The scattering of ff- and pp-modes from ensembles of thin magnetic flux tubes - An analytical approach

Motivated by the observational results of Braun (1995), we extend the model of Hanson & Cally (2014) to address the effect of multiple scattering of f and p-modes by an ensemble of thin vertical magnetic flux tubes in the surface layers of the Sun. As in observational Hankel analysis we measure the scatter and phase shift from an incident cylindrical wave in a coordinate system roughly centred in the core of the ensemble. It is demonstrated that, although thin flux tubes are unable to interact with high order fluting modes individually, they can indirectly absorb energy from these waves through the scatters of kink and sausage components. It is also shown how the distribution of absorption and phase shift across the azimuthal order m depends strongly on the tube position, as well as on the individual tube characteristics. This is the first analytical study into an ensembles multiple scattering regime, that is embedded within a stratified atmosphere.Comment: 20 pages, 8 Figure

Multiple Scattering of Seismic Waves from Ensembles of Upwardly Lossy Thin Flux Tubes

Our previous semi-analytic treatment of f- and p-mode multiple scattering from ensembles of thin flux tubes (Hanson and Cally, Astrophys. J. 781, 125; 791, 129, 2014) is extended by allowing both sausage and kink waves to freely escape at the top of the model using a radiative boundary condition there. As expected, this additional avenue of escape, supplementing downward loss into the deep solar interior, results in substantially greater absorption of incident f- and p-modes. However, less intuitively, it also yields mildly to substantially smaller phase shifts in waves emerging from the ensemble. This may have implications for the interpretation of seismic data for solar plage regions, and in particular their small measured phase shifts.Comment: 9 Pages, 5 Figures. Accepted by Solar Physic

Resonant Absorption as Mode Conversion? II. Temporal Ray Bundle

A fast-wave pulse in a simple, cold, inhomogeneous MHD model plasma is constructed by Fourier superposition over frequency of harmonic waves that are singular at their respective Alfven resonances. The pulse partially reflects before reaching the resonance layer, but also partially tunnels through to it to mode convert to an Alfven wave. The exact absorption/conversion coefficient for the pulse is shown to be given precisely by a function of transverse wavenumber tabulated in Paper I of this sequence, and to be independent of frequency and pulse width.Comment: 6 pages, 4 figures, accepted (15 Nov 2010) by Solar Physics. Ancillary file (animation) attache

Enhanced Acoustic Emission in Relation to the Acoustic Halo Surrounding Active Region 11429

The use of acoustic holography in the high-frequency $p$-mode spectrum can resolve the source distributions of enhanced acoustic emissions within halo structures surrounding active regions. In doing so, statistical methods can then be applied to ascertain relationships with the magnetic field. This is the focus of this study. The mechanism responsible for the detected enhancement of acoustic sources around solar active regions has not yet been explained. Furthermore the relationship between the magnetic field and enhanced acoustic emission has not yet been comprehensively examined. We have used vector magnetograms from the \Helioseismic and Magnetic Imager (HMI) on-board the Solar Dynamics Observatory (SDO) to image the magnetic-field properties in the halo. We have studied the acoustic morphology of an active region, with a complex halo and "glories," and we have linked some acoustic properties to the magnetic-field configuration. In particular, we find that acoustic sources are significantly enhanced in regions of intermediate field strength with inclinations no different from the distributions found in the quiet Sun. Additionally we have identified a transition region between the active region and the halo, in which the acoustic source power is hindered by inclined fields of intermediate field strength. Finally, we have compared the results of acoustic emission maps, calculated from holography, and the commonly used local acoustic maps, finding that the two types of maps have similar properties with respect to the magnetic field but lack spatial correlation when examining the highest-powered regions.Comment: 19 pages, 8 figures, Accepted by Solar Physic

Sensitivity kernels for time-distance helioseismology: efficient computation for spherically-symmetric solar models

