Galactic mass and anisotropy profile with halo K-giant and blue horizontal branch stars from LAMOST/SDSS and Gaia

Abstract A major uncertainty in the determination of the mass profile of the Milky Way using stellar kinematics in the halo is the poorly determined anisotropy parameter, , where σr is the Galactocentric radial velocity dispersion, and σθ and σφ are the tangential components of the velocity dispersion. We have used a sample of over 24,000 Galactic halo K giant and blue horizontal branch stars from the LAMOST stellar spectroscopic survey and SDSS/SEGUE, combined with proper motions from Gaia Data Release 2, to measure β(rgc) over a wide range of Galactocentric distances rgc from 5 to 80 kpc. Kinematic substructures have been carefully removed to reveal the underlying diffuse stellar halo prior to measuring β. We find that orbits are generally radial (β > 0) and β is constant out to distances of about 40 kpc, with a dependence on metallicity of the stars, such that β declines with lower metallicity. Similar behavior is seen in both the K giant and BHB samples.


Introduction
Our current knowledge of the Milky Way's total mass is uncertain by a factor of two (see related discussions, e.g. Wang et al. 2015;Eadie & Harris 2016;Eadie & Jurić 2019;Callingham et al. 2019). Via the Jeans equation the mass can be estimated from the density and anisotropy β profile of tracer objects. Measurements of the β profile have eluded our grasp before Gaia due to the lack of large samples of halo stars covering a wide range of distances with both radial velocities and proper motions. We describe here a very large sample of such stars which is part of an ongoing program using LAMOST. 92 S. A. Bird et al.

Data Sample and Method
We select halo stars from samples of K-giants in LAMOST DR5 (Wu et al. 2011;Cui et al. 2012;Deng et al. 2012;Zhao et al. 2012;Luo et al. 2012;Wu et al. 2014;Luo et al. 2015) and SDSS/SEGUE (Yanny et al. 2009;Ahn et al. 2012) and BHBs from SDSS. We define K giants from LAMOST by 4000 < T eff /K < 4600 with log g < 3.5 dex and 4600 < T eff /K < 5600 with log g < 4 dex (Liu et al. 2014;Bird et al. 2019). We include K giants from SDSS/SEGUE as selected by Xue et al. (2014). We derive spectroscopic distances using the method presented by Xue et al. (2014). We use the Xue et al. (2011) BHB sample which selects stars based on limits in their color and Balmer line profiles. The distances are photometrically derived as in Xue et al. (2011) and have typical uncertainties of ∼ 10%. The large surveys LAMOST and SDSS provide line-of-sight velocities. To these we add proper motions from Gaia DR2 (Gaia Collaboration et al. 2018).
We define Galactocentric spherical coordinates as in Bird et al. (2019). To clean our sample of disk stars, we keep only those with |Z| > 5 kpc (all metallicities) and to this add stars with 2 < |Z| < 5 kpc and [Fe/H] < −1. In total, our stellar halo sample consists of >15,000 LAMOST DR5 K giants, >5,000 SDSS K giants, and >4,000 SDSS BHBs.
We use the method of Xue et al. (2020, in preparation) to remove kinematic substructure. Substructure is identified in integral-of-motion space E, L X , L Y , L Z using a friends-of-friends algorithm. We determine orbital parameters e, a, (l orbit , b orbit ), l apo . Stream-members share similar orbits. We flag these as substructure and remove them to define a smooth, diffuse halo sample. The sample is further cleaned keeping only stars of E < 0 (km s −1 ) 2 . Our smooth halo sample consists of 15,280 K giants and BHBs.

Results and Discussion
We show the spherical coordinate velocities of our LAMOST halo K-giants in Figure 1. The corresponding results for BHBs will be presented in Bird et al. (2020, in preparation).
The resulting anisotropy profiles and their dependency on metallicity are shown in Figure 2. The key results are • LAMOST/SDSS + Gaia DR2 yield over 24,000 halo K-giant and BHB stars • first presentation of 3D velocity profiles for such a large and spatially far-reaching halo star sample • β profile is found to be constant out to distances exceeding r gc = 40 kpc where β ∼ 0.4 to 0.8 depending on the stellar metallicity • orbits are thus predominantly radial (β > 0) • K giants and BHBs both share similar radially dominated stellar orbits and β dependence on [Fe/H].
Our results are in agreement with the recent analyses of Belokurov et al. (2018) and Lancaster et al. (2019) who also use 3D velocities for main sequence and BHB, respectively, halo stars, as seen in Figure 2.
Fresh evidence of chemo-dynamically different stellar halo components has emerged in combination with Gaia data (e.g. Belokurov et al. 2018;Deason et al. 2018;Koppelman et al. 2018;Helmi et al. 2018;Myeong et al. 2018aMyeong et al. ,b,c,d, 2019Bird et al. 2019;Kruijssen et al. 2019;Lancaster et al. 2019;Mackereth et al. 2019;Matsuno et al. 2019;Simion et al. 2019;Vasiliev 2019), revealing a major contributor to the Milky Way's  dependency of anisotropy and metallicity is likely the recently uncovered large merger remnant, which goes by such names as "Gaia Sausage," "Gaia-Enceladus," "Kracken," and "blob." Our sample of stars extending to greater distances shows a continuation of the anisotropy-metallicity dependency extending out to 40 kpc.