Supergranular Flows Research Articles

Recurrence of fragmenting granules and their relation to meso- and supergranular flow fields

The 3D analysis ( x , y , t ) of the granulation intensity field (11-hour time sequence from Swedish Vacuum Solar Telescope on La Palma, Canary Islands), demonstrated that the granules in the phostosphere are organized in `` Trees of Fragmenting Granules (TFGs). A TFG consists of a family of repeatedly splitting granules, issued from one granule at its beginning. A striking result is that TFGs can live much longer (up to 8h10) than individual granules (10 mn). When averaged in time, such long-lived TFGs can be identified to the mesogranules. We also found a correlation between the network and the spatial distribution of TFGs.

Statistical Flux Tube Properties of 3D Magnetic Carpet Fields

The quiet-Sun photosphere consists of numerous magnetic flux fragments of both polarities that evolve with granular and supergranular flow fields. These concentrations give rise to a web of intermingled magnetic flux tubes which characterise the coronal magnetic field. Here, the nature of these flux tubes is studied. The photosphere is taken to be the source plane and each photospheric fragment is represented by a series of point sources. By analysing the potential field produced by these sources, it is found that the distribution of flux tube lengths obtained by (i) integrating forward from positive sources and (ii) tracing back from negative sources is highly dependent on the total flux imbalance within the region of interest. It is established that the relation between the footpoint separation of a flux tube and its height cannot be assumed to be linear. Where there is a significant imbalance of flux within a region, it is found that fragments of the dominant polarity will have noticeably more connections, on average, than the minority polarity fragments. Despite this difference, the flux from a single fragment of either polarity is typically divided such that (i) 60–70% connects to one opposite-polarity fragment, (ii) 25–30% goes to a further 1 to 2 opposite-polarity fragments, and (iii) any remaining flux may connect to as many as another 50 or more other opposite-polarity fragments. This is true regardless of any flux imbalance within the region. It is found that fragments connect preferentially to their nearest neighbours, with, on average, around 60–70% of flux closing down within 10 Mm of a typical fragment. Only 50% of the flux in a quiet region extends higher than 2.5 Mm above the solar surface and 5–10% extends higher than 25 Mm. The fragments that contribute to the field above this height cover a range of sizes, with even the smallest of fragments contributing to the field at heights of over 50 Mm.

Radial Flows in Supergranules

We determine the radial component of the supergranular flow velocity by examining the center-to-limb variation of the Doppler velocity signal. We acquire individual Doppler images obtained with the MDI instrument on the SOHO spacecraft and process them to remove the p-mode oscillation signal, the axisymmetric flows, the convective blueshift signal, and instrumental artifacts. The remaining Doppler signal contains only non-axisymmetric flow structures. The Doppler signal from the horizontal flows in these structures varies like sin ρ, where ρ is the heliocentric angle from disk center. The Doppler signal from radial flows varies like cos ρ. We fit the center-to-limb variation of the mean squared velocity signal to a straight line in sin2 ρ over the central portion of the disk. The intercept of this line at disk center gives the amplitude of the radial component of the flow. The slope of the line gives the amplitude of the horizontal component. We find that the radial flows for typical supergranules have speeds about 10% that of their associated horizontal flows or about 30 m s−1. The ratio of the radial to horizontal flow speed increases from 9% to about 18% as the size of the structure decreases from > 60 Mm to ∼ 5 Mm. We use data simulations to check these results and find a ratio that increases from 5% to only about 12% over the same range of sizes. These smaller ratios are attributed to an underestimation of the horizontal flow speeds due to the fact that the transverse component of the horizontal flow is not detected by Doppler measurements.

Stellar differential rotation from direct star-spot tracking

On the Sun, the rotation periods of individual sunspots not only trace the latitude-dependence of the surface rotation rate, but also provide clues as to the amount of subsurface fluid shear. In this paper we present the first measurements of stellar differential rotation made by tracking the rotation of individual star-spots with sizes comparable to the largest sunspots. To achieve this we re-analyse four sequences of densely sampled, high signal-to-noise ratio echelle spectra of AB Doradus spanning several stellar rotations in 1996 December. Using spectral subtraction, least-squares deconvolution and matched-filter analysis, we demonstrate that it is possible to measure directly the velocity amplitudes and rotation periods of large numbers of individual star-spots at low to intermediate latitude. We derive values for the equatorial rotation rate and the magnitude of the surface differential rotation, both of which are in excellent agreement with those obtained by Donati & Collier Cameron from cross-correlation of Doppler images derived a year earlier in 1995 December, and with a re-analysis of the 1996 data by the Χ 2 landscape method. The differences between the rotation rates of individual spots and the fitted differential rotation law are substantially greater than the observational errors. The smaller spots show a greater scatter about the mean relation than the larger ones, which suggests that buffeting by turbulent supergranular flows could be responsible.

