Vertical motion and expansion of the Gould Belt

The kinematics of the Gould Belt is considered taking into account its orientation in space and the motions of its member stars parallel and perpendicular to the galactic plane. An analysis of Hipparcos data for these stars, complemented with published radial velocities, shows that there is a mild gradient along the galactic plane in the velocity component perpendicular to it. The maintenance of the arrangement of Gould Belt stars forming a plane, even for times that are at least a considerable fraction of the vertical oscillation period of stars around the galactic plane, is a rather strong constraint on any kinematical models of the Gould Belt. It is shown that such a constraint can be satisfied if the stars had initial velocities linearly dependent on their positions in the plane of the Belt. Adopting such linear patterns and the epicyclic approximation to galactic orbits, analytical expressions are derived that allow the calculation, for any age of the Gould Belt, of the direction of its nodal line, its inclination, the values of the Oort constants A, B, C, and K, the gradient of the velocity component perpendicular to the galactic disk, and the direction of the axis of oscillation of the stars of the Belt perpendicular to the galactic plane. The evolution of all these quantities is calculated for several cases: a purely circular motion of the Gould Belt stars around the galactic center; the radial expansion from a small volume or over an extended area; the expansion along a line; and an initial rotation to the Gould Belt stars around an axis perpendicular to its plane. Pure expansion models seem to be ruled out by observations, as none of them, under any combination of initial parameters, is able to simultaneously reproduce all the observed values of the orientation, the Oort constants, and the characteristics of the vertical motion. Nevertheless, a good agreement is found between measured values of the quantities defining the orientation and kinematics of the Gould Belt, and the predictions of the rotation model. This model is the only one among those considered here able to account for the large observed offset between the nodal line of the Gould Belt with respect to the galactic plane and the axis of vertical oscillation of its stars. The best fit is achieved for an age of the Gould Belt of (3.4 ± 0.3) × 107 years, consistent with individual ages determined for Gould Belt stars. The implications that the rotation model has concerning the possible origin of the Gould Belt is briefly discussed. It is found that the disruption of a rotating, star forming giant molecular cloud is unlikely to be at the origin of the Gould Belt, due to the significant tilt with respect to the direction perpendicular to the galactic plane that it should have had.