Global evolution of the magnetic field in a thin disc and its consequences for protoplanetary systems

The strength and structure of the large-scale magnetic field in protoplanetary discs are still unknown, although they could have important consequences for the dynamics and evolution of the disc. Using a mean-field approach in which we model the effects of turbulence through enhanced diffusion coefficients, we study the time-evolution of the large-scale poloidal magnetic field in a global model of a thin accretion disc, with particular attention to protoplanetary discs. With the transport coefficients usually assumed, the magnetic field strength does not significantly increase radially inwards, leading to a relatively weak magnetic field in the inner part of the disc. We show that with more realistic transport coefficients that take into account the vertical structure of the disc and the back-reaction of the magnetic field on the flow as obtained by Guilet & Ogilvie (2012), the magnetic field can significantly increase radially inwards. The magnetic-field profile adjusts to reach an equilibrium value of the plasma $\beta$ parameter (the ratio of midplane thermal pressure to magnetic pressure) in the inner part of the disc. This value of $\beta$ depends strongly on the aspect ratio of the disc and on the turbulent magnetic Prandtl number, and lies in the range $10^4-10^7$ for protoplanetary discs. Such a magnetic field is expected to affect significantly the dynamics of protoplanetary discs by increasing the strength of MHD turbulence and launching an outflow. We discuss the implications of our results for the evolution of protoplanetary discs and for the formation of powerful jets as observed in T-Tauri star systems.Comment: 19 pages, 12 figures, accepted for publication in MNRA

A Shallow Water Analogue of the Standing Accretion Shock Instability: Experimental Demonstration and Two-Dimensional Model

Despite the sphericity of the collapsing stellar core, the birth conditions of neutron stars can be highly non spherical due to a hydrodynamical instability of the shocked accretion flow. Here we report the first laboratory experiment of a shallow water analogue, based on the physics of hydraulic jumps. Both the experiment and its shallow water modeling demonstrate a robust linear instability and nonlinear properties of symmetry breaking, in a system which is one million times smaller and about hundred times slower than its astrophysical analogue.Comment: 4 pages, 4 figures, accepted for publication in Phys. Rev. Letters. Supplementary Material (6 movies) available at http://irfu.cea.fr/Projets/SN2NS/outreach.htm

Toward a magnetohydrodynamic theory of the stationary accretion shock: toy model of the advective-acoustic cycle in a magnetized flow

The effect of a magnetic field on the linear phase of the advective-acoustic instability is investigated, as a first step toward a magnetohydrodynamic (MHD) theory of the stationary accretion shock instability taking place during stellar core collapse. We study a toy model where the flow behind a planar stationary accretion shock is adiabatically decelerated by an external potential. Two magnetic field geometries are considered: parallel or perpendicular to the shock. The entropy-vorticity wave, which is simply advected in the unmagnetized limit, separates into five different waves: the entropy perturbations are advected, while the vorticity can propagate along the field lines through two Alfven waves and two slow magnetosonic waves. The two cycles existing in the unmagnetized limit, advective-acoustic and purely acoustic, are replaced by up to six distinct MHD cycles. The phase differences among the cycles play an important role in determining the total cycle efficiency and hence the growth rate. Oscillations in the growth rate as a function of the magnetic field strength are due to this varying phase shift. A vertical magnetic field hardly affects the cycle efficiency in the regime of super-Alfvenic accretion that is considered. In contrast, we find that a horizontal magnetic field strongly increases the efficiencies of the vorticity cycles that bend the field lines, resulting in a significant increase of the growth rate if the different cycles are in phase. These magnetic effects are significant for large-scale modes if the Alfven velocity is a sizable fraction of the flow velocity.Comment: 13 pages, 9 figures, accepted for publication in ApJ. Cosmetic changes after proof reading corrections

On the linear growth mechanism driving the stationary accretion shock instability

During stellar core collapse, which eventually leads to a supernovae explosion, the stalled shock is unstable due to the standing accretion shock instability (SASI). This instability induces large-scale non spherical oscillations of the shock, which have crucial consequences on the dynamics and the geometry of the explosion. While the existence of this instability has been firmly established, its physical origin remains somewhat uncertain. Two mechanisms have indeed been proposed to explain its linear growth. The first is an advective-acoustic cycle, where the instability results from the interplay between advected perturbations (entropy and vorticity) and an acoustic wave. The second mechanism is purely acoustic and assumes that the shock is able to amplify trapped acoustic waves. Several arguments favouring the advective-acoustic cycle have already been proposed, however none was entirely conclusive for realistic flow parameters. In this article we give two new arguments which unambiguously show that the instability is not purely acoustic, and should be attributed to the advective-acoustic cycle. First, we extract a radial propagation timescale by comparing the frequencies of several unstable harmonics that differ only by their radial structure. The extracted time matches the advective-acoustic time but strongly disagrees with a purely acoustic interpretation. Second, we present a method to compute purely acoustic modes, by artificially removing advected perturbations below the shock. All these purely acoustic modes are found to be stable, showing that the advected wave is essential to the instability mechanism.Comment: 17 pages, 10 figures, accepted for publication in MNRA