Sustaining the Sun’s Magnetic Network with Emerging Bipoles

The Michelson Doppler Imager experiment on SOHO has revealed a carpet dominated by the emergence of bipolar magnetic flux in ephemeral active regions, which subsequently split into small flux elements that drift into the magnetic network. The effects of granular and supergranular convection on these flux elements are represented here by kinematic modeling: Elementary flux tubes are transported passively by the supergranular flow, while experiencing small random displacements produced by granulation. They end up in the magnetic network that surrounds the supergranules, where they eventually meet oppositely directed fields and are annihilated. The model calculations show that the total unsigned magnetic flux will decay within a few days unless it is continually replenished. A statistically steady state with a total unsigned flux of 2-3 × 1023 Mx over the whole solar surface can be maintained if bipolar flux emerges at a rate of 7 × 1022 Mx day-1, as indicated by published measurements of the rate at which ephemeral active regions appear.

New approach to study extended evolution of supergranular flows and their advection of magnetic elements

Using velocity and magnetogram data extracted from the full-disk field of view of MDI during the 1999 Dynamics Program, we have studied the dynamics of small-scale magnetic elements (3–7 Mm in size) over time periods as long as six days while they are readily visible on the solar disk. By exploiting concurrent time series of magnetograms and Doppler images, we have compared the motion of magnetic flux elements with the supergranular velocity field inferred from the correlation tracking of mesogranular motions. Using this new method (which combines the results from correlation tracking of mesogranules with detailed analysis of simultaneous magnetograms), it is now possible to correlate the motions of the velocity field and magnetic flux for long periods of time and at high temporal resolution. This technique can be utilized to examine the long-term evolution of supergranulation and associated magnetic fields, for it can be applied to data that span far longer time durations than has been possible previously. As tests of its efficacy, we are able to use this method to verify many results of earlier investigations. We confirm that magnetic elements travel at approximately 350 m s −1 throughout the duration of their lifetime as they are transported by supergranular outflows. We also find that the positions of the magnetic flux elements coincide with the supergranular network boundaries and adjust as the supergranular network itself evolves over the six days of this data set. Thus we conclude that this new method permits us to study the extended evolution of the supergranular flow field and its advection of magnetic elements. Since small-scale magnetic elements are strongly advected by turbulent convection, their dynamics can give important insight into the properties of the subsurface convection.

On the Origin of Magnetic Fields in the Quiet Photosphere

We consider the possibility that a substantial fraction of the magnetic field in the quiet photosphere is generated locally by dynamo action associated with the granular and supergranular flows. The argument is based on recent advances in the theory of fast dynamos and is supported by large-scale numerical simulations that show that thermally driven turbulent convection can indeed be an efficient source of small-scale, highly intermittent magnetic fields. Some aspects of the resulting magnetic field, such as its strength and degree of intermittency, are discussed.

Time Series of Solar Granulation Images. II. Evolution of Individual Granules

The properties of the evolution of solar granulation have been studied using an 80 minute time series of high spatial resolution white-light images obtained with the Swedish Vacuum Solar Telescope at the Observatorio del Roque de los Muchachos, La Palma. An automatic tracking algorithm has been developed to follow the evolution of individual granules, and a sample of 2643 granules has been analyzed. To check the reliability of this automatic procedure, we have manually tracked a sample of 481 solar granules and compared the results of both procedures. An exponential law gives a good fit to the distribution of granular lifetimes, T. Our estimated mean lifetime is about 6 minutes, which is at the lower limit of the ample range of values reported in the literature. We note a linear increase in the time-averaged granular sizes and intensities with the lifetime. T=12 minutes marks a sizeable change in the slopes of these linear trends. Regarding the location of granules with respect to the meso- and supergranular flow field, we find only a small excess of long-lived granules in the upflows. Fragmentation, merging, and emergence from (or dissolution into) the background are the birth and death mechanisms detected, resulting in nine granular families from the combination of these six possibilities. A comparative study of these families leads to the following conclusions: (1) fragmentation is the most frequent birth mechanism, while merging is the most frequent death mechanism; (2) spontaneous emergence from the background occurs very rarely, but dissolution into the background is much more frequent; and (3) different granular mean lifetimes are determined for each of these families; the granules that are born and die by fragmentation have the longest mean lifetime (9.23 minutes). From a comparison of the evolution of granules belonging to the most populated families, two critical values appear for the initial area in a granular evolution: 0.8 Mm2 (dg=139) and 1.3 Mm2 (dg=177). These values mark limits characterizing the birth mechanism of a granule, and predict its evolution to some extent. The findings of the present work complement the earlier results presented in this series of papers and reinforce with new inputs, as far as the evolutionary aspects are concerned, the conclusion stated there that granules can be classified into two populations with different underlying physics. The boundary between these two classes could be established at the scale of dg=14.

