Theoretical astrophysics and plasma physics at RPC

Abstract:

Abstract We demonstrate using linear theory and particle-in-cell (PIC) simulations that a synchrotron-cooling collisionless plasma acquires pressure anisotropy and, if the plasma beta is sufficiently high, becomes unstable to the firehose instability, in a process that we dub the synchrotron firehose instability (SFHI). The SFHI channels free energy from the pressure anisotropy of the radiating, relativistic electrons (and/or positrons) into small-amplitude, kinetic-scale, magnetic-field fluctuations, which pitch-angle scatter the particles and bring the plasma to a near-thermal state of marginal instability. The PIC simulations reveal a nonlinear cyclic evolution of firehose bursts interspersed by periods of stable cooling. We compare the SFHI for electron–positron and electron–ion plasmas. As a byproduct of the growing electron-firehose magnetic-field fluctuations, magnetized ions gain a pressure anisotropy opposite to that of the electrons. If these ions are relativistically hot, we find that they also experience cooling due to collisionless thermal coupling with the electrons, which we argue is mediated by a secondary ion-cyclotron instability. We suggest that the SFHI may be activated in a number of astrophysical scenarios, such as within ejecta from black hole accretion flows and relativistic jets, where the redistribution of energetic electrons from low to high pitch angles may cause transient bursts of radiation.

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.