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Abstract:

We present a second-order calculation of relativistic large-scale-structure observables in cosmological perturbation theory, specifically the “cosmic rulers and clock”, which are the building-blocks of any other large-scale-structure observable, including galaxy number counts, on large scales. We calculate the scalar rulers (longitudinal perturbation and magnification) and the cosmic clock to second order, using a fully non-linear covariant definition of the observables. We validate our formulæ on three non-trivial space-time metrics: two of them are null tests on metrics which are obtained by applying a gauge transformation to the background space-time, while the third is the “separate universe” curved background, for which we can also compute the observables exactly. We then illustrate the results by evaluating the second-order observables in a simplified symmetric setup. On large scales, they are suppressed over the linear contributions by ∼10-4, while they become comparable to the linear contributions on mildly non-linear scales. The results of this paper form a significant (and the most complicated) part of the relativistic galaxy number density at second order.

Abstract:

We investigate the evolution of black holes on orbits with small inclinations () to the gaseous discs of active galactic nuclei (AGNs). We perform 3D adiabatic hydrodynamic simulations within a shearing frame, studying the damping of inclination by black hole-gas gravitation. We find that for objects with , where is the disc aspect ratio, the inclination lost per mid-plane crossing is proportional to the inclination preceding the crossing, resulting in a net exponential decay in inclination. For objects with , damping efficiency decreases for higher inclinations. We consider a variety of different AGN environments, finding that damping is stronger for systems with a higher ambient Hill mass: the initial gas mass within the BH sphere of influence. We provide a fitting formula for the inclination changes as a function of Hill mass. We find reasonable agreement between the damping driven by gas gravity in the simulations and the damping driven by accretion under a Hill-limited Bondi–Hoyle–Lyttleton prescription. We find that gas dynamical friction consistently overestimates the strength of damping, especially for lower inclination systems, by at least an order of magnitude. For regions in the AGN disc where coplanar binary black hole formation by gas dissipation is efficient, we find that the simulated damping time-scales are especially short with . We conclude that as the time-scales for inclination damping are shorter than the expected interaction time between isolated black holes, the vast majority of binaries formed from gas capture should form from components with negligible inclination to the AGN disc.

Abstract:

Within hierarchical triple stellar systems, there exists a tidal process unique to them, known as tertiary tides. In this process, the tidal deformation of a tertiary in a hierarchical triple drains energy from the inner binary, causing the inner binary’s orbit to shrink. Previous work has uncovered the rate at which tertiary tides drain energy from inner binaries, as a function of orbital and tidal parameters, for hierarchical triples in which the orbits are all circular and coplanar. However, not all hierarchical triples have orbits which are circular and coplanar, which requires an understanding of what happens when this condition is relaxed. In this paper, we study how eccentricities affect tertiary tides, and their influence on the subsequent dynamical evolution of the host hierarchical triple. We find that eccentricities in the outer orbit undergo tidal circularization as quickly as binary tidal synchronization, and are therefore trivial, but that eccentricities in the inner binary completely change the behaviour of tertiary tides, draining energy from the outer orbit as well as the inner orbit. As with the circular orbit case, tertiary tides become significant when the tertiary is large enough to come close to filling its Roche Lobe, and dominate tidal evolution when interactions between the inner binary pair are weak. Empirical equations that approximate this behaviour are provided for ease of implementing this process in other stellar evolution codes, and the implications of these results are discussed.

Abstract:

ABSTRACT Turbulent, relativistic non-thermal plasmas are ubiquitous in high-energy astrophysical systems, as inferred from broad-band non-thermal emission spectra. The underlying turbulent non-thermal particle acceleration (NTPA) processes have traditionally been modelled with a Fokker–Planck (FP) diffusion–advection equation for the particle energy distribution. We test FP-type NTPA theories by performing and analysing particle-in-cell simulations of turbulence in collisionless relativistic pair plasma. By tracking large numbers of particles in simulations with different initial magnetization and system size, we first test and confirm the applicability of the FP framework. We then measure the FP energy diffusion (D) and advection (A) coefficients as functions of particle energy $\gamma m c^2$, and compare their dependence to theoretical predictions. At high energies, we robustly find $D \sim \gamma ^2$ for all cases. Hence, we fit $D = D_0 \gamma ^2$ and find a scaling consistent with $D_0 \sim \sigma ^{3/2}$ at low instantaneous magnetization $\sigma (t)$, flattening to $D_0 \sim \sigma$ at higher $\sigma \sim 1$. We also find that the power-law index $\alpha (t)$ of the particle energy distribution converges exponentially in time. We build and test an analytic model connecting the FP coefficients and $\alpha (t)$, predicting $A(\gamma) \sim \gamma \log \gamma$. We confirm this functional form in our measurements of $A(\gamma ,t)$, which allows us to predict $\alpha (t)$ through the model relations. Our results suggest that the basic second-order Fermi acceleration model, which predicts $D_0 \sim \sigma$, may not be a complete description of NTPA in turbulent plasmas. These findings encourage further application of tracked particles and FP coefficients as a diagnostic in kinetic simulations of various astrophysically relevant plasma processes like collisionless shocks and magnetic reconnection.

Abstract:

We study the evolution of collisionless plasmas that, due to their macroscopic evolution, are susceptible to the firehose instability, using both analytic theory and hybrid-kinetic particle-in-cell simulations. We establish that, depending on the relative magnitude of the plasma , the characteristic time scale of macroscopic evolution and the ion-Larmor frequency, the saturation of the firehose instability in high- plasmas can result in three qualitatively distinct thermodynamic (and electromagnetic) states. By contrast with the previously identified ‘ultra-high-beta’ and ‘Alfvén-inhibiting’ states, the newly identified ‘Alfvén-enabling’ state, which is realised when the macroscopic evolution time exceeds the ion-Larmor frequency by a -dependent critical parameter, can 91̽�� linear Alfvén waves and Alfvénic turbulence because the magnetic tension associated with the plasma’s macroscopic magnetic field is never completely negated by anisotropic pressure forces. We characterise these states in detail, including their saturated magnetic-energy spectra. The effective collision operator associated with the firehose fluctuations is also described; we find it to be well approximated in the Alfvén-enabling state by a simple quasi-linear pitch-angle scattering operator. The box-averaged collision frequency is , in agreement with previous results, but certain subpopulations of particles scatter at a much larger (or smaller) rate depending on their velocity in the direction parallel to the magnetic field. Our findings are essential for understanding low-collisionality astrophysical plasmas including the solar wind, the intracluster medium of galaxy clusters and black hole accretion flows. We show that all three of these plasmas are in the Alfvén-enabling regime of firehose saturation and discuss the implications of this result.