Supergranular Scales Research Articles

Magnetic Imbalance at Supergranular Scale: A Driving Mechanism for Coronal Hole Formation

Unraveling the intricate interplay between the solar photosphere’s magnetic field and the dynamics of the upper solar atmosphere is paramount to understanding the organization of solar magnetic fields and their influence on space weather events. This study delves into the organization of photospheric magnetic fields particularly in the context of coronal holes (CHs), as they are believed to harbor the sources of fast solar wind. We employed the signed measure technique on synthetic images that depict various arrangements of magnetic fields, encompassing imbalances in the sign of the magnetic field (inward and outward) and spatial organization.This study provides compelling evidence that the cancellation functions of simulated regions with imbalanced magnetic fields along the boundaries of supergranular cells align with cancellation function trends of observed photospheric magnetic regions associated with CHs. Thus the analysis serves as a significant proof that CHs arise from the formation of imbalanced magnetic patterns on the edges of supergranular cells.

Organization scale of photospheric magnetic imbalance in coronal holes

To investigate the statistical properties of the photospheric magnetic fields underlying coronal holes (CHs) and “normal” coronal regions a classical technique, the signed measure, is used. This technique allows to characterize the scaling behavior and the topology of sign-oscillating magnetic structures in selected regions of line of sigth (LoS) magnetograms recorded by the Heliosismic Magnetic Imager on board of the Solar Dynamic Observatory (SDO/HMI). To this end we have compared the properties of the photospheric magnetic field underlying 60 CHs and 60 non-coronal holes (NCHs). In particular, in addition to having studied distributions and momenta of photospheric magnetic fields associated to the selected regions, we have performed the sign singularity analysis computing the cancellation functions of the highly fluctuating photospheric magnetic fields. We have found that photospheric magnetic fields associated to CHs are imbalanced in the sign and that this imbalance emerges mainly at the supergranular scales.

The Sun’s Magnetic Power Spectra over Two Solar Cycles. I. Calibration between SDO/HMI and SOHO/MDI Magnetograms

The Sun’s magnetic field is strongly structured over a broad range of scales. Magnetic spatial power spectral analysis provides a powerful tool for understanding the various scales of magnetic fields and their interactions with plasma motions. We aim to investigate the power spectra using spherical harmonic decomposition of high-resolution Solar and Heliospheric Observatory (SOHO)/Michelson Doppler Imager (MDI) and Solar Dynamics Observatory (SDO)/Helioseismic and Magnetic Imager (HMI) synoptic magnetograms covering three consecutive solar cycle minima, in a series of papers. As the first of the series, we calibrate and analyze the power spectra based on cotemporal SDO/HMI and SOHO/MDI data in this paper. For the first time, we find that the calibration factor r between SOHO/MDI and SDO/HMI varies with the spatial scale l of the magnetic field, where l is the degree of the spherical harmonic. The calibration factor satisfies . With the calibration function, most contemporaneous SOHO/MDI and SDO/HMI magnetograms show consistent power spectra from about 8 Mm to the global scales over about three orders of magnitude. Moreover, magnetic power spectra from SOHO/MDI and SDO/HMI maps show peaks/knees at l ≈ 120, corresponding to the typical supergranular scale (about 35 Mm) constrained from direct velocimetric measurements. This study paves the way for investigating the solar cycle dependence of supergranulation and magnetic power spectra in subsequent studies.