Dispersal of Magnetic Flux in the Quiet Solar Photosphere

We study the random walk of magnetic flux concentrations on two sequences of high-resolution magnetograms, observed with the Michelson Doppler Imager on board SOHO. The flux contained in the concentrations ranges from |Φ|=1018 Mx to |Φ|=1019 Mx, with an average of |Φ|=2.5×1018 Mx. Larger concentrations tend to move slower and live longer than smaller ones. On short timescales, the observed mean-square displacements are consistent with a random walk, characterized by a diffusion coefficient D(t<10 ks)=70-90 km2 s−1. On longer timescales, the diffusion coefficient increases to D(t>30 ks)=200-250 km2 s−1, approaching the measurements for a five-day set of Big Bear magnetograms, D≃250 km2 s−1. The transition between the low and large diffusion coefficients is explained with a model and simulations of the motions of test particles, subject to random displacements on both the granular and supergranular scales, simultaneously. In this model, the supergranular flow acts as a negligible drift on short timescale, but dominates the granular diffusion on longer timescales. We also investigate the possibility that concentrations are temporarily confined, as if they were caught in supergranular vertices, that form short-lived, relatively stable environments. The best agreement of model and data is found for step lengths of 0.5 and 8.5 Mm, associated evolution times of 14 minutes and 24 hr, and a confinement time of no more than a few hours. On our longest timescale, DSim(t>105)→285 km2 s−1, which is the sum of the small- and large-scale diffusion coefficients. Models of random walk diffusion on the solar surface require a larger value: DWang=600±200 km2 s−1. One possible explanation for the difference is a bias in our measurements to the longest lived, and therefore slower concentrations in our data sets. Another possibility is the presence of an additional, much larger diffusive scale.

Velocities in Solar Pores

We use high spatial and spectral resolution filtergrams to examine the three-dimensional morphology and velocity fields associated with solar pores in a region of newly emerged magnetic flux. The observed amplitude of the horizontal surface velocities decreases near the pores. Most of the pores exhibit a downflow in the surrounding region. Time-averaged line-of-sight velocities in and near the pores increased with the strength of the associated magnetic field. The LOS velocities are such that the maximum downflow is not centered about the continuum intensity and sometimes traces an annulus ringlike structure around the pore. From a time sequence of continuum images, it appears that some pores shed flux at the photospheric level. Cork movies of the surface velocities show that the are advected toward weak downflows near the pore locations and that the loci of the advected corks trace boundaries that resemble mesogranular and supergranular flows. We analyze the vertical velocity structure in pores and show that the downflow decreases exponentially with height, with a scale height that is a factor of 2 smaller than the photospheric scale height for granules. The line-of-sight flow associated with the pores appears to expand with height. Our observations are compared with previous measurements of flows in and around pores that were based on both spectrograms and filtergrams. Finally, we provide a phenomenological description for pores.

Time-distance helioseismology

The time-distance helioseismology (or helioseismic tomography) is a new promising method for probing 3-D structures and flows beneath the solar surface, which is potentially important for studying the birth of active regions in the sun's interior and for understanding the relation between the internal dynamics of active regions and chromospheric and coronal activity. In this method, the time for waves to travel along subsurface ray paths is determined from the temporal cross correlation of signals at two separated surface points. By measuring the times for many pairs of points from Dopplergrams covering the visible hemisphere, a tremendous quantity of information about the state of the solar interior is derived. As an example, we present the results for supergranular flows and for an active region which emerged near the center of the solar disk in July 1996, and was studied from SOHO/MDI for nine days, both before and after its emergence at the surface. Initial results show a complicated structure of the emerging region in the interior, and suggest that the emerging flux ropes travel very quickly through the depth range of our observations.

