Modelling Fast-Alfv\'en Mode Conversion Using SPARC

We successfully utilise the SPARC code to model fast-Alfv\'en mode conversion in the region $c_A \gg c_S$ via 3-D MHD numerical simulations of helioseismic waves within constant inclined magnetic field configurations. This was achieved only after empirically modifying the background density and gravitational stratifications in the upper layers of our computational box, as opposed to imposing a traditional Lorentz Force limiter, to ensure a manageable timestep. We found that the latter approach inhibits the fast-Alfv\'en mode conversion process by severely damping the magnetic flux above the surface.Comment: Proceedings of GONG 2012 / LWS/SDO-5 / SOHO 27 (Eclipse on the Coral Sea: Cycle 24 Ascending) Conference, November 12 -16, 2012, Palm Cove, Australi

Directional Time-Distance Probing of Model Sunspot Atmospheres

A crucial feature not widely accounted for in local helioseismology is that surface magnetic regions actually open a window from the interior into the solar atmosphere, and that the seismic waves leak through this window, reflect high in the atmosphere, and then re-enter the interior to rejoin the seismic wave field normally confined there. In a series of recent numerical studies using translation invariant atmospheres, we utilised a "directional time-distance helioseismology" measurement scheme to study the implications of the returning fast and Alfv\'en waves higher up in the solar atmosphere on the seismology at the photosphere (Cally & Moradi 2013; Moradi & Cally 2014). In this study, we extend our directional time-distance analysis to more realistic sunspot-like atmospheres to better understand the direct effects of the magnetic field on helioseismic travel-time measurements in sunspots. In line with our previous findings, we uncover a distinct frequency-dependant directional behaviour in the travel-time measurements, consistent with the signatures of MHD mode conversion. We found this to be the case regardless of the sunspot field strength or depth of its Wilson depression. We also isolated and analysed the direct contribution from purely thermal perturbations to the measured travel times, finding that waves propagating in the umbra are much more sensitive to the underlying thermal effects of the sunspot.Comment: 9 pages, 8 figures, accepted for publication in Monthly Notices of the Royal Astronomical Society Main Journa

Fast-to-Alfv\'en mode conversion mediated by Hall current. II Application to the solar atmosphere

Coupling between fast magneto-acoustic and Alfv\'en waves can be observe in fully ionized plasmas mediated by stratification and 3D geometrical effects. In Paper I, Cally & Khomenko (2015) have shown that in a weakly ionized plasma, such as the solar photosphere and chromosphere, the Hall current introduces a new coupling mechanism. The present study extends the results from Paper I to the case of warm plasma. We report on numerical experiments where mode transformation is studied using quasi-realistic stratification in thermodynamic parameters resembling the solar atmosphere. This redresses the limitation of the cold plasma approximation assumed in Paper I, in particular allowing the complete process of coupling between fast and slow magneto-acoustic modes and subsequent coupling of the fast mode to the Alfv\'en mode through the Hall current. Our results confirm the efficacy of the mechanism proposed in Paper I for the solar case. We observe that the efficiency of the transformation is a sensitive function of the angle between the wave propagation direction and the magnetic field, and of the wave frequency. The efficiency increases when the field direction and the wave direction are aligned for increasing wave frequencies. After scaling our results to typical solar values, the maximum amplitude of the transformed Alfv\'en waves, for a frequency of 1 Hz, corresponds to an energy flux (measured above the height of peak Hall coupling) of $\sim10^3$ $\rm W\,m^{-2}$, based on an amplitude of 500 $\rm m\,s^{-1}$ at $\beta=1$, which is sufficient to play a major role in both quiet and active region coronal heating

Alfv\'en waves in simulations of solar photospheric vortices

Using advanced numerical magneto-hydrodynamic simulations of the magnetised solar photosphere, including non-grey radiative transport and a non-ideal equation of state, we analyse plasma motions in photospheric magnetic vortices. We demonstrate that apparent vortex-like motions in photospheric magnetic field concentrations do not exhibit "tornado"-like behaviour or a "bath-tub" effect. While at each time instance the velocity field lines in the upper layers of the solar photosphere show swirls, the test particles moving with the time-dependent velocity field do not demonstrate such structures. Instead, they move in a wave-like fashion with rapidly changing and oscillating velocity field, determined mainly by magnetic tension in the magnetised intergranular downflows. Using time-distance diagrams, we identify horizontal motions in the magnetic flux tubes as torsional Alfv\'en perturbations propagating along the nearly vertical magnetic field lines with local Alfv\'en speed.Comment: 5 pages, 4 figures, accepted to ApJ

