Sunspot Regions Research Articles

Are There Local Dynamos Acting in Sunspot Regions?

In solar physics, a long-unanswered question is whether or not there are local dynamos acting in sunspot regions. Here we report an observed pattern of magnetic evolution that makes the sunspots alive with ample complexity and energy. This anomalous pattern manifests as peculiar bipolar magnetic emergences (BMEs), exhibiting the following characteristics: (1) the BMEs persistently appear beyond the penumbra, encircling the sunspot in an end-to-end configuration; (2) each BME gradually grows and separates its two polarities along an arc trajectory centered on the sunspot; (3) a circular brightening belt is manifested in the ultraviolet/extreme-ultraviolet radiations during the BMEs’ evolution; and (4) the sunspot regions with such an evolution pattern often exhibit vigorous solar activity, such as homogeneous major flares. The magnetic evolving pattern and relevant flare activity indicate the presence of a local dynamo, and we characterize it as a twisting-reconnecting dynamo.

Turbulent convection as a significant hidden provider of magnetic helicity in solar eruptions

Solar flares and coronal mass ejections, the primary space weather disturbances affecting the entire heliosphere and near-Earth environment, mainly emanate from sunspot regions harbouring high degrees of magnetic twist. However, it is not clear how magnetic helicity, the quantity for measuring the magnetic twist, is supplied to the upper solar atmosphere via the emergence of magnetic flux from the turbulent convection zone. Here, we report state-of-the-art numerical simulations of magnetic flux emergence from the deep convection zone. By controlling the twist of emerging flux, we find that with the support of convective upflow, the untwisted emerging flux can reach the solar surface without collapsing, in contrast to previous theoretical predictions, and eventually create sunspots. Because of the turbulent twisting of magnetic flux, the produced sunspots exhibit rotation and inject magnetic helicity into the upper atmosphere, amounting to a substantial fraction of injected helicity in the twisted cases that is sufficient to produce flare eruptions. This result indicates that the turbulent convection is responsible for supplying a non-negligible amount of magnetic helicity and potentially contributes to solar flares.

On the propagation of gravity waves in the lower solar atmosphere in different magnetic configurations

Gravity waves are generated by turbulent subsurface convection overshooting or penetrating locally into a stably stratified medium. While propagating energy upwards, their characteristic negative phase shift over height is a well-recognized observational signature. Since their first detailed observational detection and estimates of energy content, a number of studies have explored their propagation characteristics and interaction with magnetic fields and other waves modes in the solar atmosphere. Here, we present a study of the atmospheric gravity wave dispersion diagrams utilizing intensity observations that cover photospheric to chromospheric heights over different magnetic configurations of quiet-Sun (magnetic network regions), a plage, and a sunspot as well as velocity observations within the photospheric layer over a quiet and a sunspot region. In order to investigate the propagation characteristics, we construct two–height intensity - intensity and velocity- velocity cross-spectra and study phase and coherence signals in the wavenumber - frequency dispersion diagrams and their association with background magnetic fields. We find signatures of association between magnetic fields and much reduced coherence and phase shifts over height from intensity-intensity and velocity-velocity phase and coherence diagrams, both indicating suppression/scattering of gravity waves by the magnetic fields. Our results are consistent with the earlier numerical simulations, which indicate that gravity waves are suppressed or scattered and reflected back into the lower solar atmosphere in the presence of magnetic fields.

