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Context. The Sun experienced a period of unprecedented activity during the 20th century, now called the Modern Maximum (MM). The decay of the MM after its maximum in cycle 19 has changed the Sun, the heliosphere, and the planetary environments in many ways. However, studies disagree on whether this decay has proceeded synchronously in different solar parameters or not. Aims. One of the related key issues is if the relation between two long parameters of solar activity, the sunspot number and the solar 10.7 cm radio flux, has remained the same during this decay. A recent study argues that there is an inhomogeneity in the 10.7 cm radio flux in 1980, which leads to a step-like jump ("1980 jump") in this relation. If true, this result would reduce the versatility of possible long-term studies of the Sun during the MM. Here we aim to show that the relation between sunspot number and 10.7 cm radio flux does indeed vary in time, not due to an inhomogeneous radio flux but due to physical changes in the solar atmosphere. Methods. We used radio flux measurements made in Japan at four different wavelengths, and studied their long-term relation with the sunspot number and the 10.7 cm radio flux during the decay of MM. We also used two other solar parameters, the MgII index and the number of solar active regions, in order to study the nature of the observed long-term changes in more detail. Results. We find that the 1980 jump is only the first of a series of 1–2-year "humps" that mainly occur during solar maxima. All five radio fluxes depict an increasing trend with respect to the sunspot number from the 1970s to 2010s. These results exclude the interpretation of the 1980 jump as an inhomogeneity in the 10.7 cm flux, and reestablish the 10.7 cm flux as a homogeneous measure of solar activity. The fluxes of the longer radio waves are found to increase with respect to the shorter waves, which suggests a long-term change in the solar radio spectrum. We also find that the MgII index of solar UV irradiance and the number of active regions also increased with respect to the sunspot number, further verifying the difference in the long-term evolution in chromospheric and photospheric parameters. Conclusions. Our results provide evidence for important structural changes in solar magnetic fields and the solar atmosphere during the decay of the MM, which have not been reliably documented so far. We also emphasize that the changing relation between the different (e.g., photospheric and chromospheric) solar parameters should be taken into account when using the sunspot number or any single parameter in long-term studies of solar activity. [ABSTRACT FROM AUTHOR]

Active regions (ARs) are magnetic structures typically found in the solar atmosphere. We calculated several magnetohydrostatic (MHS) equilibrium models that include the effect of a finite plasma-β and gravity and that are representative of AR structures in three dimensions. The construction of the models is based on the use of two Euler potentials, α and β, that represent the magnetic field as B = ∇α × ∇β. The ideal MHS nonlinear partial differential equations were solved numerically using finite elements in a fixed 3D rectangular domain. The boundary conditions were initially chosen to correspond to a potential magnetic field (current-free) with known analytical expressions for the corresponding Euler potentials. The distinctive feature of our model is that we incorporated the effect of shear by progressively deforming the initial potential magnetic field. This procedure is quite generic and allowed us to generate a vast variety of MHS models. The thermal structure of the ARs was incorporated through the dependence of gas pressure and temperature on the Euler potentials. Using this method, we achieved the characteristic hot and overdense plasma found in ARs, but we demonstrate that the method can also be applied to study configurations with open magnetic field lines. Furthermore, we investigated basic topologies that include neutral lines. Our focus is on the force balance of the structures, and we do not consider the energy balance in the constructed models. In addition, we addressed the difficult question of the stability of the calculated 3D models. We find that if the plasma is convectively stable, then the system is not prone, in general, to develop magnetic Rayleigh-Taylor instabilities. However, when the plasma-β is increased or the density at the core of the AR is high, then the magnetic configuration becomes unstable due to magnetic buoyancy. [ABSTRACT FROM AUTHOR]

Context. Activity on the far side of the Sun is routinely studied through the analysis of the seismic oscillations detected on the near side using helioseismic techniques such as phase-shift sensitive holography. Detections made through those methods are limited to strong active regions due to the need for a high signal-to-noise ratio. Recently, the neural network FarNet was developed to improve these detections. This network extracts more information from helioseismic far-side maps, enabling the detection of smaller and weaker active regions. Aims. We aim to create a new machine learning tool, FarNet-II, which further increases FarNet's scope, and to evaluate its performance in comparison to FarNet and the standard helioseismic method for detecting far-side activity. Methods. We developed FarNet-II, a neural network that retains some of the general characteristics of FarNet but improves the detections in general, as well as the temporal coherence among successive predictions. The main novelties of the new neural network are the implementation of attention and convolutional long short-term memory (ConvLSTM) modules. A cross-validation approach, training the network 37 times with a different validation set for each run, was employed to leverage the limited amount of data available. We evaluate the performance of FarNet-II using three years of extreme ultraviolet observations of the far side of the Sun acquired with the Solar Terrestrial Relations Observatory (STEREO) as a proxy of activity. The results from FarNet-II were compared with those obtained from FarNet and the standard helioseismic method using the Dice coefficient as a metric. Given that the application of the ConvLSTM modules can affect the accuracy as a function of the position on the sequence, we take this potential dependency into account in the evaluation. Results. FarNet-II achieves a Dice coefficient that improves that of FarNet by over 0.2 points for every output position on the sequences from the evaluation dates. Its improvement over FarNet is higher than that of FarNet over the standard method. Conclusions. The new network is a very promising tool for improving the detection of activity on the far side of the Sun given by pure helioseismic techniques. Space weather forecasts can potentially benefit from the higher sensitivity provided by this novel method. [ABSTRACT FROM AUTHOR]

Context. Ellerman bombs are regions with enhanced Balmer line wing emission and mark magnetic reconnection in the deep solar atmosphere in active regions and the quiet Sun. They are often found in regions where opposite magnetic polarities are in close proximity. Recent high-resolution observations suggest that Ellerman bombs are more prevalent than previously thought. Aims. We aim to determine the occurrence of Ellerman bombs in the penumbra of sunspots. Methods. We analyzed high spatial resolution observations of sunspots in the Balmer Hα and Hβ lines as well as auxiliary continuum channels obtained with the Swedish 1-m Solar Telescope and applied the k-means clustering technique to systematically detect and characterize Ellerman Bombs. Results. Features with all the defining characteristics of Ellerman bombs are found in large numbers over the entire penumbra. The true prevalence of these events is only fully appreciated in the Hβ line due to the highest spatial resolution and lower chromospheric opacity. We find that the penumbra hosts some of the highest Ellerman bomb densities, surpassed only by the moat in the immediate surroundings of the sunspot. Some penumbral Ellerman bombs show flame morphology and rapid dynamical evolution. Many penumbral Ellerman bombs are fast moving with typical speed of 3.7 km s−1 and sometimes more than 10 km s−1. Many penumbral Ellerman bombs migrate from the inner to the outer penumbra over hundreds of km, and some continue moving beyond the outer penumbral boundary into the moat. Many penumbral Ellerman bombs are found in the vicinity of regions with opposite magnetic polarity. Conclusions. We conclude that reconnection is a near continuous process in the low atmosphere of the penumbra of sunspots that manifest in the form of penumbral Ellerman bombs. These are so prevalent that they may be a major sink of sunspot magnetic energy. [ABSTRACT FROM AUTHOR]

Coverage of plasma motions is limited to the line-of-sight component at the Sun's surface. Multiple tracking and inversion methods were developed to infer the transverse motions from observational data. Recently, the DeepVel neural network was trained with computations performed by numerical simulations of the solar photosphere to recover the missing transverse component at the surface and at two additional optical depths simultaneously from the surface white light intensity in the Quiet Sun. We argue that deep learning could provide additional spatial coverage to existing observations in the form of depth-dependent synthetic observations, i.e. estimates generated through the emulation of numerical simulations. We trained different versions of DeepVel using slices from numerical simulations of both the Quiet Sun and Active Region at various optical and geometrical depths in the solar atmosphere, photosphere and upper convection zone to establish the upper and lower limits at which the neural network can generate reliable synthetic observations of plasma motions from surface intensitygrams. Flow fields inferred in the photosphere and low chromosphere s 2 [0.1, 1) are comparable to inversions performed at the surface (s " 1) and are deemed to be suitable for use as synthetic estimates in data assimilation processes and data-driven simulations. This upper limit extends closer to the transition region (s " 0.01) in the Quiet Sun, but not for Active Regions. Subsurface flows inferred from surface intensitygrams fail to capture the small-scale features of turbulent convective motions as depth crosses a few hundred kilometers. We suggest that these reconstructions could be used as first estimates of a model's velocity vector in data assimilation processes to nowcast and forecast short term solar activity and space weather. [ABSTRACT FROM AUTHOR]

Aims. We aim to investigate the temperature enhancements and formation heights of solar active-region brightenings such as Ellerman bombs (EBs), ultraviolet bursts (UVBs), and flaring active-region fibrils (FAFs) using interferometric observations in the millimeter (mm) continuum provided by the Atacama Large Millimeter/submillimeter Array (ALMA). Methods. We examined 3 mm signatures of heating events identified in Solar Dynamics Observatory observations of an active region and compared the results with synthetic spectra from a 3D radiative magnetohydrodynamic simulation. We estimated the contribution from the corona to the mm brightness using differential emission measure analysis. Results. We report the null detection of EBs in the 3 mm continuum at ∼1.2″ spatial resolution, which is evidence that they are sub-canopy events that do not significantly contribute to heating the upper chromosphere. In contrast, we find the active region to be populated with multiple compact, bright, flickering mm-bursts – reminiscent of UVBs. The high brightness temperatures of up to ∼14 200 K in some events have a contribution (up to ∼7%) from the corona. We also detect FAF-like events in the 3 mm continuum. These events show rapid motions of > 10 kK plasma launched with high plane-of-sky velocities (37 − 340 km s−1) from bright kernels. The mm FAFs are the brightest class of warm canopy fibrils that connect magnetic regions of opposite polarities. The simulation confirms that ALMA should be able to detect the mm counterparts of UVBs and small flares and thus provide a complementary diagnostic for localized heating in the solar chromosphere. [ABSTRACT FROM AUTHOR]

