Magnetically Controlled Accretion Flows onto Young Stellar Objects

TL;DR

This paper develops a formalism using orthogonal coordinate systems aligned with magnetic field lines to analytically describe magnetically controlled accretion flows onto young stars, considering complex magnetic geometries and flow conditions.

Contribution

It introduces a new analytic approach to model accretion flows along arbitrary magnetic field configurations, extending previous dipole models to include multipole fields like octupoles.

Findings

Flow must be near isothermal for steady transonic solutions with octupole fields.

Higher multipole order requires a stiffer equation of state for smooth flow.

Including octupole components affects surface densities, hot spot locations, and magnetic truncation radius.

Abstract

(abridged) Accretion from disks onto young stars is thought to follow magnetic field lines from the inner disk edge to the stellar surface. The accretion flow thus depends on the geometry of the magnetic field. This paper extends previous work by constructing a collection of orthogonal coordinate systems, including the corresponding differential operators, where one coordinate traces the magnetic field lines. This formalism allows for an (essentially) analytic description of the geometry and the conditions required for the flow to pass through sonic points. Using this approach, we revisit the problem of magnetically controlled accretion flow in a dipole geometry, and then generalize the treatment to consider magnetic fields with multiple components, including dipole, octupole, and split monopole contributions. This approach can be generalized further to consider more complex magnetic field configurations. Observations indicate that accreting young stars have substantial dipole and octupole components, and that accretion flow is transonic. If the effective equation of state for the fluid is too stiff, the flow cannot pass smoothly through the sonic points in steady state. For a multipole field of order \ell, we derive a constraint on the polytropic index, n>\ell+3/2, required for steady transonic flow to reach free-fall velocities. For octupole fields, inferred on surfaces of T Tauri stars, n>9/2, so that the flow must be close to isothermal. The inclusion of octupole field components produces higher densities at the stellar surface and smaller hot spots, which occur at higher latitudes; the magnetic truncation radius is also modified. This contribution thus increases our understanding of magnetically controlled accretion for young stellar objects and can be applied to a variety of additional astrophysical problems.