We present a new numerical code, PLUTO, for the solution of hypersonic flows in 1, 2, and 3 spatial dimensions and different systems of coordinates. The code provides a multiphysics, multialgorithm modular environment particularly oriented toward the treatment of astrophysical flows in presence of discontinuities. Different hydrodynamic modules and algorithms may be independently selected to properly describe Newtonian, relativistic, MHD, or relativistic MHD fluids. The modular structure exploits a general framework for integrating a system of conservation laws, built on modern Godunov-type shock-capturing schemes. Although a plethora of numerical methods has been successfully developed over the past two decades, the vast majority shares a common discretization recipe, involving three general steps: a piecewise polynomial reconstruction followed by the solution of Riemann problems at zone interfaces and a final evolution stage. We have checked and validated the code against several benchmarks available in literature. Test problems in 1, 2, and 3 dimensions are discussed.

https://iopscience.iop.org/article/10.1086/513316/pdf

PLUTO: A Numerical Code for Computational Astrophysics

Black hole accretion flows can be divided into two broad classes: cold and hot. Whereas cold accretion flows consist of cool optically thick gas and are found at relatively high mass accretion rates, hot accretion flows, the topic of this review, are virially hot and optically thin, and occur at lower mass accretion rates. They are described by accretion solutions such as the advection-dominated accretion flow and luminous hot accretion flow. Because of energy advection, the radiative efficiency of these flows is in general lower than that of a standard thin accretion disk. Moreover, the efficiency decreases with decreasing mass accretion rate. Observations show that hot accretion flows are associated with jets. In addition, theoretical arguments suggest that hot flows should produce strong winds. Hot accretion flows are believed to be present in low-luminosity active galactic nuclei and in black hole X-ray binaries in the hard and quiescent states. The prototype is Sgr A*, the ultralow-luminosity supermassive black hole at our Galactic center. The jet, wind, and radiation from a supermassive black hole with a hot accretion flow can interact with the external interstellar medium and modify the evolution of the host galaxy.

Hot Accretion Flows Around Black Holes

A new code for astrophysical magnetohydrodynamics (MHD) is described. The code has been designed to be easily extensible for use with static and adaptive mesh refinement. It combines higher order Godunov methods with the constrained transport (CT) technique to enforce the divergence-free constraint on the magnetic field. Discretization is based on cell-centered volume averages for mass, momentum, and energy, and face-centered area averages for the magnetic field. Novel features of the algorithm include (1) a consistent framework for computing the time- and edge-averaged electric fields used by CT to evolve the magnetic field from the time- and area-averaged Godunov fluxes, (2) the extension to MHD of spatial reconstruction schemes that involve a dimensionally split time advance, and (3) the extension to MHD of two different dimensionally unsplit integration methods. Implementation of the algorithm in both C and FORTRAN95 is detailed, including strategies for parallelization using domain decomposition. Results from a test suite which includes problems in one-, two-, and three-dimensions for both hydrodynamics and MHD are given, not only to demonstrate the fidelity of the algorithms, but also to enable comparisons to other methods. The source code is freely available for download on the web.

/pdf/athena-a-new-code-for-astrophysical-mhd-1de7wtkkl8.pdf

Athena: a new code for astrophysical mhd

We describe new optically thin solutions for rotating accretion flows around black holes and neutron stars. These solutions are advection dominated, so that most of the viscously dissipated energy is advected radially with the flow. We model the accreting gas as a two temperature plasma and include cooling by bremsstrahlung, synchrotron, and Comptonization. We obtain electron temperatures $T_e\sim 10^{8.5}-10^{10}$K. The new solutions are present only for mass accretion rates $\dot M$ less than a critical rate $\dot M_{crit}$ which we calculate as a function of radius $R$ and viscosity parameter $\alpha$. For $\dot M<\dot M_{crit}$ we show that there are three equilibrium branches of solutions. One of the branches corresponds to a cool optically thick flow which is the well-known thin disk solution of Shakura \& Sunyaev (1973). Another branch corresponds to a hot optically thin flow, discovered originally by Shapiro, Lightman \& Eardley (1976, SLE). This solution is thermally unstable. The third branch corresponds to our new advection-dominated solution. This solution is hotter and more optically thin than the SLE solution, but is viscously and thermally stable. It is related to the ion torus model of Rees et al. (1982) and may potentially explain the hard X-ray and $\gamma$-ray emission from X-ray binaries and active galactic nuclei.

/pdf/advection-dominated-accretion-underfed-black-holes-and-cc41v8tdhl.pdf

Advection-Dominated Accretion: Underfed Black Holes and Neutron Stars

Short-hard gamma-ray bursts

We present numerical simulations of axisymmetric, magnetically driven relativistic jets. Our special-relativistic, ideal-magnetohydrodynamics numerical scheme is specifically designed to optimize accuracy and resolution and to minimize numerical dissipation. In addition, we implement a grid-extension method that reduces the computation time by up to three orders of magnitude and makes it possible to follow the flow up to six decades in spatial scale. To eliminate the dissipative effects induced by a free boundary with an ambient medium we assume that the flow is confined by a rigid wall of a prescribed shape, which we take to be α r a (in cylindrical coordinates, with a ranging from 1 to 3). We also prescribe, through the rotation profile at the inlet boundary, the injected poloidal current distribution: we explore cases where the return current flows either within the volume of the jet or on the outer boundary. The outflows are initially cold, sub-Alfvenic and Poynting flux-dominated, with a total-to-rest-mass energy flux ratio μ ∼ 15. We find that in all cases they converge to a steady state characterized by a spatially extended acceleration region. The acceleration process is very efficient: on the outermost scale of the simulation as much as ∼ 77 percent of the Poynting flux has been converted into kinetic energy flux, and the terminal Lorentz factor approaches its maximum possible value (Γ ≃ μ). We also find a high collimation efficiency: all our simulated jets (including the limiting case of an unconfined flow) develop a cylindrical core. We argue that this could be the rule for current-carrying outflows that start with a low initial Lorentz factor (Γ 0 ∼ 1). Our conclusions on the high acceleration and collimation efficiencies are not sensitive to the particular shape of the confining boundary or to the details of the injected current distribution, and they are qualitatively consistent with the semi-analytic self-similar solutions derived by Vlahakis and Konigl. We apply our results to the interpretation of relativistic jets in active galactic nuclei: we argue that they naturally account for the spatially extended accelerations inferred in these sources (Γ ∞ ≥ 10 attained on radial scales R ≥ 10 17 cm) and are consistent with the transition to the matter-dominated regime occurring already at R ≥ 10 16 cm.

