Equation of state in relativistic magnetohydrodynamics: variable versus constant adiabatic index

By Andrea Mignone, J. McKinney. 2007

147 citations recorded by the source corpus.

The role of the equation of state (EoS) for a perfectly conducting, relativistic magnetized fluid is the main subject of this work. The ideal constant Γ-law EoS, commonly adopted in a wide range of astrophysical applications, is compared with a more realistic EoS that better approximates the single-specie relativistic gas. The paper focuses on three different topics. First, the influence of a more realistic EoS on the propagation of fast magnetosonic shocks is investigated. This calls into question the validity of the constant Γ-law EoS in problems where the temperature of the gas substantially changes across hydromagnetic waves. Secondly, we present a new inversion scheme to recover primitive variables (such as rest-mass density and pressure) from conservative ones that allows for a general EoS and avoids catastrophic numerical cancellations in the non-relativistic and ultrarelativistic limits. Finally, selected numerical tests of astrophysical relevance (including magnetized accretion flows around Kerr black holes) are compared using different equations of state. Our main conclusion is that the choice of a realistic EoS can considerably bear upon the solution when transitions from cold to hot gas (or vice versa) are present. Under these circumstances, a polytropic EoS can significantly endanger the solution.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/f02b50f2adb7bf02179412ede4f5f54400ef6ea4

How researchers see this paper

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In Astronomy and Astrophysics

1. Ramesh Narayan
2. A. Tchekhovskoy
3. A. Sa̧dowski
4. J. McKinney
5. J. E. McClintock
6. F. Yuan
7. R. Penna
8. Harvard

In Nuclear and High Energy Physics

1. Ramesh Narayan
2. A. Tchekhovskoy
3. J. McKinney
4. A. Sa̧dowski
5. J. E. McClintock
6. R. Penna
7. F. Yuan
8. Harvard

Citations in the corpus

• EFFICIENCY OF MAGNETIC TO KINETIC ENERGY CONVERSION IN A MONOPOLE MAGNETOSPHERE (2009, methodology): “For example, the conversion of conserved to primitive quantities is performed identically to the thermal case (Mignone & McKinney 2007), but pressure and internal energy and all their derivatives are set to zero.”
• The Athena++ Adaptive Mesh Refinement Framework: Design and Magnetohydrodynamic Solvers (2020, methodology): “…(Del Zanna et al. 2007) uses a velocity-based 1D method, RAMSES (Teyssier 2002; Lamberts et al. 2012) uses a modified enthalpy-based method from Mignone & McKinney (2007), PLUTO (Mignone et al. 2007; Mignone 2014) uses the enthalpy-based 1D method of Mignone & Bodo (2006), and BHAC uses both…”
• Stability of relativistic jets from rotating, accreting black holes via fully three-dimensional magnetohydrodynamic simulations (2008, methodology): “We us the conservative unsplit 3D GRMHD code HARM (Gammie et al. 2003), Kerr-Schild coordinates, 4th-order interpolationa d 4thorder Runge-Kutta (McKinney 2006a), a robust inversion scheme (Mignone & McKinney 2007), a staggered field scheme (McKinney et al., in prep.)”
• Relativistic jet feedback in high-redshift galaxies – I. Dynamics (2016, background): “We assume an ideal equation of state with γ ad = 5/3, which is a reasonable approximation for a relativistic gas in with χ 1 (Synge 1957; Mignone & McKinney 2007).”
• Three-Dimensional Simulations of Magnetized Thin Accretion Disks around Black Holes: Stress in the Plunging Region (2008, methodology): “…were performed using a 3D GRMHD code HARM (Gammie et al. 2003) in Kerr-Schild coordinates using the interpolation scheme described by McKinney (2006), inversion scheme described by Noble et al. (2006) and Mignone & McKinney (2007), and other advances described by Tchekhovskoy et al. (2007).”
• Gamma-Ray Burst Afterglows in the Multimessenger Era: Numerical Models and Closure Relations (2019, background): “An accurate equation of state is essential in transrelativistic calculations (Mignone & McKinney 2007).”
• Relativistic jet feedback – III. Feedback on gas discs (2018, background): “We assume an ideal equation of state (Mignone & McKinney 2007), where the specific MNRAS 000, ??”
• Simulations of magnetized discs around black holes: Effects of black hole spin, disc thickness and magnetic field geometry (2010, methodology): “…we set the cooling function dU/dτ = 0 if (1) the time-step, dt, obeys dt > τ cool, which ensures that the cooling does not create negative entropy gas; or (2) log(K/Kc) < 1Models with = 5/3 show some minor differences compared to models with = 4/3 (McKinney & Gammie 2004; Mignone & McKinney 2007).”
• General relativistic magnetohydrodynamic simulations of magnetically choked accretion flows around black holes (2012, methodology): “The initial mass for the thick disk models is an isentropic hydro-equilibrium torus (Fishbone & Moncrief 1976; Gammie et al. 2003) with inner edge at rin = 10rg and pressure maximum at rmax = 100rg.”
• Three-dimensional general relativistic radiation magnetohydrodynamical simulation of super-Eddington accretion, using a new code HARMRAD with M1 closure (2013, methodology): “We choose Γ = 5/3, where Γ = 4/3 may lead to somewhat different results (McKinney & Gammie 2004; Mignone & McKinney 2007).”
• A Reconnection Switch to Trigger gamma-Ray Burst Jet Dissipation (2010, methodology): “…steady-state jet solution is presented as based upon approximate analytical solutions that have been confirmed numerically (Tchekhovskoy et al. 2008, 2009, 2010b) using the HARM code (Gammie, McKinney & Tóth 2003; Noble et al. 2006; Mignone & McKinney 2007; Tchekhovskoy, McKinney & Narayan 2007).”
• GRMHD simulations of magnetized advection‐dominated accretion on a non‐spinning black hole: role of outflows (2012, background): “In the simulations presented here we have set = 5/3, which is close enough, although technically in the ‘unphysical region’ discussed by Mignone & McKinney (2007).”
• BLACK HOLE SPIN AND THE RADIO LOUD/QUIET DICHOTOMY OF ACTIVE GALACTIC NUCLEI (2009, methodology): “…the simulations using the GR MHD code HARM (Gammie et al. 2003; McKinney & Gammie 2004; McKinney 2006a, 2006b; Noble et al. 2006) using Kerr– Schild coordinates in the Kerr metric; the code includes a number of recent improvements (Mignone & McKinney 2007; Tchekhovskoy et al. 2007, 2008, 2009a).”
• Simulations of ultrarelativistic magnetodynamic jets from gamma‐ray burst engines (2008, methodology): “For this we will use the same numerical scheme as in the present numerical work but optimized for the ultrarelativistic MHD regime (Gammie, McKinney & Tóth 2003; Mignone & McKinney 2007; Tchekhovskoy, McKinney & Narayan 2007).”