The method of choice for integrating the equations of motion of the general Nbody problem has been to use an individual time step scheme. For the sake of efficiency, block time steps have been the most popular, where all time step sizes are smaller than a maximum time step size by an integer power of two. We present the first successful attempt to construct a time-symmetric integration scheme, based on block time steps. We demonstrate how our scheme shows a vastly better long-time behavior of energy errors, in the form of a random walk rather than a linear drift. Increasing the number of particles makes the improvement even more pronounced.

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Context. The Centaur (10199) Chariklo has the first ring system discovered around a small object. It was first observed using stellar occultation in 2013. Stellar occultations allow sizes and shapes to be determined with kilometre accuracy, and provide the characteristics of the occulting object and its vicinity. Aims. Using stellar occultations observed between 2017 and 2020, our aim is to constrain the physical parameters of Chariklo and its rings. We also determine the structure of the rings, and obtain precise astrometrical positions of Chariklo. Methods. We predicted and organised several observational campaigns of stellar occultations by Chariklo. Occultation light curves were measured from the datasets, from which ingress and egress times, and the ring widths and opacity values were obtained. These measurements, combined with results from previous works, allow us to obtain significant constraints on Chariklo’s shape and ring structure. Results. We characterise Chariklo’s ring system (C1R and C2R), and obtain radii and pole orientations that are consistent with, but more accurate than, results from previous occultations. We confirm the detection of W-shaped structures within C1R and an evident variation in radial width. The observed width ranges between 4.8 and 9.1 km with a mean value of 6.5 km. One dual observation (visible and red) does not reveal any differences in the C1R opacity profiles, indicating a ring particle size larger than a few microns. The C1R ring eccentricity is found to be smaller than 0.022 (3σ), and its width variations may indicate an eccentricity higher than ~0.005. We fit a tri-axial shape to Chariklo’s detections over 11 occultations, and determine that Chariklo is consistent with an ellipsoid with semi-axes of 143.8−1.5+1.4, 135.2−2.8+1.4, and 99.1−2.7+5.4 km. Ultimately, we provided seven astrometric positions at a milliarcsecond accuracy level, based on Gaia EDR3, and use it to improve Chariklo’s ephemeris.

Several mechanisms have been proposed for the formation of brown dwarfs, but there is as yet no consensus as to which -- if any -- are operative in nature. Any theory of brown dwarf formation must explain the observed statistics of brown dwarfs. These statistics are limited by selection effects, but they are becoming increasingly discriminating. In particular, it appears (a) that brown dwarfs that are secondaries to Sun-like stars tend to be on wide orbits, $a\ga 100\,{\rm AU}$ (the Brown Dwarf Desert), and (b) that these brown dwarfs have a significantly higher chance of being in a close ($a\la 10\,{\rm AU}$) binary system with another brown dwarf than do brown dwarfs in the field. This then raises the issue of whether these brown dwarfs have formed {\it in situ}, i.e. by fragmentation of a circumstellar disc; or have formed elsewhere and subsequently been captured. We present numerical simulations of the purely gravitational interaction between a close brown-dwarf binary and a Sun-like star. These simulations demonstrate that such interactions have a negligible chance ($<0.001$) of leading to the close brown-dwarf binary being captured by the Sun-like star. Making the interactions dissipative by invoking the hydrodynamic effects of attendant discs might alter this conclusion. However, in order to explain the above statistics, this dissipation would have to favour the capture of brown-dwarf binaries over single brown-dwarfs, and we present arguments why this is unlikely. The simplest inference is that most brown-dwarf binaries -- and therefore possibly also most single brown dwarfs -- form by fragmentation of circumstellar discs around Sun-like protostars, with some of them subsequently being ejected into the field.Comment: 10 pages, 8 figures, Accepted for publication in Astrophysics and Space Scienc

Abstract. We argue that brown dwarfs (BDs) and planemos form by the same mechanisms as low-mass hydrogen-burning stars, but that as one moves to lower and lower masses, an increasing fraction of these objects is formed by fragmentation of the outer parts (R 100 AU) of protostellar accretion discs around more massive primary protostars, which in turn formed in their own very-low-mass prestellar cores. Numerical simulations of disc fragmentation with realistic thermodynamics show that low-mass objects are readily formed by fragmentation of short-lived massive, extended protostellar accretion discs. Such objects tend subsequently to be liberated into the field at low speed, due to mutual interactions with the primary protostar. Many (∼20%) are in low-mass (M 1 + M2 < 0.2 M ) binary systems with semi-major axes a ∼ 1 to 2 AU or ∼200 AU and mass ratios q ≡ M2 /M1 0.7. Most of the brown dwarfs have sufficiently large attendant discs to sustain accretion and outflows. Most of the BDs that remain bound to the primary protostar have wide orbits (i.e., there is a BD desert), and these BDs also have a significantly higher probability of being in a BD/BD binary system than do the brown dwarfs that are liberated into the field (just as observed). In this picture, the multiplicity statistics and velocity dispersion of brown dwarfs are largely determined by the eigen evolution of a small-N system, born from a single prestellar core, rather than the larger-scale dynamics of the parent cluster. Consequently, many of the statistical properties of brown dwarfs should not differ very much from one star-formation region to another.