Magnetized Accretion and Dead Zones in Protostellar Disks

The edges of magnetically-dead zones in protostellar disks have been proposed as locations where density bumps may arise, trapping planetesimals and helping form planets. Magneto-rotational turbulence in magnetically-active zones provides both accretion of gas on the star and transport of mass to the dead zone. We investigate the location of the magnetically-active regions in a protostellar disk around a solar-type star, varying the disk temperature, surface density profile, and dust-to-gas ratio. We also consider stellar masses between 0.4 and 2 $M_\odot$, with corresponding adjustments in the disk mass and temperature. The dead zone's size and shape are found using the Elsasser number criterion with conductivities including the contributions from ions, electrons, and charged fractal dust aggregates. The charged species' abundances are found using the approach proposed by S. Okuzumi. The dead zone is in most cases defined by the ambipolar diffusion. In our maps, the dead zone takes a variety of shapes, including a fish-tail pointing away from the star and islands located on and off the midplane. The corresponding accretion rates vary with radius, indicating locations where the surface density will increase over time, and others where it will decrease. We show that density bumps do not readily grow near the dead zone's outer edge, independently of the disk parameters and the dust properties. Instead, the accretion rate peaks at the radius where the gas-phase metals freeze out. This could lead to clearing a valley in the surface density, and to a trap for pebbles located just outside the metal freeze-out line.Comment: 58 pages, 25 figures, 2 tables, accepted to Ap

Magnetic diffusivities in 3D radiative chemo-hydrodynamic simulations of protostellar collapse

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Magnetic diffusivities in 3D radiative chemo-hydrodynamic simulations of protostellar collapse

International audienceContext. Both theory and observations of star-forming clouds require simulations that combine the co-evolving chemistry, magneto-hydrodynamics, and radiative transfer in protostellar collapse simulation. A detailed knowledge of self-consistent chemical evolution for the main charge carriers (both gas species and dust grains) allows us to correctly estimate the rate and nature of magnetic dissipation in the collapsing core. This knowledge is critical to answer one of the most significant issues of star and planet formation: what is the magnitude and spatial distribution of magnetic flux as the initial condition to protoplanetary disk evolution?Aims. We use a chemo-dynamical version of RAMSES, which is described in a companion publication, to follow the chemo-dynamical evolution of collapsing dense cores with various dust properties and interpret differences that occur in magnetic diffusivity terms. These differences are crucial to circumstellar disk formation. Methods. We performed 3D chemo-dynamical simulations of 1 M⊙ isolated dense core collapse for a range in dust size assumptions. The number density of dust and its mean size affect the efficiency of charge capturing and the formation of ices. The radiative hydrodynamics and dynamical evolution of chemical abundances were used to reconstruct the magnetic diffusivity terms for clouds with various magnetisation. Results. The simulations are performed for a mean dust size ranging from 0.017 μm to 1 μm, and we adopt both a fixed dust size and a dust size distribution. The chemical abundances for this range of dust sizes are produced by RAMSES and serve as inputs to calculations of Ohmic, ambipolar, and Hall diffusivity terms. Ohmic resistivity only plays a role at the late stage of the collapse in the innermost region of the cloud where gas density is in excess of a few times 1013 cm-3. Ambipolar diffusion is a dominant magnetic diffusivity term in cases where mean dust size is a typical ISM value or larger. We demonstrate that the assumption of a fixed dominant ion mass can lead to a one order of magnitude mismatch in the ambipolar diffusion magnitude. The negative Hall effect is dominant during the collapse in case of small dust, i.e. for the mean dust size of 0.02 μm and smaller; we connect this effect to the dominance of negatively charged grains. We find that the Hall effect reverses its sign for mean dust size of 0.1 μm and smaller. The phenomenon of the sign reversal strongly depends on the number of negatively charged dust relative to the ions and the quality of coupling of the charged dust to the magnetic fields. We have adopted different strengths of magnetic fields, β = Pgas/Pmag = 2,5,25. We observe that the variation on the field strength only shifts the Hall effect reversal along the radius of the collapsing cloud, but does not prevent it. Conclusions. The dust grain mean size appears to be the parameter with the strongest impact on the magnitude of the magnetic diffusivity, dividing the collapsing clouds in Hall-dominated and ambipolar-dominated clouds and affecting the size of the resulting disks. We propose to link the dust properties and occurrence and size of disk structures in Class 0 young stellar objects. The proper accounting for dust grain growth in the radiative magneto-hydrodynamical collapse models are as important as coupling the dynamics of the collapse with the chemistry

Steady-state accretion in magnetized protoplanetary disks

Context. The transition between magnetorotational instability (MRI)-active and magnetically dead regions corresponds to a sharp change in the disk turbulence level, where pressure maxima may form, hence potentially trapping dust particles and explaining some of the observed disk substructures. Aims. We aim to provide the first building blocks toward a self-consistent approach to assess the dead zone outer edge as a viable location for dust trapping, under the framework of viscously driven accretion. Methods. We present a 1+1D global magnetically driven disk accretion model that captures the essence of the MRI-driven accretion, without resorting to 3D global nonideal magnetohydrodynamic (MHD) simulations. The gas dynamics is assumed to be solely controlled by the MRI and hydrodynamic instabilities. For given stellar and disk parameters, the Shakura–Sunyaev viscosity parameter, α, is determined self-consistently under the adopted framework from detailed considerations of the MRI with nonideal MHD effects (Ohmic resistivity and ambipolar diffusion), accounting for disk heating by stellar irradiation, nonthermal sources of ionization, and dust effects on the ionization chemistry. Additionally, the magnetic field strength is numerically constrained to maximize the MRI activity. Results. We demonstrate the use of our framework by investigating steady-state MRI-driven accretion in a fiducial protoplanetary disk model around a solar-type star. We find that the equilibrium solution displays no pressure maximum at the dead zone outer edge, except if a sufficient amount of dust particles has accumulated there before the disk reaches a steady-state accretion regime. Furthermore, the steady-state accretion solution describes a disk that displays a spatially extended long-lived inner disk gas reservoir (the dead zone) that accretes a few times 10−9 M⊙ yr−1. By conducting a detailed parameter study, we find that the extent to which the MRI can drive efficient accretion is primarily determined by the total disk gas mass, the representative grain size, the vertically integrated dust-to-gas mass ratio, and the stellar X-ray luminosity. Conclusions. A self-consistent time-dependent coupling between gas, dust, stellar evolution models, and our general framework on million-year timescales is required to fully understand the formation of dead zones and their potential to trap dust particles