The tilting rate of the Milky Way's disc

We present tilting rates for galaxies comparable to the Milky Way (MW) in a $\Lambda$ cold dark matter cosmological hydrodynamical simulation, and compare these with the predicted tilting rate detection limit of the {\it Gaia} satellite $0.28\degrees$Gyr$^{-1}$. We first identify galaxies with mass comparable to the MW ($9 \times 10^{11} \le M_{200} \le 1.2 \times 10^{12} \Msun $) and consider the tilting rates between $z=0.3$ and $0$. This sample yields a tilting rate of $7.6\degrees \pm 4.5\degrees$Gyr$^{-1}$. We constrain our sample further to exclude any galaxies that have high stellar accretion during the same time. We still find significant tilting, with an average rate of $6.3\degrees$Gyr$^{-1}$. Both subsamples tilt with rates significantly above {\it Gaia}'s predicted detection limit. We show that our sample of galaxies covers a wide range of environments, including some similar to the MW's. We find galaxies in denser regions tilt with higher rates then galaxies in less dense regions. We also find correlations between the angular misalignment of the hot gas corona, and the tilting rate. {\it Gaia} is likely to be able to directly measure tilting in the MW. Such a detection will provide an important constraint on the environment of the MW, including the rate of gas cooling onto the disc, the shape and orientation of its dark matter halo, and the mass of the Large Magellanic Cloud. Conversely, failure to detect tilting may suggest the MW is in a very quiet configuration.