We discuss the potential use of an algebraic method to compute the value of the solar axial dipole moment at solar minimum, widely considered to be the most reliable precursor of the activity level in the next solar cycle. The method consists of summing up the ultimate contributions of individual active regions to the solar axial dipole moment at the end of the cycle. A potential limitation of the approach is its dependence on the underlying surface flux transport (SFT) model details. We demonstrate by both analytical and numerical methods that the factor relating the initial and ultimate dipole moment contributions of an active region displays a Gaussian dependence on latitude with parameters that only depend on details of the SFT model through the parameter η/Δu where η is supergranular diffusivity and Δu is the divergence of the meridional flow on the equator. In a comparison with cycles simulated in the 2 × 2D dynamo model we further demonstrate that the inaccuracies associated with the algebraic method are minor and the method may be able to reproduce the dipole moment values in a large majority of cycles. [ABSTRACT FROM AUTHOR]

Aims. We aim to study the magnetic field in solar spicules using high-resolution spectropolarimetric observations in the Ca II 8542 Å line obtained with the Swedish 1-m Solar Telescope. Methods. The equations that result from the application of the weak field approximation (WFA) to the radiative transfer equations were used to infer the line-of-sight (LOS) component of the magnetic field (BLOS). Two restrictive conditions were imposed on the Stokes I and V profiles at each pixel before they could be used in a Bayesian inversion to compute its BLOS. Results. The LOS magnetic field component was inferred in six data sets totalling 448 spectral scans in the Ca II 8542 Å line and containing both active region and quiet Sun areas, with values of hundreds of Gauss being abundantly inferred. There seems to be no difference, from a statistical point of view, between the magnetic field strength of spicules in the quiet Sun or near an active region. On the other hand, the BLOS distributions present smaller values on the disc than off-limb, a fact that can be explained by the effect of superposition on the chromosphere of on-disc structures. We show that on-disc pixels in which the BLOS is determined are possibly associated with spicular structures because these pixels are co-spatial with the magnetic field concentrations at the network boundaries and the sign of their BLOS agrees with that of the underlying photosphere. We find that spicules in the vicinity of a sunspot have a magnetic field polarity (i.e. north or south) equal to that of the sunspot. This paper also contains an analysis of the effect of off-limb overlapping structures on the observed Stokes I and V parameters and the BLOS obtained from the WFA. It is found that this value is equal to or smaller than the largest LOS magnetic field components of the two structures. In addition, using random BLOS, Doppler velocities, and line intensities of these two structures leads in ≃50% of the cases to Stokes I and V parameters that are unsuitable to be used with the WFA. Conclusions. Our results present a scarcity of LOS magnetic field components smaller than some 50 G, which must not be taken as evidence against the existence of these magnetic field strengths in spicules. This fact possibly arises as the consequence of signal superposition and noise in the data. We also suggest that the failure of previous works to infer the strong magnetic fields in spicules detected here is their coarser spatial and/or temporal resolution. [ABSTRACT FROM AUTHOR]

An algebraic method for the reconstruction and potentially prediction of the solar dipole moment value at sunspot minimum (known to be a good predictor of the amplitude of the next solar cycle) was suggested in the first paper in this series. The method sums up the ultimate dipole moment contributions of individual active regions in a solar cycle: for this, detailed and reliable input data would in principle be needed for thousands of active regions in a solar cycle. To reduce the need for detailed input data, here we propose a new active region descriptor called ARDoR (Active Region Degree of Rogueness). In a detailed statistical analysis of a large number of activity cycles simulated with the 2 × 2D dynamo model we demonstrate that ranking active regions by decreasing ARDoR, for a good reproduction of the solar dipole moment at the end of the cycle it is sufficient to consider the top N regions on this list explicitly, where N is a relatively low number, while for the other regions the ARDoR value may be set to zero. For example, with N = 5 the fraction of cycles where the dipole moment is reproduced with an error exceeding ±30% is only 12%, significantly reduced with respect to the case N = 0, i.e. ARDoR set to zero for all active regions, where this fraction is 26%. This indicates that stochastic effects on the intercycle variations of solar activity are dominated by the effect of a low number of large "rogue" active regions, rather than the combined effect of numerous small ARs. The method has a potential for future use in solar cycle prediction. [ABSTRACT FROM AUTHOR]

Context. Magnetic helicity is approximately conserved in resistive magnetohydrodynamic models. It quantifies the entanglement of the magnetic field within the plasma. The transport and removal of helicity is crucial in both dynamo development in the solar interior and active region evolution in the solar corona. This transport typically leads to highly inhomogeneous distributions of entanglement. Aims. There exists no consistent systematic means of decomposing helicity over varying spatial scales and in localised regions. Spectral helicity decompositions can be used in periodic domains and is fruitful for the analysis of homogeneous phenomena. This paper aims to develop methods for analysing the evolution of magnetic field topology in non-homogeneous systems. Methods. The method of multi-resolution wavelet decomposition is applied to the magnetic field. It is demonstrated how this decomposition can further be applied to various quantities associated with magnetic helicity, including the field line helicity. We use a geometrical definition of helicity, which allows these quantities to be calculated for fields with arbitrary boundary conditions. Results. It is shown that the multi-resolution decomposition of helicity has the crucial property of local additivity. We demonstrate a general linear energy-topology conservation law, which significantly generalises the two-point correlation decomposition used in the analysis of homogeneous turbulence and periodic fields. The localisation property of the wavelet representation is shown to characterise inhomogeneous distributions, which a Fourier representation cannot. Using an analytic representation of a resistive braided field relaxation, we demonstrate a clear correlation between the variations in energy at various length scales and the variations in helicity at the same spatial scales. Its application to helicity flows in a surface flux transport model show how various contributions to the global helicity input from active region field evolution and polar field development are naturally separated by this representation. Conclusions. The multi-resolution wavelet decomposition can be used to analyse the evolution of helicity in magnetic fields in a manner which is consistently additive. This method has the advantage over more established spectral methods in that it clearly characterises the inhomogeneous nature of helicity flows where spectral methods cannot. Further, its applicability in aperiodic models significantly increases the range of potential applications. [ABSTRACT FROM AUTHOR]

Context. Some high-resolution observations have revealed that the active region solar corona is filled with a myriad of thin strands even in apparently uniform regions with no resolved loops. This fine structure can host collective oscillations involving a large portion of the corona due to the coupling of the motions of the neighbouring strands. Aims. We study these vibrations and the possible observational effects. Methods. We theoretically investigated the collective oscillations inherent to the fine structure of the corona. We have called them fundamental vibrations because they cannot exist in a uniform medium. We used the T-matrix technique to find the normal modes of random arrangements of parallel strands. We considered an increasing number of tubes to understand the vibrations of a huge number of tubes of a large portion of the corona. We additionally generated synthetic time-distance Doppler and line-broadening diagrams of the vibrations of a coronal region to compare with observations. Results. We have found that the fundamental vibrations are in the form of clusters of tubes where not all the tubes participate in the collective mode. The periods are distributed over a wide band of values. The width of the band increases with the number of strands but rapidly reaches an approximately constant value. We have found an analytic approximate expression for the minimum and maximum periods of the band. The frequency band associated with the fine structure of the corona depends on the minimum separation between strands. We have found that the coupling between the strands is on a large extent and the motion of one strand is influenced by the motions of distant tubes. The synthetic Dopplergrams and line-broadening maps show signatures of collective vibrations, not present in the case of purely random individual kink vibrations. Conclusions. We conclude that the fundamental vibrations of the corona can contribute to the energy budget of the corona and they may have an observational signature. [ABSTRACT FROM AUTHOR]

Aims. We investigated the possibility of diagnosing the degree of departure from the Maxwellian distribution using the Fe XVII–Fe XVIII spectra originating in plasmas in collisional ionization equilibrium, such as in the cores of solar active regions or microflares. Methods. The original collision strengths for excitation are integrated over the non-Maxwellian electron κ-distributions characterized by a high-energy tail. Synthetic X-ray emission line spectra were calculated for a range of temperatures and κ. We focus on the 6–24 Å spectral range to be observed by the upcoming Marshall Grazing-Incidence X-ray Spectrometer MaGIXS. Results. We find that many line intensity ratios are sensitive to both T and κ. Best diagnostic options are provided if a ratio involving both Fe XVII and Fe XVIII is combined with another ratio involving lines formed within a single ion. The sensitivity of such diagnostics to κ is typically a few tens of per cent. Much larger sensitivity, of about a factor of two to three, can be obtained if the Fe XVIII 93.93 Å line observed by SDO/AIA is used in conjuction with the X-ray lines. Conclusions. We conclude that the MaGIXS instrument is well-suited for detection of departures from the Maxwellian distribution, especially in active region cores. [ABSTRACT FROM AUTHOR]

