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NASA NTRS1973

Convection and magnetic fields in an atmosphere with constant temperature gradient. I - Hydrodynamic flows

In order to deduce the fluid and field conditions deep in the supergranules from the fluid motions and magnetic fields observed in the solar photosphere, it is necessary to have some idea of the depth to which the supergranules extend and the form of their internal fluid velocities. Toward this end a number of analytic solutions of the Navier-Stokes equations are given for circumstances possessing various facets of the supergranule environment in the sun. These solutions, together with the earlier work by others, shows that the granules extend to depths in excess of their mean diameters, that the convective velocities probably do not diminish much, if any, with depth, and that across the tops of the supergranules at the photosphere the horizontal velocity is more or less independent of depth.

Parker, E. N.↗
NASA NTRS1995

Kinematic models of supergranular diffusion on the Sun

We develop kinematic models of diffusion generated by supergranulation at the solar surface. These models use current observations for the size, horizontal velocity, and lifetime of supergranules. Because there is no observational description of the appearance and disappearance of supergranules, we investigate models using several plausible evolution processes, including the effect of different lifetime distribution functions for the cells. The results are quite insensitive to the methods chosen to replace old supergranules, the distribution of cell lifetimes, and even the cell lifetime itself, for mean lifetimes between 15 to 30 hr. Calculated diffusion coefficients range between 500 and 700 sq km/s, in agreement with the best fit diffusion coefficients used by Sheeley and his collaborators to model the large-scale distribution of magnetic fields over the solar surface. However, our models do not explain the field distribution in plage, and they predict that virtually all the strong field in quiet Sun exists in relatively isolated clumps. We suggest possible mechanisms for the creation of plage and the bright network seen in quiet Sun.

Simon, G. W.↗
NASA NTRS2012

Subsurface Supergranular Vertical Flows as Measured Using Large Distance Separations in Time-Distance Helioseismology

As large-distance rays (say, 10 - 24deg) approach the solar surface approximately vertically, travel times measured from surface pairs for these large separations are mostly sensitive to vertical flows, at least for shallow flows within a few Mm of the solar surface. All previous analyses of supergranulation have used smaller separations and have been hampered by the difficulty of separating the horizontal and vertical flow components. We find that the large-separation travel times associated with supergranulation cannot be studied using the standard phase-speed filters of time-distance helioseismology. These filters, whose use is based upon a refractive model of the perturbations, reduce the resultant travel time signal by at least an order of magnitude at some distances. More effective filters are derived. Modeling suggests that the center-annulus travel-time difference [outward-going time minus inward-going time] in the separation range delta= 10 - 24deg is insensitive to the horizontally diverging flow from the centers of the supergranules and should lead to a constant signal from the vertical flow. Our measurement of this quantity, 5.1+/-0.1 seconds, is constant over the distance range. This magnitude of the signal cannot be caused by the level of upflow at cell centers seen at the photosphere of 10 ms(exp−1) extended in depth. It requires the vertical flow to increase with depth. A simple Gaussian model of the increase with depth implies a peak upward flow of 240 ms(exp−1) at a depth of 2.3 Mm and a peak horizontal flow of 700 ms(exp−1) at a depth of 1.6 Mm.

