On the diffusive propagation of warps in thin accretion discs

By G. Lodato, D. P. D. D. Fisica, U. Milano, Isaac Newton Institute for Mathematical Studies, Cambridge Centre for Stellar, P. Astrophysics, Monash University School of Physics, U. Exeter. 2010

236 citations recorded by the source corpus.

In this paper, we revisit the issue of the propagation of warps in thin and viscous accretion discs. In this regime, warps are known to propagate diffusively, with a diffusion coefficient approximately inversely proportional to the disc viscosity. Previous numerical investigations of this problem did not find a good agreement between the numerical results and the predictions of the analytic theories of warp propagation, both in the linear and in the non-linear case. Here, we take advantage of a new, low-memory and highly efficient smoothed particle hydrodynamics (SPH) code to run a large set of very high-resolution simulations (up to 20 million SPH particles) of warp propagation, implementing an isotropic disc viscosity in different ways, to investigate the origin of the discrepancy between the theory and the numerical results. We identify the cause of the discrepancy in an incorrect calibration of disc viscosity in previous investigations. Our new and improved analysis now shows a remarkable agreement with the analytic theory both in the linear and in the non-linear regime, in terms of warp diffusion coefficient and precession rate. It is worth noting that the resulting diffusion coefficient is inversely proportional to the disc viscosity only for small amplitude warps and small values of the disc α coefficient (α≲ 0.1). For non-linear warps, the diffusion coefficient is a function of both radius and time, and is significantly smaller than the standard value. Warped accretion discs are present in many contexts, from protostellar discs to accretion discs around supermassive black holes. In all such cases, the exact value of the warp diffusion coefficient may strongly affect the evolution of the system and therefore its careful evaluation is critical in order to correctly estimate the system dynamics.

Subfields: Astronomy and Astrophysics, Physical and Theoretical Chemistry

View Paper: https://www.semanticscholar.org/paper/ce71bfa2eed000b65750ef3d30149c21b9997e04

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Citations in the corpus

Gravitational Instabilities in Circumstellar Disks (2016, background): “Paradoxically, this reduction of the viscosity coefficient has the counter-intuitive effect of increasing artificial dissipation, since it generates artificially large velocity gradients (Lodato & Price 2010).”
Disc formation from tidal disruptions of stars on eccentric orbits by Schwarzschild black holes (2015, methodology): “For the fallback phase, we do not consider self-gravity and make use of the highly efficient code PHANTOM (Price & Federrath 2010; Lodato & Price 2010) that is optimized for studying non-self-gravitating problems.2 This choice is legitimate because the self-gravity force is only needed during the…”
Smoothed particle hydrodynamics and magnetohydrodynamics (2010, unknown): “[3,52,64,72]”
A review of quasi-periodic oscillations from black hole X-ray binaries: Observation and theory (2019, background): “For very large β0 and/or very small H/R, the smooth transition of the Bardeen-Petterson configuration is predicted to become rather sharp (disc breaking [125]), or even separate into discrete, individually precessing rings (disc tearing [170]).”
Tearing up the disc: misaligned accretion on to a binary (2013, methodology): “PHANTOM has been extensively benchmarked for performing simulations of warped discs (Lodato & Price 2010), showing excellent agreement with the analytical treatment of Ogilvie (1999).”
On planet formation in HL Tau (2015, methodology): “We perform 3D global simulations of dust/gas discs with embedded protoplanets using thePHANTOM smoothed particle hydrodynamics (SPH) code written by DP (rice & Federrath 2010; Lodato & Price 2010; Price 2012; Nixon, King & Price 2013).”
Phantom: A Smoothed Particle Hydrodynamics and Magnetohydrodynamics Code for Astrophysics (2017, methodology): “Details of the fitting procedure are given in Lodato & Price (2010).”
Kinematic Evidence for an Embedded Protoplanet in a Circumstellar Disk (2018, methodology): “We set the artificial viscosity in the code in order to obtain an average Shakura & Sunyaev (1973) viscosity of 10−3 (Lodato & Price 2010), in agreement with the upper limits found by Flaherty et al. (2015, 2017).”
The Masses and Spins of Neutron Stars and Stellar-Mass Black Holes (2014, background): “There is considerable discussion of where this is [72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82], with typical estimates being hundreds to thousands of times the gravitational radius rg ≡ GM/c(2), but it may also be that alignment is less effective when the accretion rate approaches Eddington [83].”