Solar coronal magnetic fields derived using seismology techniques applied to omnipresent sunspot waves

Sunspots on the surface of the Sun are the observational signatures of intense manifestations of tightly packed magnetic field lines, with near-vertical field strengths exceeding 6,000 G in extreme cases1. It is well accepted that both the plasma density and the magnitude of the magnetic field strength decrease rapidly away from the solar surface, making high-cadence coronal measurements through traditional Zeeman and Hanle effects difficult as the observational signatures are fraught with low-amplitude signals that can become swamped with instrumental noise2, 3. Magneto-hydrodynamic (MHD) techniques have previously been applied to coronal structures, with single and spatially isolated magnetic field strengths estimated as 9–55 G (refs 4,5,6,7). A drawback with previous MHD approaches is that they rely on particular wave modes alongside the detectability of harmonic overtones. Here we show, for the first time, how omnipresent magneto-acoustic waves, originating from within the underlying sunspot and propagating radially outwards, allow the spatial variation of the local coronal magnetic field to be mapped with high precision. We find coronal magnetic field strengths of 32 ± 5 G above the sunspot, which decrease rapidly to values of approximately 1 G over a lateral distance of 7,000 km, consistent with previous isolated and unresolved estimations. Our results demonstrate a new, powerful technique that harnesses the omnipresent nature of sunspot oscillations to provide magnetic field mapping capabilities close to a magnetic source in the solar corona.

On the Source of Propagating Slow Magnetoacoustic Waves in Sunspots

Recent high-resolution observations of sunspot oscillations using simultaneously operated ground- and space-based telescopes reveal the intrinsic connection between different layers of the solar atmosphere. However, it is not clear whether these oscillations are externally driven or generated in situ. We address this question by using observations of propagating slow magnetoacoustic waves along a coronal fan loop system. In addition to the generally observed decreases in oscillation amplitudes with distance, the observed wave amplitudes are also found to be modulated with time, with similar variations observed throughout the propagation path of the wave train. Employing multi-wavelength and multi-instrument data, we study the amplitude variations with time as the waves propagate through different layers of the solar atmosphere. By comparing the amplitude modulation period in different layers, we find that slow magnetoacoustic waves observed in sunspots are externally driven by photospheric p-modes, which propagate upward into the corona before becoming dissipated.

Time-lapse monitoring of climate effects on earthworks using surface waves

The UK’s transportation network is supported by critical geotechnical assets (cuttings/embankments/dams) that require sustainable, cost-effective management, while maintaining an appropriate service level to meet social, economic, and environmental needs. Recent effects of extreme weather on these geotechnical assets have highlighted their vulnerability to climate variations. We have assessed the potential of surface wave data to portray the climate-related variations in mechanical properties of a clay-filled railway embankment. Seismic data were acquired bimonthly from July 2013 to November 2014 along the crest of a heritage railway embankment in southwest England. For each acquisition, the collected data were first processed to obtain a set of Rayleigh-wave dispersion and attenuation curves, referenced to the same spatial locations. These data were then analyzed to identify a coherent trend in their spatial and temporal variability. The relevance of the observed temporal variations was also verified with respect to the experimental data uncertainties. Finally, the surface wave dispersion data sets were inverted to reconstruct a time-lapse model of S-wave velocity for the embankment structure, using a least-squares laterally constrained inversion scheme. A key point of the inversion process was constituted by the estimation of a suitable initial model and the selection of adequate levels of spatial regularization. The initial model and the strength of spatial smoothing were then kept constant throughout the processing of all available data sets to ensure homogeneity of the procedure and comparability among the obtained VS sections. A continuous and coherent temporal pattern of surface wave data, and consequently of the reconstructed VS models, was identified. This pattern is related to the seasonal distribution of precipitation and soil water content measured on site.

Ultra-high-resolution Observations of MHD Waves in Photospheric Magnetic Structures

Here we review the recent progress made in the detection, examination, characterisation and interpretation of oscillations manifesting in small-scale magnetic elements in the solar photosphere. This region of the Sun's atmosphere is especially dynamic, and importantly, permeated with an abundance of magnetic field concentrations. Such magnetic features can span diameters of hundreds to many tens of thousands of km, and are thus commonly referred to as the `building blocks' of the magnetic solar atmosphere. However, it is the smallest magnetic elements that have risen to the forefront of solar physics research in recent years. Structures, which include magnetic bright points, are often at the diffraction limit of even the largest of solar telescopes. Importantly, it is the improvements in facilities, instrumentation, imaging techniques and processing algorithms during recent years that have allowed researchers to examine the motions, dynamics and evolution of such features on the smallest spatial and temporal scales to date. It is clear that while these structures may demonstrate significant magnetic field strengths, their small sizes make them prone to the buffeting supplied by the ubiquitous surrounding convective plasma motions. Here, it is believed that magnetohydrodynamic waves can be induced, which propagate along the field lines, carrying energy upwards to the outermost extremities of the solar corona. Such wave phenomena can exist in a variety of guises, including fast and slow magneto-acoustic modes, in addition to Alfven waves. Coupled with rapid advancements in magnetohydrodynamic wave theory, we are now in an ideal position to thoroughly investigate how wave motion is generated in the solar photosphere, which oscillatory modes are most prevalent, and the role that these waves play in supplying energy to various layers of the solar atmosphere.

Ultra-High-Resolution Observations of MHD Waves in Photospheric Magnetic Structures

This chapter reviews the recent observations of waves and oscillations manifesting in fine-scale magnetic structures in the solar photosphere, which are often interpreted as the "building blocks' of the magnetic Sun. The authors found, through phase relationships between the various waveforms, that small-scale magnetic bright points (MBPs) in the photosphere demonstrated signatures of specific magnetoacoustic waves, in particular the sausage and kink modes. Modern magnetohydrodynamic (MHD) simulations of the lower solar atmosphere clearly show how torsional motions can easily be induced in magnetic elements in the photosphere through the processes of vortical motions and/or buffeting by neighboring granules. The authors detected significant power associated with high-frequency horizontal motions, and suggested that these cases may be especially important in the creation of a turbulent environment that efficiently promotes Alfvén wave dissipation.

A Schamel equation for ion acoustic waves in superthermal plasmas

An investigation of the propagation of ion acoustic waves in nonthermal plasmas in the presence of trapped electrons has been undertaken. This has been motivated by space and laboratory plasma observations of plasmas containing energetic particles, resulting in long-tailed distributions, in combination with trapped particles, whereby some of the plasma particles are confined to a finite region of phase space. An unmagnetized collisionless electron-ion plasma is considered, featuring a non-Maxwellian-trapped electron distribution, which is modelled by a kappa distribution function combined with a Schamel distribution. The effect of particle trapping has been considered, resulting in an expression for the electron density. Reductive perturbation theory has been used to construct a KdV-like Schamel equation, and examine its behaviour. The relevant configurational parameters in our study include the superthermality index κ and the characteristic trapping parameter β. A pulse-shaped family of solutions is proposed, also depending on the weak soliton speed increment u₀. The main modification due to an increase in particle trapping is an increase in the amplitude of solitary waves, yet leaving their spatial width practically unaffected. With enhanced superthermality, there is a decrease in both amplitude and width of solitary waves, for any given values of the trapping parameter and of the incremental soliton speed. Only positive polarity excitations were observed in our parametric investigation.