convection↗
NASA NTRS2001

Coronal Heating and the Magnetic Flux Content of the Network

Previously, from analysis of SOHO coronal images in combination with Kitt Peak magnetograms, we found that the quiet corona is the sum of two components: the large-scale corona and the coronal network. The large-scale corona consists of all coronal-temperature (T approximately 10(exp 6) K) structures larger than supergranules (greater than approximately 30,000 kilometers). The coronal network (1) consists of all coronal-temperature structures smaller than supergranules, (2) is rooted in and loosely traces the photospheric magnetic network, (3) has its brightest features seated on polarity dividing lines (neutral lines) in the network magnetic flux, and (4) produces only about 5% of the total coronal emission in quiet regions. The heating of the coronal network is apparently magnetic in origin. Here, from analysis of EIT coronal images of quiet regions in combination with magnetograms of the same quiet regions from SOHO/MDI and from Kitt Peak, we examine the other 95% of the quiet corona and its relation to the underlying magnetic network. We find: (1) Dividing the large-scale corona into its bright and dim halves divides the area into bright "continents" and dark "oceans" having spans of 2-4 supergranules. (2) These patterns are also present in the photospheric magnetograms: the network is stronger under the bright half and weaker under the dim half. (3) The radiation from the large-scale corona increases roughly as the cube root of the magnetic flux content of the underlying magnetic network. In contrast, the coronal radiation from an active region increases roughly linearly with the magnetic flux content of the active region. We assume, as is widely held, that nearly all of the large-scale corona is magnetically rooted in the network. Our results suggest that either the coronal heating in quiet regions has a large non-magnetic component, or, if the heating is predominantly produced via the magnetic field, the mechanism is significantly different than in active regions.

Falconer, D. A.↗
NASA NTRS2001

Coronal Heating and the Magnetic Flux Content of the Network

Previously, from analysis of SOHO/EIT coronal images in combination with Kitt Peak magnetograms (Falconer et al 1998, ApJ, 501, 386-396), we found that the quiet corona is the sum of two components: the e-scale corona and the coronal network. The large-scale corona consists of all coronal-temperature (T approx. 10(exp 6) K) structures larger than supergranules (>approx.30,000 km). The coronal network (1) consists of all coronal-temperature structures smaller than supergranules, (2) is rooted in and loosely traces the photospheric magnetic network, (3) has its brightest features seated on polarity dividing fines (neutral lines) in the network magnetic flux, and (4) produces only about 5% of the total coronal emission in quiet regions. The heating of the coronal network is apparently magnetic in origin. Here, from analysis of EIT coronal images of quiet regions in combination with magnetograms of the same quiet regions from SOHO/MDI and from Kitt Peak, we examine the other 95% of the quiet corona and its relation to the underlying magnetic network. We find: (1) Dividing the large-scale corona into its bright and dim halves divides the area into bright "continents" and dark "oceans" having spans of 2-4 supergranules. (2) These patterns are also present in the photospheric magnetograms: the network is stronger under the bright half and weaker under the dim half. (3) The radiation from the large-scale corona increases roughly as the cube root of the magnetic flux content of the underlying magnetic network. In contrast, Fisher et A (1998, ApJ, 508, 985-998) found that the coronal radiation from an active region increases roughly linearly with the magnetic flux content of the active region. We assume, as is widely held, that nearly all of the large-scale corona is magnetically rooted in the network. Our results, together with the result of Fisher et al (1999), suggest that either the coronal heating in quiet regions has a large non-magnetic component, or, if the heating is predominantly produced via the magnetic field, the mechanism is significantly different than in active regions. This work is funded by NASA's Office of Space Science through the Solar Physics Supporting Research and Technology Program and the Sun-Earth Connection Guest Investigator Program.

Falconer, D. A.↗
NASA NTRS2004

Flows in the Solar Convection Zone

Flows within the solar convection zone are the primary drivers of the Sun's magnetic activity cycle. Differential rotation stretches out the magnetic field and converts poloidal fields into toroidal fields. Zones of strong radial shear are found at both the surface and at the base of the convection zone (the tachocline). The poleward meridional flow near the surface transports magnetic flux that is observed to reverse the magnetic poles near the time of cycle maxima. The deeper (and as yet unobserved), equatorward meridional flow should carry magnetic flux toward the equator where it reconnects with oppositely directed fields in the other hemisphere. The non-axisymmetric flows (granules, supergranules, and giant cells) also transport magnetic flux but in a more random, diffusive, manner. Supergranules and giant cells also play significant roles in driving the large-scale, axisymmetric flows themselves. The effect of solar rotation on supergranulation produces the shear layer near the surface and enhances the meridional flow. The effect of solar rotation on giant cells should produce the latitudinal differential rotation, the shear in the tachocline, and the meridional circulation. In this presentation I will describe the observed and theorized characteristics of the flows in the solar convection zone and discuss their connections to the solar activity cycle.

