Ambipolar diffusion in smoothed particle magnetohydrodynamics

111

We extend recently-developed mesh-free Lagrangian methods for numerical magnetohydrodynamics (MHD) to arbitrary anisotropic diffusion equations, including: passive scalar diffusion, Spitzer-Braginskii conduction and viscosity, cosmic ray diffusion/streaming, anisotropic radiation transport, non-ideal MHD (Ohmic resistivity, ambipolar diffusion, the Hall effect), and turbulent "eddy diffusion." We study these as implemented in the code GIZMO for both new meshless finite-volume Godunov schemes (MFM/MFV). We show the MFM/MFV methods are accurate and stable even with noisy fields and irregular particle arrangements, and recover the correct behavior even in arbitrarily anisotropic cases. They are competitive with state-of-the-art AMR/moving-mesh methods, and can correctly treat anisotropic diffusion-driven instabilities (e.g. the MTI and HBI, Hall MRI). We also develop a new scheme for stabilizing anisotropic tensor-valued fluxes with high-order gradient estimators and non-linear flux limiters, which is trivially generalized to AMR/moving-mesh codes. We also present applications of some of these improvements for SPH, in the form of a new integral-Godunov SPH formulation that adopts a moving-least squares gradient estimator and introduces a flux-limited Riemann problem between particles.

Section: Discussionmentioning

confidence: 99%

Anisotropic diffusion in mesh-free numerical magnetohydrodynamics

Hopkins¹

2016

111

“…The radiative transfer was treated by the FLD-SPH method (Whitehouse & Bate 2004;Whitehouse, Bate & Monaghan 2005). We treated Ohmic and ambipolar diffusion with the method described by Tsukamoto, Iwasaki & Inutsuka (2013) and Wurster, Price & Ayliffe (2014), respectively. Both diffusion processes were accelerated by super time stepping method (Alexiades, Amiez & Gremaud 1996).…”

Section: Numerical Methods and Initial Conditionsmentioning

confidence: 99%

Effects of Ohmic and ambipolar diffusion on formation and evolution of first cores, protostars, and circumstellar discs

Tsukamoto

Iwasaki

Okuzumi

et al. 2015

124

116

We investigate the formation and evolution of a first core, protostar, and circumstellar disc with a three-dimensional non-ideal (including both Ohmic and ambipolar diffusion) radiation magnetohydrodynamics simulation. We found that the magnetic flux is largely removed by magnetic diffusion in the first core phase and that the plasma β of the centre of the first core becomes large, β > 10 4 . Thus, proper treatment of first core phase is crucial in investigating the formation of protostar and disc. On the other hand, in an ideal simulation, β ∼ 10 at the centre of the first core. The simulations with magnetic diffusion show that the circumstellar disc forms at almost the same time of protostar formation even with a relatively strong initial magnetic field (the value for the initial mass-to-flux ratio of the cloud core relative to the critical value is µ = 4). The disc has a radius of r ∼ 1 AU at the protostar formation epoch. We confirm that the disc is rotationally supported. We also show that the disc is massive (Q ∼ 1) and that gravitational instability may play an important role in the subsequent disc evolution.

“…For the C-shock test presented in Mac Low et al (1995) and Wurster et al (2014), the timestep was 30-40 times shorter for the case that included ambipolar diffusion compared to the case using ideal MHD.…”

Section: Timesteppingmentioning

confidence: 96%

“…To calculate the non-ideal MHD terms in (37), we follow the procedure described in Wurster et al (2014). First, the current density, J ≡ ∇ × B, is calculated using the difference operator (c.f.…”

Section: Pmentioning

confidence: 99%

“…Therefore, no a priori knowledge is required of which term is dominant. This algorithm has been thoroughly tested for ambipolar diffusion with constant resistivity in Wurster et al (2014); given the non-diffusive nature of the Hall effect, we present the results from two tests in Appendix C1. We compute the artificial resistivity term (Price & Monaghan 2004 in (37) using…”

Section: Pmentioning

confidence: 99%

See 1 more Smart Citation

Can non-ideal magnetohydrodynamics solve the magnetic braking catastrophe?

Wurster

Price

Bate

2016

Self Cite

149

235

We investigate whether or not the low ionisation fractions in molecular cloud cores can solve the 'magnetic braking catastrophe', where magnetic fields prevent the formation of circumstellar discs around young stars. We perform three-dimensional smoothed particle non-ideal magnetohydrodynamics (MHD) simulations of the gravitational collapse of one solar mass molecular cloud cores, incorporating the effects of ambipolar diffusion, Ohmic resistivity and the Hall effect alongside a self-consistent calculation of the ionisation chemistry assuming 0.1µm grains. When including only ambipolar diffusion or Ohmic resistivity, discs do not form in the presence of strong magnetic fields, similar to the cases using ideal MHD. With the Hall effect included, disc formation depends on the direction of the magnetic field with respect to the rotation vector of the gas cloud. When the vectors are aligned, strong magnetic braking occurs and no disc is formed. When the vectors are anti-aligned, a disc with radius of 13 AU can form even in strong magnetic when all three non-ideal terms are present, and a disc of 38 AU can form when only the Hall effect is present; in both cases, a counter-rotating envelope forms around the first hydrostatic core. For weaker, anti-aligned fields, the Hall effect produces massive discs comparable to those produced in the absence of magnetic fields, suggesting that planet formation via gravitational instability may depend on the sign of the magnetic field in the precursor molecular cloud core.