Approximate Riemann solvers for the cosmic ray magnetohydrodynamical equations

Kudoh, Yuki; Hanawa, Tomoyuki

doi:10.1093/mnras/stw1937

Cited by 11 publications

(16 citation statements)

References 26 publications

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“…The above energy equation does not have a flux-conservative form. Kudoh and Hanawa (2016) (see also Pfrommer et al (2006)) propose an alternative approach leading to a full set of flux-conservative equations for the CR-MHD system. To proceed the authors introduce the CR mass density ρ CR = p 1/γCR CR , thus approximating CRs as a polytropic gas.…”

Section: Model Equationsmentioning

confidence: 99%

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Multi-scale simulations of particle acceleration in astrophysical systems

Marcowith

Ferrand

Grech

et al. 2020

Preprint

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This review aims at providing an up-to-date status and a general introduction to the subject of the numerical study of energetic particle acceleration and transport in turbulent astrophysical flows. The subject is also complemented by a short overview of recent progresses obtained in the domain of laser plasma experiments. We review the main physical processes at the heart of the production of a non-thermal distribution in both Newtonian and relativistic astrophysical flows, namely the first and second order Fermi acceleration processes. We also discuss shock drift and surfing acceleration, two processes important in the context of particle injection in shock acceleration. We analyze with some details the particle-in-cell (PIC) approach used to describe particle kinetics. We review the main results obtained with PIC simulations in the recent years concerning particle acceleration at shocks and in reconnection events. The review discusses the solution of Fokker-Planck problems with application to the study of particle acceleration at shocks but also in hot coronal plasmas surrounding compact objects. We continue by considering large scale physics. We describe recent developments in magnetohydrodynamic (MHD) simulations. We give a special emphasize on the way energetic particle dynamics can be coupled to MHD solutions either using a multi-fluid calculation or directly coupling kinetic and fluid calculations. This aspect is mandatory to investigate the acceleration of particles in the deep relativistic regimes to explain the highest Cosmic Ray energies.

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Section: Model Equationsmentioning

confidence: 99%

“…5.4), Miniati (2007) develop a modified Glimm-Godunov solver where the CR mediation is included in the Riemann problem. Kudoh and Hanawa (2016) propose a CR+MHD solver, second order accurate in space and time for a bi-fluid system based on a Roe solver.…”

Section: Specific Numerical Schemes Of Cr-fluid Systemsmentioning

confidence: 99%

Multi-scale simulations of particle acceleration in astrophysical systems

Marcowith

Ferrand

Grech

et al. 2020

Preprint

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“…Assuming that all the dissipated energy at the shock front is transferred to ions, we solved the entropy equation for electrons using Equation (5). Here, we followed the method adopted by Kudoh and Hanawa [35] to simulate the two component fluid including thermal plasma and cosmic rays, in which they assume that the cosmic ray fluid is adiabatic at the shock front. We neglected electron dissipative heating at the shock front in this paper.…”

Section: Basic Equationsmentioning

confidence: 99%

Two-Temperature Magnetohydrodynamics Simulations of Propagation of Semi-Relativistic Jets

