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Constraints on the Galactic Bar from the Hercules stream as traced with RAVE across the Galaxy

Non-axisymmetries in the Galactic potential (spiral arms and bar) induce kinematic groups such as the Hercules stream. Assuming that Hercules is caused by the effects of the Outer Lindblad Resonance of the Galactic bar, we model analytically its properties as a function of position in the Galaxy and its dependence on the bar's pattern speed and orientation. Using data from the RAVE survey we find that the azimuthal velocity of the Hercules structure decreases as a function of Galactocentric radius, in a manner consistent with our analytical model. This allows us to obtain new estimates of the parameters of the Milky Way's bar. The combined likelihood function of the bar's pattern speed and angle has its maximum for a pattern speed of $Ω_b=(1.89 \pm 0.08) \times Ω_0$ where $Ω_0$ is the local circular frequency. Assuming a Solar radius of 8.05 kpc and a local circular velocity of 238 km/s, this corresponds to $Ω_b=56\pm 2$ km/s/kpc. On the other hand, the bar's orientation $ϕ_b$ cannot be constrained with the available data. In fact, the likelihood function shows that a tight correlation exists between the pattern speed and the orientation, implying that a better description of our best fit results is given by the linear relation $Ω_b/Ω_0=1.91 + 0.0044[ϕ_b(°)-48]$, with standard deviation of 0.02. For example, for an angle of $ϕ_b=30°$ the pattern speed is $54.0\pm0.5$ km/s/kpc. These results are not very sensitive to the other Galactic parameters such as the circular velocity curve or the peculiar motion of the Sun, and are robust to biases in distance.