Dust within the old nuclear star cluster in the Milky Way
  The mean absolute extinction towards the central parsec of the Milky Way is
A_K~3 mag, including both foreground and Galactic center dust. Here we present
a measurement of dust extinction within the Galactic old nuclear star cluster
(NSC), based on combining differential extinctions of NSC stars with their u_l
proper motions along Galactic longitude. Extinction within the NSC
preferentially affects stars at its far side, and because the NSC rotates, this
causes higher extinctions for NSC stars with negative u_l, as well as an
asymmetry in the u_l-histograms. We model these effects using an axisymmetric
dynamical model of the NSC in combination with simple models for the dust
distribution. Comparing the predicted asymmetry to data for ~7100 stars in
several NSC fields, we find that dust associated with the Galactic center
mini-spiral with extinction A_K~=0.15-0.8 mag explains most of the data. The
largest extinction A_K~=0.8 mag is found in the region of the Western arm of
the mini-spiral. Comparing with total A_K determined from stellar colors, we
determine the extinction in front of the NSC. Finally, we estimate that for a
typical extinction of A_K~=0.4 the statistical parallax of the NSC changes by
~0.4%.
