We report new constraints on the local escape speed of our Galaxy. Our analysis is based on a sample of high velocity stars from the RAVE survey and two previously published datasets. We use cosmological simulations of disk galaxy formation to motivate our assumptions on the shape of the velocity distribution, allowing for a significantly more precise measurement of the escape velocity compared to previous studies. We find that the escape velocity lies within the range $498kms < ve < 608 kms$ (90 per cent confidence), with a median likelihood of $544kms$. The fact that $ve^2$ is significantly greater than $2vc^2$ (where $vc=220kms$ is the local circular velocity) implies that there must be a significant amount of mass exterior to the Solar circle, i.e. this convincingly demonstrates the presence of a dark halo in the Galaxy. For a simple isothermal halo, one can calculate that the minimum radial extent is $sim58$ kpc. We use our constraints on $ve$ to determine the mass of the Milky Way halo for three halo profiles. For example, an adiabatically contracted NFW halo model results in a virial mass of $1.42^{+1.14}_{-0.54}times10^{12}M_odot$ and virial radius of $305^{+66}_{-45}$ kpc (90 per cent confidence). For this model the circular velocity at the virial radius is $142^{+31}_{-21}kms$. Although our halo masses are model dependent, we find that they are in good agreement with each other.
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