High-speed molecular cloudlets around the Galactic center’s supermassive black hole

We present 1″-resolution ALMA observations of the circumnuclear disk (CND) and the interstellar environment around Sgr A*. The images unveil the presence of small spatial scale 12CO (J = 3–2) molecular “cloudlets” (≲20 000 AU size) within the central parsec of the Milky Way, in other words, inside the cavity of the CND, and moving at high speeds, up to 300 km s−1 along the line-of-sight. The 12CO-emitting structures show intricate morphologies: extended and filamentary at high negative-velocities (vLSR ≲−150 km s−1), more localized and clumpy at extreme positive-velocities (vLSR ≳+200 km s−1). Based on the pencil-beam 12CO absorption spectrum toward Sgr A* synchrotron emission, we also present evidence for a diffuse molecular gas component producing absorption features at more extreme negative-velocities (vLSR < −200 km s−1). The CND shows a clumpy spatial distribution traced by the optically thin H13CN (J = 4–3) emission. Its motion requires a bundle of non-uniformly rotating streams of slightly different inclinations. The inferred gas density peaks, molecular cores of several 105 cm−3, are lower than the local Roche limit. This supports that CND cores are transient. We apply the two standard orbit models, spirals vs. ellipses, invoked to explain the kinematics of the ionized gas streamers around Sgr A*. The location and velocities of the 12CO cloudlets inside the cavity are inconsistent with the spiral model, and only two of them are consistent with the Keplerian ellipse model. Most cloudlets, however, show similar velocities that are incompatible with the motions of the ionized streamers or with gas bounded to the central gravity. We speculate that they are leftovers of more massive molecular clouds that fall into the cavity and are tidally disrupted, or that they originate from instabilities in the inner rim of the CND that lead to fragmentation and infall from there. In either case, we show that molecular cloudlets, all together with a mass of several 10 M⊙, exist around Sgr A*. Most of them must be short-lived, ≲104 yr: photoevaporated by the intense stellar radiation field, G0 ≃ 105.3–104.3, blown away by winds from massive stars in the central cluster, or disrupted by strong gravitational shears.

On the shapes of Newton's revolving orbits

Newton's beautiful theorem on revolving orbits is described in propositions 43 and 44 of Principia . From Motte's translation revised by Cajori (see also Chandrasekhar, who first drew our attention to this theorem). 43. It is required to make a body move in a curve that revolves about the centre of force in the same manner as another body in the same curve at rest 4. The difference of the forces by which two bodies may be made to move equally, one in a fixed, the other in the same orbit revolving varies inversely as the cubes of their common altitudes (radii). Those who read these propositions without consulting the expositions that follow them are likely to believe that Newton was considering two orbits, the first in fixed axes and the second in uniformly rotating axes. This is not the case. Indeed, that could not be so because unless the orbits were circular, the second particle would not then sweep out equal areas in equal times relative to fixed axes, so the force could not be central. Newton's subtlety lies in choosing the rate of rotation of the axes proportional to the øof the particle in the fixed orbit, where ø is the azimuth. With that construction the second particle, when seen from fixed axes, sweeps in equal times equal areas proportional to those swept by the first. A Keplerian ellipse in fixed axes will generate the same ellipse in Newton's nonuniformly rotating axes when we add an inverse cube force. But what shape will that ellipse make relative to axes rotating uniformly at the same mean rate as Newton's?

A discussion on orbital analysis - Determination of the Earth’s gravitational field from satellite orbits: methods and results

The structure of theories used in determining the gravitational field from the perturbations of orbits of artificial satellites is discussed and it is shown how it corresponds to the fact that small departures from a Keplerian ellipse are readily observed. Some current problems are mentioned. Statistical problems in the estimation of parameters of the field from orbital data are considered and recent estimates are summarized