Kinematics and dynamics of the Galactic bar revealed by Gaia long-period variables

We use low-amplitude, long period variable (LA-LPV) candidates in \textit{Gaia} DR3 to trace the kinematics and dynamics of the Milky Way bar. LA-LPVs, like other LPVs, are intrinsically bright and follow a tight period-luminosity relation, but unlike e.g. Mira variables, their radial velocity measurements are reliable due to their smaller pulsation amplitudes. We supplement the \textit{Gaia} astrometric and radial velocity measurements with distance moduli assigned using a period-luminosity relation to acquire full 6D phase space information. The assigned distances are validated by comparing to geometric distances and StarHorse distances, which shows biases less than $\sim5\%$. Our sample provides an unprecedented panoramic picture of the inner Galaxy with minimal selection effects. We map the kinematics of the inner Milky Way and find a significant kinematic signature corresponding to the Galactic bar. We measure the pattern speed of the Galactic bar using the continuity equation and find $\Omega_{\rm b}=34.1\pm2.4$ km s$^{-1}$ kpc$^{-1}$. We develop a simple, robust and potential-independent method to measure the dynamical length of the bar using only kinematics and find $R_{\rm b}\sim4.0$ kpc. We validate both measurements using N-body simulations. Assuming knowledge of the gravitational potential of the inner Milky Way, we analyse the orbital structure of the Galactic bar using orbital frequency ratios. The $x_1$ orbits are the dominant bar-supporting orbital family in our sample. Amongst the selected bar stars, the $x_1 v_1$ or "banana" orbits constitute a larger fraction ($\sim 15\%$) than other orbital families in the bar, implying that they are the dominant family contributing to the Galactic X-shape, although contributions from other orbital families are also present.