Evolution of the flow field in decaying active regions

Context. In a previous work, we investigated the evolution of the flow field around sunspots during sunspot decay and compared it with the flow field of supergranular cells. The decay of a sunspot proceeds as it interacts with its surroundings. This is manifested by the changes observed in the flow field surrounding the decaying spot. Aims. We now investigate in detail the evolution of the flow field in the direct periphery of the sunspots of the same sample and aim to provide a complete picture of the role of large-scale flows present in sunspot cells. Methods. We analyse the horizontal velocity profiles of sunspots obtained from observations by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO). We follow their evolution across the solar disc from their stable phase to their decay and their final disappearance. Results. We find two different scenarios for the evolution of the flow region surrounding a spot in the final stage of its decay: (i) either the flow cell implodes and disappears under the action of the surrounding supergranules or (ii) it outlives the spot. In the later case, an inwards flow towards the remaining naked spot develops in the vicinity closest to the spot followed by an outflow further out. These findings provide observational evidence to theoretical predictions by realistic magnetohydrodynamic (MHD) sunspot and moat region simulations. Conclusions. The Evershed flow and the moat flow, both connected to the presence of fully fledged sunspots in a spot cell, vanish when penumbrae decay. Moat flows decline into supergranular flows. The final fate of a spot cell depends on its interaction with the surrounding supergranular cells. In the case of non-imploding spot cells, the remaining naked spot develops a converging inflow driven by radiative cooling and a geometrical alignment of granules in its periphery which is similar to that observed in pores.

Origin of extreme solar eruptive activity from the active region NOAA 12673 and the largest flare of solar cycle 24

AbstractDuring 2017, when the Sun was moving toward the minimum phase of solar cycle 24, an exceptionally eruptive active region (AR) NOAA 12673 emerged on the Sun during August 28-September 10. During the highest activity level, the AR turned into a δ-type sunspot region, which manifests the most complex configuration of magnetic fields from the photosphere to the coronal heights. The AR 12673 produced four X-class and 27 M-class flares, along with numerous C-class flares, making it one of the most powerful ARs of solar cycle 24. Notably, it produced the largest flare of solar cycle 24, namely, the X9.3 event on 2017 September 6. In this work, we highlight the results of our comprehensive analysis involving multi-wavelength imaging and coronal magnetic field modeling to understand the evolution and eruptivity from AR 12673. We especially focus on the morphological, spectral and kinematical evolution of the two X-class flares on 6 September 2017. We explore various large- and small-scale magnetic field structures of the active region which are associated with the triggering and subsequent outbursts during the powerful solar transients.

Propagating Alfvénic Waves Observed in the Chromosphere around a Small Sunspot: Tales of 3-minute Waves and 10-minute Waves

Recent observations provided evidence that the solar chromosphere of sunspot regions is pervaded by Alfvénic waves—transverse magnetohydrodynamic (MHD) waves (Alfvén waves or kink waves). In order to systematically investigate the physical characteristics of Alfvénic waves over a wide range of periods, we analyzed the time series of line-of-sight velocity maps constructed from the Hα spectral data of a small sunspot region taken by the Fast Imaging Solar Spectrograph of the Goode Solar Telescope at Big Bear. We identified each Alfvénic wave packet by examining the cross-correlation of band-filtered velocity between two points that are located a little apart presumably on the same magnetic field line. As result, we detected a total of 279 wave packets in the superpenumbral region around the sunspot and obtained their statistics of period, velocity amplitude, and propagation speed. An important finding of ours is that the detected Alfvénic waves are clearly separated into two groups: 3-minute period (<7 minutes) waves and 10-minute period (>7 minutes) waves. We propose two tales on the origin of Alfvénic waves in the chromosphere; the 3-minute Alfvénic waves are excited by the upward-propagating slow waves in the chromosphere through the slow-to-Alfvénic mode conversion, and the 10-minute Alfvénic waves represent the chromospheric manifestation of the kink waves driven by convective motions in the photosphere.

Observing the Development of Two Solar Flares by Monitoring AR 12882 which Produces a Kp6 Geomagnetic Storm in October 2021

In this paper, we study active region 12882 in conjunction with the level of geomagnetic storm based on space weather data. Several flares occurred in this region in October 2021, including M1.6 and C2.1. Data were also collected from the online solar monitor and space weather live database provided by NOAA and SDO/AIA. The study of the solar flare events was done by monitoring the sunspot region for the past four days to observed changes in the earth’s atmosphere. The M-class flare event made by AR 12882 produced a CME with a speed exceeding 500 km/sec which directed towards Earth and produced an intense geomagnetic storm with kp6 index.

