Discrete cellular scales of solar convection

The theoretical power spectrum of velocity fields and flux fluctuations at the solar photosphere is calculated using a quasi-nonlinear framework of superposition of unstable convective eigenmodes excited in the solar convection zone. It is demonstrated that this power spectrum exhibits at least three distinct peaks corresponding to granulation, mesogranulation and supergranulation. The vertical velocity and the brightness fluctuation at the solar surface are found to be correlated. The theoretical framework can be adopted for application to other types of stars in order to predict the dominant length scales in the power spectrum of convection in these stars.     

Specifics of the solar photospheric convection at granulation,mesogranulation, and supergranulation scales

The power spectra of temperature and vertical velocity variations in the solar photosphere are calculated using the data obtained through observations of a nonperturbed region near the solar disk center in the neutral iron line λ ≈ 639.3 nm conducted at the 70 cm German Vacuum Tower Telescope (VTT) located in the Canary Islands (Spain). The variations of these spectra with altitude are analyzed. It is found that the primary power in the lower photosphere is localized in the range of frequencies that correspond to granulation with a peak at the λ ≈ 1.5–2.0 Mm scale and is reduced with altitude, the power spectrum maximum in the upper photospheric layers is shifted towards larger scales (Δλ ≤ 1 Mm), and the power of variations of the vertical supergranulation velocity (λ ≈ 20–30 Mm) virtually does not change with altitude. An isolated mesogranulation regime (λ ≈ 5–12 Mm) is not found at any of the studied altitudes. The obtained results suggest that the convective structure of the solar photosphere at mesogranulation scales behaves like granulation: the mesostructures are a part of an extended distribution of granulation scales. It is shown that the supergranulation flows are stable throughout the entire photosphere and reach much higher altitudes than the granulation flows.     

Inferring the depth extent of the horizontal supergranular flow

The 2D horizontal velocity field determined from local correlation tracking of granulation and its divergence have remarkably different appearances. The 2D horizontal velocity shows the classical 32 Mm supergranular cellular outflow bounded by the chromospheric network, whereas the divergence is dominated by distinct long-lived sources and sinks of about 7 Mm size. The 2D horizontal velocity shows no obvious evidence for 7 Mm cells, and the divergence exhibits little power with the 32 Mm scale. However, by mass continuity for a steady 3D flow in a stratified atmosphere, the divergence of the 2D horizontal component is equal to the vertical velocity divided by a height scale. Thus the 3D steady solar flow field at the bottom of the photosphere has a vertical component consisting primarily of 7 Mm sources and sinks, which define the 2D cellular-like 32 Mm continuous horizontal outflows.Simultaneous Doppler vertical velocity measurements verify the mass-continuity relation, and give a height scale equal to the density scale height in the photosphere within observational error. The observational result is consistent with our theoretical expectation. Any height scale other than the density scale height would indicate a vertical velocity thate-folds on a scale comparable to or smaller than the density scale height, which we argue is unphysical near the top of the convection zone. The continuity relation indicates that vortex-free steady horizontal velocities seen at the solar surface, i.e., the horizontal supergranular flow, must diminish with depth due to the increasing density scale height. We estimate that the horizontal supergranular flow cannot extend much more than onee-fold increase in the density scale height below the visible solar surface, about 2.4 Mm. Therefore the convection below the solar surface should be characterized by the scale of the principal steady vertical velocity component, i.e., by vertical plumes having a dimension of 7 Mm - what we have called mesogranulation - rather than closed 32 Mm cells as is widely believed.Operated by the Association of Universities for Research in Astronomy, Inc. (AURA) under cooperative agreement with National Science Foundation.     

Structure Properties of Supergranulation and Granulation

We investigate spatial dislocation ordering of the solar structures associated with supergranulation and granulation scales. The supergranular and granular structures are automatically segmented from time-distance divergence maps and from broad-band images, respectively. The spatial dislocation ordering analysis is accomplished by applying the statistical method of Pair Correlation Function, g ₂(r), to segmented features in the solar fields. We compare the computed g ₂(r) functions obtained from both single and persistent, i.e., time-averaged, fields associated with supergranulation and granulation. We conclude that supergranulation and granulation patterns present a different topological order both in single and persistent fields. The analysis carried out on single fields suggests that the granulation behaves as an essentially random distribution of soft plasma features with a very broad distribution in size, while supergranulation behaves as a random distribution of close packed, coherent stiff features with a rather defined mean size.     

