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The Sun’s interior magnetic field

From helioseismology it is known that the Sun’s radiation zone rotates as a solid body, whereas the convection zone rotates differentially — slower at the poles and faster at the equator.  The shear layer in between is known as the ‘tachocline’.

The Sun's interior rotation
Angular velocity in the solar interior
(Korzennik & Eff-Darwich 2011).

The solid rotation of the radiation zone can be explained by the presence of a global-scale magnetic field, in accordance with Ferraro’s law of isorotation.  This field must be confined to the radiation zone, i.e., prevented from diffusing out into the convection zone.

The differential rotation of the convection zone is maintained by the transport of angular momentum by convective turbulence.  The convection zone exerts a retrograde drag on the high-latitude tachocline, which drives meridional flows that try to burrow into and thereby spin down the interior.  To prevent this burrowing, the magnetic field must transport angular momentum to the poles from lower latitudes.

My research concerns the processes that confine the interior magnetic field below the convection zone, and the transport of angular momentum by the magnetic field in the tachocline.

In middle and low latitudes the internal magnetic field can be confined by “magnetic pumping” by overshooting convective plumes.  In high latitudes the field must be confined by the tachocline’s meridional flow, which is expected to be downwelling near the pole.

Confinement of polar field
Numerical simulations demonstrating confinement of the Sun’s interior magnetic field (red) in high latitudes.
Simulations were performed with the HPS code (see Tobias et al. 1998, ApJ, 502, L177).

In middle latitudes, the shear within the tachocline winds up the magnetic field lines, transmitting a prograde Maxwell torque to the poles that maintains the solid rotation of the radiation zone.

The global magnetic field geometry in the tachocline.
The global magnetic field geometry in the tachocline.

Semi-convection in stars and planets

The interiors of stars and planets are often subject to double-diffusive instabilities, because temperature diffuses much more rapidly than either momentum or chemical composition.  Near the cores of massive stars and giant planets, a stabilizing vertical gradient of composition can inhibit thermal convection, but may still allow a type of double-diffusive convection known as “semi-convection”.

Vertical profiles of temperature, composition, and density in a semi-convective region. Initially linear profiles (dashed) spontaneously develop into a staircase of layers (solid).

Under certain conditions, a semi-convective region can spontaneously develop into layered convection, which leads to an enormous increase in the transport of heat and composition (Wood et al. 2013, ApJ, 768, 157).

Density perturbations at the interface between semi-convective layers.
Density perturbations at the interface between semi-convective layers.

My research concerns the transport of heat and composition through layered convection, and its impact on the internal structure of stars and planets.

The magnetic field of a neutron star

Neutron stars have the strongest magnetic fields in the observable universe, and their fields strongly affect their evolution and observational properties.  Within the outer 10% of the star, the ions are tightly squeezed into a rigid crystalline “crust,” and the flow of free electrons through the crust generates the star’s magnetic field.  The evolution of the field is described by the electron-MHD equation, which depends nonlinearly on the field strength (the Hall effect), and somewhat resembles the vorticity equation for a non-magnetic fluid.

The imperfect analogy between electron MHD and non-magnetic fluid dynamics leaves open the possibility of turbulent cascades (either forward or inverse) in the magnetic spectrum.  This might explain why the large-scale component of neutron star fields are observed to evolve on a faster timescale than large-scale ohmic diffusion.

The structure of the crustal magnetic field also strongly affects the flow of heat out of the star. Conversely, the temperature gradient affects the evolution of the field through thermoelectric effects (including the Biermann battery effect).

My research concerns the evolution of magnetic fields in the crust of neutron stars, and the interactions between the field and the heat flow.

The magnetic field of a neutron star
Magnetic field lines of a neutron star. The coloring indicates regions at the surface of the star that are susceptible to starquakes.