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.
Solar active regions are one of the most magnetically dynamic locations in the Sun’s tenuous atmosphere. The intrinsically embedded magnetic fields support a wide variety of coronal compressive MHD wave phenomena, with EUV observations dating back to the late 1990s revealing a wealth of magneto-acoustic oscillations travelling upwards from the solar surface along magnetic fields to distances far exceeding many tens of thousands of km (refs 8,9,10,11). The weak dissipation mechanisms experienced in the solar corona, in the forms of thermal conduction, compressive viscosity and optically thin radiation12, allow features to be probed through seismology techniques in an attempt to uncover atmospheric changes and sub-resolution structuring that would otherwise be difficult, if not impossible to determine13. MHD seismology of sunspots is a powerful tool that has risen in popularity in recent years, with insights into atmospheric structuring, expansion and emission gained through the comparison of wave periods, velocities and dissipation rates14,15. Importantly, evidence continues to be brought forward that suggests compressive MHD wave phenomena originating in sunspots are not simply a rare occurrence, but instead an omnipresent feature closely tied to all atmospheric layers16.
Using previously deployed MHD seismology techniques to infer the strength of the coronal magnetic field is a difficult task, often limited by substantial errors (up to 80% in some cases4). Critical problems are its inability to deduce the magnetic field strength as a function of spatial position, and by the relative rareness of oscillatory phenomena in the solar corona demonstrating measurable harmonic overtones7. Other methods, including deep exposures of coronal magnetic Stokes profiles17 and the examination of brightness–temperature spectra from gyro-resonance emission18, also bring about their own distinct impediments, including crosstalk between Stokes signals, poor temporal resolutions often exceeding 1 h and ambiguous cyclotron frequency reference points19. Therefore, although diverse, yet encouraging attempts have been made to constrain the magnitude of the coronal magnetic field in previous years, each process is hindered by its inability to accurately and simultaneously deduce spatially resolved, unambiguous and high-cadence field strengths. In this Letter we document and apply a novel MHD-based technique that combines high-resolution observations from modern space-based observatories, vector magnetic field extrapolations and differential emission measure techniques to accurately measure the spatial dependence of the coronal magnetic field strength with potential temporal resolutions orders-of-magnitude better than current imaging approaches.
Observations at high spatial (435 km per pixel) and temporal (12 s) resolution with the Atmospheric Imaging Assembly20 (AIA) on-board the Solar Dynamics Observatory (SDO) spacecraft have allowed us to resolve fine-scale and rapidly dynamic coronal features associated with a powerful magnetic sunspot. The data were obtained through six independent EUV filters on 10 December 2011, with the resulting fields of view cropped to 50 × 50 Mm2 to closely match simultaneous ground-based observations obtained with the Rapid Oscillations in the Solar Atmosphere21 (ROSA) and Hydrogen-Alpha Rapid Dynamics camera14 (HARDcam) instruments on the Dunn Solar Telescope (see Supplementary Methods for further information on the processing of the observational data). The images (Fig. 1) show a number of elongated structures extending away from the underlying sunspot, which are particularly apparent in AIA 171 Å data known to correspond to lower coronal plasma with temperatures ∼700,000 K. Differential emission measure (DEM) techniques22 are employed on the six EUV AIA channels, producing emission measure (EM) and temperature (Te) estimates for the sunspot and its locality. The resulting Te map reveals that the elongated structures, seen to extend away from the underlying sunspot, are comprised of relatively cool coronal material (<1,000,000 K), hence explaining why they demonstrate such visibility in the AIA 171 Å channel. Examination of time-lapse movies (Supplementary Movie 1) reveals a multitude of wavefronts seen to propagate radially outwards from the sunspot, particularly along the relatively cool, elongated coronal fan structures.
Fourier-filtered images (Fig. 2 and Supplementary Movie 2) reveal a wealth of oscillatory signatures covering a wide range of frequencies, with longer periodicities preferentially occurring at increasing distances from the sunspot umbra, and propagating with reduced phase speeds. Importantly, the waves are apparently continuous in time, suggesting that such oscillatory phenomena are driven from a regular, powerful and coherent source. Through centre-of-gravity techniques the centre of the sunspot (or umbral barycentre) is defined, as indicated by the white crosses in Fig. 1c. A series of expanding annuli, centred on the umbral barycentre, are used to map the azimuthally averaged phase velocities as a function of period through the creation of time–distance diagrams (Fig. 2). Phase speeds are calculated from the gradients of the diagonal bands in the time–distance diagrams and found to span 92 km s−1 (60 s periodicity) through to 23 km s−1 (660 s periodicity), which are characteristic of coronal slow magneto-acoustic tube speeds9,10,11,12, ct. Owing to the continuous nature of the propagating waves, Fourier methods are applied to the unfiltered data to create power maps allowing the signatures of the wave phenomena to be easily extracted as a function of period. Employing the same expanding annuli technique, the period-dependent power spectra are studied as a function of the radial distance from the umbral barycentre (Supplementary Fig. 1). A gradual change in the dominant period as a function of distance is found, with periodicities of approximately 3 min within the underlying sunspot umbra, increasing rapidly within the penumbral locations, and eventually plateauing at periodicities of approximately 13 min further along the coronal fan structures (Fig. 2d). This suggests that the waves detected within the immediate periphery of the underlying sunspot are the lower coronal counterpart of propagating compressive magneto-acoustic oscillations driven upwards by the underlying sunspot.
