The pattern speed of the Milky Way bar from transverse velocities. (arXiv:1903.02009v1 [astro-ph.GA])
<a href="http://arxiv.org/find/astro-ph/1/au:+Sanders_J/0/1/0/all/0/1">Jason L. Sanders</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Smith_L/0/1/0/all/0/1">Leigh Smith</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Evans_N/0/1/0/all/0/1">N. Wyn Evans</a>

We use the continuity equation to derive a method for measuring the pattern
speed of the Milky Way’s bar from proper motion data. The method has minimal
assumptions but requires complete coverage of the non-axisymmetric component in
two of the three Galactic coordinates. We apply our method to the proper motion
data from a combination of Gaia DR2 and VISTA Variables in the Via Lactea (VVV)
to measure the pattern speed of the bar as $Omega_mathrm{p}=(41pm
3),mathrm{km,s^{-1},kpc^{-1}}$. This puts the corotation radius at
$(5.5pm0.3),mathrm{kpc}$, under the assumptions of the standard peculiar
motion of the Sun and the absence of non-axisymmetric streaming in the Solar
neighbourhood. We demonstrate using a dynamically-formed bar/bulge simulation
that even with the limited field of view of the VVV survey our method robustly
recovers the pattern speed.

We use the continuity equation to derive a method for measuring the pattern
speed of the Milky Way’s bar from proper motion data. The method has minimal
assumptions but requires complete coverage of the non-axisymmetric component in
two of the three Galactic coordinates. We apply our method to the proper motion
data from a combination of Gaia DR2 and VISTA Variables in the Via Lactea (VVV)
to measure the pattern speed of the bar as $Omega_mathrm{p}=(41pm
3),mathrm{km,s^{-1},kpc^{-1}}$. This puts the corotation radius at
$(5.5pm0.3),mathrm{kpc}$, under the assumptions of the standard peculiar
motion of the Sun and the absence of non-axisymmetric streaming in the Solar
neighbourhood. We demonstrate using a dynamically-formed bar/bulge simulation
that even with the limited field of view of the VVV survey our method robustly
recovers the pattern speed.

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