Radial velocity field in the lower atmosphere of the solar active region during a flare with an ejection: The initial phase of the flare

Horizontal motion has been studied of the matter along the active region at different heights of the photosphere (115–580 km) in the initial phase of the two-ribbon solar flare on September 4, 1990, near the solar limb, accompanied by the ejection. Photospheric velocities varied in the range −3.5 ... 2.5 km/s. The direction of motion in the photosphere and the chromosphere was mainly toward the observer. Kinematic elements have been discovered in the structure of the horizontal velocity field. Their size reduced as they approached the maximum of the flare from 7–12 to 4–5 Mm, and the velocity amplitude decreased. Throughout the whole investigated active region, vortex motions were observed in the photosphere and chromosphere. Temporal changes in the horizontal velocity field in node areas and in their vicinity were oscillatory in nature and occurred almost simultaneously along the entire height of the photosphere.     

On convection in the sun

Convective motions driven by a superadiabatic temperature gradient in a viscous thermally conductive medium are considered. Approximate linearized equations governing the perturbation are derived under the following conditions: (i) The ratio of the excess temperature gradient over the adiabatic gradient is small compared with the gradient itself, (ii) The perturbation is of low-frequency type, (iii) The rotation is slow. Only the convective mode is described by these equations (as in the Boussinesq approximation), and the equations are valid for compressible configurations with any ratio between the scale heights of the equilibrium and perturbed quantities. Results of a numerical calculation of unstable perturbations for configurations with a large density stratification are given. They show that under conditions appropriate for the solar convection zone an extremely strong instability is expected to occur if the mixing length is assumed to be equal to 1.5 times the pressure scale height. The horizontal scale of the instability is intermediate between those of granulation and supergranulation. The larger the mixing length, the smaller the growth rate of the instability, and the larger its horizontal scale. Therefore it seems possible to adjust the mixing length to obtain the characteristics corresponding to those of the solar supergranulation. The possible origin of the granulation as an instability in a subsurface zone, where a local increase in the density scale height takes place, is also discussed. To achieve agreement with observations, it seems necessary to assume that the ratio of the mixing length to pressure scale height is an increasing function of the pressure.     

Overstability of acoustic modes and the solar five-minute oscillations

The stability of linear convective and acoustic modes in solar envelope models is investigated by incorporating the thermal and mechanical effects of turbulence through the eddy transport coefficients. With a reasonable value of the turbulent Prandtl number it is possible to obtain the scales of motion corresponding to granulation, supergranulation and the five-minute oscillations. Several of the acoustic modes trapped in the solar convection zone are found to be overstable and the most unstable modes, spread over a region centred predominantly around a period of 300 s with a wide range of horizontal length scales, are in reasonable accord with the observed power-spectrum of the five-minute oscillations. It is demonstrated that these oscillations are driven by a simultaneous action of the -mechanism and the radiative and turbulent conduction mechanisms operating in the strongly superadiabatic region in the hydrogen ionization zone, the turbulent transport being the dominant process in overstabilizing the acoustic modes.     

Radial velocities of the photospheric matter in a solar flare with matter ejection

We present results of a study of photospheric horizontal motions at the initial and main phases of the solar flare which happened on September 4, 1990, near the solar limb. The flare was accompanied by matter ejection. Spectra of the flare were obtained using the AZU-26 horizontal solar telescope at the MAO NAS (Terskol observatory). We found variations of the matter motion velocity’s value and direction at different stages of the photosphere during the flare development. The velocity changed in a range from −4 to 2 km/s. Comparisons of the obtained data with variations of the chromospheric radial velocities showed that the horizontal matter motions in the photosphere and chromosphere are mostly directed toward the observer but at particular time moments their direction changed. At two different knots, the time shift of the photospheric velocities is different. The highest velocities were observed at the main phase of the flare. At the initial phase of the flare, in the matter ejection region, we note a velocity increase compared with its preflare value and at the flare knots.     

Photospheric brightness differences associated with the solar supergranulation

The large scale (> 5000 km) intensity structure of the photosphere has been examined. The power per frequency unit indicates a continuous increase towards smaller spatial frequency. No excess power exists at wavelengths near the size of the supergranulation (30000 km) or at any other wavelength between 5000 and 100000 km. However, direct measurement of the intensity distribution in 1652 supergranulation cells shows a very small increase of the intensity towards the cell boundary. The amount of this increase is larger near the solar limb. It is probably due to a weak continuum emission associated with the chromospheric network. Any temperature difference arising from the supergranulation convection is obscured by this emission and is probably less than 1 K.     

