catalog with line-of-sight velocities and distances, matched to proper motions from the second Gaia data release. We construct full 6-D positions and velocities for the K giants to directly measure the 3 components of the velocity dispersion (σ r , σ θ , σ φ ) (in spherical coordinates). We find that the orbits in the halo are radial over our full Galactocentric distance range reaching over 100 kpc. The anisotropy remains remarkably unchanged with Galactocentric radius from approximately 5 to 25 kpc, with an amplitude that depends on the metallicity of the stars, dropping from β ≈ 0.9 for −1.8 ≤ [Fe/H] < −1.3 (for the bulk of the stars) to β ≈ 0.6 for the lowest metallicities ([Fe/H] < −1.8). Considering our sample as a whole, β ≈ 0.8 and, beyond 25 kpc, the orbits gradually become less radial and anisotropy decreases to β < 0.3 past 100 kpc. Within 8 kpc, β < 0.8. The measurement of anisotropy is affected by substructure and streams, particularly beyond a Galactocentric distance of approximately 25 kpc, where the Sagittarius stream is prominent in the data. These results are complimentary to recent analysis of simulations by Loebman et al. and of SDSS/Gaia DR1 data by Belokurov et al.

We use a distribution function analysis to estimate the mass of the Milky Way (MW) out to 100 kpc using a large sample of halo stars. These stars are compiled from the literature, and the vast majority (${\sim } 98{{\ \rm per\ cent}}$) have 6D phase-space information. We pay particular attention to systematic effects, such as the dynamical influence of the Large Magellanic Cloud (LMC), and the effect of unrelaxed substructure. The LMC biases the (pre-LMC infall) halo mass estimates towards higher values, while realistic stellar haloes from cosmological simulations tend to underestimate the true halo mass. After applying our method to the MW data, we find a mass within 100 kpc of M (&lt;100 kpc) = 6.07 ± 0.29 (stat.) ± 1.21 (sys.) × 1011 M⊙. For this estimate, we have approximately corrected for the reflex motion induced by the LMC using the Erkal et al. model, which assumes a rigid potential for the LMC and MW. Furthermore, stars that likely belong to the Sagittarius stream are removed, and we include a 5 per cent systematic bias, and a 20 per cent systematic uncertainty based on our tests with cosmological simulations. Assuming the mass–concentration relation for Navarro–Frenk–White haloes, our mass estimate favours a total (pre-LMC infall) MW mass of M200c = 1.01 ± 0.24 × 1012 M⊙, or (post-LMC infall) mass of M200c = 1.16 ± 0.24 × 1012 M⊙ when a 1.5 × 1011 M⊙ mass of a rigid LMC is included.

Radial velocity (RV) is among the most fundamental physical quantities obtainable from stellar spectra and is rather important in the analysis of time-domain phenomena. LAMOST Medium-resolution Survey (MRS) DR7 contains five million single-exposure stellar spectra with spectral resolution R ∼ 7500. However, the temporal variation of the RV zero-points (RVZPs) of the MRS, which makes the RVs from multiple epochs inconsistent, has not been addressed. In this paper, we measure the RVs of 3.8 million single-exposure spectra (for 0.6 million stars) with signal-to-noise ratios (S/N) higher than 5 based on the cross-correlation function method, and propose a robust method to self-consistently determine the RVZPs exposure by exposure for each spectrograph with the help of Gaia DR2 RVs. Such RVZPs are estimated for 3.6 million RVs and can reach a mean precision of ∼0.38 km s−1. The result of the temporal variation of RVZPs indicates that our algorithm is efficient and necessary before we use the absolute RVs to perform time-domain analyses. Validating the results with APOGEE DR16 shows that our absolute RVs can reach an overall precision of 0.84/0.80 km s−1 in the blue/red arm at 50 < S/N < 100 and of 1.26/1.99 km s−1 at 5 < S/N < 10. The cumulative distribution function of the standard deviations of multiple RVs (N obs ≥ 8) for 678 standard stars reaches 0.45/0.54, 1.07/1.39, and 1.45/1.86 km s−1 in the blue/red arm at the 50%, 90%, and 95% levels, respectively. Catalogs of the RVs, RVZPs, and selected candidate RV standard stars are available at https://github.com/hypergravity/paperdata.