We determine the total dynamical density in the solar neighbourhood using the Tycho-Gaia Astrometric Solution ( TGAS ) catalogue .
Astrometric measurements of proper motion and parallax of stars inform us of both the stellar number density distribution and the velocity distribution of stars close to the plane .
Assuming equilibrium , these distributions are interrelated through the local dynamical density .
For the first time , we do a full joint fit of the velocity and stellar number density distributions while accounting for the astrometric error of individual stars , in the framework of Bayesian hierarchical modelling .
We use a sample of stars whose distance extends to approximately 160 pc from the Sun .
We find a local matter density of \rho _ { 0 } = 0.119 ^ { +0.015 } _ { -0.012 } ~ { } M _ { \odot } n { pc } ^ { -3 } , where the result is presented as the median to the posterior distribution , plus/minus its 16th and 84th percentiles .
We find the Sun ’ s position above the Galactic plane to be z _ { \odot } = 15.29 ^ { +2.24 } _ { -2.16 } ~ { } n { pc } , and the Sun ’ s velocity perpendicular to the Galactic plane to be W _ { \odot } = 7.19 ^ { +0.18 } _ { -0.18 } ~ { } n { km } n { s } ^ { -1 } .