What is the horizontal scale of the 5-min oscillations?

If wrong, all the early reports of a small horizontal scale ( 2000 km) for the 5-min oscillations may be due to unfortunate similarities between the velocity and overturning time of the solar granule convection and the corresponding velocity and period typical of the oscillations. A large horizontal scale ( 30000 km) for the oscillations seems consistent with the old data and almost required by more recent measurements. The large scales recently measured would imply that a sizeable fraction of the solar volume is involved in the oscillation and would cast some doubt on all the old theories of the 5-min oscillations which were based on plane parallel atmospheres.     

Simulating photospheric Doppler velocity fields

A method is described for constructing artificial data that realistically simulate photospheric velocity fields. The velocity fields include rotation, differential rotation, meridional circulation, giant cell convection, supergranulation, convective limb shift, p-mode oscillations, and observer motion. Data constructed by this method can be used for testing algorithms designed to extract and analyze these velocity fields in real Doppler velocity data.     

Convective instability in the solar envelope

The characteristics of the most unstable fundamental mode and the first harmonic excited in the convection zone of a variety of solar envelope models are shown to be in reasonable agreement with the observed features of granulation and supergranulation. On leave of absence from Government Digvijai College, Rajnandgaon 491441     

Comparisons of Supergranule Characteristics During the Solar Minima of Cycles 22/23 and 23/24

Supergranulation is a component of solar convection that manifests itself on the photosphere as a cellular network of around 35 Mm across, with a turnover lifetime of 1 – 2 days. It is strongly linked to the structure of the magnetic field. The horizontal, divergent flows within supergranule cells carry local field lines to the cell boundaries, while the rotational properties of supergranule upflows may contribute to the restoration of the poloidal field as part of the dynamo mechanism, which controls the solar cycle. The solar minimum at the transition from cycle 23 to 24 was notable for its low level of activity and its extended length. It is of interest to study whether the convective phenomena that influence the solar magnetic field during this time differed in character from periods of previous minima. This study investigates three characteristics (velocity components, sizes and lifetimes) of solar supergranulation. Comparisons of these characteristics are made between the minima of cycles 22/23 and 23/24 using MDI Doppler data from 1996 and 2008, respectively. It is found that whereas the lifetimes are equal during both epochs (around 18 h), the sizes are larger in 1996 (35.9 ± 0.3 Mm) than in 2008 (35.0 ± 0.3 Mm), while the dominant horizontal velocity flows are weaker (139 ± 1 m s⁻¹ in 1996; 141 ± 1 m s⁻¹ in 2008). Although numerical differences are seen, they are not conclusive proof of the most recent minimum being inherently unusual.     

Streamer Belt and Chains as the Main Sources of Quasi-Stationary Slow Solar Wind

Synoptic maps of white-light coronal brightness from SOHO/LASCO C2 and distributions of solar wind velocity obtained from interplanetary scintillation are studied. Regions with velocity V≈300 – 450 km s⁻¹ and increased density N>10 cm⁻³, typical of the “slow” solar wind originating from the belt and chains of streamers, are shown to exist at Earth’s orbit, between the fast solar wind flows (with a maximum velocity V _max≈450 – 800 km s⁻¹). The belt and chains of streamers are the main sources of the “slow” solar wind. As the sources of “slow” solar wind, the contribution from the chains of streamers may be comparable to that from the streamer belt.     

Some properties of convective motions in the upper solar atmosphere. II

Using a three-dimensional hydrodynamical model of the solar atmosphere, we calculated profiles of the Fe I λ 639.361 nm and Fe II λ 523.462 nm lines with consideration for deviations from the local thermodynamic equilibrium. We determined heights for intensity contrast reversal and for velocity sign reversal of convective elements. Both of these parameters depend strongly on the convective velocity and intensity measured in the continuum. The larger the parameters, the greater is the atmosphere altitude where the reversal takes place. We compared all the calculated relations with the observations obtained at the German Vacuum Tower Telescope in Izana (Tenerife, Spain). In our opinion, the 3D hydrodynamical model of the solar atmosphere satisfactorily describes all the main features of observed convective velocities and intensities.     

