Large-scale magnetic field in the accretion discs of young stars: the influence of magnetic diffusion, buoyancy and Hall effect

TL;DR

This study models the magnetic field structure in young star accretion discs considering various diffusion and buoyancy effects, revealing how these processes influence magnetic field geometry and polarization signatures.

Contribution

It provides a comprehensive, accurate solution for magnetic field evolution in discs, including effects like Hall, buoyancy, and ionization, which were not simultaneously addressed before.

Findings

Magnetic fields in dead zones are quasi-vertical due to diffusion constraints.

Buoyancy limits the toroidal magnetic field near the disc's inner edge.

Polarization maps show reduced polarization in dead zones.

Abstract

We investigate the fossil magnetic field in the accretion and protoplanetary discs using the Shakura and Sunyaev approach. The distinguishing feature of this study is the accurate solution of the ionization balance equations and the induction equation with Ohmic diffusion, magnetic ambipolar diffusion, buoyancy and the Hall effect. We consider the ionization by cosmic rays, X-rays and radionuclides, radiative recombinations, recombinations onto dust grains, and also thermal ionization. The buoyancy appears as the additional mechanism of magnetic flux escape in the steady-state solution of the induction equation. Calculations show that Ohmic diffusion and magnetic ambipolar diffusion constraint the generation of the magnetic field inside the `dead' zones. The magnetic field in these regions is quasi-vertical. The buoyancy constraints the toroidal magnetic field strength close to the disc inner edge. As a result, the toroidal and vertical magnetic fields become comparable. The Hall effect is important in the regions close to the borders of the `dead' zones because electrons are magnetized there. The magnetic field in these regions is quasi-radial. We calculate the magnetic field strength and geometry for the discs with accretion rates $(10^{-8}-10^{-6})\,\rm{M}_{\odot}\,\rm{yr}^{-1}$. The fossil magnetic field geometry does not change significantly during the disc evolution while the accretion rate decreases. We construct the synthetic maps of dust emission polarized due to the dust grain alignment by the magnetic field. In the polarization maps, the `dead' zones appear as the regions with the reduced values of polarization degree in comparison to those in the adjacent regions.