Hathaway, D. H.↗
NASA NTRS2010

Flux Transport and the Sun's Global Magnetic Field

The Sun s global magnetic field is produced and evolved through the emergence of magnetic flux in active regions and its transport across the solar surface by the axisymmetric differential rotation and meridional flow and the non-axisymmetric convective flows of granulation, supergranulation, and giant cell convection. Maps of the global magnetic field serve as the inner boundary condition for space weather. The photospheric magnetic field and its evolution determine the coronal and solar wind structures through which CMEs must propagate and in which solar energetic particles are accelerated and propagate. Producing magnetic maps which best represent the actual field configuration at any instant requires knowing the magnetic field over the observed hemisphere as well as knowing the flows that transport flux. From our Earth-based vantage point we only observe the front-side hemisphere and each pole is observable for only six months of the year at best. Models for the surface magnetic flux transport can be used to provide updates to the magnetic field configuration in those unseen regions. In this presentation I will describe successes and failures of surface flux transport and present new observations on the structure, the solar cycle variability, and the evolution of the flows involved in magnetic flux transport. I find that supergranules play the dominant role due to their strong flow velocities and long lifetimes. Flux is transported by differential rotation and meridional flow only to the extent that the supergranules participate in those two flows.

Hathaway, David H.↗
NASA NTRS2012

Subsurface Supergranular Vertical Flows as Measured Using Large Distance Separations in Time-Distance Helioseismology

As large-distance rays (say, 10-24 deg) approach the solar surface approximately vertically, travel times measured from surface pairs for these large separations are mostly sensitive to vertical flows, at least for shallow flows within a few Mm of the solar surface. All previous analyses of supergranulation have used smaller separations and have been hampered by the difficulty of separating the horizontal and vertical flow components. We find that the large separation travel times associated with upergranulation cannot be studied using the standard phase-speed filters of time-distance helioseismology. These filters, whose use is based upon a refractive model of the perturbations,reduce the resultant travel time signal by at least an order of magnitude at some distances. More effective filters are derived. Modeling suggests that the center-annulus travel time difference in the separation range 10-24 deg is insensitive to the horizontally diverging flow from the centers of the supergranules and should lead to a constant signal from the vertical flow. Our measurement of this quantity for the average supergranule, 5.1 s, is constant over the distance range. This magnitude of signal cannot be caused by the level of upflow at cell centers seen at the photosphere of 10 m/s extended in depth. It requires the vertical flow to increase with depth. A simple Gaussian model of the increase with depth implies a peak upward flow of 240 m/s at a depth of 2.3 Mm and a peak horizontal flow of 700 m/s at a depth of 1.6 Mm.

Duvall, T. L., Jr.↗
NASA NTRS1974

Hydraulic concentration of magnetic fields in the solar photosphere. I - Turbulent pumping

Observations suggest that most of the magnetic flux through the solar photosphere is concentrated in vertical filaments in the supergranule boundaries. Each filament appears to contain about 3 times 10 to the 18-th power maxwells, in the form of a field of 500 gauss or more, over a diameter of 700 km or less. The magnetic energy density in the filaments is 100 times the observed kinetic energy density of the observed supergranule motions, but comparable to the kinetic energy density of the granules. Force-free field configurations cannot duplicate the observational numbers, nor can such cooling effects as are believed responsible for the intense fields in sunspot umbrae. We point out a simple hydraulic mechanism (turbulent pumping) that appears to account for the observed concentration of fields.