Context. The details of the spectral profiles of extreme UV emission lines from solar active regions contain key information for investigating the structure, dynamics, and energetics of the solar upper atmosphere. Aims. We characterize the line profiles not only through the Doppler shift and intensity of the bulk part of the profile. More importantly, we investigate the excess emission and asymmetries in the line wings to study twisting motions and helicity. Methods. We used a raster scan of the Interface Region Imaging Spectrograph (IRIS) in an active region. We concentrated on the Si IV line at 1394 Å, which forms just below 0.1 MK, and followed the plasma that moves in a cool loop from one footpoint to the other. We applied single-Gaussian fits to the line core, determined the excess emission in the red and blue wings, and derived the asymmetry of the red and blue wings. Results. The blue wing excess at one footpoint shows injection of plasma into the loop that then flows to the other side. At the same footpoint, redshifts in the line core indicate that energy is deposited at around 0.1 MK. The enhanced pressure would then push the cool plasma down and inject some plasma into the loop. In the middle part of the loop, the spectral tilts of the line profiles indicate that the magnetic field has a helical structure, and the line wings are symmetrically enhanced. This is an indication that the loop is driven through the injection of helicity at the loop feet. Conclusions. If the loop is driven to be helical, then the magnetic field can be expected to be in a turbulent state, as has been shown by existing magnetohydrodynamics models. The turbulent motions might explain the (symmetric) line wing enhancements that have also been seen in loops at coronal temperatures, but are not understood so far. [ABSTRACT FROM AUTHOR]

Ellerman bombs are transient brightenings in the wings of Hα 6563 Å that pinpoint photospheric sites of magnetic reconnection in solar active regions. Their partial visibility in the 1600 Å and 1700 Å continua registered routinely by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) offers a unique opportunity to inventory such magnetic-field disruptions throughout the AIA database if a reliable recipe for their detection can be formulated. This is done here. We have improved and applied an Hα Ellerman bomb detection code to ten data sets spanning viewing angles from solar disc centre to the limb. They combine high-quality Hα imaging spectroscopy from the Swedish 1 m Solar Telescope with simultaneous AIA imaging around 1600 Å and 1700 Å. A trial grid of brightness, lifetime and area constraints is imposed on the AIA images to define optimal recovery of the 1735 Ellerman bombs detected in Hα. The best results when optimising simultaneously for recovery fraction and reliability are obtained from 1700 Å images by requiring 5σ brightening above the average 1700 Å nearby quiet-Sun intensity, lifetime above one minute, area of 1–18 AIA pixels. With this recipe 27% of the AIA detections are Hα-detected Ellerman bombs while it recovers 19% of these (of which many are smaller than the AIA resolution). Better yet, among the top 10% AIA 1700 Å detections selected with combined brightness, lifetime and area thresholds as many as 80% are Hα Ellerman bombs. Automated selection of the best 1700 Å candidates therefore opens the entire AIA database for detecting most of the more significant photospheric reconnection events. This proxy is applicable as a flux-dynamics tell-tale in studying any Earth-side solar active region since early 2010 up to the present. [ABSTRACT FROM AUTHOR]

Aims. We aim to reproduce the structure of the corona above a solar active region as seen in the extreme ultraviolet (EUV) using a three-dimensional magnetohydrodynamic (3D MHD) model. Methods. The 3D MHD data-driven model solves the induction equation and the mass, momentum, and energy balance. To drive the system, we feed the observed evolution of the magnetic field in the photosphere of the active region AR 12139 into the bottom boundary. This creates a hot corona above the cool photosphere in a self-consistent way. We synthesize the coronal EUV emission from the densities and temperatures in the model and compare this to the actual coronal observations. Results. We are able to reproduce the overall appearance and key features of the corona in this active region on a qualitative level. The model shows long loops, fan loops, compact loops, and diffuse emission forming at the same locations and at similar times as in the observation. Furthermore, the low-intensity contrast of the model loops in EUV matches the observations. Conclusions. In our model the energy input into the corona is similar as in the scenarios of fieldline-braiding or flux-tube tectonics, that is, energy is transported to the corona through the driving of the vertical magnetic field by horizontal photospheric motions. The success of our model shows the central role that this process plays for the structure, dynamics, and heating of the corona. [ABSTRACT FROM AUTHOR]

Context. Densely packed coronal loops are rooted in photospheric plages in the vicinity of active regions on the Sun. The photospheric magnetic features underlying these plage areas are patches of mostly unidirectional magnetic field extending several arcsec on the solar surface. Aims. We aim to explore the transient nature of the magnetic field, its mixed-polarity characteristics, and the associated energetics in the active region plage using high spatial resolution observations and numerical simulations. Methods. We used photospheric Fe I 6173 Å spectropolarimetric observations of a decaying active region obtained from the Swedish 1-m Solar Telescope (SST). These data were inverted to retrieve the photospheric magnetic field underlying the plage as identified in the extreme-ultraviolet emission maps obtained from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). To obtain better insight into the evolution of extended unidirectional magnetic field patches on the Sun, we performed 3D radiation magnetohydrodynamic simulations of magnetoconvection using the MURaM code. Results. The observations show transient magnetic flux emergence and cancellation events within the extended predominantly unipolar patch on timescales of a few 100 s and on spatial scales comparable to granules. These transient events occur at the footpoints of active region plage loops. In one case the coronal response at the footpoints of these loops is clearly associated with the underlying transient. The numerical simulations also reveal similar magnetic flux emergence and cancellation events that extend to even smaller spatial and temporal scales. Individual simulated transient events transfer an energy flux in excess of 1 MW m−2 through the photosphere. Conclusions. We suggest that the magnetic transients could play an important role in the energetics of active region plage. Both in observations and simulations, the opposite-polarity magnetic field brought up by transient flux emergence cancels with the surrounding plage field. Magnetic reconnection associated with such transient events likely conduits magnetic energy to power the overlying chromosphere and coronal loops. [ABSTRACT FROM AUTHOR]

Context. Whilst there are observational indications that transverse magnetohydrodynamic (MHD) waves carry enough energy to maintain the thermal structure of the solar corona, it is not clear whether such energy can be efficiently and effectively converted into heating. Phase-mixing of Alfvén waves is considered a candidate mechanism, as it can develop transverse gradient where magnetic energy can be converted into thermal energy. However, phase-mixing is a process that crucially depends on the amplitude and period of the transverse oscillations, and only recently have we obtained a complete measurement of the power spectrum for transverse oscillations in the corona. Aims. We aim to investigate the heating generated by phase-mixing of transverse oscillations triggered by buffeting of a coronal loop that follows from the observed coronal power spectrum as well as the impact of these persistent oscillations on the structure of coronal loops. Methods. We considered a 3D MHD model of an active region coronal loop and we perturbed its footpoints with a 2D horizontal driver that represents a random buffeting motion of the loop footpoints. Our driver was composed of 1000 pulses superimposed to generate the observed power spectrum. Results. We find that the heating supply from the observed power spectrum in the solar corona through phase-mixing is not sufficient to maintain the million-degree active region solar corona. We also find that the development of Kelvin–Helmholtz instabilities could be a common phenomenon in coronal loops that could affect their apparent life time. Conclusions. This study concludes that is unlikely that phase-mixing of Alfvén waves resulting from an observed power spectrum of transverse coronal loop oscillations can heat the active region solar corona. However, transverse waves could play an important role in the development of small scale structures. [ABSTRACT FROM AUTHOR]

Aims. In a previous study we analysed the C IV 1548.189 Å and 1550.775 Å lines observed with the Solar Ultraviolet Measurements of Emitted Radiation (SUMER), showing cases where the 1548.189 Å spectral profile was noticeably different from the 1550.775 Å one, profiles that we dubbed differentially shaped profiles. We explained this differential behaviour by an important radiative contribution, affecting multiple plasma motions happening at the instrument sub-resolution scale. In the present study we examine more general cases where radiative effects may contribute to the emission from the transition region of an active region. Here we analyse the lines Si IV 1393.757 Å and 1402.772 Å observed with the Interface Region Imaging Spectrograph (IRIS). Methods. We study active region NOAA 12529, observed with IRIS on 18 April 2016. Using sorting techniques we selected individual profiles for which the intensity line ratio 1393.757 Å/1402.772 Å is significantly higher or lower than 2 and we also tracked differentially shaped profiles. We analyse the physical conditions that create these profiles and in some cases we estimate electron densities. Results. We found more than 4000 individual profiles with line ratios higher than 2, about 500 profiles for which the line ratio is in the range 1.3–1.6, and 15 differentially shaped profiles. Line ratios higher than 2, are found along loops, and mostly at the y = 250 to 300″ part of the plage. There, we estimated the incident radiation and derived electron densities that can vary from 109 to a few times 1011 cm−3, depending on the plasma temperature. For the low line ratios, the sources are concentrated at the periphery of the active region plage, mostly along fibrils and present optical depths, τ, between 1.5 and 3. in most cases. The electron densities calculated from these Si IV profiles are comparable with electron densities derived using the O IV 1399.766 Å-1401.163 Å ratios. Conclusions. We found that about 2.4% of the individual profiles for which we can perform a Gaussian fit present a line ratio higher than 2. In profiles with a high line ratio, the resonant scattering appears to be due to the combination of an average incident radiation field with a relatively low local electron density and not due to the vicinity of an ephemeral strong light source. As far as low intensity ratios are concerned, non-negligible optical depths are found at the edge of the plage, near the footpoints of fibrils that are oriented towards quiet Sun areas, where the electron density can be as high as (7 − 9) × 1011 cm−3 if we assume a plasma in ionization equilibrium. [ABSTRACT FROM AUTHOR]