Three Dimensional MHD Wave Propagation and Conversion to Alfven Waves near the Solar Surface. I. Direct Numerical Solution

The efficacy of fast/slow MHD mode conversion in the surface layers of sunspots has been demonstrated over recent years using a number of modelling techniques, including ray theory, perturbation theory, differential eigensystem analysis, and direct numerical simulation. These show that significant energy may be transferred between the fast and slow modes in the neighbourhood of the equipartition layer where the Alfven and sound speeds coincide. However, most of the models so far have been two dimensional. In three dimensions the Alfven wave may couple to the magneto-acoustic waves with important implications for energy loss from helioseismic modes and for oscillations in the atmosphere above the spot. In this paper, we carry out a numerical ``scattering experiment'', placing an acoustic driver 4 Mm below the solar surface and monitoring the acoustic and Alfvenic wave energy flux high in an isothermal atmosphere placed above it. These calculations indeed show that energy conversion to upward travelling Alfven waves can be substantial, in many cases exceeding loss to slow (acoustic) waves. Typically, at penumbral magnetic field strengths, the strongest Alfven fluxes are produced when the field is inclined 30-40 degrees from the vertical, with the vertical plane of wave propagation offset from the vertical plane containing field lines by some 60-80 degrees.Comment: Accepted for the HELAS II/ SOHO 19/ GONG 2007 Topical Issue of Solar Physic

Resonant Absorption as Mode Conversion?

Resonant absorption and mode conversion are both extensively studied mechanisms for wave "absorption" in solar magnetohydrodynamics (MHD). But are they really distinct? We re-examine a well-known simple resonant absorption model in a cold MHD plasma that places the resonance inside an evanescent region. The normal mode solutions display the standard singular resonant features. However, these same normal modes may be used to construct a ray bundle which very clearly undergoes mode conversion to an Alfv\'en wave with no singularities. We therefore conclude that resonant absorption and mode conversion are in fact the same thing, at least for this model problem. The prime distinguishing characteristic that determines which of the two descriptions is most natural in a given circumstance is whether the converted wave can provide a net escape of energy from the conversion/absorption region of physical space. If it cannot, it is forced to run away in wavenumber space instead, thereby generating the arbitrarily small scales in situ that we recognize as fundamental to resonant absorption and phase mixing. On the other hand, if the converted wave takes net energy way, singularities do not develop, though phase mixing may still develop with distance as the wave recedes.Comment: 23 pages, 8 figures, 2 tables; accepted by Solar Phys (July 9 2010

Probing sunspots with two-skip time-distance helioseismology

Previous helioseismology of sunspots has been sensitive to both the structural and magnetic aspects of sunspot structure. We aim to develop a technique that is insensitive to the magnetic component so the two aspects can be more readily separated. We study waves reflected almost vertically from the underside of a sunspot. Time-distance helioseismology was used to measure travel times for the waves. Ray theory and a detailed sunspot model were used to calculate travel times for comparison. It is shown that these large distance waves are insensitive to the magnetic field in the sunspot. The largest travel time differences for any solar phenomena are observed. With sufficient modeling effort, these should lead to better understanding of sunspot structure

Helioseismic analysis of the solar flare-induced sunquake of 2005 January 15

We report the discovery of one of the most powerful sunquakes detected to date, produced by an X1.2-class solar flare in active region 10720 on 2005 January 15. We used helioseismic holography to image the source of seismic waves emitted into the solar interior from the site of the flare. Acoustic egression power maps at 3 and 6 mHz with a 2 mHz bandpass reveal a compact acoustic source strongly correlated with impulsive hard X-ray and visible-continuum emission along the penumbral neutral line separating the two major opposing umbrae in the $\delta$-configuration sunspot that predominates AR10720. The acoustic emission signatures were directly aligned with both hard X-ray and visible continuum emission that emanated during the flare. The visible continuum emission is estimated at $2.0 \times 10^{23}$ J, approximately 500 times the seismic emission of $\sim 4 \times 10^{20}$ J. The flare of 2005 January 15 exhibits the same close spatial alignment between the sources of the seismic emission and impulsive visible continuum emission as previous flares, reinforcing the hypothesis that the acoustic emission may be driven by heating of the low photosphere. However, it is a major exception in that there was no signature to indicate the inclusion of protons in the particle beams thought to supply the energy radiated by the flare. The continued strong coincidence between the sources of seismic emission and impulsive visible continuum emission in the case of a proton-deficient white-light flare lends substantial support to the ``back -- warming'' hypothesis, that the low photosphere is significantly heated by intense Balmer and Paschen continuum-edge radiation from the overlying chromosphere in white-light flares.Comment: 12 pages, 7 figures, published in MNRA