Magnetorotational Instability in Core-Collapse Supernovae

We discuss the relevance of the magnetorotational instability (MRI) in core-collapse supernovae (CCSNe). Our recent numerical studies show that in CCSNe, the MRI is terminated by parasitic instabilities of the Kelvin-Helmholtz type. To determine whether the MRI can amplify initially weak magnetic fields to dynamically relevant strengths in CCSNe, we performed three-dimensional simulations of a region close to the surface of a differentially rotating proto-neutron star in non-ideal magnetohydrodynamics with two different numerical codes. We find that under the conditions prevailing in proto-neutron stars, the MRI can amplify the magnetic field by (only) one order of magnitude. This severely limits the role of MRI channel modes as an agent amplifying the magnetic field in proto-neutron stars starting from small seed fields.Comment: Proceedings in Acta Physica Polonica B, Proceedings Supplement, Vol. 10, No. 2, p.361, 4 pages, 1 figur

The saturation of SASI by parasitic instabilities

The Standing Accretion Shock Instability (SASI) is commonly believed to be responsible for large amplitude dipolar oscillations of the stalled shock during core collapse, potentially leading to an asymmetric supernovae explosion. The degree of asymmetry depends on the amplitude of SASI, which nonlinear saturation mechanism has never been elucidated. We investigate the role of parasitic instabilities as a possible cause of nonlinear SASI saturation. As the shock oscillations create both vorticity and entropy gradients, we show that both Kelvin-Helmholtz and Rayleigh-Taylor types of instabilities are able to grow on a SASI mode if its amplitude is large enough. We obtain simple estimates of their growth rates, taking into account the effects of advection and entropy stratification. In the context of the advective-acoustic cycle, we use numerical simulations to demonstrate how the acoustic feedback can be decreased if a parasitic instability distorts the advected structure. The amplitude of the shock deformation is estimated analytically in this scenario. When applied to the set up of Fernandez & Thompson (2009a), this saturation mechanism is able to explain the dramatic decrease of the SASI power when both the nuclear dissociation energy and the cooling rate are varied. Our results open new perspectives for anticipating the effect, on the SASI amplitude, of the physical ingredients involved in the modeling of the collapsing star.Comment: 14 pages, 16 figures, accepted for publication in ApJ. Minor changes following the referee report

The stress–pressure relationship in simulations of MRI-induced turbulence

We determine how MRI (magnetorotational instability)-turbulent stresses depend on gas pressure via a suite of unstratified shearing box simulations. Earlier numerical work reported only a very weak dependence at best, results that call into question the canonical α-disc model and the thermal stability results that follow from it. Our simulations, in contrast, exhibit a stronger relationship, and show that previous work was box-size limited: turbulent ‘eddies’ were artificially restricted by the numerical domain rather than by the scaleheight. Zero-net-flux runs without physical diffusion coefficients yield a stress proportional to P^0.5, where P is pressure. The stresses are also proportional to the grid length and hence remain numerically unconverged. The same runs with physical diffusivities, however, give a result closer to an α-disc: the stress is ∝P^0.9. Net-flux simulations without explicit diffusion exhibit stresses ∝P^0.5, but stronger imposed fields weaken this correlation. In summary, compressibility is important for the saturation of the MRI, but the exact stress–pressure relationship is difficult to ascertain in local simulations because of numerical convergence issues and the influence of any imposed flux. As a consequence, the interpretation of thermal stability behaviour in local simulations is a problematic enterprise.Some of the simulations were run on the DiRAC Complexity system, operated by the University of Leicester IT Services, which forms part of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment is funded by BIS National E-Infrastructure capital grant ST/K000373/1 and STFC DiRAC Operations grant ST/K0003259/1. DiRAC is part of the UK National E-Infrastructure run. JR and HNL are partially funded by STFC grants ST/L000636/1 and ST/K501906/1. JG acknowledges support from the Max-Planck-Princeton Center for Plasma Physics.This is the final version of the article. It first appeared from Oxford University Press via http://dx.doi.org/10.1093/mnras/stv228