The Velocity Fields of Gas and Stars within Five KPC of the Sun

Abstract

If the velocity field around the sun is assumed to be sufficiently smooth so that it can be represented by a second order Taylor series, then the most probable value of the line of sight velocity, Vr, of an element at galactic longitude ℓ and distance projected onto the plane of the galactic disk r = d • cos(b), where d is the distance to the object, can be represented as;

$$ {V_{r}} = \cos (b)\cdot [{c_{1}}\cdot \cos (\ell + {c_{2}}) + r({c_{3}} + {c_{4}}\cdot \sin (2(\ell + {c_{5}}))) + {r^{2}}({c_{6}}\cdot \sin (\ell + {c_{7}}) + {c_{8}}\cdot \sin (3(\ell + {c_{9}})))]$$

where the coefficients are determined by a least squares fit.