Coronal condensation as the source of transition-region supersonic downflows above a sunspot

Context. Plasma loops or plumes rooted in sunspot umbrae often harbor downflows with speeds of 100 km s−1. These downflows are supersonic at transition region temperatures of ∼0.1 MK. The source of these flows is not well understood. Aims. We aim to investigate the source of sunspot supersonic downflows (SSDs) in active region 12740 using simultaneous spectroscopic and imaging observations. Methods. We identified SSD events from multiple raster scans of a sunspot by the Interface Region Imaging Spectrograph, and we calculated the electron densities, mass fluxes, and velocities of these SSDs. The extreme-ultraviolet (EUV) images provided by the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory and the EUV Imager onboard the Solar Terrestrial Relations Observatory were employed to investigate the origin of these SSDs and their associated coronal rain. Results. Almost all the identified SSDs appear at the footpoints of sunspot plumes and are temporally associated with the appearance of chromospheric bright dots inside the sunspot umbra. Dual-perspective EUV imaging observations reveal a large-scale closed magnetic loop system spanning the sunspot region and a remote region. We observed that the SSDs are caused by repeated coronal rain that forms and flows along these closed magnetic loops toward the sunspot. One episode of coronal rain clearly indicates that reconnection near a coronal X-shaped structure first leads to the formation of a magnetic dip. Subsequently, hot coronal plasma catastrophically cools from ∼2 MK in the dip region via thermal instability. This results in the formation of a transient prominence in the dip, from which the cool gas mostly slides into the sunspot along inclined magnetic fields under the gravity. This drainage process manifests as a continuous rain flow, which lasts for ∼2 h and concurrently results in a nearly steady SSD event. The total mass of condensation (1.3 × 1014 g) and condensation rate (1.5 × 1010 g s−1) in the dip region were found to be sufficient to sustain this long-lived SSD event, which has a mass transport rate of 0.7 − 1.2 × 1010 g s−1. Conclusions. Our results demonstrate that coronal condensation in magnetic dips can result in the quasi-steady sunspot supersonic downflows.

A Study on Correcting the Effect of Polarization Crosstalk in Full-Disk Solar Photospheric Magnetic Field Observations

Magnetography using magnetic sensitive lines is regarded traditionally as the main instrument for measuring the magnetic field of the whole Sun. Full polarized Stokes parameters (\(I\), \(Q\), \(U\), \(V\)) can be used to deduce the magnetic field under specific theoretical models or inversion algorithms. Due to various reasons, there are often cross-talk effects among Stokes signals observed directly by magnetographs. Especially, the circularly polarized signal \(V\) usually seriously affects the linearly polarized \(Q\) and \(U\) signals, which is one of the main errors in the value of the transverse magnetic field (parallel to the solar surface) that is related to \(Q\) and \(U\). The full-disk magnetograph onboard the Advanced Space based Solar Observatory (ASO-S/FMG) is designed to observe Stokes parameters and deduce the magnetic-field vector. In this article, the methods for correcting the effects of cross-talk \(V\) on \(Q\) and \(U\) based on the assumption of perfectly symmetric \(Q\) and \(U\) and anti-symmetric Stokes \(V\) profiles and a new method for reducing the crosstalk effect under observation mode of the FMG are developed. Through the test, it is found that the two methods are effective in cross-talk removal in the sunspot region and have better consistency. Additionally, the developed method can be applied to remove the cross-talk effect by using only one group of \(Q\), \(U\) and \(V\) images observed at one wavelength position.