Context. Sixteen years ago local helioseismology detected spatially extended converging surface flows into solar active regions. These flows play an important role in flux-transport models of the solar dynamo. Aims. We aim to validate the existence of the inflows by deriving horizontal flow velocities around active regions with local correlation tracking of granulation. Methods. We generate a six-year time series of full-disk maps of the horizontal velocity at the solar surface by tracking granules in continuum intensity images provided by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO). Results. On average, active regions are surrounded by inflows extending up to 10° from the center of the active region of magnitudes of 20-30 m/s, reaching locally up to 40 m/s, which is in agreement with results from local helioseismology. By computing an ensemble average consisting of 243 individual active regions, we show that the inflows are not azimuthally symmetric, but converge predominantly towards the trailing polarity of the active region with respect to the longitudinally and temporally averaged flow field. [ABSTRACT FROM AUTHOR]

Context. The magnetic field plays a dominant role in the solar irradiance variability. Determining the contribution of various magnetic features to this variability is important in the context of heliospheric studies and Sun-Earth connection. Aims. We studied the solar irradiance variability and its association with the underlying magnetic field for a period of five years (January 2011-January 2016). We used observations from the Large Yield Radiometer (LYRA), the Sun Watcher with Active Pixel System detector and Image Processing (SWAP) on board PROBA2, the Atmospheric Imaging Assembly (AIA), and the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO). Methods. The Spatial Possibilistic Clustering Algorithm (SPoCA) is applied to the extreme ultraviolet (EUV) observations obtained from the AIA to segregate coronal features by creating segmentation maps of active regions (ARs), coronal holes (CHs) and the quiet sun (QS). Further, these maps are applied to the full-disk SWAP intensity images and the full-disk (FD) HMI line-of-sight (LOS) magnetograms to isolate the SWAP coronal features and photospheric magnetic counterparts, respectively. We then computed full-disk and feature-wise averages of EUV intensity and line of sight (LOS) magnetic flux density over ARs/CHs/QS/FD. The variability in these quantities is compared with that of LYRA irradiance values. Results. Variations in the quantities resulting from the segmentation, namely the integrated intensity and the total magnetic flux density of ARs/CHs/QS/FD regions, are compared with the LYRA irradiance variations. We find that the EUV intensity over ARs/CHs/QS/FD is well correlated with the underlying magnetic field. In addition, variations in the full-disk integrated intensity and magnetic flux density values are correlated with the LYRA irradiance variations. Conclusions. Using the segmented coronal features observed in the EUV wavelengths as proxies to isolate the underlying magnetic structures is demonstrated in this study. Sophisticated feature identification and segmentation tools are important in providing more insights into the role of various magnetic features in both the short- and long-term changes in the solar irradiance. [ABSTRACT FROM AUTHOR]

Context: The discovery of clear criteria that can deterministically describe the eruptive state of a solar active region would lead to major improvements on space weather predictions. Aims: Using series of numerical simulations of the emergence of a magnetic flux rope in a magnetized coronal, leading either to eruptions or to stable configurations, we test several global scalar quantities for the ability to discriminate between the eruptive and the non-eruptive simulations. Methods: From the magnetic field generated by the three-dimensional magnetohydrodynamical simulations, we compute and analyze the evolution of the magnetic flux, of the magnetic energy and its decomposition into potential and free energies, and of the relative magnetic helicity and its decomposition. Results: Unlike the magnetic flux and magnetic energies, magnetic helicities are able to markedly distinguish the eruptive from the non-eruptive simulations. We find that the ratio of the magnetic helicity of the current-carrying magnetic field to the total relative helicity presents the highest values for the eruptive simulations, in the pre-eruptive phase only. We observe that the eruptive simulations do not possess the highest value of total magnetic helicity. Conclusions: In the framework of our numerical study, the magnetic energies and the total relative helicity do not correspond to good eruptivity proxies. Our study highlights that the ratio of magnetic helicities diagnoses very clearly the eruptive potential of our parametric simulations. Our study shows that magnetic-helicity-based quantities may be very efficient for the prediction of solar eruptions. [ABSTRACT FROM AUTHOR]

Aims. The aim of this work is to investigate and characterise particle behaviour in an (observationally-driven) 3D magnetohydrodynamic (MHD) model of the solar atmosphere above a slowly evolving, non-flaring active region. Methods. We use a relativistic guiding-centre particle code to investigate the behaviour of selected particle orbits, distributed throughout a single snapshot of the 3D MHD simulation. Results. Two distinct particle acceleration behaviours are recovered, which affect both electrons and protons: (i) direct acceleration along field lines and (ii) tangential drifting of guiding centres with respect to local magnetic field. However, up to 40% of all particles actually experience a form of (high energy) particle trap, because of changes in the direction of the electric field and unrelated to the strength of the magnetic field; such particles are included in the first category. Additionally, category (i) electron and proton orbits undergo surprisingly strong acceleration to non-thermal energies (≲42 MeV), because of the strength and extent of super-Dreicer electric fields created by the MHD simulation. Reducing the electric field strength of the MHD model does not significantly affect the efficiency of the (electric field-based) trapping mechanism, but does reduce the peak energies gained by orbits. We discuss the implications for future experiments, which aim to simulate non-flaring active region heating and reconnection. [ABSTRACT FROM AUTHOR]

Context. We have conducted a 3D MHD simulation of the solar corona above an active region (AR) in full scale and high resolution, which shows coronal loops, and plasma flows within them, similar to observations. Aims. We want to find the connection between the photospheric energy input by field-line braiding with the coronal energy conversion by Ohmic dissipation of induced currents. Methods. To this end we compare the coronal energy input and dissipation within our simulation domain above di erent fields of view, e.g. for a small loops system in the AR core. We also choose an ensemble of field lines to compare, e.g., the magnetic energy input to the heating per particle along these field lines. Results. We find an enhanced Ohmic dissipation of currents in the corona above areas that also have enhanced upwards-directed Poynting flux. These regions coincide with the regions where hot coronal loops within the AR core are observed. The coronal density plays a role in estimating the coronal temperature due to the generated heat input. A minimum flux density of about 200 Gauss is needed in the photosphere to heat a field line to coronal temperatures of about 1MK. Conclusions. This suggests that the field-line braiding mechanism provides the coronal energy input and that the Ohmic dissipation of induced currents dominates the coronal heating mechanism. [ABSTRACT FROM AUTHOR]

Solar electron spike events are a special subclass of near-relativistic electron events characterized by their short duration, symmetric time profile, and their strong anisotropic pitch angle distribution. All previous studied events were only observed by a single spacecraft (s/c). For the first time, we present measurements of this kind of an electron spike event that was observed simultaneously by both close-spaced STEREO s/c on 2 May 2014. The longitudinal separation angle between STEREO-A (STA) and STEREO-B (STB) was 38°. The spikes at STA and STB are characterized by very short durations of ≤12 min at full-width at half maximum (FWHM) and almost identical and symmetric time profiles. They exhibit similar properties in durations, pitch angle distributions (PADs), energy spectra, and peak intensities. The spike parent source was situated close to the STA nominal magnetic footpoint and was separated by 48° from STB's footpoint. The intensity distribution and the relative onset timing behaved opposite to what is expected: STB measured a higher intensity and an earlier onset than the nominally better connected STA. We suggest that the spike electrons undergo a substantial nonradial injection into interplanetary (IP) space from the parent source, a flaring active region (AR), and propagate in a strong nonradial diverging magnetic field. In addition we show that because of the spike properties it is evident that, irrespective of how the electrons were injected into the IP medium, the en route particle scattering conditions along the paths to STA and STB were very similar. Evidently both s/c detected different parts of the same beam whose angular extension was at least 38° at 1 AU, comparable to the longitudinal separation between STA and STB. [ABSTRACT FROM AUTHOR]

We study the spatial distribution and evolution of the slope of the emission measure (EM) between 1 MK and 3 MK in the core of the active region (AR) NOAA 11193, first when it appeared near the central meridian and then again when it reappeared after a solar rotation. We use observations recorded by the Extreme-ultraviolet Imaging Spectrometer (EIS) aboard Hinode, with a new radiometric calibration. We also use observations from the Atmospheric Imaging Assembly (AIA) aboard the Solar Dynamics Observatory (SDO). We present the first spatially resolved maps of the EM slope in the 1-3 MK range within the core of the AR using several methods, either from approximations or from the differential emission measure (DEM). A significant variation of the slope is found at different spatial locations within the active region. We selected two regions that were not greatly affected by lower temperature emission along the line of sight. We found that the EM had a power law of the form EM ? Tb, with b = 4.4 ± 0.4, and 4.6 ± 0.4, during the first and second appearance of the active region, respectively. During the second rotation, line-of-sight effects become more important, although difficult to estimate. We found that the use of the ground calibration for Hinode/EIS and the approximate method to derive the EM, used in previous publications, produce an underestimation of the slopes. The EM distribution in active region cores is generally found to be consistent with high frequency heating, and does not change much during the evolution of the active region. [ABSTRACT FROM AUTHOR]