The interpretation of helioseismic measurements, such as wave travel-time, is based on the computation of kernels that give the sensitivity of the measurements to localized changes in the solar interior. These are computed using the ray or the Born approximation. The Born approximation is preferable as it takes finite-wavelength effects into account, but can be computationally expensive. We propose a fast algorithm to compute travel-time sensitivity kernels under the assumption that the background solar medium is spherically symmetric. Kernels are typically expressed as products of Green's functions that depend upon depth, latitude and longitude. Here, we compute the spherical harmonic decomposition of the kernels and show that the integrals in latitude and longitude can be performed analytically. In particular, the integrals of the product of three associated Legendre polynomials can be computed thanks to the algorithm of Dong and Lemus (2002). The computations are fast and accurate and only require the knowledge of the Green's function where the source is at the pole. The computation time is reduced by two orders of magnitude compared to other recent computational frameworks. This new method allows for flexible and computationally efficient calculations of a large number of kernels, required in addressing key helioseismic problems. For example, the computation of all the kernels required for meridional flow inversion takes less than two hours on 100 cores

Supervised Neural Networks for Helioseismic Ring-Diagram Inversions

The inversion of ring fit parameters to obtain subsurface flow maps in ring-diagram analysis for 8 years of SDO observations is computationally expensive, requiring ~3200 CPU hours. In this paper we apply machine learning techniques to the inversion in order to speed up calculations. Specifically, we train a predictor for subsurface flows using the mode fit parameters and the previous inversion results, to replace future inversion requirements. We utilize Artificial Neural Networks as a supervised learning method for predicting the flows in 15 degree ring tiles. To demonstrate that the machine learning results still contain the subtle signatures key to local helioseismic studies, we use the machine learning results to study the recently discovered solar equatorial Rossby waves. The Artificial Neural Network is computationally efficient, able to make future flow predictions of an entire Carrington rotation in a matter of seconds, which is much faster than the current ~31 CPU hours. Initial training of the networks requires ~3 CPU hours. The trained Artificial Neural Network can achieve a root mean-square error equal to approximately half that reported for the velocity inversions, demonstrating the accuracy of the machine learning (and perhaps the overestimation of the original errors from the ring-diagram pipeline). We find the signature of equatorial Rossby waves in the machine learning flows covering six years of data, demonstrating that small-amplitude signals are maintained. The recovery of Rossby waves in the machine learning flow maps can be achieved with only one Carrington rotation (27.275 days) of training data. We have shown that machine learning can be applied to, and perform more efficiently than the current ring-diagram inversion. The computation burden of the machine learning includes 3 CPU hours for initial training, then around 0.0001 CPU hours for future predictions.Comment: 10 pages, 10 Figures, Accepted by A&

A linear model for inertial modes in a differentially rotating Sun

Inertial wave modes in the Sun are of interest owing to their potential to reveal new insight into the solar interior. These predominantly retrograde-propagating modes in the solar subsurface appear to deviate from the thin-shell Rossby-Haurwitz model at high azimuthal orders. We present new measurements of sectoral equatorial inertial modes at $m>15$ where the modes appear to become progressively less retrograde compared to the canonical Rossby-Haurwitz dispersion relation in a co-rotating frame. We use a spectral eigenvalue solver to compute the spectrum of solar inertial modes in the presence of differential rotation. Focussing specifically on equatorial Rossby modes, we find that the numerically obtained mode frequencies lie along distinct ridges, one of which lies strikingly close to the observed mode frequencies in the Sun. We also find that the $n=0$ ridge is deflected strongly in the retrograde direction. This suggests that the solar measurements may not correspond to the fundamental $n=0$ Rossby-Haurwitz solutions as was initially suspected, but to a those for a higher $n$. The numerically obtained eigenfunctions also appear to sit deep within the convection zone -- unlike those for the $n=0$ modes -- which differs substantially from solar measurements and complicates inference.Comment: 16 pages, 12 figure

Magnetic flux in the Sun emerges unaffected by supergranular-scale surface flows

Magnetic flux emergence from the convection zone into the photosphere and beyond is a critical component of the behaviour of large-scale solar magnetism. Flux rarely emerges amid field-free areas at the surface, but when it does, the interaction between magnetism and plasma flows can be reliably explored. Prior ensemble studies identified weak flows forming near emergence locations, but the low signal-to-noise required averaging over the entire dataset, erasing information about variation across the sample. Here, we apply deep learning to achieve improved signal-to-noise, enabling a case-by-case study. We find that these associated flows are dissimilar across instances of emergence and also occur frequently in the quiet convective background. Our analysis suggests diminished influence of supergranular-scale convective flows and magnetic buoyancy on flux rise. Consistent with numerical evidence, we speculate that small-scale surface turbulence and / or deep-convective processes play an outsize role in driving flux emergence.Comment: 20 pages, 13 figures, Accepted in Ap