Computational Modelling of Magneto-Hydrodynamic Mode Conversion in Sunspot Atmospheres
An enhancement in high-frequency time-averaged Doppler velocity and intensity Fourier power (with respect to quiet-Sun values) is commonly observed amongst the weak and highly inclined field around the penumbra of sunspots and active regions in the solar photosphere and chromosphere. This well documented phenomenon is known as the acoustic (or seismic) halo.
In this thesis we attempt to model the halo numerically by initiating 3D linear wave modelling in a realistic magneto-hydrostatic sunspot atmosphere. It is our goal to ascertain whether the formation of the acoustic halo in regions of moderate and inclined magnetic field is caused by the refraction and return of fast waves via fast-slow MHD mode conversion.
We begin (chapter 2) by initiating a very simple wavelet pulse source below the photospheric surface of our sunspot atmosphere and analysing the structure of the power enhancements that form. In this scenario we observe a strong halo-like enhancement that exhibits many observationally verified characteristics. In particular we find a strong spatial relationship between halo formation and the equipartition surface at which the Alfvén speed a matches the sound speed c. This is significant as the a = c layer is where the fast-slow mode conversion takes place and so this correlation lends weight to the mode conversion halo mechanism. It also explains the fact that the halo is seen to undergo a spreading with height.
In order to model halos that are directly comparable to observations we also utilise a realistic wave source, designed to mimic the wave bath of the solar photosphere (chapter 3). We directly compare these enhancements with multi-height SDO halo observations of an active region similar (in size and field strength) to our simulated sunspot. We find that these more realistic simulated halos are in good qualitative agreement with observations, except for the fact that the simulation halo magnitudes are consistently greater than those observed. We discuss at length why this may be the case. Significantly, in simulations (both in the pulse source and realistic stochastic source cases) where we have capped the atmospheric Alfvén speed such that waves are not permitted to refract and return downwards after reaching the a = c height, halos are non-existent; indeed the halo magnitude itself seems to be a smooth function of the height at which the cap is implemented, which suggests that the power enhancement is wholly dependent on returning fast waves. In addition, we also find strong evidence that fast-Alfvén mode conversion plays a significant role in the structure of the halo, taking energy away from photospheric and chromospheric heights in the form of field-aligned Alfvén waves. This conversion process may explain the observed dual-ring halo structure that we see at higher (> 8 mHz) frequencies.
Finally (chapter 4) we sidestep somewhat from the large-scale numerical to the semi-analytical regime. Here we investigate the efficiency of the fast-Alfvén mode conversion process in the chromosphere in the context of a simplified force-free twisted magnetic field in a gravitationally stratified cold plasma. The validity of Alfvén wave production at photospheric and chromospheric heights is a contested issue, and our simple study only aims to highlight the conditions under which the conversion is most efficient in the twisted field, stratified case. We find that the production of the upwards-travelling Alfvén wave is maximised in the weakly twisted case where the field is largely vertical. However the conversion is identically zero in the case where the field is precisely vertical. The conversion is also strongly dependent on the wavevector-to-field attack angle (Φ) when the wave reaches the fast wave reflection height, being maximised when Φ = 90°. Finally, the upwards (field-aligned) Alfvén wave appears to be strongly favoured by fast waves with Φ < 90°, i.e. with a component in the direction of the field, rather than against it. These results more or less match the conclusions of Cally & Hansen (2011) who conducted a similar parameter study in uniform untwisted field.