Diffuse solar coronal features and their spicular footpoints

Context. In addition to a component of the emission that originates from clearly distinguishable coronal loops, the solar corona also exhibits extreme-ultraviolet (EUV) and X-ray ambient emission that is rather diffuse and is often considered undesirable background. Importantly, unlike the generally more structured transition region and chromosphere, the diffuse corona appears to be rather featureless. Aims. The magnetic nature of the diffuse corona, and in particular, its footpoints in the lower atmosphere, are not well understood. We study the origin of the diffuse corona above the quiet-Sun network on supergranular scales. Methods. We identified regions of diffuse EUV emission in the coronal images from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). To investigate their connection to the lower atmosphere, we combined these SDO/AIA data with the transition region spectroscopic data from the Interface Region Imaging Spectrograph (IRIS) and with the underlying surface magnetic field information from the Helioseismic and Magnetic Imager (HMI), also on board SDO. Results. The region of the diffuse emission is of supergranular size and persists for more than five hours, during which it shows no obvious substructure. It is associated with plasma at about 1 MK that is located within and above a magnetic canopy. The canopy is formed by unipolar magnetic footpoints that show highly structured spicule-like emission in the overlying transition region. Conclusions. Our results suggest that the diffuse EUV emission patch forms at the base of long-ranging loops, and it overlies spicular structures in the transition region. Heated material might be supplied to it by means of spicular upflows, conduction-driven upflows from coronal heating events, or perhaps by flows originating from the farther footpoint. Therefore, the question remains open how the diffuse EUV patch might be sustained. Nevertheless, our study indicates that heated plasma trapped by long-ranging magnetic loops might substantially contribute to the featureless ambient coronal emission.

Solar-cycle variation of quiet-Sun magnetism and surface gravity oscillation mode

Context. The origins of quiet-Sun magnetism (QS) is still under debate and investigating the solar cycle variation observationally in greater detail can provide clues on how to resolve the ensuing controversies. Aims. We investigate the solar cycle variation of the most magnetically quiet regions and their surface gravity oscillation (f-) mode-integrated energy, Ef. Methods. We used 12 years of Helioseismic and Magnetic Imager (HMI) data and applied a stringent selection criteria based on spatial and temporal quietness to avoid any influence from active regions (ARs). We developed an automated high-throughput pipeline to go through all available magnetogram data and to compute the value of Ef for the selected quiet regions. Results. We observed a clear solar cycle dependence of the magnetic field strength in the most quiet regions containing several supergranular cells. For patch sizes smaller than a supergranular cell, no significant cycle dependence was detected. The Ef at the supergranular scale is not constant over time. During the late ascending phase of Cycle 24 (SC24, 2011-2012), it is roughly constant, but starts diminishing in 2013, as the maximum of SC24 is approached. This trend continues until mid-2017, when hints of strengthening at higher southern latitudes are seen. Slow strengthening continues, stronger at higher latitudes than at the equatorial regions, but Ef never returns to the values seen in 2011-2012. In addition, the strengthening trend continues past the solar minimum, to the years when SC25 is already clearly ascending. Hence, the Ef behavior is not in phase with the solar cycle. Conclusions. The dependence of Ef on the solar cycle at supergranular scales is indicative of the fluctuating magnetic field being replenished by tangling from the large-scale magnetic field – and not solely due to the action of a fluctuation dynamo process in the surface regions. The absence of variations on smaller scales might be an effect of the limited spatial resolution and magnetic sensitivity of HMI. The anticorrelation of Ef with the solar cycle in gross terms is expected, but the phase shift of several years indicates a connection to the large-scale poloidal magnetic field component rather than the toroidal one. Calibrating AR signals with the QS Ef does not reveal significant enhancement of the f-mode prior to AR emergence.

Power spectra of the Sun’s large-scale magnetic field during solar cycles 23 and 24

AbstractThe magnetic power spectrum analysis provides an effective way to understand the observed distribution of the photospheric magnetic fields and their interaction with plasma motions. We aim to investigate the power spectra using spherical harmonic decomposition of SOHO/MDI and SDO/HMI synoptic magnetograms for cycles 23 and 24. We find that the calibration factor between MDI and HMI power spectral density is spatial scale-dependent. The magnetic power spectra show two peaks at the AR scale (l≈30) and supergranular scale (l≈120). The power law indices between these show a good anti-correlation with the amplitude of magnetic activity.

Investigating Toroidal Flows in the Sun Using Normal-mode Coupling

Abstract Helioseismic observations have provided valuable data sets with which to pursue the detailed investigation of solar interior dynamics. Among various methods to analyze these data, normal-mode coupling has proven to be a powerful tool, used to study Rossby waves, differential rotation, meridional circulation, and nonaxisymmetric multiscale subsurface flows. Here, we invert mode-coupling measurements from the Helioseismic Magnetic Imager and the Michelson Doppler Imager to obtain mass-conserving toroidal convective flow as a function of depth, spatial wavenumber, and temporal frequency. To ensure that the estimates of velocity magnitudes are proper, we also evaluate correlated realization noise, caused by the limited visibility of the Sun. We benchmark the near-surface inversions against results from local correlation tracking. The convective power likely assumes greater latitudinal isotropy with a decrease in spatial scale of the flow. We note the absence of a peak in toroidal-flow power at supergranular scales, in line with observations that show that supergranulation is dominantly poloidal in nature.