et al. 2019

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In astrophysical jets observed in active galactic nuclei and in microquasars, the energy exchange rate by Coulomb collision is insufficient for thermal equilibrium between ions and electrons. Therefore, it is necessary to consider the difference between the ion temperature and the electron temperature. We present the results of two-temperature magnetohydrodynamics(MHD) simulations to demonstrate the effects of Coulomb coupling. It is assumed that the thermal dissipation heats only ions. We find that the ion and electron temperatures are separated through shocks. Since the ion entropy is increased by energy dissipation at shocks and the Coulomb collisions are inefficient, electron temperature becomes about 10 times lower than the ion temperature in the hotspot ahead of the jet terminal shock. In the cocoon, electron temperature decreases by gas mixing between high temperature cocoon gas and low temperature shocked-ambient gas even when we neglect radiative cooling, but electrons can be heated through collisions with ions. Radiation intensity maps are produced by post processing numerical results. Distributions of the thermal bremsstrahlung radiation computed from electron temperature have bright filament and cavity around the jet terminal shock.propagation of light supersonic jets, which exhibited the basic structures of jets such as a bow shock, a terminal shock (a reverse shock), internal shocks, and a cocoon. Recently, jet propagation and its feedback to inter cluster medium has been studied in realistic environments of galaxy cluster by Guo et al. [6,7]. The spacial variation of the propagation velocity of the jet has been reported by analytical methods (e.g., [8,9]) and by numerical simulations (e.g., [10]).The magnetic field structure of jets has been studied using polarized radiation. Faraday tomography have revealed that jets in 3C273 and SS433/W50 [11,12] have a helical magnetic field. The effects of magnetic fields on the jet dynamics have been examined for both non-relativistic and relativistic jets assuming axisymmetry [13][14][15]. In three-dimensional calculations, jets develop current-driven kink instability (m = 1) [16,17]. In addition, some studies compared numerical results with observations [18][19][20].Previous studies, however, did not focus on thermal non-equilibrium between ions and electrons in optically thin plasmas. When the relaxation time of ions and electrons by Coulomb collisions is longer than the dynamical time, the electron temperature can be lower than the ion temperature partly because electrons are cooled by radiation, and partly because shock waves primarily heat ions. Therefore, the electron temperature becomes lower than the ion temperature under such circumstances [21,22]. Such a two-temperature plasma has been studied extensively in the context of optically thin hot accretion flows in galactic black hole candidates (Shapiro, Lightman and Eardley [23]) and in the jet launching region in low luminosity active galactic nucleis (AGNs). Ressler et al. [24] and Sadowski et al. [2...

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“…To overcome this potential numerical flaw, alternative schemes have been developed to integrate CR physics into the simulations based on ideas by Ryu et al (1993). Here, rather than CR energy, a modified CR entropy density (𝜌𝐾 cr = 𝑃 cr /𝜌 𝛾 cr −1 ) is used as the relevant quantity to describe the CR fluid (Kudoh & Hanawa 2016;Semenov et al 2021). This approach has the evident benefit that the CR equation is in conservative form so that Godunov-type solvers can be straightforwardly applied.…”

Section: Introductionmentioning

confidence: 99%

Comparing energy and entropy formulations for cosmic ray hydrodynamics

Weber¹,

Thomas²,

Pfrommer³

2022

Preprint

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Cosmic rays (CRs) play an important role in many astrophysical systems. Acting on plasma scales to galactic environments, CRs are usually modeled as a fluid, using the CR energy density as the evolving quantity. This method comes with the flaw that the corresponding CR evolution equation is not in conservative form as it contains an adiabatic source term that couples CRs to the thermal gas. In the absence of non-adiabatic changes, instead evolving the CR entropy density is a physically equivalent option that avoids this potential numerical inconsistency. In this work, we study both approaches for evolving CRs in the context of magneto-hydrodynamic (MHD) simulations using the massively parallel moving-mesh code A . We investigate the performance of both methods in a sequence of shock-tube tests with various resolutions and shock Mach numbers. We find that the entropy-conserving scheme performs best for the idealized case of purely adiabatic CRs across the shock while both approaches yield similar results at lower resolution. In this setup, both schemes operate well and almost independently of the shock Mach number. Taking active CR acceleration at the shock into account, the energy-based method proves to be numerically much more stable and significantly more accurate in determining the shock velocity, in particular at low resolution, which is more typical for astrophysical large-scale simulations. For a more realistic application, we simulate the formation of several isolated galaxies at different halo masses and find that both numerical methods yield almost identical results with differences far below common astrophysical uncertainties.

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Approximate Riemann solvers for the cosmic ray magnetohydrodynamical equations

Cited by 11 publications

References 26 publications

Multi-scale simulations of particle acceleration in astrophysical systems

Multi-scale simulations of particle acceleration in astrophysical systems

Two-Temperature Magnetohydrodynamics Simulations of Propagation of Semi-Relativistic Jets

Comparing energy and entropy formulations for cosmic ray hydrodynamics

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