Theoretical astrophysics and plasma physics at RPC

Abstract:

Vector resonant relaxation (VRR) is known to be the fastest gravitational process that shapes the geometry of stellar orbits in nuclear star clusters. This leads to the realignment of the orbital planes on the corresponding VRR time-scale tVRR of a few million years, while the eccentricity e and semimajor axis a of the individual orbits are approximately conserved. The distribution of orbital inclinations reaches an internal equilibrium characterized by two conserved quantities, the total potential energy among stellar orbits, Etot, and the total angular momentum, Ltot. On time-scales longer than tVRR, the eccentricities and semimajor axes change slowly, and the distribution of orbital inclinations are expected to evolve through a series of VRR equilibria. Using a Monte Carlo Markov Chain method, we determine the equilibrium distribution of orbital inclinations in the microcanonical ensemble with fixed Etot and Ltot for isolated nuclear star clusters with a power-law distribution of a, e, and m, where m is the stellar mass. We explore the possible equilibria for nine representative Etot–Ltot pairs that cover the possible parameter space. For all cases, the equilibria show anisotropic mass segregation, where the distribution of more massive objects is more flattened than that for lighter objects. Given that stellar black holes are more massive than the average main-sequence stars, these findings suggest that black holes reside in disc-like structures within nuclear star clusters for a wide range of initial conditions.

Abstract:

The time-step criterion plays a crucial role in direct N-body codes. If not chosen carefully, it will cause a secular drift in the energy error. Shared, adaptive time-step criteria commonly adopt the minimum pairwise time-step, which suffers from discontinuities in the time evolution of the time-step. This has a large impact on the functioning of time-step symmetrization algorithms. We provide new demonstrations of previous findings that a smooth and weighted average over all pairwise time-steps in the N-body system, improves the level of energy conservation. Furthermore, we compare the performance of 27 different time-step criteria, by considering three methods for weighting time-steps and nine symmetrization methods. We present performance tests for strongly chaotic few-body systems, including unstable triples, giant planets in a resonant chain, and the current Solar System. We find that the harmonic symmetrization methods (methods A3 and B3 in our notation) are the most robust, in the sense that the symmetrized time-step remains close to the time-step function. Furthermore, based on our Solar System experiment, we find that our new weighting method based on direct pair-wise averaging (method W2 in our notation), is slightly preferred over the other methods.

Abstract:

We formulate a generalized periodic boundary condition as a limit of the standard twist-and-shift parallel boundary condition that is suitable for simulations of plasmas with low magnetic shear. This is done by applying a phase shift in the binormal direction when crossing the parallel boundary. While this phase shift can be set to zero without loss of generality in the local flux-tube limit when employing the twist-and-shift boundary condition, we show that this is not the most general case when employing periodic parallel boundaries, and may not even be the most desirable. A non-zero phase shift can be used to avoid the convective cells that plague simulations of the three-dimensional Hasegawa–Wakatani system, and is shown to have measurable effects in periodic low-magnetic-shear gyrokinetic simulations. We propose a numerical program where a sampling of periodic simulations at random pseudo-irrational flux surfaces are used to determine physical observables in a statistical sense. This approach can serve as an alternative to applying the twist-and-shift boundary condition to low-magnetic-shear scenarios, which, while more straightforward, can be computationally demanding.