Network Activity and the Evaporative Formation of Polar Plumes

It has previously been suggested that polar plumes are generated and maintained by strong, localized heating within coronal holes and that this heating is somehow associated with the interaction between small magnetic bipoles and nearby unipolar flux concentrations. These ideas are used here as the basis of a model for the formation and evolution of coronal plumes. The energy deposition rate in a plume is taken to be proportional to the rate at which magnetic flux becomes reconnected to the nearby monopole as the poles of the bipole are separated by the supergranular flow field. The heat input is conducted down to the base of the newly opened flux tube (located at the majority-polarity end of the bipole), where a small fraction of the energy goes into lifting chromospheric gas into the corona, while the rest is radiated away. The evaporation timescale (?evap${r evap}$ -->$t SUBgt {r evap}t/SUBgt $ --> ~6 hr) represents the characteristic time for a new plume to form following the emergence of a bipole. Once flux exchange between the bipole and the unipolar flux concentration ceases, the plume decays on the radiative cooling timescale ?cool${r cool}$ -->$t SUBgt {r cool}t/SUBgt $ --> ~4 hr. In the absence of new bipole eruptions, the total lifetime of a plume is found to be 12-24 hr. The model accounts for the quiescent nature of polar plumes and the tendency for the diffuse plume emission to strengthen as the underlying bright network features disperse and decay.

Real-Time Frame Selector and its Application to Observations of the Horizontal Velocity Field in the Solar Photosphere

A real-time frame selector (RTFS), a new observational system, was developed at the Domeless Solar Telescope of Hida Observatory, Kyoto University. Our RTFS allows us to automatically select out a video frame with the highest spatial resolution in a series of live video images during a prescribed time span, and stores the selected one in digital format to a hard disk file. We applied the RTFS to observations of solar granulation in the G-band wavelength (λ 4308 Å, passband 20 Å) and obtained a time series of data with a step of 15 seconds. By the method of local-correlation tracking, we derived the horizontal velocity field with the granulation pattern as tracers. In a quiet photosphere, we found the so-called mesogranulation flow field, clearly. Supergranular flow patterns were also detected and identified from a comparison with an Hα wing image. On the other hand, in a sunspot area, we found new evidence of horizontal inflow from penumbral areas to umbral areas as well as the presence of another circumferential inflow from the surrounding photosphere to the penumbral outer edge.

On the Patterns of the Solar Granulation and Supergranulation

We study the cellular patterns of the white light granulation and of the chromospheric Ca II K supergranular network. We apply a gradient-based tessellation algorithm to define the cell outlines. The geometry of the patterns formed by the associated granular and supergranular flows are very similar, in spite of the substantial difference in length scale. We compare these patterns to generalized Voronoi foams and conclude that both convective patterns are very nearly compatible with an essentially random distribution of upflow centers, with the downflow boundaries determined by the competing strengths of outflows of neighboring upwellings. There appears to be a slight clustering in upflow positions for the granulation, consistent with the granular evolution. This slight preference for large granules to be surrounded by somewhat smaller ones makes the granular and supergranular patterns differ enough to allow a correct identification in three out of four cases by eye. The model analogy suggests that the range in outflow strengths is remarkably small. The patterns appear to be rather insensitive to the details of the competing forces that establish the pattern of the downflow network: similar patterns result under very different conditions, so that little can be learned about the details of the forces involved by studying the geometry of these patterns only.

Simulating exploding granules and mesogranular flows

Cellular convective motion at the solar surface can be simulated by a suitable distribution of axisymmetric sources /1/. With this model we represent randomly distributed exploding granules or mesogranules. The effect of a given velocity field on the magnetic field is modelled by inserting test particles (“corks”) and following their resultant motions. An important question raised by the observations is whether mesogranular flows are generated entirely by exploding granules which recur in approximately the same location or whether there is a persistent underlying circulation. Our model calculations suggest that a combination of systematic cellular motion on a mesogranular scale and recurrent exploding granules located near the mesogranular centers is compatible with observed magnetic structures. We also generate randomly-distributed exploders not tethered to mesogranular sites, and the resulting cork patterns do not resemble those observed on the solar surface. Finally we introduce a large-scale persistent supergranular flow which transports the mesogranules and exploders towards the supergranular network and obtain patterns not unlike those seen on the Sun.

Vertical flows of supergranular and mesogranular scale observed on the sun with OSO 8

A program of observations was carried out in order to study the penetration of supergranular flows over a broad range of heights in the solar atmosphere. Steady Doppler velocities are determined from observations of a Si II spectral line using the Ultraviolet Spectrometer on the Orbiting Solar Observatory 8 (OSO 8) satellite and Fe I and Mg I lines with the diode-array instrument on the vacuum telescope at Sacramento Peak Observatory (SPO). The heights of formation of these spectral lines span about 1400 km or nearly 11 density scale heights from the photosphere to the middle chromosphere. Steady vertical flows on spatial scales typical of supergranulation and mesogranulation have been detected in the middle chromosphere with OSO 8. The patterns of intensity and steady velocity of granular scale are reproducible in successive data sets. The patterns appear to evolve slowly over the 9 hr period spanned by six orbits.

