Dynamically constraining the length of the Milky Way bar

We present a novel method for constraining the length of the Galactic bar using 6D phase space information to directly integrate orbits. We define a pseudo-length for the Galactic bar, named $R_{Freq}$, based on the maximal extent of trapped bar orbits. We find the $R_{Freq}$ measured from orbits is consistent with the $R_{Freq}$ of the assumed potential only when the length of the bar and pattern speed of said potential is similar to the model from which the initial phase-space coordinates of the orbits are derived. Therefore, one can measure the model's or the Milky Way's bar length from 6D phase-space coordinates by determining which assumed potential leads to a self-consistent measured $R_{Freq}$. When we apply this method to $\approx$210,000 stars in APOGEE DR17 and $Gaia$ eDR3 data, we find a consistent result only for potential models with a dynamical bar length of $\approx$3.5 kpc. We find the Milky Way's trapped bar orbits extend out to only $\approx$3.5 kpc, but there is also an overdensity of stars at the end of the bar out to 4.8 kpc which could be related to an attached spiral arm. We also find that the measured orbital structure of the bar is strongly dependent on the properties of the assumed potential.