Context. Bright points (BPs) are small-scale, magnetic features ubiquitous across the solar surface. Previously, we have observed and noted their properties for quiet Sun regions. Here, we determine the dynamic properties of BPs using simultaneous quiet Sun and active region data. Aims. The aim of this paper is to compare the properties of BPs in both active and quiet Sun regions and to determine any difference in the dynamics and general properties of BPs as a result of the varying magnetic activity within these two regions. Methods. High spatial and temporal resolution G-band observations of active region AR11372 were obtained with the Rapid Oscillations in the Solar Atmosphere instrument at the Dunn Solar Telescope. Three subfields of varying polarity and magnetic flux density were selected with the aid of magnetograms obtained from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. Bright points within these subfields were subsequently tracked and analysed. Results. It is found that BPs within active regions display attenuated velocity distributions with an average horizontal velocity of~0.6 km?s-1, compared to the quiet region which had an average velocity of 0.9 km?s-1. Active region BPs are also ~21% larger than quiet region BPs and have longer average lifetimes (~132 s) than their quiet region counterparts (88 s). No preferential flow directions are observed within the active region subfields. The diffusion index (?) is estimated at ~1.2 for the three regions. Conclusions. We confirm that the dynamic properties of BPs arise predominately from convective motions. The presence of stronger field strengths within active regions is the likely reason behind the varying properties observed. We believe that larger amounts of magnetic flux will attenuate BP velocities by a combination of restricting motion within the intergranular lanes and by increasing the number of stagnation points produced by inhibited convection. Larger BPs are found in regions of higher magnetic flux density and we believe that lifetimes increase in active regions as the magnetic flux stabilises the BPs. [ABSTRACT FROM AUTHOR]

A brief review of studies of elemental abundances and emission measures in quiescent solar active region cores is presented. Hinode EUV Imaging Spectrometer (EIS) observations of strong iron spectral lines have shown sharply peaked distributions around 3 MK. EIS observations of lines emitted by a range of elements have allowed good estimates of abundances relative to iron. However, X-ray observations are required to measure the plasma emission above 3 MK and the abundances of oxygen and neon. We revisit, using upto- date atomic data, older X-ray observations obtained by a sounding rocket and by the Solar Maximum Mission (SMM) Flat Crystal Spectrometer (FCS). We find that the Fe/O and Fe/Ne ratios are normally increased by a factor of 3.2, compared to the photospheric values. Similar results are obtained from FCS observations of six quiescent active region cores. The FCS observations also indicate that the emission measure above 3 MK has a very steep negative slope, with very little plasma observed at 5 MK or above. [ABSTRACT FROM AUTHOR]

For the first time, we present and discuss EUV radiances of the solar transition region (TR) and corona obtained during a solar cycle. The measurements were obtained with the SOHO/coronal diagnostic spectrometer (CDS) during the period from 1996 to 2010. We find that limb-brightening significantly affects any characterisation of the solar radiances. We present the limb-brightening function for the main lines and find that it does not change measurably during the cycle. We confirm earlier findings that the radiance histogram of the cooler lines have a well defined, log-normal quiet-Sun component, although our results differ from previous ones. The width of the lowest-radiance log-normal distribution is constant along the cycle. Both the analysis of the centre-to-limb variation and of the radiance statistical distribution point to a constant quiet Sun emission along solar cycle 23. Lines formed above 1 MK are dramatically affected by the presence of active regions, and indeed, no "quiet Sun" region can be defined during periods of maximum activity. Much of the irradiance variability in lines formed below 1.5 MK is due to a change in the emitting area. For hotter lines, the emitting area saturates to almost 100% of full solar disk at the maximum of activity, while simultaneously the emission due to active regions increases by more than an order of magnitude. We show that structures around active regions, sometimes referred to as dark halos or dark canopies, are common and discuss their similarities and differences with coronal holes. In particular, we show how they are well visible in TR lines, contrary to coronal holes. [ABSTRACT FROM AUTHOR]

Context. Solar energetic transients such as flares and coronal mass ejections occur mostly within active regions (ARs) and release large amounts of energy, which is expected to excite acoustic waves by transferring the mechanical impulse of the thermal expansion of the flare on the photosphere. On the other hand, strong magnetic fields of AR sunspots absorb the power of the photospheric oscillation modes. Aims. We study the properties of high-degree p-mode oscillations in flaring and dormant ARs and compare them with those in corresponding quiet regions (QRs) to find the association of the mode parameters with magnetic- and flare-related activities. Methods. We computed the mode parameters using the ring-diagram technique. The magnetic-activity indices (MAIs) of ARs and QRs were determined from the line-of-sight magnetograms. The flare indices (FIs) of ARs were obtained from the GOES X-ray fluxes. Mode parameters were corrected for foreshortening, duty cycle, and MAI using multiple non-linear regression. Results. Our analysis of several flaring and dormant ARs observed during the Carrington rotations 1980-2109 showed a strong association of the mode amplitude, width, and energy with magnetic and flare activities, although their changes are combined effects of foreshortening, duty cycle, magnetic-activity, flare-activity, and measurement uncertainties. We find that the largest reduction in mode amplitude and background power of an AR are caused by the angular distance of the AR from the solar disc centre. After correcting the mode parameters for foreshortening and duty cycle, we find that the mode amplitudes of flaring and dormant ARs are lower than in corresponding QRs reducing with increasing MAI, suggesting a stronger mode power suppression in ARs with larger magnetic fields. The mode widths in ARs are larger than in corresponding QRs and increase with MAI, indicating shorter lifetimes of modes in ARs than in QRs. The variations in mode amplitude and width with MAI are not same in different frequency bands. The largest amplification (reduction) in mode amplitude (mode width) of dormant ARs is found in the five-minute frequency band. The average mode energy of both the flaring and dormant ARs is smaller than in their corresponding QRs, reducing with increasing MAI. But the average mode energy reduction rate in flaring ARs is smaller than in dormant ARs. Moreover, the increase in mode width rate in dormant (flaring) ARs is followed by a decrease (increase) in the amplitude variation rate. Furthermore, including the mode corrections for MAI shows that mode amplitude and mode energy of flaring ARs escalate with FI, while the mode width shows an opposite trend, suggesting excitations of modes and growth in their lifetimes by flares. The increase (decrease) in mode amplitude (width) is larger in the five-minute and higher-frequency bands. The enhancement in width variation rate is followed by a rapid decline in the amplitude variation rate. [ABSTRACT FROM AUTHOR]

Context. Abreu et al. (2012, A&A. 548, A88) have recently compared the periodicities in a 14C - 10Be proxy record of solar variability during the Holocene and found a strong similarity with the periodicities predicted on the basis of a model of the time-dependent torque exerted by the planets on the sun's tachocline. If verified, this effect would represent a dramatic advance not only in the basic understanding of the Sun's variable activity, but also in the potential influence of this variability on the Earth's climate. Cameron and Schussler (2013, A&A. 557, A83) have seriously criticized the statistical treatment used by Abreu et al. to test the significance of the coincidences between the periodicities of their model with the Holocene proxy record. Aims. If the Abreu et al. hypothesis is correct, it should be possible to find the same periodicities in the records of cosmogenic nuclides at earlier times. Methods. We present here a high-resolution record of 10Be in the EPICA Dome C (EDC) ice core from Antarctica during the Marine Interglacial Stage 9.3 (MIS 9.3), 325-336 kyr ago, and investigate its spectral properties. Results. We find very limited similarity with the periodicities seen in the proxy record of solar variability during the Holocene, or with that of the model of Abreu et al. Conclusions. We find no support for the hypothesis of a planetary influence on solar activity, and raise the question of whether the centennial periodicities of solar activity observed during the Holocene are representative of solar activity variability in general. [ABSTRACT FROM AUTHOR]

Context. Precise localization and characterization of active regions (AR) and coronal holes (CH) as observed by extreme ultra violet (EUV) imagers are crucial for a wide range of solar and helio-physics studies. Aims. We introduce a set of segmentation procedures (known as the SPoCA-suite) that allows one to retrieve AR and CH properties on EUV images taken from SOHO-EIT, STEREO-EUVI, PROBA2-SWAP, and SDO-AIA. Methods. We build upon our previous work on the Spatial Possibilistic Clustering Algorithm (SPoCA), that we have improved substantially in several ways. Results. We apply our algorithm on the synoptic EIT archive from 1997 to 2011 and decompose this dataset into regions that can clearly be identified as AR, quiet Sun, and CH. An antiphase between AR and CH filling factor is observed, as expected. The SPoCAsuite is next applied to datasets from EUVI, SWAP, and AIA. The time series pertaining to ARs or CHs are presented. Conclusions. The SPoCA-suite enables the extraction of several long time series of AR andCH properties from the data files of EUV imagers and also allows tracking individual ARs or CHs over time. For AIA images, AR and CH catalogs are available in near-real time fromthe Heliophysics Events Knowledgebase. The full code, which allows processing any EUV images, is available upon request to the authors. [ABSTRACT FROM AUTHOR]

Aims. We examine the response of the Hinode X-Ray Telescope (XRT), using simultaneous observations with the Hinode Extremeultraviolet Imaging Spectrometer (EIS), for a flare, an active region and a quiet Sun region. We also examine the relative intensity calibration of EIS and XRT. Methods. EIS differential emission measure distribution (DEM) curves were used to create synthetic spectra with the CHIANTI atomic database. The contribution of spectral lines and continuum emission to each of the XRT channels was determined from the synthetic spectra, which were then convolved with the effective area of each XRT channel. The predicted total count rates for each channel were compared with the observed count rates. The effects of varying elemental abundances and the temperature range for the inversion were investigated. DEMs obtained from the XRT bands were also computed and compared to those obtained with EIS. Results. For the active region observations, the observed XRT count rates for most of the channels are in reasonable agreement with those predicted using EIS observations, but are dependent on the elemental abundances chosen. Significant discrepancies between predicted and observed count rates were found and are discussed for the adjacent quiet Sun region and also for the flare. Synthetic spectra and continuum emission contributing to the XRT channels are presented and discussed for the active region, quiet Sun and flare observations. [ABSTRACT FROM AUTHOR]

