Theoretical astrophysics and plasma physics at RPC

Abstract:

In this work, we compare gyrokinetic simulations in stellarators using different computational domains, namely, flux tube (FT), full-flux-surface (FFS), and radially global (RG) domains. Two problems are studied: the linear relaxation of zonal flows (ZFs) and the linear stability of ion temperature gradient (ITG) modes. Simulations are carried out with the codes EUTERPE, GENE, GENE-3D, and stella in magnetic configurations of LHD and W7-X using adiabatic electrons. The ZF relaxation properties obtained in different FTs are found to differ with each other and with the RG result, except for sufficiently long FTs, in general. The FT length required for convergence is configuration-dependent. Similarly, for ITG instabilities, different FTs provide different results, but the discrepancy between them diminishes with increasing FT length. FFS and FT simulations show good agreement in the calculation of the growth rate and frequency of the most unstable modes in LHD, while for W7-X differences in the growth rates are found between the FT and the FFS domains. RG simulations provide results close to the FFS ones. The radial scale of unstable ITG modes is studied in global and FT simulations finding that in W7-X, the radial scale of the most unstable modes depends on the binormal wavenumber, while in LHD no clear dependency is found.

Abstract:

We study the influence of relativity on the chaotic properties and dynamical outcomes of an unstable triple system; the Pythagorean three-body problem. To this end, we extend the brutus N-body code to include post-Newtonian pairwise terms up to 2.5 order, and the first order Taylor expansion to the Einstein-Infeld-Hoffmann equations of motion. The degree to which our system is relativistic depends on the scaling of the total mass (the unit size was 1 parsec). Using the brutus method of convergence, we test for time-reversibility in the conservative regime, and demonstrate that we are able to obtain definitive solutions to the relativistic three-body problem. It is also confirmed that the minimal required numerical accuracy for a successful time-reversibility test correlates with the amplification factor of an initial perturbation, as was found previously for the Newtonian case. When we take into account dissipative effects through gravitational wave emission, we find that the duration of the resonance, and the amount of exponential growth of small perturbations depend on the mass scaling. For a unit mass , the system behavior is indistinguishable from Newton’s equations of motion, and the resonance always ends in a binary and one escaping body. For a mass scaling up to , relativity gradually becomes more prominent, but the majority of the systems still dissolve in a single body and an isolated binary. The first mergers start to appear for a mass of , and between and all systems end prematurely in a merger. These mergers are preceded by a gravitational wave driven in-spiral. For a mass scaling , all systems result in a gravitational wave merger upon the first close encounter. Relativistic three-body encounters thus provide an efficient pathway for resolving the final parsec problem. The onset of mergers at the characteristic mass scale of potentially leaves an imprint in the mass function of supermassive black holes.