Rare Event Sampling Improves Mercury Instability Statistics

Due to the chaotic nature of planetary dynamics, there is a non-zero probability that Mercury’s orbit will become unstable in the future. Previous efforts have estimated the probability of this happening between 3 and 5 billion years in the future using a large number of direct numerical simulations with an N-body code, but were not able to obtain accurate estimates before 3 billion years in the future because Mercury instability events are too rare. In this paper we use a new rare-event sampling technique, Quantile Diffusion Monte Carlo (QDMC), to estimate that the probability of a Mercury instability event in the next 2 billion years is approximately 10−4 in the REBOUND N-body code. We show that QDMC provides unbiased probability estimates at a computational cost of up to 100 times less than direct numerical simulation. QDMC is easy to implement and could be applied to many problems in planetary dynamics in which it is necessary to estimate the probability of a rare event.

The Diversity of Exoplanets: From Interior Dynamics to Surface Expressions

The coupled interior–atmosphere system of terrestrial exoplanets remains poorly understood. Exoplanets show a wide variety of sizes, densities, surface temperatures, and interior structures, with important knock-on effects for this coupled system. Many exoplanets are predicted to have a “stagnant lid” at the surface, with a rigid stationary crust, sluggish mantle convection, and only minor volcanism. However, if exoplanets have Earth-like plate tectonics, which involves several discrete, slowly moving plates and vigorous tectono-magmatic activity, then this may be critical for planetary habitability and have implications for the development (and evolution) of life in the galaxy. Here, we summarize our current knowledge of coupled planetary dynamics in the context of exoplanet diversity.

SpaceHub: A high-performance gravity integration toolkit for few-body problems in astrophysics

We present the open source few-body gravity integration toolkit SpaceHub. SpaceHub offers a variety of algorithmic methods, including the unique algorithms AR-Radau, AR-Sym6, AR-ABITS and AR-chain+ which we show out-perform other methods in the literature and allow for fast, precise and accurate computations to deal with few-body problems ranging from interacting black holes to planetary dynamics. We show that AR-Sym6 and AR-chain+, with algorithmic regularization, chain algorithm, active round-off error compensation and a symplectic kernel implementation, are the fastest and most accurate algorithms to treat black hole dynamics with extreme mass ratios, extreme eccentricities and very close encounters. AR-Radau, the first regularized Radau integrator with round off error control down to 64 bits floating point machine precision, has the ability to handle extremely eccentric orbits and close approaches in long-term integrations. AR-ABITS, a bit efficient arbitrary precision method, achieves any precision with the least CPU cost compared to other open source arbitrary precision few-body codes. With the implementation of deep numerical and code optimization, these new algorithms in SpaceHub prove superior to other popular high precision few-body codes in terms of performance, accuracy and speed.

Insights into the planetary dynamics of HD 206893 with ALMA

ABSTRACT Radial substructure in the form of rings and gaps has been shown to be ubiquitous among protoplanetary discs. This could be the case in exo-Kuiper belts as well, and evidence for this is emerging. In this paper, we present ALMA observations of the debris/planetesimal disc surrounding HD 206893, a system that also hosts two massive companions at 2 and 11 au. Our observations reveal a disc extending from 30 to 180 au, split by a 27 au wide gap centred at 74 au, and no dust surrounding the reddened brown dwarf (BD) at 11 au. The gap width suggests the presence of a 0.9MJup planet at 74 au, which would be the third companion in this system. Using previous astrometry of the BD, combined with our derived disc orientation as a prior, we were able to better constrain its orbit finding it is likely eccentric ($0.14^{+0.05}_{-0.04}$). For the innermost companion, we used radial velocity, proper motion anomaly, and stability considerations to show its mass and semimajor axis are likely in the ranges 4–100MJup and 1.4–4.5 au. These three companions will interact on secular time-scales and perturb the orbits of planetesimals, stirring the disc and potentially truncating it to its current extent via secular resonances. Finally, the presence of a gap in this system adds to the growing evidence that gaps could be common in wide exo-Kuiper belts. Out of six wide debris discs observed with ALMA with enough resolution, four to five show radial substructure in the form of gaps.

Hall Effect on Radiative Casson Fluid Flow with Chemical Reaction on a Rotating Cone through Entropy Optimization

Magnetohydrodynamic (MHD) flow with Hall current has numerous applications in industrial areas such as Hall current accelerators, MHD power generators, planetary dynamics, Hall current sensors, etc. In this paper, the analysis of an unsteady MHD Casson fluid with chemical reaction over a rotating cone is presented. The impacts of Hall current, joule heating, thermal radiation, and viscous dissipation are analyzed. Entropy optimization is also considered in the present analysis. The system of coupled equations is tackled with homotopy analysis method (HAM). The convergence of HAM is also shown through figures. Deviations in the flow due to dimensionless parameters are shown graphically. Similarly, the variation in skin friction, Nusselt number, and Sherwood number are deliberated through Tables. A justification of the current consequences is presented.

High-order symplectic integrators for planetary dynamics and their implementation in rebound

ABSTRACT Direct N-body simulations and symplectic integrators are effective tools to study the long-term evolution of planetary systems. The Wisdom–Holman (WH) integrator in particular has been used extensively in planetary dynamics as it allows for large time-steps at good accuracy. One can extend the WH method to achieve even higher accuracy using several different approaches. In this paper, we survey integrators developed by Wisdom et al., Laskar & Robutel, and Blanes et al. Since some of these methods are harder to implement and not as readily available to astronomers compared to the standard WH method, they are not used as often. This is somewhat unfortunate given that in typical simulations it is possible to improve the accuracy by up to six orders of magnitude (!) compared to the standard WH method without the need for any additional force evaluations. To change this, we implement a variety of high-order symplectic methods in the freely available N-body integrator rebound. In this paper, we catalogue these methods, discuss their differences, describe their error scalings, and benchmark their speed using our implementations.

Hybrid symplectic integrators for planetary dynamics

Hybrid symplectic integrators such as MERCURY are widely used to simulate complex dynamical phenomena in planetary dynamics that could otherwise not be investigated. A hybrid integrator achieves high accuracy during close encounters by using a high-order integration scheme for the duration of the encounter while otherwise using a standard second-order Wisdom–Holman scheme, thereby optimizing both speed and accuracy. In this paper we reassess the criteria for choosing the switching function that determines which parts of the Hamiltonian are integrated with the high-order integrator. We show that the original motivation for choosing a polynomial switching function in MERCURY is not correct. We explain the nevertheless excellent performance of the MERCURY integrator and then explore a wide range of different switching functions including an infinitely differentiable function and a Heaviside function. We find that using a Heaviside function leads to a significantly simpler scheme compared to MERCURY , while maintaining the same accuracy in short-term simulations.