Effect of latitudinal differential rotation on solar Rossby waves: Critical layers, eigenfunctions, and momentum fluxes in the equatorialβplane

Context.Retrograde-propagating waves of vertical vorticity with longitudinal wavenumbers between 3 and 15 have been observed on the Sun with a dispersion relation close to that of classical sectoral Rossby waves. The observed vorticity eigenfunctions are symmetric in latitude, peak at the equator, switch sign near 20°–30°, and decrease at higher latitudes.Aims.We search for an explanation that takes solar latitudinal differential rotation into account.Methods.In the equatorialβplane, we studied the propagation of linear Rossby waves (phase speedc < 0) in a parabolic zonal shear flow,U= −U̅ξ2< 0, whereU̅= 244 m s−1, andξis the sine of latitude.Results.In the inviscid case, the eigenvalue spectrum is real and continuous, and the velocity stream functions are singular at the critical latitudes whereU = c. We add eddy viscosity to the problem to account for wave attenuation. In the viscous case, the stream functions solve a fourth-order modified Orr-Sommerfeld equation. Eigenvalues are complex and discrete. For reasonable values of the eddy viscosity corresponding to supergranular scales and above (Reynolds number 100 ≤ Re ≤ 700), all modes are stable. At fixed longitudinal wavenumber, the least damped mode is a symmetric mode whose real frequency is close to that of the classical Rossby mode, which we call the R mode. ForRe ≈ 300, the attenuation and the real part of the eigenfunction is in qualitative agreement with the observations (unlike the imaginary part of the eigenfunction, which has a larger amplitude in the model).Conclusions.Each longitudinal wavenumber is associated with a latitudinally symmetric R mode trapped at low latitudes by solar differential rotation. In the viscous model, R modes transport significant angular momentum from the dissipation layers toward the equator.

Inferring Plasma Flows at Granular and Supergranular Scales With a New Architecture for the DeepVel Neural Network

The wealth of observational data available has been instrumental in investigating physical features relevant to solar granulation, supergranulation and Active Regions. Meanwhile, numerical models have attempted to bridge the gap between the physics of the solar interior and such observations. However, there are relevant physical quantities that can be modelled but that cannot be directly measured and must be inferred. For example, direct measurements of plasma motions at the photosphere are limited to the line-of-sight component. Methods have consequently been developed to infer the transverse plasma motions from continuum images in the case of the Quiet Sun and magnetograms in the case of Active Regions. Correlation-based tracking methods calculate the optical flows by correlating series of images locally while other methods like “Coherent Structure Tracking” or "Balltracking” exploit the coherency of photospheric granules to track them and use the group motions of the granules as a proxy of the average plasma flows advecting them. Recently, neural network computing has been used in conjunction with numerical models of the Sun to be able to recover the full velocity vector in photospheric plasma from continuum images. We experiment with a new architecture for the DeepVel neural network which takes inspiration from the U-Net architecture. Simulation data of the Quiet Sun and Active Regions are then used to evaluate the response at granular and supergranular scales of the aforementioned method.

Characterizing the spatial pattern of solar supergranulation using the bispectrum