Complementary 171 Å data from the EUVI instrument on-board the leading Solar TErrestrial RElations Observatory23 (STEREO-A) provides a side-on view of the coronal fan, allowing the spatial variation of the structure with atmospheric height to be measured directly (Fig. 3). Magnetic field extrapolations24 of vector magnetograms from SDO’s Helioseismic and Magnetic Imager25 (HMI) are also used to calculate magnetic field vectors over a wide range of atmospheric heights, allowing field inclination angles to be compared with direct STEREO-A imaging as a function of distance from the umbral barycentre (Fig. 4). We find that increasing the distance from the centre of the sunspot results in more inclined magnetic fields. Importantly, this means that the measured phase speeds of the propagating waves will have been underestimated to a certain degree, particularly for locations close to the umbral barycentre, where the magnetic field inclination is minimal. To compensate for this, we first use the velocity–period and period–distance relationships to convert the measured tube speeds into a function of distance from the centre of the underlying sunspot (Fig. 4). Then, the inclination angles at this spatial position are used to calculate the true wave velocity irrespective of inclination-angle effects (Fig. 4d). Tube speeds of approximately 185 km s−1 are found towards the centre of the umbra, decreasing radially within several Mm to values of approximately 25 km s−1.
Because the sound speed, cs, is dependent on the local plasma temperature, we use the Te maps to derive the spatial distribution of the sound speed through the relation where γ = 5/3 is the adiabatic index, μ = 1.3 g mol−1 is the mean molecular weight assuming H:He = 10:1 for the solar corona26, and R is the gas constant. This provides sound speeds greater than the compensated tube speeds, and of the order of 160–210 km s−1 (Fig. 4d). With the distributions of cs and ct known, we estimate the spatial distribution of the Alfvén speed, vA, through the relationship27 The derived Alfvén speeds, shown in Fig. 4d, are highest (1,500 km s−1) towards the centre of the sunspot umbra, dropping to their lowest values (25 km s−1) at the outermost extremity of the active region. The large values found towards the sunspot core are consistent with previous coronal fast-mode wave observations related to magnetically confined structures28.
The Alfvén speed depends on two key parameters: the magnitude of the magnetic field strength, |B|, and the local plasma density, ρ. We calculate22 spatially resolved plasma densities from the EM and Te maps, resulting in a range of densities of the order of (2.1–5.6) × 10−12 kg m−3. With the Alfvén speeds and local plasma densities known, we derive the magnitude of the azimuthally averaged magnetic field at each radial location through the relationship27 where μ0 is the magnetic permeability. The resulting values for |B| range from 32 ± 5 G at the centre of the underlying sunspot, rapidly decreasing to 1 G over a lateral distance of approximately 7,000 km (Fig. 5a). Both our maximal and minimal values are consistent with previous, yet isolated and/or error-prone independent estimations of magnetically dominated coronal loops4,5,6,7 and quiet Sun locations29. However, importantly, we show for the first time a novel way of harnessing the omnipresent nature of propagating slow-mode waves in the corona to more accurately constrain the magnetic field topology as a function of spatial location, with the potential to provide coronal B-field maps with cadences as high as 1 min. This would provide more than an order-of-magnitude improvement in temporal resolution compared with deep exposures of coronal Stokes profiles17. A key science goal of the upcoming 4 m Daniel K. Inouye Solar Telescope (DKIST) is to directly image the full coronal Stokes profiles using near-infrared spectral lines. The novel techniques presented here will therefore serve as an important long-term tool that can be used to compare directly with the DKIST observations following first light in 2019. Furthermore, because magnetic reconnection phenomena are often observed in the vicinity of active regions, a high-cadence approach to monitoring the spatial variations of the coronal magnetic field would be critical when attempting to understand the precursor events leading to solar flares.
D.B.J. wishes to thank the UK Science and Technology Facilities Council (STFC) for the award of an Ernest Rutherford Fellowship in addition to a dedicated Research Grant. D.B.J. also wishes to thank Invest NI for their Research & Development Grants. This work was supported by a UKIERI trilateral research grant of The British Council.