Exploring possibilities for solar irradiance prediction from solar photosphere images using recurrent neural networks

Studies of the Sun and the Earth’s atmosphere and climate consider solar variability as an important driver, and its constant monitoring is essential for climate models. Solar total and spectral irradiance are among the main relevant parameters. Physical semi-empirical and empirical models have been developed and made available, and they are crucial for the reconstruction of irradiance during periods of data failure or their absence. However, ionospheric and climate models would also benefit from solar irradiance prediction through prior knowledge of irradiance values hours or days ahead. This paper presents a neural network-based approach, which uses images of the solar photosphere to extract sunspot and active region information and thus generate inputs for recurrent neural networks to perform the irradiance prediction. Experiments were performed with two recurrent neural network architectures for short- and long-term predictions of total and spectral solar irradiance at three wavelengths. The results show good quality of prediction for total solar irradiance (TSI) and motivate further effort in improving the prediction of each type of irradiance considered in this work. The results obtained for spectral solar irradiance (SSI) point out that photosphere images do not have the same influence on the prediction of all wavelengths tested but encourage the bet on new spectral lines prediction.

The study of the strongest solar event on a minimum of the 24th solar cycle

The strongest solar flares of the 24th solar cycle erupted on September 6, 2017, and it was the 8th strongest solar flare recorded since 1996. This extreme solar flare occurred at the minimum of the 24th solar cycle. The active region is located in the Western Hemisphere and produced the violent explosion of class X9.3 and X2.2 on September 6, X1.3 on September 7, and X8.2 on September 10, 2017. The injection duration of the solar energetic particles of the solar event was 17 minutes. All data for this solar event was collected from the Advanced Composition Explorer and simulated for particles’ motion using the transport equation and solved by the numerical technique. We obtained the injection time of the solar energetic particle propagation by comparing fitting between the simulation results and the spacecraft data. Injection time taken by high-energy particles to travel from the Sun to the Earth was found to be in the range of 39 to 743 minutes. At the peak of this solar flare, the coronal mass ejection was detected, which increased the injection time. The Kp-index of this solar flare was 4; thus, there was no effect on the Earth. The Kp-index value increased to 8 on September 7-8, 2017, due to another solar event from the same sunspot region, indicating the effect of solar flare and CME, which resulted in the appearance of aurora.

Ti I lines at 2.2 μm as probes of the cooler regions of sunspots

Context. The sunspot umbra harbours the coolest plasma on the solar surface due to the presence of strong magnetic fields. The atomic lines that are routinely used to observe the photosphere have weak signals in the umbra and are often swamped by molecular lines. This makes it harder to infer the properties of the umbra, especially in the darkest regions. Aims. The lines of the Ti I multiplet at 2.2 μm are formed mainly at temperatures ≤4500 K and are not known to be affected by molecular blends in sunspots. Since the first systematic observations in the 1990s, these lines have been seldom observed due to the instrumental challenges involved at these longer wavelengths. We revisit these lines and investigate their formation in different solar features. Methods. We synthesized the Ti I multiplet using a snapshot from 3D magnetohydrodynamic (MHD) simulations of a sunspot and explored the properties of two of its lines in comparison with two commonly used iron lines, at 6302.5 Å and 1.5648 μm. Results. We find that the Ti I lines have stronger signals than the Fe I lines in both intensity and polarization in the sunspot umbra and in penumbral spines. They have little to no signal in the penumbral filaments and the quiet Sun, at μ = 1. Their strong and well-split profiles in the dark umbra are less affected by stray light. Consequently, inside the sunspot, it is easier to invert these lines and to infer the atmospheric properties as compared to the iron lines. Conclusions. The Cryo-NIRSP instrument at the DKIST will provide the first-ever high-resolution observations in this wavelength range. In this preparatory study, we demonstrate the unique temperature and magnetic sensitivities of the Ti multiplet by probing the Sun’s coolest regions, which are not favourable for the formation of other commonly used spectral lines. We thus expect such observations to advance our understanding of sunspot properties.