Context. The study of solar irradiance variability is of great importance in heliophysics, the Earth's climate, and space weather applications. These studies require careful identifying, tracking and monitoring of active regions (ARs), coronal holes (CHs), and the quiet Sun (QS). Aims. We studied the variability of solar irradiance for a period of two years (January 2011-December 2012) using the Large Yield Radiometer (LYRA), the Sun Watcher using APS and image Processing (SWAP) on board PROBA2, and the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). Methods. We used the spatial possibilistic clustering algorithm (SPoCA) to identify and segment coronal features from the EUV observations of AIA. The AIA segmentation maps were then applied on SWAP images, and parameters such as the intensity, fractional area, and contribution of ARs/CHs/QS features were computed and compared with the full-disk integrated intensity and LYRA irradiance measurements. Results. We report the results obtained from SDO/AIA and PROBA2/SWAP images taken from January 2011 to December 2012 and compare the resulting integrated full-disk intensity with PROBA2/LYRA irradiance. We determine the contributions of the segmented features to EUV and UV irradiance variations. The variations of the parameters resulting from the segmentation, namely the area, integrated intensity, and relative contribution to the solar irradiance, are compared with LYRA irradiance. We find that the active regions have a great impact on the irradiance fluctuations. In the EUV passbands considered in this study, the QS is the greatest contributor to the solar irradiance, with up to 63% of total intensity values. Active regions, on the other hand, contribute to about 10%, and off-limb structures to about 24%. We also find that the area of the features is highly variable suggesting that their area has to be taken into account in irradiance models, in addition to their intensity variations. Conclusions. We successfully show that the feature extraction allows us to use EUV telescopes to measure irradiance fluctuations and to quantify the contribution of each part to the EUV spectral solar irradiance observed with a calibrated radiometer. This study also shows that SPoCA is viable, and that the segmentation of images can be a useful tool. We also provide the measurement correlation between SWAP and AIA during this analysis. [ABSTRACT FROM AUTHOR]

Context. The distribution of magnetic fields in the atmosphere of the quiet Sun has been extensively studied with various methods, but it is still a matter of debate. Previous analyses mostly rely on the inversion of spectro-polarimetric data and different methods lead to somewhat different results. Aims. Here we do not intend to determine the magnetic field vector, but we use total polarization images as tracers of the magnetic field distribution and we study their cross-correlations with granulation and reversed-granulation images. Methods. We used high-resolution spectro-polarimetric scans obtained in the 630 nm FeI line pair at varying heliocentric angles along the north-south polar axis of the Sun, with the Solar Optical Telescope (SOT) onboard Hinode. We obtain polarization images by summing the total polarization (linear and circular) in each line. We compute the 2D correlation of polarization images and their cross-correlations with images of the granulation observed simultaneously in the line wings and with the reversed granulation observed in the line cores, and we examine their center-to-limb variations. Results. The correlation-widths of polarization images have on the average, the same value (1.3") as the correlation-width of the granulation, showing that the granular scale is a characteristic scale of the quiet Sun magnetic field distribution. At disk center the cross-correlation between total polarization and the granulation shows a negative peak. Out of disk-center both a negative and a positive peak are detected. The cross-correlation of polarization images with the reversed granulation always shows a positive peak. We assign these cross-correlation signals to the presence of two kinds of magnetized regions spatially separated, one of them is located in the intergranular lanes (anti-correlated with the granulation), the other one lies within the bright granules. For images obtained out of disk center, the correlation and anti-correlation peaks are shifted along the north-south direction and the shifts measured at the same limb-distance in the southern and northern hemispheres have opposite values. A consistent interpretation of these shifts is proposed in terms of a perspective effect arising when two images formed at different heights are observed at an angle. We were able to measure the perspective effect for the magnetic component correlated with the reversed granulation. Its polarization signals observed in the FeI 630.25 nm line and in the 630.15 nm line, are formed respectively 100 km and 150 km below the bright features seen at line centers. [ABSTRACT FROM AUTHOR]

Aims. A broad jet was observed in a weak magnetic field area at the edge of active region NOAA 11106 that also produced other nearby recurring and narrow jets. The peculiar shape and magnetic environment of the broad jet raised the question of whether it was created by the same physical processes of previously studied jets with reconnection occurring high in the corona. Methods. We carried out a multi-wavelength analysis using the EUV images from the Atmospheric Imaging Assembly (AIA) and magnetic fields from the Helioseismic and Magnetic Imager (HMI) both on-board the Solar Dynamics Observatory, which we coupled to a high-resolution, nonlinear force-free field extrapolation. Local correlation tracking was used to identify the photospheric motions that triggered the jet, and time-slices were extracted along and across the jet to unveil its complex nature. A topological analysis of the extrapolated field was performed and was related to the observed features. Results. The jet consisted of many different threads that expanded in around 10 minutes to about 100 Mm in length, with the bright features in later threads moving faster than in the early ones, reaching a maximum speed of about 200 km s-1. Time-slice analysis revealed a striped pattern of dark and bright strands propagating along the jet, along with apparent damped oscillations across the jet. This is suggestive of a (un)twisting motion in the jet, possibly an Alfvén wave. Bald patches in field lines, low-altitude flux ropes, diverging flow patterns, and a null point were identified at the basis of the jet. Conclusions. Unlike classical λ or Eiffel-tower-shaped jets that appear to be caused by reconnection in current sheets containing null points, reconnection in regions containing bald patches seems to be crucial in triggering the present jet. There is no observational evidence that the flux ropes detected in the topological analysis were actually being ejected themselves, as occurs in the violent phase of blowout jets; instead, the jet itself may have gained the twist of the flux rope(s) through reconnection. This event may represent a class of jets different from the classical quiescent or blowout jets, but to reach that conclusion, more observational and theoretical work is necessary. [ABSTRACT FROM AUTHOR]

We present simultaneous SDO AIA and Hinode EIS observations of the hot cores of active regions (ARs) and assess the dominant contributions to the AIA EUV bands. This is an extension of our previous work. We find good agreement between SDO AIA, EVE and EIS observations, using our new EIS calibration and the latest EVE v.3 data. We find that all the AIA bands are multi-thermal, with the exception of the 171 and 335 Å, and provide ways to roughly estimate the main contributions directly from the AIA data. We present and discuss new atomic data for the AIA bands, showing that they are now sufficiently complete to obtain temperature information in the cores of ARs, with the exception of the 211 Å band. We found that the newly identified Fe xiv 93.61 Å line is the dominant contribution to the 94 Å band, whenever Fe xviii is not present. Three methods to estimate the Fe xviii emission in this band are presented, two using EIS and one directly from the AIA data. Fe xviii emission is often present in the cores of ARs, but we found cases where it is formed at 3 MK and not 7 MK, the temperature of peak ion abundance in equilibrium. The best EIS lines for elemental abundance determination and differential emission measure (DEM) analysis are discussed. A new set of abundances for many elements are obtained from EIS observations of hot 3 MK loops. The abundances of the elements with low first ionisation potential (FIP), relative to those of the high-FIP elements, are found to be enhanced by about a factor of three, compared to the photospheric values. A measurement of the path length implies that the absolute abundances of the low-FIP elements are higher than the photospheric values by at least a factor of three. We present a new DEM method customised for the AIA bands, to study the thermal structure of ARs at 1'' resolution. This was tested on a few ARs, including one observed during the Hi-C rocket flight. We found excellent agreement between predicted and observed AIA count rates and EIS radiances. Overall we found few differences between the AIA and Hi-C 193 Å images of coronal structures, despite the higher Hi-C resolution (0.25''). The Hi-C images and the AIA DEM modelling suggest that some of the cooler loops (below 1 MK) are already resolved by AIA, while the hotter (1.5-2.5 MK) "background" emission is in most places still unresolved even at the Hi-C resolution. This unresolved emission is significantly lower than previously observed with TRACE, the SOHO CDS, and Hinode EIS spectrometers. Its enhancement appears to be mostly due to increased iron abundance. We find an ubiquitous presence of emission at different temperatures that is not co-spatial, and suggest that future high-resolution imaging is carried out with isothermal bands. [ABSTRACT FROM AUTHOR]

We investigate two candidate solar sources or active regions (ARs) in association with a solar impulsive energetic electron (SIEE) event on 2002 October 20. The solar particle release (SPR) times of SIEEs are derived by using their velocity dispersion with consideration of the instrumental effect. It is found that there are double electron injections at the Sun. The low-energy (⩽13 keV) electron injection coincides with a C6.6 flare in AR10154 and is accompanied with prominent type III radio bursts rather than a stronger M1.8 flare in AR10160. The M1.8 flare produces, however, faint type III radio bursts. Electrons of ∼25 to ∼300 keV are released ∼9 min later when a jet-like CME travels to ~2.6 solar radii. We further examine the coronal magnetic configurations above the two ARs based on the potential field source surface (PFSS) model. It is found that open field lines, rooted in AR10154 and well connected to the Earth, provide escaping channels for energetic electrons. Only a small portion of magnetic fields are opened above AR10160, being responsible for the faint type III radio bursts. These lines are, however, not well connected, making it impossible for SIEEs detection by near-Earth spacecraft. The results appear to establish a physical link between coronal magnetic topology, formation of type III radio bursts, and production of SIEEs. [ABSTRACT FROM AUTHOR]

