We recently proposed that the star-forming potential of dense molecular clouds in the Central Molecular Zone ( CMZ , i.e .
the central few 100 ~ { } \mbox { $ { 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 _ { red } ^ { 2 } = 2.0 ) to the observed position-velocity distribution of dense ( n > { several } ~ { } 10 ^ { 3 } ~ { } \mbox { $ { 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 ~ { } \mbox { $ { 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 ~ { } \mbox { $ { Myr } $ } ago .
Given their short free-fall times ( t _ { ff } \sim 0.34 ~ { } \mbox { $ { 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 .