DETEKSI OTOMATIS DAERAH TERANG DI SISI JAUH MATAHARI UNTUK PREDIKSI KEMUNCULAN BINTIK

Active regions that responsible to flare occurrences often appear at east limb as mature active regions. Therefore, we use EUVI instrument onboard STEREO-A spacecraft to observe far-side extreme ultra violet (EUV) for the automatic detection system. The procedure running on the system is by combining the latest STEREO/EUVI and the SDO/AIA data into a single composite heliographic coordinate system map. Active regions are detected based on their intensities on the heliographic map and their duration after they are detected. The program has successfully detected far-side bright-regions in an automatically near real-time system. 85 % of active regions that have been detected for more than 4 days appear in the east limb as sunspots. On the other hand, bright-regions that have detected between 2-3 days develop to be plagues or decay before reaching the east limb. We find that the different between the mean intensities of the bright-regions that develop to sunspot and no-sunspot regions is about 200 DN//s, which is insignificant to determine the threshold.

Absorption of High-frequency Oscillations and Its Relation to Emissivity Reduction

Abstract Sunspots are known to be strong absorbers of solar oscillation modal power. The most convincing way to demonstrate this is done via Fourier–Hankel decomposition (FHD), where the local oscillation field is separated into in- and outgoing waves, showing the reduction in power. Due to the Helioseismic and Magnetic Imager’s high-cadence Doppler measurements, power absorption can be investigated at frequencies beyond the acoustic cutoff frequency. We perform an FHD on five sunspot regions and two quiet-Sun control regions and study the resulting absorption spectra α ℓ (ν), specifically at frequencies ν &gt; 5.3 mHz. We observe an unreported high-frequency absorption feature, which only appears in the presence of a sunspot. This feature is confined to phase speeds of one-skip waves whose origins coincide with the sunspot’s center, with v ph = 85.7 km s−1 in this case. By employing a fit to the absorption spectra at a constant phase speed, we find that the peak absorption strength lies between 0.166 and 0.222 at a noise level of about 0.009 (5%). The well-known absorption along ridges at lower frequencies can reach up to . Thus our finding in the absorption spectrum is weaker, but nevertheless significant. From first considerations regarding the energy budget of high-frequency waves, this observation can likely be explained by the reduction of emissivity within the sunspot. We derive a simple relation between emissivity and absorption. We conclude that sunspots yield a wave power absorption signature (for certain phase speeds only), which may help in understanding the effect of strong magnetic fields on convection and source excitation and potentially in understanding the general sunspot subsurface structure.

Spectroscopic Detection of Alfvénic Waves in the Chromosphere of Sunspot Regions

Abstract Transverse magnetohydrodynamic waves often called Alfvénic (or kink) waves have been often theoretically put forward to solve the outstanding problems of the solar corona like coronal heating, solar wind acceleration, and chemical abundance enhancement. Here we report the first spectroscopic detection of Alfvénic waves around a sunspot at chromospheric heights. By analyzing the spectra of the Hα line and Ca ii 854.2 nm line, we determined line-of-sight velocity and temperature as functions of position and time. As a result, we identified transverse magnetohydrodynamic waves pervading the superpenumbral fibrils. These waves are characterized by the periods of 2.5 to 4.5 minutes, and the propagation direction parallel to the fibrils, the supersonic propagation speeds of 45 to 145 km s−1, and the close association with umbral oscillations and running penumbral waves in sunspots. Our results support the notion that the chromosphere around sunspots abounds with Alfvénic waves excited by the mode conversion of the upward-propagating slow magnetoacoustic waves.