Context. Waves have long been thought to contribute to the heating of the solar corona and the generation of the solar wind. Recent observations have demonstrated evidence of quasi-periodic longitudinal disturbances and ubiquitous transverse wave propagation in many different coronal environments. Aims. This paper investigates signatures of different types of oscillatory behaviour, both above the solar limb and on-disk, by comparing findings from the Coronal Multi-channel Polarimeter (CoMP) and the Atmospheric Imaging Assembly (AIA) on-board the Solar Dynamics Observatory (SDO) for the same active region. Methods. We study both transverse and longitudinal motion by comparing and contrasting time-distance images of parallel and perpendicular cuts along/across active region fan loops. Comparisons between parallel space-time diagram features in CoMP Doppler velocity and transverse oscillations in AIA images are made, together with space-time analysis of propagating quasi-periodic intensity features seen near the base of loops in AIA. Results. Signatures of transverse motions are observed along the same magnetic structure using CoMP Doppler velocity (vphase = 600 → 750 km s-1, P = 3 → 6min) and in AIA/SDO above the limb (P = 3 → 8min). Quasi-periodic intensity features (vphase = 100 → 200 km s-1, P = 6 → 11 min) also travel along the base of the same structure. On the disk, signatures of both transverse and longitudinal intensity features were observed by AIA, and both show similar properties to signatures found along structures anchored in the same active region three days earlier above the limb. Correlated features are recovered by space-time analysis of neighbouring tracks over perpendicular distances of ≲2.6Mm. [ABSTRACT FROM AUTHOR]

An assessment of the in-flight radiometric calibration of the Hinode EUV Imaging Spectrometer (EIS) is presented. This is done with the line ratio technique applied to a wide range of observations of the quiet Sun, active regions, and flares from 2006 until 2012. The best diagnostic lines and the relevant atomic data are discussed in detail. Radiances over the quiet Sun are also considered, with comparisons with previous measurements. Some departures in the shapes of the ground calibration responsivities are found at the start of the mission. These shapes do not change significantly over time, with the exception of the shorter wavelengths of the EIS short-wavelength (SW) channel, which shows some degradation. The sensitivity of the SW channel at longer wavelengths does not show significant degradation, while that of the long-wavelength (LW) channel shows a significant degradation with time. By the beginning of 2010 the responsivity of the LW channel was already lower than the values measured on the ground by a factor of two or more. A first-order correction is proposed. With this correction, the main ratios of lines in the two channels become constant to within a relative 20%, and the He ii 256 Å radiances over the quiet Sun also become constant over time. This correction removes long-standing discrepancies for a number of lines and ions, in particular those involving the strongest Fe x, Fexiii, Fexiv, Fexvii, and Fe xxiv lines, where discrepancies of factors of more than two were found. These results have important implications for various EIS science analyses, in particular for measurements of temperatures, emission measures and elemental abundances. [ABSTRACT FROM AUTHOR]

Aims. We report for the first time the hot and cool components of two flux ropes simultaneously observed by SDO and STEREO, and the relationship between the flux rope eruptions and the coronal mass ejection (CME). Methods. Employing SDO and STEREO A and B observations, we investigated the eruptive event of two flux ropes and their associated activities in active region (AR) 11402 on January 23, 2012. Results. In SDO/AIA 94 Å (~6.4 MK) and 131 Å (~10 MK) images, a twisted flux rope appeared from 00:44 UT, which was located in AR 11402. Another longer saddle-shaped flux rope, with twisted fine structures, appeared 25 min later. This was located across the two ARs 11401 and 11402. These two flux ropes initially rose rapidly, then slowly, and finally were again accelerated fast. The two flux ropes are also identified in the STEREO A and B 195 Å (~1.4MK), 304 Å (0.06-0.08 MK), 284 Å (~1.8 MK), and 171 Å (~1.0 MK) observations. We suggest that the flux ropes may have both hot and cool components. Investigating the flux rope eruptions with their associated CME, we find that the erupting flux ropes are co-spatial with the CME bright core and the expanding overlying flux loops with the CME bright front. [ABSTRACT FROM AUTHOR]

Context. Solar active longitudes and their rotation have been studied for a long time using various forms of solar activity. However, the results on the long-term evolution of rotation rates and the hemispheric asymmetry obtained by earlier authors differ significantly from each other. Aims. We aim to find a consistent result on the long-term migration of active longitudes of sunspots in 1877-2008 separately for the two hemispheres. Methods. We used a dynamic, differentially rotating reference system to determine the best-fit values of the differential rotation parameters of active longitudes for each year in 1877-2008. With these parameters we determined the momentary rotation rates at the reference latitude of 17° and calculated the non-axisymmetries of active longitudes. We repeated this with five different fit intervals and two weighting methods and compared the results. Results. The evolution of solar surface rotation in each hemisphere suggests a quasi-periodicity of about 80-90 years. The long-term variations of solar rotation in the northern and southern hemisphere have a close anti-correlation, leading to a significant 80-90-year quasi-periodicity in the north-south asymmetry of solar rotation. The north-south asymmetry of solar rotation is found to have an inverse relationship with the area of large sunspots. The latitudinal contrast of differential rotation is also found to be anti-correlated with the sunspot area. Different fit and weight methods yield similar results. Conclusions. Our results give strong evidence for the anti-correlation of the rotation of the two solar hemispheres. The long-term oscillation of solar rotation suggests that a systematic interchange of angular momentum takes place between the two hemispheres at a period of about 80-90 years. [ABSTRACT FROM AUTHOR]

Context. Monitoring of the photometric and chromospheric HK emission data series of stars similar to the Sun in age and average activity level showed that there is an empirical correlation between the average stellar chromospheric activity level and the photometric variability. In general, more active stars show larger photometric variability. Interestingly, the measurements and reconstructions of the solar irradiance show that the Sun is significantly less variable than indicated by the empirical relationship. Aims. We aim to identify possible reasons for the Sun to be currently outside of this relationship. Methods. We employed different scenarios of solar HK emission and irradiance variability and compared them with available time series of Sun-like stars. Results. We show that the position of the Sun on the diagram of photometric variability versus chromospheric activity changes with time. The present solar position is different from its temporal mean position as the satellite era of continuous solar irradiance measurements has accidentally coincided with a period of unusually high and stable solar activity. Our analysis suggests that although present solar variability is significantly smaller than indicated by the stellar data, the temporal mean solar variability might be in agreement with the stellar data. We propose that the continuation of the photometric program and its expansion to a larger stellar sample will ultimately allow us to constrain the historical solar variability. [ABSTRACT FROM AUTHOR]

Context. Radial velocity (RV) time series are strongly impacted by the presence of stellar activity. In a series of papers, we have reconstructed solar RV variations over a full solar cycle from observed solar structures (spots and plages) and studied their impact on the detectability of an Earth-mass planet in the habitable zone of the Sun as seen edge-on from a neighbour star in several typical cases. We found that the convective contribution dominates the RV times series. Aims. The objective of this paper is twofold: to determine detection limits on a Sun-like star seen edge-on with different levels of convection and to estimate the performance of the activity correction using a Ca index. Methods. We apply two methods to compute the detection limits: a correlation-based method and a local power analysis method, which both take into account the temporal structure of the observations. Furthermore, we test two methods using a Ca index to correct for the convective contribution to the RV: a sinusoidal fit to the Ca variations and a linear fit to the RV-Ca relation. In both cases, we use observed Ca and reconstructed Ca to study the various effects and limitations of our estimations. Results. We confirm that an excellent sampling is necessary to have detection limits below 1 MEarth (e.g. 0.2-0.3 MEarth) when there is no convection and a low RV noise. With convection, the detection limit is always above 7 MEarth. The two correction methods perform similarly when the Ca time series are noisy, leading to a significant improvement (down to a few MEarth), which is above the 1 MEarth limit. With a very good Ca noise (signal to noise ratio, S/N, around 130), the sinusoidal method does not get significantly better because it is dominated by the fact that the solar cycle is not sinusoidal, but the RV-Ca method can reach the 1 MEarth for an excellent Ca noise level. Conclusions. For Sun-like conditions and under the simplifying assumptions considered, we first conclude that the detection limit of a few MEarth planet can be reached providing good sampling and Ca noise. The detection of a 1 MEarth may be possible, but only with an excellent temporal sampling and an excellent Ca index noise level: we estimate that a probability larger than 50% to detect a 1 MEarth at 1.2 AU requires more than 1000 well-sampled observations and a Ca S/N larger than 130. [ABSTRACT FROM AUTHOR]

Context. Particle acceleration during solar flares results in departures of the distribution of particle energies from the Maxwellian distribution. Apart from the high-energy tail, the bulk of the distribution was recently also found to be significantly affected, due, e.g., to the presence of double layers. Aims. We investigate the influence of several proposed non-Maxwellian distribution functions on the X-ray flare line spectra. The distribution functions considered are sharply peaked and include the n-distribution, the moving Maxwellian distribution, and the distribution formed in strong double layers in the flaring plasma. Methods. Synthetic Si XIId-Si XIV spectra involving allowed and dielectronic transitions at 5-6 Å are calculated numerically. The parameters chosen for the calculations correspond to the impulsive phase of solar flares, as inferred by previous authors. Results. The Si XIId λ5.56/Si XIII λ5.68 and Si XIId λ5.82/Si XIII λ5.68 ratios depend on the relative number of electrons at energies corresponding to the formation of the Si XIId lines. Therefore, these ratios increase with the increasing narrowness of the peak of the electron distribution function. The highest ratios are achieved for the distribution formed in double layers, while the moving Maxwellian distribution is less likely to reproduce the observed enhancement of Si XIId intensities. However, the ratio of the allowed Si XIV λ5.22/Si XIII λ5.68 transitions depends on the ionization equilibrium. This ratio is very small for the double-layer distribution. Combination of the double-layer distribution with a Maxwellian distribution with the same mean energy significantly enhances this ratio, while keeping the Si XIId intensities sufficiently increased to explain the characteristics of the observed spectra. Conclusions. These results support the presence of double layers in the plasma during impulsive phase of solar flares. [ABSTRACT FROM AUTHOR]

