we use the solar peculiar motions $(U_\odot, V_\odot, W_\odot)=(11.1, 12.24, 7.25)$ km s$^{-1}$ derived by [@schonrich10]. Thus, in our analysis, the circular speed at the position of the Sun is $V_c = 238$ km s$^{-1}$ (where $V_{g, \odot}= V_c +V_\odot$). We note that the combination of $R_0=8.5$ kpc and $V_c = 220$ km s$^{-1}$ has been used widely in the literature, so in Section \[sec:res\] we show how our halo rotation signal is affected if we instead adopt these parameters.

Model
-----

We define a (rotating) 3D velocity ellipsoid aligned in spherical coordinates:

$$\begin{aligned}
\label{eqn:fv}
&&P(v_r,v_\theta,v_\phi|\sigma_r,\sigma_\phi,\sigma_\theta,\langle V_\phi \rangle) = \\ 
&&\frac{1}{\left(2\pi\right)^{3/2}\sigma_r \sigma_\theta
  \sigma_\phi} \mathrm{exp}\left[-\frac{v^2_r}{2\sigma^2_r}-\frac{v^2_\theta}{2
    \sigma^2_\theta}-\frac{\left(v_\phi-\langle V_{\phi} \rangle\right)^2}{2
    \sigma^2_\phi}\right] \notag\end{aligned}$$

Here, we only allow net streaming motion in the $v_\phi$ velocity coordinate, and assume Gaussian velocity distributions. Note that positive $\langle V_{\phi} \rangle$ is in the same direction as the disc rotation. For simplicity, we assume an isotropic ellipsoid where $\sigma_r=\sigma_\theta=\sigma_\phi=\sigma_*$, but we have ensured that this assumption of isotropy does not significantly affect our rotation estimates (see also Section \[sec:sims\]).

This velocity distribution function can be transformed to Galactic coordinates $(\mu_l, \mu_b, v_{\rm los})$ by using the Jacobian of the transformation $J=4.74047^2 D^2$, which gives $P(\mu_l, \mu_b,v_{\rm los}|\sigma_*,\langle V_\phi \rangle, 