Magnetic acceleration of relativistic active galactic nucleus jets

This is a brief review of the recent developments in the theory of magnetic acceleration of relativistic jets. We attempt to explain the key results of this complex theory using basic physical arguments and simple calculations. The main focus is on the standard model, which describes steady-state axisymmetric ideal MHD flows. We argue that this model is over-restrictive and discuss various alternatives.

Magnetic acceleration of relativistic jets

We present numerical simulations of axi symmetric, magnetically driven outflows that reproduce the inferred properties of ultrarelativistic gamma-ray burst (GRB) jets. These results extend our previous simulations of outflows accelerated to moderately relativistic speeds, which are applicable to jets of active galactic nuclei. In contrast to several recent investigations, which have employed the magnetodynamics approximation, our numerical scheme solves the full set of equations of special relativistic, ideal magnetohydrodynamics, which enables us to explicitly calculate the jet velocity and magnetic-to-kinetic energy conversion efficiency - key parameters of interest for astrophysical applications. We confirm that the magnetic acceleration scheme remains robust into the ultrarelativistic regime, as previously indicated by semi-analytic self-similar solutions. We find that all current-carrying outflows exhibit self-collimation and consequent acceleration near the rotation axis, but that unconfined outflows lose causal connectivity across the jet and therefore do not collimate or accelerate efficiently in their outer regions. We show that magnetically accelerated jets confined by an external pressure that varies as z -α (0 1), and we obtain analytic expressions for the one-to-one correspondence between the pressure distribution and the asymptotic jet shape. We demonstrate that the acceleration efficiency of jets with paraboloidal streamlines is ≥50 per cent, with the numerical value being higher the lower the initial magnetization. We derive asymptotic analytic expressions for the acceleration of initially cold outflows along paraboloidal streamlines and verify that they provide good descriptions of the simulated flows. Our modelled jets (corresponding to 3/2 < a < 3) attain Lorentz factors Γ ≥ 10 2 on scales ∼ 10 10 -10 12 cm, consistent with the possibility that long/soft GRB jets are accelerated within envelopes of collapsing massive stars, and r ≥ 30 on scales ∼9 x 10 8 -3 x 10 10 cm, consistent with the possibility that short/hard GRB jets are accelerated on scales where they can be confined by moderately relativistic winds from accretion discs. We also find that Γθ v ∼ 1 for outflows that undergo an efficient magnetic-to-kinetic energy conversion, where θ v is the opening half-angle of the poloidal streamlines. This relation implies that the γ-ray emitting components of GRB outflows accelerated in this way are very narrow, with θ v ≤ 1° in regions where Γ ≥ 100, and that the afterglow light curves of these components would either exhibit a very early jet break or show no jet break at all.

Magnetic acceleration of ultrarelativistic jets in gamma-ray burst sources

We present a relativistic-MHD numerical study of axisymmetric, magnetically driven jets with parameters applicable to gamma-ray burst (GRB) flows. We also present analytic expressions for the asymptotic jet shape and other flow parameters that agree very well with the numerical results. All current-carrying outflows exhibit self-collimation and consequent acceleration near the rotation axis, but unconfined outflows lose causal connectivity across the jet and therefore do not collimate or accelerate efficiently in their outer regions. Magnetically accelerated jets confined by an external pressure that varies with distance with a power-law index 50%. They attain Lorentz factors > 30 on scales 10^9-3x10^10 cm, consistent with the possibility that short/hard GRB jets are accelerated on scales where they can be confined by moderately relativistic winds from accretion discs, and > 100 on scales 10^10-10^12 cm, consistent with the possibility that long/soft GRB jets are accelerated within the envelopes of collapsing massive stars. We also find that the Lorentz factor of a magnetically accelerated jet is approximately inversely proportional to the opening half-angle of the poloidal streamlines. This implies that the gamma-ray emitting components of GRB outflows are very narrow, with a half-angle < 1 degree in regions where the Lorentz factor exceeds 100, and that the afterglow light curves of these components would either exhibit a very early jet break or show no jet break at all.

Magnetic acceleration of ultra-relativistic jets in gamma-ray burst sources

The basic properties of relativistic magnetohydrodynamics, as a hyperbolic system of quasi-linear conservation laws, are discussed. These are then used to develop a multidimensional Godunov-type numerical scheme that enforces the magnetic flux conservation. This scheme is based on linear Riemann solvers and has second-order accuracy in smooth regions. The results of thorough test calculations demonstrate that the scheme is robust and can cope with truly ultrarelativistic problems.

Serguei S. Komissarov

Papers

Magnetic acceleration of relativistic active galactic nucleus jets

Magnetic acceleration of relativistic jets

Magnetic acceleration of ultrarelativistic jets in gamma-ray burst sources

Magnetic acceleration of ultra-relativistic jets in gamma-ray burst sources

A Godunov-type scheme for relativistic magnetohydrodynamics