Parker, E. N.↗
NASA NTRS1976

The EUV chromospheric network in the quiet sun

Investigations on the structure and intensity of the chromospheric network from quiet solar regions have been carried out with EUV data obtained with a spectroheliometer on the Apollo Telescope Mount of Skylab. The distribution of intensities within supergranulation cell interiors follows a near-normal function, where the standard deviation exceeds the value expected from the counting rate, which indicates fine-scale structure below the 5 arcsec resolution of the data. The intensities from the centers of supergranulation cells appear to be the same in both quiet regions and coronal holes, although the network is significantly different in the two types of regions. The average halfwidth of the network elements was measured as 10 arcsec and was independent of the temperature of formation of the observing line for effective-temperature logarithms (log Te) from 3.8 to 5.8. The contrast between the network and the centers of cells is greatest for lines with log Te about equal to 5.2, where the network contributes approximately 75% of the intensity of quiet solar regions. The contrast and fractional-intensity contributions decrease to higher and lower temperatures characteristic of the corona and chromosphere.

Reeves, E. M.↗
NASA NTRS1985

Channeled propagation of solar particles

Bartley (1966) and McCracken and Ness (1966) identified bundles of interplanetary magnetic field (IMF) lines that differed in direction from the interplanetary field lines in which they were imbedded. These bundles, called filaments differed in direction by as much as several tens of degrees from the surrounding field. The filaments werre first noticed due to the large and sudden change in flow direction of highly anisotropic solar flare protons in the energy range 1 to 13 MeV. Passage of the filaments over the spacecraft required a few hours, implying a diameter for the filaments of approximately 3 x 10 to the 6th power km at a distance of 1 AU from the Sun. In 1968, Jakipii and Parker used Leighton's hypothesis of random walk of magnetic field lines associated with granules and supergranules (1964) to develop a picture of an interplanetary medium composed of a tangle of field lines frozen into the solar wind, but whose feet were carried about by the random motions at the solar surface. Jakipii and Parker noted that using a correlation length of 15,000 km - about the radius of a supergranule - the magnetic structure would be 3 x 10 to the 6th power km in size of the filaments as determined by Bartley and McCracken and Ness. These workers did not find changes in the solar particle intensity, anisotropy ratio or energy spectrum as the spacecraft entered the filament.

Anderson, K. A.↗
NASA NTRS1988

Temporal filters for isolating steady photospheric flows

A variety of temporal filters are tested on artificial data with 60 and 75 s sampling intervals to determine their accuracy in separating the nearly-steady photospheric flows from the p-mode oscillations in Doppler velocity data. Longer temporal averages are better at reducing the residual signal due to p-modes but they introduce additional errors from the rotation of the supergranule pattern across the solar disk. Unweighted filters (boxcar averages) leave residual rms errors of about 6 m/s from the p-modes after 60 min of averaging. Weighted filters, with nearly Gaussian shapes, leave similar residual errors after only 20 min of averaging and introduce smaller errors from the rotation of the supergranule pattern. The best filters found are weighted filters that use data separated by 150 or 120 s so that the p-modes are sampled at opposite phases.

Hathaway, David H.↗
NASA NTRS1989

Do mesogranules exist?

The application of spatial and temporal averaging techniques to several long sequences of Dopplergrams obtained at the solar disk center and near the limb confirmed the persistent supergranule velocity pattern. After excluding the 5-min oscillation and supergranule velocity fields from the disk center Doppler data, it is found that the velocity structure shows a typical scale of 7 Mm, consistent with the scale of mesogranules found by November, Toomre, and Gebbie (1981) and November et al. (1982). However, this velocity pattern does not show properties of the cellular convection. It is proposed that the mesogranule velocity structure found by November et al. might be the uncorrected part of the 5-min oscillations and granule velocity.

Wang, Haimin↗
NASA NTRS1991

Power spectra of solar convection

The properties of convective motions on the sun are studied using Kitt Peak Doppler images and power spectra of convection. The power peaks at a scale of about 29,000 km and drops off smoothly with wavenumber. There is no evidence of apparent energy excess at the scale of the mesogranulation proposed by other authors. The vertical and horizontal power for each wavenumber are obtained and used to calculate the vertical and horizontal velocities of the supergranulation. The amplitude of vertical and horizontal velocities of the supergranulation are 0.034 (+ or - 0.002) km/s and 0.38 (+ or - 0.01) km/s, respectively. The corresponding rms values are 0.024 (+ or - 0.002) km/s and 0.27 (+ or - 0.01) km/s.