Context. The spatial power spectrum of supergranulation does not fully characterize the underlying physics of turbulent convection. For example, it does not describe the non-Gaussianity in the horizontal flow divergence. Aims. Our aim is to statistically characterize the spatial pattern of solar supergranulation beyond the power spectrum. The next-order statistic is the bispectrum. It measures correlations of three Fourier components and is related to the nonlinearities in the underlying physics. It also characterizes how a skewness in the dataset is generated by the coupling of three Fourier components. Methods. We estimated the bispectrum of supergranular horizontal surface divergence maps that were obtained using local correlation tracking (LCT) and time-distance helioseismology (TD) from one year of data from the helioseismic and magnetic imager on-board the solar dynamics observatory starting in May 2010. Results. We find significantly nonzero and consistent estimates for the bispectrum using LCT and TD. The strongest nonlinearity is present when the three coupling wave vectors are at the supergranular scale. These are the same wave vectors that are present in regular hexagons, which have been used in analytical studies of solar convection. At these Fourier components, the bispectrum is positive, consistent with the positive skewness in the data and consistent with supergranules preferentially consisting of outflows surrounded by a network of inflows. We use the bispectral estimates to generate synthetic divergence maps that are very similar to the data. This is done by a model that consists of a Gaussian term and a weaker quadratic nonlinear component. Using this method, we estimate the fraction of the variance in the divergence maps from the nonlinear component to be of the order of 4–6%. Conclusions. We propose that bispectral analysis is useful for understanding the dynamics of solar turbulent convection, for example for comparing observations and numerical models of supergranular flows. This analysis may also be useful to generate synthetic flow fields.

Link between trees of fragmenting granules and deep downflows in MHD simulation

Context. Trees of fragmenting granules (TFG) and associated flows are suspected to play a major role in the formation of the network in the quiet Sun. We investigate the counterparts, in terms of dynamics, of surface structures detectable by high resolution observations in deeper layers up to 15 Mm, which are only available from numerical simulations. Aims. The first aim is to demonstrate that TFG can be evidenced either from surface intensitites, vertical (Vz), or Doppler (Vdop) velocities. The second is to show that horizontal flows, which are derived from intensities or Vz/Vdop flows, are in good agreement, and that this is the case for observations and numerical simulations. The third objective is to apply this new Vz-based method to a 3D simulation to probe relationships between horizontal surface flows, TFG, and deep vertical motions. Methods. The TFG were detected after oscillation filtering of intensities or Vz/Vdop flows, using a segmentation and labelling technique. Surface horizontal flows were derived from local correlation tracking (LCT) and from intensities or Vz/Vdop flows. These methods were applied to Hinode observations, 2D surface results of a first simulation, and 3D Vz data of a second simulation. Results. We find that TFG and horizontal surface flows (provided by the LCT) can be detected either from intensities or Vz/Vdop component, for high resolution observations and numerical simulations. We apply this method to a 3D run providing the Vz component in depth. This reveals a close relationship between surface TFG (5 Mm mesoscale) and vertical downflows 5 Mm below the surface. We suggest that the dynamics of TFG form larger scales (the 15–20 Mm supergranulation) associated with 15 Mm downflowing cells below the surface. Conclusions. The TFG and associated surface flows seem to be essential to understanding the formation and evolution of the network at the meso and supergranular scale.

Reconstruction of Horizontal Plasma Motions at the Photosphere from Intensitygrams: A Comparison Between DeepVel, LCT, FLCT, and CST

Direct measurements of plasma motions in the photosphere are limited to the line-of-sight component of the velocity. Several algorithms have therefore been developed to reconstruct the transverse components from observed continuum images or magnetograms. We compare the space and time averages of horizontal velocity fields in the photosphere inferred from pairs of consecutive intensitygrams by the LCT, FLCT, and CST methods and the DeepVel neural network in order to identify the method that is best suited for generating synthetic observations to be used for data assimilation. The Stein and Nordlund (Astrophys. J. Lett. 753, L13, 2012) magnetoconvection simulation is used to generate synthetic SDO/HMI intensitygrams and reference flows to train DeepVel. Inferred velocity fields show that DeepVel performs best at subgranular and granular scales and is second only to FLCT at mesogranular and supergranular scales.

Association of Supergranule Mean Scales with Solar Cycle Strengths and Total Solar Irradiance

Abstract We analyze the long-term behavior of the supergranule scale parameter, in active regions (ARs) and quiet regions (QRs), using the Kodaikanal digitized data archive. This database provides century-long daily full disk observations of the Sun in Ca ii K wavelengths. In this paper, we study the distributions of the supergranular scales, over the whole data duration, which show identical shape in these two regimes. We found that the AR mean scale values are always higher than that of the QR for every solar cycle. The mean scale values are highly correlated with the sunspot number cycle amplitude and also with total solar irradiance (TSI) variations. Such a correlation establishes the cycle-wise mean scale as a potential calibrator for the historical data reconstructions. We also see an upward trend in the mean scales, as has already been reported in TSI. This may provide new input for climate forcing models. These results also give us insight into the different evolutionary scenarios of the supergranules in the presence of strong (AR) and weak (QR) magnetic fields.