A novel approach to identify resonant MHD wave modes in solar pores and sunspot umbrae: B − ω analysis

The umbral regions of sunspots and pores in the solar photosphere are generally dominated by 3 mHz oscillations, which are due to p-modes penetrating the magnetic region. In these locations, wave power is also significantly reduced with respect to the quiet Sun. However, here we study a pore where not only is the power of the oscillations in the umbra comparable to, or even larger than, that of the quiet Sun, but the main dominant frequency is not 3 mHz as expected, but instead 5 mHz. By combining Doppler velocities and spectropolarimetry and analysing the relationship between magnetic field strength and frequency, the resultant B − ω diagram reveals distinct ridges that are remarkably clear signatures of resonant magneto-hydrodynamic (MHD) oscillations confined within the pore umbra. We demonstrate that these modes, in addition to velocity oscillations, are also accompanied by magnetic oscillations, as predicted from MHD theory. The novel technique of B − ω analysis proposed in this article opens up an exciting new avenue for identifying MHD wave modes in the umbral regions of both pores and sunspots.

The configuration and failed eruption of a complex magnetic flux rope above aδsunspot region

Aims.We aim to investigate the configuration of a complex flux rope above theδsunspot region in the National Oceanic and Atmospheric Administration AR 11515 and its eruptive expansion during a confined M5.3-class flare.Methods.We studied the formation of theδsunspot using the continuum intensity images and photospheric vector magnetograms provided by the Helioseismic and Magnetic Imager on-board the Solar Dynamics Observatory (SDO). We employed the extreme-ultraviolet and ultraviolet images provided by the Atmospheric Imaging Assembly on-board SDO and the hard X-ray emission recorded by theReuven RamatyHigh-Energy Solar Spectroscopic Imager to investigate the eruptive details. The coronal magnetic field is extrapolated from the photospheric field using a nonlinear force free field (NLFFF) method, based on which the flux rope is identified through calculating the twist numberTwand squashing factorQ. We searched the null point via a modified Powell hybrid method.Results.The collision between two newly emerged spot groups form theδsunspot. A bald patch (BP) configuration forms at the collision location between one umbra and the penumbra, above which a complex flux rope structure is identified. The flux rope has a multilayer configuration, with one compact end and the other end bifurcating into different branches. It has a non-uniformTwprofile, which decreases from the core to the boundary. The outmost layer is merely sheared. A null point is located above the flux rope. The eruptive process consists of precursor flarings at av-shaped coronal structure, rise of the filament, and brightening below the filament, corresponding well with the topological structures deduced from the NLFFF, including a higher null point, a flux rope, and a BP and a hyperbolic flux tube (HFT) below the flux rope. Two sets of post-flare loops and three flare ribbons in theδsunspot region further support the bifurcation configuration of the flux rope.Conclusions.Combining the observations and magnetic field extrapolation, we conclude that the precursor reconnection, which occurs at the null point, weakens the overlying confinement to allow the flux rope to rise, fitting the breakout model. The main phase reconnection, which may occur at the BP or HFT, facilitates the flux rope rising. The results suggest that theδspot configuration presents an environment prone to the formation of complex magnetic configurations that work together to produce activities.

