The dynamical evolution of molecular clouds near the Galactic Centre - I. Orbital structure and evolutionary timeline

We recently proposed that the star-forming potential of dense molecular clouds in the Central Molecular Zone (CMZ, i.e. the central few 100 pc) of the Milky Way is intimately linked to their orbital dynamics, potentially giving rise to an absolute-time sequence of star-forming clouds. In this paper, we present an orbital model for the gas stream(s) observed in the CMZ. The model is obtained by integrating orbits in the empirically constrained gravitational potential and represents a good fit (chi(2)(red) = 2.0) to the observed position-velocity distribution of dense (n > several10(3) cm(-3)) gas, reproducing all of its key properties. The orbit is also consistent with observational constraints not included in the fitting process, such as the 3D space velocities of Sgr B2 and the Arches and Quintuplet clusters. It differs from previous, parametric models in several respects: (1) the orbit is open rather than closed due to the extended mass distribution in the CMZ, (2) its orbital velocity (100-200 km s(-1)) is twice as high as in previous models, and (3) Sgr A* coincides with the focus of the (eccentric) orbit rather than being offset. Our orbital solution supports the recently proposed scenario in which the dust ridge between G0.253+0.016 ('the Brick') and Sgr B2 represents an absolute-time sequence of star-forming clouds, of which the condensation was triggered by the tidal compression during their most recent pericentre passage. We position the clouds on a common timeline and find that their pericentre passages occurred 0.30-0.74 Myr ago. Given their short free-fall times (t(ff) similar to 0.34 Myr), the quiescent cloud G0.253+0.016 and the vigorously star-forming complex Sgr B2 are separated by a single free-fall time of evolution, implying that star formation proceeds rapidly once collapse has been initiated. We provide the complete orbital solution, as well as several quantitative predictions of our model (e.g. proper motions and the positions of star formation 'hotspots'). The paper is concluded with a discussion of the assumptions and possible caveats, as well as the position of the model in the Galactic context, highlighting its relation to large-scale gas accretion, the dynamics of the bar, the x(2) orbital family, and the origin of the Arches and Quintuplet clusters.