The detection of mesogranulation on the sun

Time averages of velocity measurements at disk center on the quiet sun reveal the presence of a fairly stationary pattern of cellular flow with a spatial scale of 5-10 Mm. Such mesogranulation has a spatial rms vertical velocity amplitude of about 60 m/s superposed on the larger scale supergranular flows. The lifetimes of mesogranules appear to be at least 2 hr.

Mechanical wave-energy fluxin magnetoatmospheres: Discrete and continuous spectra

This paper deals with a rather general class of magnetoatmospheres — media for which the restoring forces of buoyancy, compressibility and magnetic tension/pressure are important in sustaining wave motion. The magnetic field has the general form (B0(z), 0,0) and there is also an aligned shear flow (U0(z), 0, 0) present. After discussion of the equilibrium and stability of such systems, and certain mathematical properties of a particular system (an isothermal atmosphere with uniform magnetic field, of interest in solar physics), theory is developed which enables expressions to be written down for the mechanical wave energy flux associated with wave motion due to a transient source. These analytic expressions are very general and contain contributions from the continuous and discrete frequency spectra, corresponding respectively to freely propagating and trapped (or surface) waves. These fluxes are evaluated for various ranges of magnetic field, horizontal wavenumber, characteristic source times and frequency, for a simple constant-parameter atmosphere. The source is taken to be a transient fluctuation of the lower boundary, (modelling convective overshoot) which is taken to be located at the level τ5000=0.08 in the solar atmosphere. The relative distribution of wave energy flux in the various modes is discussed in the context of solar physics parameters. The possible significance of ‘leaky’ modes arising from supergranular or other flow, for the local flux balance in the solar chromosphere is outlined.

Supergranulation and the dynamics of gas and magnetic field below the solar photosphere

We suggest that the scale of supergranular flow may simply reflect the depth dapprox. =1.5 x 10/sup 4/ km below the photosphere over which the magnetic field occupies a relatively small volume and the nonmagnetic fluid is allowed to convect and rotate freely. If magnetic buoyancy is important in bringing flux to the photosphere from a deep region of either primordial or dynamo field, then a sharp increase of magnetic flux inward below the photosphere is required to satisfy a simple continuity argument. It is remarkable that the angular velocity of the nonmagnetic fluid seems to increase with depth over this supergranular layer at the rate expected if angular momentum per unit mass is conserved in radial convection. From this rotation law in the supergranular layer, we suggest that the effective eddy viscosity ..nu.. at this scale exceeds 10/sup 11/ cm/sup 2/ s/sup -1/. This means that large values of viscosity in the range ..nu..> or approx. =10/sup 13/ cm/sup 2/ s/sup -1/ may be reasonable in dynamical models of deep (d> or =10/sup 5/ km) convection on the Sun. We demonstrate that the radial gradient of the rotation velocity in the nonmagnetic gas is capable of bending flux tubesmore » that extend upward through this supergranular layer through an angle which agrees closely with that inferred from observations by Howard. If this inferred tilt of the photospheric fields were ascribed to the torque of the interplanetary field, it would imply a rate of loss of angular momentum from the Sun exceeding by two orders of magnitude the value estimated from the rate of mass loss in the solar wind at the present epoch.« less

Hydrodynamic instability of convectively unstable atmospheres in shear flow

Results are presented concerning the interaction between regions of convectively unstable fluid, bounded above and below by stable fluid, with a basic horizontal flow field, sheared in a vertical direction. The analysis is conveniently based on the definition of the mechanical energy flux associated with wave motion in a stratified compressible fluid, and enables bounds to be placed on the real and complex phase velocities of overstable modes, in addition to some general results on the net upward wave energy flux. It is shown that purely exponentially growing modes (with horizontal wavevectors spanwise to the shear) do not exist. A known sufficient condition for the stability of stable atmospheres is reproduced here with an interesting modification, and details of energy-flux discontinuities at certain singular points of the equations are given. The work is relevant to any astrophysical and geophysical situations in which convectively unstable regions and shear flows are likely to be together present, but the special motivation here is that of describing some aspects of the interaction between supergranular flow and granular convection.