The automated prediction of solar flares from SDO images using deep learning

In the last few years, there has been growing interest in near-real-time solar data processing, especially for space weather applications. This is due to space weather impacts on both space-borne and ground-based systems, and industries, which subsequently impacts our lives. In the current study, the deep learning approach is used to establish an automated hybrid computer system for a short-term forecast; it is achieved by using the complexity level of the sunspot group on SDO/HMI Intensitygram images. Furthermore, this suggested system can generate the forecast for solar flare occurrences within the following 24 h. The input data for the proposed system are SDO/HMI full-disk Intensitygram images and SDO/HMI full-disk magnetogram images. System outputs are the “Flare or Non-Flare” of daily flare occurrences (C, M, and X classes). This system integrates an image processing system to automatically detect sunspot groups on SDO/HMI Intensitygram images using active-region data extracted from SDO/HMI magnetogram images (presented by Colak and Qahwaji, 2008) and deep learning to generate these forecasts. Our deep learning-based system is designed to analyze sunspot groups on the solar disk to predict whether this sunspot group is capable of releasing a significant flare or not. Our system introduced in this work is called ASAP_Deep. The deep learning model used in our system is based on the integration of the Convolutional Neural Network (CNN) and Softmax classifier to extract special features from the sunspot group images detected from SDO/HMI (Intensitygram and magnetogram) images. Furthermore, a CNN training scheme based on the integration of a back-propagation algorithm and a mini-batch AdaGrad optimization method is suggested for weight updates and to modify learning rates, respectively. The images of the sunspot regions are cropped automatically by the imaging system and processed using deep learning rules to provide near real-time predictions. The major results of this study are as follows. Firstly, the ASAP_Deep system builds on the ASAP system introduced in Colak and Qahwaji (2009) but improves the system with an updated deep learning-based prediction capability. Secondly, we successfully apply CNN to the sunspot group image without any pre-processing or feature extraction. Thirdly, our system results are considerably better, especially for the false alarm ratio (FAR); this reduces the losses resulting from the protection measures applied by companies. Also, the proposed system achieves a relatively high scores for True Skill Statistics (TSS) and Heidke Skill Score (HSS).

Wave amplitude modulation in fan loops as observed by AIA/SDO

Aims. We perform a detailed analysis to understand the evolution and dynamics of propagating intensity disturbances observed in a fan loop system. Methods. We performed multiwavelength time-distance analysis of a fan loop system anchored in an isolated sunspot region (AR 12553). The active region was observed by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. We measured the phase speeds of the propagating intensity disturbances by employing cross-correlation analysis, and by obtaining the slopes in xt-plots. We obtained original and detrended light curves at different heights of the time-distance maps and characterised them by performing Fourier and wavelet analysis, respectively. Results. The time-distance maps reveal clear propagation of intensity oscillations in all the coronal extreme ultraviolet (EUV) channels except AIA 94 and 335 Å. We determine the nature of the intensity disturbances as slow magneto-acoustic waves by measuring their phase speeds. The time-distance maps, as well as the detrended light curves, show an increase and decrease in the amplitude of propagating 3 min oscillations over time. The amplitude variations appear most prominently in AIA 171 Å, though other EUV channels also show such signatures. The Fourier power spectrum yields the presence of significant powers with several nearby frequencies in the range of 2–3 min (5–8 mHz), along with many other smaller peaks between 2–4 min. Wavelet analysis shows an increase and decrease of oscillating power around 3 min simultaneous to the amplitude variations. We obtain the modulation period to be in the range of 20–30 min. Conclusions. Our results provide the viability of occurrence of phenomenon like “Beat” among the nearby frequencies giving rise to the observed amplitude modulation. However, we cannot at this stage rule out the possibility that the modulation may be driven by variability in an underlying unknown source.

Scattering Matrix for the Interaction between Solar Acoustic Waves and Sunspots. II. Theory

Abstract The interaction between solar acoustic waves and an isolated sunspot is a scattering problem. A common tool to study scattering problems is the scattering matrix, which is the amplitude for the transition from one mode to another after the interaction. In the previous study (Part I), the scattering matrix elements were determined with the measured scattered wavefunction of the sunspot. In this study (Part II), we obtain an analytical relation between the scattering matrix elements and the perturbed quantities of the background medium of the sunspot region. The sunspot is considered a perturbed region relative to the quiet Sun. The perturbation of the background medium includes the magnetic field, the flow velocity, and perturbed thermodynamics quantities, such as the density and pressure perturbations. Inferring these perturbed quantities from measured quantities is one of the goals of helioseismology. Here, with the help of Green’s functions, the scattering matrix elements are expressed as a spatial integral, which contains these unknown perturbed quantities. This integral equation, together with the measured scattering matrix elements, could be used to infer the perturbed quantities with the forward and inversion methods. Besides the typical approximations for solar acoustic waves, two additional assumptions are made here: one is the Born approximation, and the other is that the background medium of the sunspot region does not change with time.