Gert Botha

Numerical simulations of rotating axisymmetric sunspots

A numerical model of axisymmetric convection in the presence of a vertical magnetic flux bundle and rotation about the axis is presented. The model contains a compressible plasma described by the non-linear MHD equations, with density and temperature gradients simulating the upper layer of the Suns convection zone. The solutions exhibit a central magnetic flux tube in a cylindrical numerical domain, with convection cells forming collar flows around the tube. When the numerical domain is rotated with a constant angular velocity, the plasma forms a Rankine vortex, with the plasma rotating as a rigid body where the magnetic field is strong, as in the flux tube, while experiencing sheared azimuthal flow in the surrounding convection cells, forming a free vortex. As a result, the azimuthal velocity component has its maximum value close to the outer edge of the flux tube. The azimuthal flow inside the magnetic flux tube and the vortex flow is prograde relative to the rotating cylindrical reference frame. A retrograde flow appears at the outer wall. The most significant convection cell outside the flux tube is the location for the maximum value of the azimuthal magnetic field component. The azimuthal flow and magnetic structure are not generated spontaneously, but decay exponentially in the absence of any imposed rotation of the cylindrical domain.

Chromospheric seismology above sunspot umbrae

The acoustic resonator is an important model for explaining the three-minute oscillations in the chromosphere above sunspot umbrae. The steep temperature gradients at the photosphere and transition region provide the cavity for the acoustic resonator, which allows waves to be both partially transmitted and partially reflected. In this paper, a new method of estimating the size and temperature profile of the chromospheric cavity above a sunspot umbra is developed. The magnetic field above umbrae is modelled numerically in 1.5D with slow magnetoacoustic wave trains travelling along magnetic fieldlines. Resonances are driven by applying the random noise of three different colours---white, pink and brown---as small velocity perturbations to the upper convection zone. Energy escapes the resonating cavity and generates wave trains moving into the corona. Line of sight (LOS) integration is also performed to determine the observable spectra through SDO/AIA. The numerical results show that the gradient of the coronal spectra is directly correlated with the chromosperic temperature configuration. As the chromospheric cavity size increases, the spectral gradient becomes shallower. When LOS integrations is performed, the resulting spectra demonstrate a broadband of excited frequencies that is correlated with the chromospheric cavity size. The broadband of excited frequencies becomes narrower as the chromospheric cavity size increases. These two results provide a potentially useful diagnostic for the chromospheric temperature profile by considering coronal velocity oscillations.

Nonaxisymmetric Instabilities of Convection around Magnetic Flux Tubes

On the surface of the Sun, magnetic flux elements collect in regions of converging flow, grow in field strength, and become pores, which have been observed to exhibit nonaxisymmetric structure over a range of scales. Around a fully developed sunspot, as well as the fine scale of the penumbra, the moat sometimes shows a clearly observable spokelike structure at low azimuthal wavenumbers. We investigate the formation of azimuthal structure by computing the linear stability properties of fully nonlinear axisymmetric magnetoconvection, which takes the form of a central flux tube surrounded by a convecting field-free region. We find steady and oscillatory instabilities with a preferred azimuthal wavenumber. The unstable modes are concentrated in the convecting region close to the outer edge of the flux tube. The instability is driven by convection and is not a magnetic fluting instability.

Observational signatures of a kink-unstable coronal flux rope using Hinode/EIS

The signatures of energy release and energy transport for a kink-unstable coronal flux rope are investigated via forward modelling. Synthetic intensity and Doppler maps are generated from a 3D numerical simulation. The CHIANTI database is used to compute intensities for three Hinode/EIS emission lines that cover the thermal range of the loop. The intensities and Doppler velocities at simulation resolution are spatially degraded to the Hinode/EIS pixel size (1\arcsec), convolved using a Gaussian point-spread function (3\arcsec), and exposed for a characteristic time of 50 seconds. The synthetic images generated for rasters (moving slit) and sit-and-stare (stationary slit) are analysed to find the signatures of the twisted flux and the associated instability. We find that there are several qualities of a kink-unstable coronal flux rope that can be detected observationally using Hinode/EIS, namely the growth of the loop radius, the increase in intensity towards the radial edge of the loop, and the Doppler velocity following an internal twisted magnetic field line. However, EIS cannot resolve the small, transient features present in the simulation, such as sites of small-scale reconnection (e.g. nanoflares)

3D WKB solution for fast magnetoacoustic wave behaviour around an X-line

We study the propagation of a fast magnetoacoustic wave in a 3D magnetic field created from two magnetic dipoles. The magnetic topology contains an X-line. We aim to contribute to the overall understanding of MHD wave propagation within inhomogeneous media, specifically around X-lines. We investigate the linearised, 3D MHD equations under the assumptions of ideal and cold plasma. We utilise the WKB approximation and Charpits method during our investigation. It is found that the behaviour of the fast magnetoacoustic wave is entirely dictated by the local, inhomogeneous, equilibrium Alfven speed profile. All parts of the wave experience refraction during propagation, where the magnitude of the refraction effect depends on the location of an individual wave element within the inhomogeneous magnetic field. The X-line, along which the Alfven speed is identically zero, acts as a focus for the refraction effect. There are two main types of wave behaviour: part of the wave is either trapped by the X-line or escapes the system, and there exists a critical starting region around the X-line that divides these two types of behaviour. For the set-up investigated, it is found that

Statistical properties of Charney-Hasegawa-Mima zonal flows

15.5\%

Predictions of DKIST/DL-NIRSP Observations for an Off-limb Kink-unstable Coronal Loop

of the fast wave energy is trapped by the X-line. We conclude that linear,

Onset of 2D magnetic reconnection in the solar photosphere,chromosphere and corona

\beta=0

Numerical simulations of sunspots

fast magnetoacoustic waves can accumulate along X-lines and thus these will be specific locations of fast wave energy deposition and thus preferential heating. The work here highlights the importance of understanding the magnetic topology of a system. We also demonstrate how the 3D WKB technique described in this paper can be applied to other magnetic configurations.

Converging and diverging convection around axisymmetric magnetic flux tubes

A theoretical interpretation of numerically generated probability density functions (PDFs) of intermittent plasma transport events in unforced zonal flows is provided within the Charney-Hasegawa-Mima (CHM) model. The governing equation is solved numerically with various prescribed density gradients that are designed to produce different configurations of parallel and anti-parallel streams. Long-lasting vortices form whose flow is governed by the zonal streams. It is found that the numerically generated PDFs can be matched with analytical predictions of PDFs based on the instanton method by removing the autocorrelations from the time series. In many instances, the statistics generated by the CHM dynamics relaxes to Gaussian distributions for both the electrostatic and vorticity perturbations, whereas in areas with strong nonlinear interactions it is found that the PDFs are exponentially distributed.