Theoretical astrophysics and plasma physics at RPC

Abstract:

This paper describes a new code for simulating astrophysical plasmas that solves a hybrid model composed of gyrokinetic ions (GKI) and an isothermal electron fluid (ITEF) [A. Schekochihin et al., Astrophys. J. Suppl. \textbf{182}, 310 (2009)]. This model captures ion kinetic effects that are important near the ion gyro-radius scale while electron kinetic effects are ordered out by an electron-ion mass ratio expansion. The code is developed by incorporating the ITEF approximation into ${\tt AstroGK}$, an Eulerian $\delta f$ gyrokinetics code specialized to a slab geometry [R. Numata et al., J. Compute. Pays. \textbf{229}, 9347 (2010)]. The new code treats the linear terms in the ITEF equations implicitly while the nonlinear terms are treated explicitly. We show linear and nonlinear benchmark tests to prove the validity and applicability of the simulation code. Since the fast electron timescale is eliminated by the mass ratio expansion, the Courant--Friedrichs--Lewy condition is much less restrictive than in full gyrokinetic codes; the present hybrid code runs $\sim 2\sqrt{m_\mathrm{i}/m_\mathrm{e}} \sim 100$ times faster than ${\tt AstroGK}\ $with a single ion species and kinetic electrons where $m_\mathrm{i}/m_\mathrm{e}$ is the ion-electron mass ratio. The improvement of the computational time makes it feasible to execute ion scale gyrokinetic simulations with a high velocity space resolution and to run multiple simulations to determine the dependence of turbulent dynamics on parameters such as electron--ion temperature ratio and plasma beta.

Abstract:

Models aiming to explain the formation of massive black hole seeds, and in particular the direct collapse scenario, face substantial difficulties. These are rooted in rather ad hoc and fine-tuned initial conditions, such as the simultaneous requirements of extremely low metallicities and strong radiation backgrounds. Here, we explore a modification of such scenarios where a massive primordial star cluster is initially produced. Subsequent stellar collisions give rise to the formation of massive (104−105 M⊙) objects. Our calculations demonstrate that the interplay among stellar dynamics, gas accretion, and protostellar evolution is particularly relevant. Gas accretion on to the protostars enhances their radii, resulting in an enhanced collisional cross-section. We show that the fraction of collisions can increase from 0.1 to 1 per cent of the initial population to about 10 per cent when compared to gas-free models or models of protostellar clusters in the local Universe. We conclude that very massive objects can form in spite of initial fragmentation, making the first massive protostellar clusters viable candidate birth places for observed supermassive black holes.

Abstract:

A class of simple kinetic systems is considered, described by the 1D Vlasov--Landau equation with Poisson or Boltzmann electrostatic response and an energy source. Assuming a stochastic electric field, a solvable model is constructed for the phase-space turbulence of the particle distribution. The model is a kinetic analog of the Kraichnan--Batchelor model of chaotic advection. The solution of the model is found in Fourier--Hermite space and shows that the free-energy flux from low to high Hermite moments is suppressed, with phase mixing cancelled on average by anti-phase-mixing (stochastic plasma echo). This implies that Landau damping is an ineffective dissipation channel at wave numbers below a certain cut off (analog of Kolmogorov scale), which increases with the amplitude of the stochastic electric field and scales as inverse square of the collision rate. The full Fourier--Hermite spectrum is derived. Its asymptotics are $m^{-3/2}$ at low wave numbers and high Hermite moments ($m$) and $m^{-1/2}k^{-2}$ at low Hermite moments and high wave numbers ($k$). The energy distribution and flows in phase space are a simple and, therefore, useful example of competition between phase mixing and nonlinear dynamics in kinetic turbulence, reminiscent of more realistic but more complicated multi-dimensional systems that have not so far been amenable to complete analytical solution.