Theoretical astrophysics and plasma physics at RPC

Abstract:

Abstract Consider a system of point masses in a spherical potential. In such systems objects execute planar orbits covering two-dimensional rings or annuli, represented by the angular-momentum vectors, which slowly reorient due to the persistent weak gravitational interaction between different rings. This process, called vector resonant relaxation, is much faster than other processes which change the size/shape of the rings. The interaction is strongest between objects with closely aligned angular-momentum vectors. In this paper, we show that nearly parallel angular-momentum vectors may form stable bound pairs in angular-momentum space. We examine the stability of such pairs against an external massive perturber, and determine the critical separation analogous to the Hill radius or tidal radius in the three-body problem, where the angular-momentum pairs are marginally disrupted, as a function of the perturber’s mass, the orbital inclination, and the radial distance. Angular-momentum pairs or multiples closer than the critical inclination will remain bound and evolve together in angular-momentum-direction space under any external influence, such as anisotropic density fluctuations, or massive perturbers. This study has applications in various astrophysical contexts, including galactic nuclei, in particular the Milky Way’s Galactic centre, globular clusters, or planetary systems. In nuclear star clusters with a central super-massive black hole, we apply this criterion to the disc of young, massive stars, and show that clusters in angular-momentum space may be used to constrain the presence of intermediate-mass black holes or the mass of the nearby gaseous torus.

Abstract:

A theory of cosmic-ray transport in multiphase diffusive media is developed, with the specific application to cases in which the cosmic-ray diffusion coefficient has large spatial fluctuations that may be inherently multiscale. We demonstrate that the resulting transport of cosmic rays is diffusive in the long-time limit, with an average diffusion coefficient equal to the harmonic mean of the spatially varying diffusion coefficient. Thus, cosmic-ray transport is dominated by areas of low diffusion even if these areas occupy a relatively small, but not infinitesimal, fraction of the volume. On intermediate time-scales, the cosmic rays experience transient effective subdiffusion, as a result of low-diffusion regions interrupting long flights through high-diffusion regions. In the simplified case of a two-phase medium, we show that the extent and extremity of the subdiffusivity of cosmic-ray transport is controlled by the spectral exponent of the distribution of patch sizes of each of the phases. We finally show that, despite strongly influencing the confinement times, the multiphase medium is only capable of altering the energy dependence of cosmic-ray transport when there is a moderate (but not excessive) level of perpendicular diffusion across magnetic-field lines.

Abstract:

We introduce a new approach to measure the magnetic pitch angle profile in tokamak plasmas with Doppler backscattering (DBS), a technique traditionally used for measuring flows and density fluctuations. The DBS signal is maximised when its probe beam’s wavevector is perpendicular to the magnetic field at the cutoff location, independent of the density fluctuations (Hillesheim et al 2015 Nucl. Fusion 55 073024). Hence, if one could isolate this effect, DBS would then yield information about the magnetic pitch angle. By varying the toroidal launch angle, the DBS beam reaches cutoff with different angles with respect to the magnetic field, but with other properties remaining similar. Hence, the toroidal launch angle which gives maximum backscattered power is thus that which is matched to the pitch angle at the cutoff location, enabling inference of the magnetic pitch angle. We performed systematic scans of the DBS toroidal launch angle for repeated DIII-D tokamak discharges. Experimental DBS data from this scan were analysed and combined with Gaussian beam-tracing simulations using the Scotty code (Hall-Chen et al 2022 Plasma Phys. Control. Fusion 64 095002). The pitch-angle inferred from DBS is consistent with that from magnetics-only and motional-Stark-effect-constrained (MSE) equilibrium reconstruction in the edge. In the core, the pitch angles from DBS and magnetics-only reconstructions differ by one to two degrees, while simultaneous MSE measurements were not available. The uncertainty in these measurements was under a degree; we show that this uncertainty is primarily due to the error in toroidal steering, the number of toroidally separated measurements, and shot-to-shot repeatability. We find that the error of pitch-angle measurements can be reduced by optimising the poloidal launch angle and initial beam properties. Since DBS has high spatial and temporal resolutions, is non-perturbative, does not require neutral beams, and is likely robust to neutron damage of and debris on the first mirrors, using DBS to measure the pitch angle in future fusion energy systems is especially appealing.

Abstract:

The generation of dense electron-positron pair beams in the laboratory can enable direct tests of theoretical models of γ-ray bursts and active galactic nuclei. We have successfully achieved this using ultrarelativistic protons accelerated by the Super Proton Synchrotron at (CERN). In the first application of this experimental platform, the stability of the pair beam is studied as it propagates through a meter-length plasma, analogous to TeV γ-ray-induced pair cascades in the intergalactic medium. It has been argued that pair beam instabilities disrupt the cascade, thus accounting for the observed lack of reprocessed GeV emission from TeV blazars. If true, this would remove the need for a moderate strength intergalactic magnetic field to explain the observations. We find that the pair beam instability is suppressed if the beam is not perfectly collimated or monochromatic, hence the lower limit to the intergalactic magnetic field inferred from γ-ray observations of blazars is robust.

Abstract:

Merging black hole (BH) binaries in active galactic nucleus (AGN) discs formed through two-body scatterings via the ‘gas-capture’ process may explain a significant fraction of BH mergers in AGN and a non-negligible contribution to the observed rate from LIGO-VIRGO-KAGRA. We perform Monte Carlo simulations of binary BH formation, evolution, and mergers across the observed AGN mass function using a novel physically motivated treatment for the gas-capture process derived from hydrodynamical simulations of BH–BH encounters in AGN. Our models suggest that gas-captured binaries could result in merger rates of Gpc yr. Mergers from AGN are dominated by AGN with supermassive BH masses of , with 90 per cent of mergers occurring in the range . The merging mass distribution is flatter than the initial BH mass power law by a factor , as larger BHs align with the disc and form binaries more efficiently. Similarly, the merging mass ratio distribution is flatter therefore the AGN channel could explain high mass and unequal mass ratio detections such as GW190521 and GW190814. Using a simpler dynamical friction treatment for the binary formation process, the results are similar, where the primary bottleneck is the alignment time with the disc. The most influential parameters are the anticipated number of BHs and their mass function. Given the many uncertainties that remain in the AGN channel, we expect the true uncertainty extends beyond our predicted rates. None the less, we conclude that AGN remain an important channel for consideration, particularly for gravitational wave detections involving one or two high mass BHs.