Dynamics of the photosphere along the solar cycle from SDO/HMI

Context. As the global magnetic field of the Sun has an activity cycle, one expects to observe some variation of the dynamical properties of the flows visible in the photosphere. Aims. We investigate the flow field during the solar cycle by analysing SDO/HMI observations of continuum intensity, Doppler velocity and longitudinal magnetic field. Methods. We first picked data at disk center during 6 yr along the solar cycle with a 48-h time step in order to study the overall evolution of the continuum intensity and magnetic field. Then we focused on thirty 6-h sequences of quiet regions without any remnant of magnetic activity separated by 6 months, in summer and winter, when disk center latitude B0 is close to zero. The horizontal velocity was derived from the local correlation tracking technique over a field of view of 216.4 Mm × 216.4 Mm located at disk center. Results. Our measurements at disk center show the stability of the flow properties between meso- and supergranular scales along the solar cycle. Conclusions. The network magnetic field, produced locally at disk center independently from large scale dynamo, together with continuum contrast, vertical and horizontal flows, seem to remain constant during the solar cycle.

THE EMERGENCE OF SOLAR SUPERGRANULATION AS A NATURAL CONSEQUENCE OF ROTATIONALLY CONSTRAINED INTERIOR CONVECTION

We investigate how rotationally-constrained, deep convection might give rise to supergranulation, the largest distinct spatial scale of convection observed in the solar photosphere. While supergranulation is only weakly influenced by rotation, larger spatial scales of convection sample the deep convection zone and are presumably rotationally influenced. We present numerical results from a series of nonlinear, 3-D simulations of rotating convection and examine the velocity power distribution realized under a range of Rossby numbers. When rotation is present, the convective power distribution possesses a pronounced peak, at characteristic wavenumber $\ell_\mathrm{peak}$, whose value increases as the Rossby number is decreased. This distribution of power contrasts with that realized in non-rotating convection, where power increases monotonically from high to low wavenumbers. We find that spatial scales smaller than $\ell_\mathrm{peak}$ behave in analogy to non-rotating convection. Spatial scales larger than $\ell_\mathrm{peak}$ are rotationally-constrained and possess substantially reduced power relative to the non-rotating system. We argue that the supergranular scale emerges due to a suppression of power on spatial scales larger than $\ell\approx100$ owing to the presence of deep, rotationally-constrained convection. Supergranulation thus represents the largest non-rotationally-constrained mode of solar convection. We conclude that the characteristic spatial scale of supergranulation bounds that of the deep convective motions from above, making supergranulation an indirect measure of the deep-seated dynamics at work in the solar dynamo. Using the spatial scale of supergranulation in conjunction with our numerical results, we estimate an upper bound of 10 m s$^{-1}$ for the Sun's bulk rms convective velocity.

SUPERGRANULATION AS THE LARGEST BUOYANTLY DRIVEN CONVECTIVE SCALE OF THE SUN

ABSTRACT The origin of solar supergranulation remains a mystery. Unlike granulation, the size of which is comparable to both the thickness of the radiative boundary layer and local scale-height in the photosphere, supergranulation does not reflect any obvious length scale of the solar convection zone. Moreover, recent observations of flows in the photosphere using Doppler imaging or correlation or feature tracking show a monotonic decrease in horizontal flow power at scales larger than supergranulation. Both local area and global spherical shell simulations of solar convection by contrast show the opposite, an increase in horizontal flow amplitudes to a low wavenumber. We examine these disparities and investigate how the solar supergranulation may arise as a consequence of nonlocal heat transport by cool diving plumes. Using three-dimensional anelastic simulations with surface driving, we show that the kinetic energy of the largest convective scales in the upper layers of a stratified domain reflects the depth of transition from strong buoyant driving to adiabatic stratification below caused by the dilution of the granular downflows. This depth is quite shallow because of the rapid increase of the mean density below the photosphere. We interpret the observed monotonic decrease in solar convective power at scales larger than supergranulation to be a consequence of this rapid transition, with the supergranular scale the largest buoyantly driven mode of convection in the Sun.