Searching for possible siblings of the sun from a common cluster based on stellar space velocities

We propose a kinematic approach to searching for the stars that could be formed with the Sun in a common “parent” open cluster. The approach consists in preselecting suitable candidates by the closeness of their space velocities to the solar velocity and analyzing the parameters of their encounters with the solar orbit in the past in a time interval comparable to the lifetime of stars. We consider stars from the Hipparcos catalog with available radial velocities. The Galactic orbits of stars have been constructed in the Allen-Santillan potential by taking into account the perturbations from the spiral density wave. We show that two stars, HIP 87382 and HIP 47399, are of considerable interest in our problem. Their orbits oscillate near the solar orbit with an amplitude of ≈250 pc; there are short-term close encounters to distances <10 pc. Both stars have an evolutionary status and metallicity similar to the solar ones.     

Convective velocities derived from granule contrast profiles in Fe i λ 6569.2

A new determination of the granular and intergranular velocities is described, based on a new approach. The method involves measurement of the granule/intergranule contrast as a function of wavelength on a sequence of filtergrams taken with the CSIRO computer-controlled 1/8 Å filter in the photospheric line Fe i 6569.2. A procedure based on a simple but realistic morphological model of the granulation pattern is used to correct for spatial smearing. The effects of spectral smearing and of scattered light are also taken into account.The present observations reveal a one hundred per cent correlation between brightness and the sense of the vertical velocity component and thus demonstrate beyond doubt the convective origin of the granulation. The new measurements yield a value of 1.8 km s^–1 for the difference between the upward and downward velocities associated with an average granule. With certain plausible assumptions this leads to granular and intergranular velocities of 0.7 km s^–1 (upward) and 1.1 km s^–1 (downward) respectively.Estimates are also obtained for the (true) central intensities and line broadening parameters of the line profile, separately for the average granule and intergranular lane.     

Testing Helioseismic-Holography Inversions for Supergranular Flows Using Synthetic Data

Supergranulation is one of the most visible length scales of solar convection and has been studied extensively by local helioseismology. We use synthetic data computed with the Seismic Propagation through Active Regions and Convection (SPARC) code to test regularized-least squares (RLS) inversions of helioseismic-holography measurements for a supergranulation-like flow. The code simulates the acoustic wavefield by solving the linearized three-dimensional Euler equations in Cartesian geometry. We model a single supergranulation cell with a simple, axisymmetric, mass-conserving flow. The use of simulated data provides an opportunity for direct evaluation of the accuracy of measurement and inversion techniques. The RLS technique applied to helioseismic-holography measurements is generally successful in reproducing the structure of the horizontal-flow field of the model supergranule cell. The errors are significant in horizontal-flow inversions near the top and bottom of the computational domain as well as in vertical-flow inversions throughout the domain. We show that the errors in the vertical velocity are due largely to cross talk from the horizontal velocity.     

Analysis of Supergranule Sizes and Velocities Using Solar Dynamics Observatory (SDO)/Helioseismic Magnetic Imager (HMI) and Solar and Heliospheric Observatory (SOHO)/Michelson Doppler Imager (MDI) Dopplergrams

Co-temporal Doppler images from Solar and Heliospheric Observatory (SOHO)/Michelson Doppler Imager (MDI) and Solar Dynamics Observatory (SDO)/Helioseismic Magnetic Imager (HMI) have been analyzed to extract quantitative information about global properties of the spatial and temporal characteristics of solar supergranulation. Preliminary comparisons show that supergranules appear to be smaller and have stronger horizontal velocity flows within HMI data than was measured with MDI. There appears to be no difference in their evolutionary timescales. Supergranule sizes and velocities were analyzed over a ten-day time period at a 15-minute cadence. While the averages of the time-series retain the aforementioned differences, fluctuations of these parameters first observed in MDI data were seen in both MDI and HMI time-series, exhibiting a strong cross-correlation. This verifies that these fluctuations are not instrumental, but are solar in origin. The observed discrepancies between the averaged values from the two sets of data are a consequence of instrument resolution. The lower spatial resolution of MDI results in larger observed structures with lower velocities than is seen in HMI. While these results offer a further constraint on the physical nature of supergranules, they also provide a level of calibration between the two instruments.     

Phase velocities of gravity waves in the solar photosphere

Space-time variations of pressure in the solar photosphere are reproduced based on the results of observations in the Fe I line. Local internal gravity waves (IGWs) are isolated by means of proper filtering. A method of determination of the phase velocities of IGWs based on 1D observations is developed. Horizontal and vertical projections of the phase velocities of isolated IGWs with different periods are determined. It is shown that the phase velocity of an IGW decreases significantly with a decrease in oscillation frequency. The horizontal wavelengths of gravity waves with periods ranging from 5 to 60 minutes are commensurable with the granulation scales. The dispersive properties of gravity waves are studied.