Differential rotation of the halo traced by the K-giant stars

We use K-giant stars selected from the LAMOST DR5 to study the variation of the rotational velocity of the galactic halo at different space positions. Modelling the rotational velocity distribution with both the halo and disk components, we find that the rotational velocity of the halo population decreases almost linearly with increasing vertical distance to the galactic disk plane, $Z$, at fixed galactocentric radius, $R$. The samples are separated into two parts with $6<R<12$ kpc and $12<R<20$ kpc. We derive that the decreasing rates along $Z$ for the two subsamples are $-3.07\pm0.63$ and $-1.89\pm0.37$ km s$^{-1}$ kpc$^{-1}$, respectively. Compared with the TNG simulations, we suggest that this trend is probably caused by the interaction between the disk and halo. The results from the simulations show that only the oblate halo can provide a decreasing rotational velocity with an increasing $Z$. This indicates that the Galactic halo is oblate with galactocentric radius $R<20$ kpc. On the other hand, the flaring of the disk component (mainly the thick disk) is clearly traced by this study, with $R$ between 12 and 20 kpc, the disk can vertically extend to $6\sim10$ kpc above the disk plane. What is more interesting is that, we find the Gaia-Enceladus-Sausage (GES) component has a significant contribution only in the halo with $R<12$ kpc, i.e. a fraction of 23$-$47\%. While in the outer subsample, the contribution is too low to be well constrained.