Context. The variations of solar activity over long time intervals using a solar activity reconstruction based on the cosmogenic radionuclide 10Be measured in polar ice cores are studied. Aims. The periodicity of the solar activity cycle is studied. The solar activity cycle is governed by a complex dynamo mechanism. Methods of nonlinear dynamics enable us to learn more about the regular and chaotic behavior of solar activity. In this work we compare our earlier findings based on 14C data with the results obtained using 10Be data. Methods. By applying methods of nonlinear dynamics, the solar activity cycle is studied using solar activity proxies that have been reaching into the past for over 9300 years. The complexity of the system is expressed by several parameters of nonlinear dynamics, such as embedding dimension or false nearest neighbors, and the method of delay coordinates is applied to the time series. We also fit a damped random walk model, which accurately describes the variability of quasars, to the solar 10Be data and investigate the corresponding power spectral distribution. The periods in the data series were searched by the Fourier and wavelet analyses. Results. The solar activity on the long-term scale is found to be on the edge of chaotic behavior. This can explain the observed intermittent period of longer lasting solar activity minima. Filtering the data by eliminating variations below a certain period (the periods of 380 yr and 57 yr were used) yields a far more regular behavior of solar activity. A comparison between the results for the 10Be data with the 14C data shows many similarities. Both cosmogenic isotopes are strongly correlated mutually and with solar activity. Finally, we find that a series of damped random walk models provides a good fit to the 10Be data with a fixed characteristic time scale of 1000 years, which is roughly consistent with the quasi-periods found by the Fourier and wavelet analyses. Conclusions. The time series of solar activity proxies used here clearly shows that solar activity behaves differently from random data. The unfiltered data exhibit a complex dynamics that becomes more regular when filtering the data. The results indicate that solar activity proxies are also influenced by other than solar variations and reflect solar activity only on longer time scales. [ABSTRACT FROM AUTHOR]

Elemental abundance effects in active coronae have eluded our understanding for almost three decades, since the discovery of the first ionization potential (FIP) effect on the sun. The goal of this paper is to monitor the same coronal structures over a time interval of six days and resolve active regions on a stellar corona through rotational modulation. We report on four iso-phase X-ray spectroscopic observations of the RS CVn binary EI Eri with XMM-Newton, carried out approximately every two days, to match the rotation period of EI Eri. We present an analysis of the thermal and chemical structure of the EI Eri corona as it evolves over the six days. Although the corona is rather steady in its temperature distribution, the emission measure and FIP bias both vary and seem to be correlated. An active region, predating the beginning of the campaign, repeatedly enters into our view at the same phase as it rotates from beyond the stellar limb. As a result, the abundances tend slightly, but consistently, to increase for high FIP elements (an inverse FIP effect) with phase. We estimate the abundance increase of high FIP elements in the active region to be of about 75% over the coronal mean. This observed fractionation of elements in an active region on time scales of days provides circumstantial clues regarding the element enrichment mechanism of non-flaring stellar coronae. [ABSTRACT FROM AUTHOR]

Context. The magnetic field configuration is essential for understanding solar explosive phenomena, such as flares and coronal mass ejections. To overcome the unavailability of coronal magnetic field measurements, photospheric magnetic field vector data can be used to reconstruct the coronal field. Two complications of this approach are that the measured photospheric magnetic field is not force-free and that one has to apply a preprocessing routine to achieve boundary conditions suitable for the force-free modeling. Furthermore the nonlinear force-free extrapolation code should take uncertainties into account in the photospheric field data. They occur due to noise, incomplete inversions, or azimuth ambiguity-removing techniques. Aims. Extrapolation codes in Cartesian geometry for modeling the magnetic field in the corona do not take the curvature of the Sun's surface into account and can only be applied to relatively small areas, e.g., a single active region. Here we apply a method for nonlinear force-free coronal magnetic field modeling and preprocessing of photospheric vector magnetograms in spherical geometry using the optimization procedure to full disk vector magnetograms. We compare the analysis of the photospheric magnetic field and subsequent force-free modeling based on full-disk vector maps from Helioseismic and Magnetic Imager (HMI) onboard the solar dynamics observatory (SDO) and Vector Spectromagnetograph (VSM) of the Synoptic Optical Long-term Investigations of the Sun (SOLIS). Methods. We used HMI and VSM photospheric magnetic field measurements to model the force-free coronal field above multiple solar active regions, assuming magnetic forces to dominate. We solved the nonlinear force-free field equations by minimizing a functional in spherical coordinates over a full disk and excluding the poles. After searching for the optimum modeling parameters for the particular data sets, we compared the resulting nonlinear force-free model fields. We compared quantities, such as the total magnetic energy content, free magnetic energy, the longitudinal distribution of the magnetic pressure, and surface electric current density, using our spherical geometry extrapolation code. Results. The magnetic field lines obtained from nonlinear force-free extrapolation based on HMI and VSMdata show good agreement. However, the nonlinear force-free extrapolation based on HMI data contain more total magnetic energy, free magnetic energy, the longitudinal distribution of the magnetic pressure, and surface electric current density than do the VSM data. [ABSTRACT FROM AUTHOR]

Context. Variations of solar irradiance are mainly determined by the changing coverage of the visible solar disk with magnetic flux concentrations. The relationship between brightness and field strength is an important ingredient for models and reconstructions of irradiance variations. Aims. We assess the effect of limited observational resolution on the relationship between brightness and magnetic field by comparing comprehensive MHD simulations with observational results. Methods. Simulations of magnetoconvection representing the near-surface layers of a plage region were used to determine maps of the continuum brightness and Stokes profiles for the Fe i line at 630.22 nm. After convolving with instrumental profiles, synthetic observations of the magnetic field were generated by applying a Stokes inversion code. We compare the resulting relation between brightness and apparent vertical magnetic field to the corresponding outcome derived from real observations of a plage region with the Hinode satellite. Results. Consideration of the image smearing effects due to the limited resolution of the observations transform the largely monotonic relation between brightness and field strength at the original resolution of the simulations into a profile with a maximum at intermediate field strength, which is in good agreement with the observations. Conclusions. Considering the effect of limited observational resolution renders the relation between brightness and magnetic field from comprehensive MHD simulations consistent with observational results. This is a necessary prerequisite for the utilization of simulations for models and reconstruction of solar irradiance variations. [ABSTRACT FROM AUTHOR]

Context. Solar flare prediction models normally depend on properties of active regions, such as sunspot area, McIntosh classifications, Mount Wilson classifications, and various measures of the magnetic field. Nevertheless, the positional information of active regions has not been used. Aims. We define a metric, DARAL (distance between active regions and predicted active longitudes), to depict the positional relationship between active regions and predicted active longitudes and add DARAL to our solar flare prediction model to improve its performance. Methods. Combining DARAL with other solar magnetic field parameters, we build a solar flare prediction model with the instancebased learning method, which is a simple and effective algorithm in machine learning. We extracted 70 078 active region instances from the Solar and Heliospheric Observatory (SOHO)/Michelson Doppler Imager (MDI) magnetograms containing 1055 National Oceanic and Atmospheric Administration (NOAA) active regions within 30? of the solar disk center from 1996 to 2007 and used them to train and test the solar flare prediction model. Results. Using four performance measures (true positive rate, true negative rate, true skill statistic, and Heidke skill score), we compare performances of the solar flare prediction model with and without DARAL. True positive rate, true negative rate, true skill statistic, and Heidke skill score increase by 6.7% ± 1.3%, 4.2% ± 0.5%, 10.8% ± 1.4% and 8.7% ± 1.0%, respectively. Conclusions. The comparison indicates that the metric DARAL is beneficial to performances of the solar flare prediction model. [ABSTRACT FROM AUTHOR]

Context. The surface layers of the Sun are strongly stratified. In the presence of turbulence with a weak mean magnetic field, a large-scale instability resulting in the formation of nonuniform magnetic structures, can be excited on the scale of many (more than ten) turbulent eddies (or convection cells). This instability is caused by a negative contribution of turbulence to the effective (mean-field) magnetic pressure and has previously been discussed in connection with the formation of active regions. Aims. We want to understand the effects of rotation on this instability in both two and three dimensions. Methods. We use mean-field magnetohydrodynamics in a parameter regime in which the properties of the negative effective magnetic pressure instability have previously been found to agree with properties of direct numerical simulations. Results. We find that the instability is already suppressed for relatively slow rotation with Coriolis numbers (i.e. inverse Rossby numbers) around 0.2. The suppression is strongest at the equator. In the nonlinear regime, we find traveling wave solutions with propagation in the prograde direction at the equator with additional poleward migration away from the equator. Conclusions. We speculate that the prograde rotation of the magnetic pattern near the equator might be a possible explanation for the faster rotation speed of magnetic tracers relative to the plasma velocity on the Sun. In the bulk of the domain, kinetic and current helicities are negative in the northern hemisphere and positive in the southern. [ABSTRACT FROM AUTHOR]