NON-POTENTIAL FIELDS IN THE QUIET SUN NETWORK: EXTREME-ULTRAVIOLET AND MAGNETIC FOOTPOINT OBSERVATIONS

The quiet Sun (QS) magnetic network is known to contain dynamics which are indicative of non-potential fields. Non-potential magnetic fields forming S-shaped loop arcades can lead to the breakdown of static activity and have only been observed in high temperature X-ray coronal structures—some of which show eruptive behavior. Thus, analysis of this type of atmospheric structuring has been restricted to large-scale coronal fields. Here we provide the first identification of non-potential loop arcades exclusive to the QS supergranulation network. High-resolution Atmospheric Imaging Assembly data from the Solar Dynamics Observatory have allowed for the first observations of fine-scale S-shaped loop arcades spanning the network. We have investigated the magnetic footpoint flux evolution of these arcades from Heliospheric and Magnetic Imager data and find evidence of evolving footpoint flux imbalances accompanying the formation of these non-potential fields. The existence of such non-potentiality confirms that magnetic field dynamics leading to the build up of helicity exist at small scales. QS non-potentiality also suggests a self-similar formation process between the QS network and high temperature corona and the existence of self-organized criticality (SOC) in the form of loop-pair reconnection and helicity dissipation. We argue that this type of behavior could lead to eruptive forms of SOC as seen in active region (AR) and X-ray sigmoids if sufficient free magnetic energy is available. QS magnetic network dynamics may be considered as a coronal proxy at supergranular scales, and events confined to the network can even mimic those in coronal ARs.

TOMOGRAPHY OF PLASMA FLOWS IN THE UPPER SOLAR CONVECTION ZONE USING TIME-DISTANCE INVERSION COMBINING RIDGE AND PHASE-SPEED FILTERING

The consistency of time--distance inversions for horizontal components of the plasma flow on supergranular scales in the upper solar convection zone is checked by comparing the results derived using two k--\omega filtering procedures -- ridge filtering and phase-speed filtering -- commonly used in time--distance helioseismology. It is shown that both approaches result in similar flow estimates when finite-frequency sensitivity kernels are used. It is further demonstrated that the performance of the inversion improves (in terms of simultaneously better averaging kernel and lower noise level) when the two approaches are combined together in one inversion. Using the combined inversion I invert for horizontal flows in the upper 10 Mm of the solar convection zone. The flows connected with supergranulation seem to be coherent only in the upper ~5 Mm depth, deeper down there is a hint on change of convection scales towards structures larger than supergranules.

Time–distance inversions for horizontal and vertical flows on supergranular scales applied to MDI and HMI data

We study the possibility of consistent extension of MDI full-disc helioseismic campaigns with the growing data set of HMI observations. To do so, we down-sample and filter the HMI Dopplegrams so that the resulting spatial power spectrum is similar to the spatial power spectrum of MDI full-disc Dopplergrams. The set of co-spatial and co-temporal datacube pairs from both instruments containing no missing and no bad frames were processed using the same codes and inverted independently for all three components of the plasma flow in the near surface layers. The results from the two instruments are highly correlated, however systematically larger (by ~ 20%) flow magnitudes are derived from HMI. We comment that this may be an effect of the different formation depth of the Doppler signal from the two instruments.

DIFFUSION OF SOLAR MAGNETIC ELEMENTS UP TO SUPERGRANULAR SPATIAL AND TEMPORAL SCALES

The study of spatial and temporal scales on which small magnetic structures (magnetic elements) are organized in the quiet Sun may be approached by determining how they are transported on the solar photosphere by convective motions. The process involved is diffusion. Taking advantage of Hinode high spatial resolution magnetograms of a quiet Sun region at the disk center, we tracked 20145 magnetic elements. The large field of view (~50 Mm) and the long duration of the observations (over 25 hours without interruption at a cadence of 90 seconds) allowed us to investigate the turbulent flows at unprecedented large spatial and temporal scales. In the field of view, in fact, an entire supergranule is clearly recognizable. The magnetic elements displacement spectrum shows a double-regime behavior: superdiffusive (gamma=1.34 +/- 0.02) up to granular spatial scales (~1500 km), and slightly superdiffusive (gamma=1.20 +/- 0.05) up to supergranular scales.