Theoretical astrophysics and plasma physics at RPC

Abstract:

It has been proposed that primordial black holes (PBHs) form binaries in the radiation dominated era. Once formed, some fraction of them may merge within the age of the Universe by gravitational radiation reaction. We investigate the merger rate of the PBH binaries when the PBHs have a distribution of masses around ${\cal O}(10) M_\odot$, which is a generalization of the previous studies where the PBHs are assumed to have the same mass. After deriving a formula for the merger time probability distribution in the PBH mass plane, we evaluate it under two different approximations. We identify a quantity constructed from the mass-distribution of the merger rate density per unit cosmic time and comoving volume $\mathcal{R}(m_1,m_2)$, $\alpha = -{(m_1+m_2)}^2\partial^2 \ln\mathcal{R}/\partial m_1\partial m_2 $, which universally satisfies $0.97 \lesssim \alpha \lesssim 1.05$ for all binary masses independently of the PBH mass function. This result suggests that the measurement of this quantity is useful for testing the PBH scenario.

Abstract:

Magnetic fields are ubiquitous in the Universe. Diffuse radiosynchrotron emission observations and Faraday rotation measurements have revealed magnetic field strengths ranging from a few nG and tens of µG in extragalactic disks, halos and clusters [1], up to hundreds of TG in magnetars, as inferred from their spin-down [2]. The energy density of these fields is typically comparable to the energy density of the fluid motions of the plasma in which they are embedded, making magnetic fields essential players in the dynamics of the luminous matter. The standard theoretical model for the origin of these strong magnetic fields is through the amplification of tiny seed fields via turbulent dynamo to the level consistent with current observations [3–7]. Here we demonstrate, using laser-produced colliding plasma flows, that turbulence is indeed capable of rapidly amplifying seed fields to near equipartition with the turbulent fluid motions. These results support the notion that turbulent dynamo is a viable mechanism responsible for the observed present-day magnetization.

Abstract:

Numerical solutions to Newtons equations of motion for chaotic self gravitating systems of more than 2 bodies are often regarded to be irreversible. This is due to the exponential growth of errors introduced by the integration scheme and the numerical round-off in the least significant figure. This secular growth of error is sometimes attributed to the increase in entropy of the system even though Newton’s equations of motion are strictly time reversible. We demonstrate that when numerical errors are reduced to below the physical perturbation and its exponential growth during integration the microscopic reversibility is retrieved. Time reversibility itself is not a guarantee for a definitive solution to the chaotic N-body problem. However, time reversible algorithms may be used to find initial conditions for which perturbed trajectories converge rather than diverge. The ability to calculate such a converging pair of solutions is a striking illustration which shows that it is possible to compute a definitive solution to a highly unstable problem. This works as follows: If you (i) use a code which is capable of producing a definitive solution (and which will therefore handle converging pairs of solutions correctly), (ii) use it to study the statistical result of some other problem, and then (iii) find that some other code produces a solution S with statistical properties which are indistinguishable from those of the definitive solution, then solution S may be deemed veracious.

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.