Chou, D.-Y.↗
NASA NTRS1992

Spherical harmonic analysis of steady photospheric flows. II

The use of the spherical harmonic functions to analyze the nearly steady flows in the solar photosphere is extended to situations in which B(0) the latitude at disk center, is nonzero and spurious velocities are present. The procedures for extracting the rotation profile and meridional circulation are altered to account for the seasonal tilt of the sun's rotation axis toward and away from the observer. A more robust and accurate method for separating the limb shift and meridional circulation signals is described. The analysis procedures include the ability to mask out areas containing spurious velocities (velocity-like signals that do not represent true flow velocities in the photosphere). The procedures are shown to work well in extracting the various flow components from realistic artificial data with a broad, continuous spectrum for the supergranulation. The presence of this supergranulation signal introduces errors of a few m/s in the measurements of the rotation profile, meridional circulation, and limb shift from a single Doppler image.

Hathaway, David H.↗
NASA NTRS1996

Observing large-scale solar surface flows with GONG: Investigation of a key element in solar activity buildup

The Global Oscillation Network Group (GONG) solar telescope network has begun regular operations, and will provide continuous Doppler images of large-scale nearly-steady motions at the solar surface, primarily those due to supergranulation. Not only the Sun's well-known magnetic network, but also flux diffusion, dispersal, and concentration at the surface appear to be controlled by supergranulation. Through such magnetoconvective interactions, magnetic stresses develop, leading to solar activity. We show a Doppler movie made from a 45.5 hr time series obtained 1995 May 9-10 using data from three of the six GONG sites (Learmonth, Tenerife, Tucson), to demonstrate the capability of this system.

Beck, John G.↗
NASA NTRS1998

Mesogranulation as A Distinct Scale of Convection in the Sun

We present evidence for the existence of mesogranulation as a scale of convection distinct from granulation and supergranulation through analysis of full-disk Doppler velocity images of the Sun collected by the Michelson Doppler Imager (MDI) aboard the NASA/ESA Solar and Heliospheric Observatory (SOHO). Our analysis procedures isolate nearly steady flows in the solar photosphere and yield power spectra of convection for spherical harmonic degrees up to I = 1000. Each spectrum exhibits an obvious supergranulation peak at I approximately 130 and a broad secondary peak at I approximately 600 with a distinct break in the spectrum between these peaks at I approximately 300. We believe that this secondary peak is a signature of mesogranulation with typical cell diameters of about 7 Mm. Our standard analysis procedure is to first remove the p-mode oscillation signal by averaging individual Dopplergrams over 17-minute intervals. Next, by fitting to standard functional forms we remove Doppler signals due to the motion of the spacecraft, the convective blueshift, solar rotation including differential rotation, and the meridional circulation in order to produce Dopplergrams dominated by convective motions. By mapping these processed images onto heliographic coordinates and projecting onto spherical harmonics, we produce a power spectrum of solar convection for each 17-minute period. We construct synthetic images and pass them through the same analysis procedure in order to determine the actual solar convection spectrum that reproduces the analyzed results. We find that a small but increasing percentage of high-degree convective power is lost in the analysis as we approach the limit of resolution of the detector but'that the broad, mesogranulation peak at I approximately 600 must be included in the convection spectrum of the synthetic images.

Bachmann, Kurt T.↗
NASA NTRS1999

Large-Scale Coronal Heating from the Solar Magnetic Network

In Fe 12 images from SOHO/EIT, the quiet solar corona shows structure on scales ranging from sub-supergranular (i.e., bright points and coronal network) to multi- supergranular. In Falconer et al 1998 (Ap.J., 501, 386) we suppressed the large-scale background and found that the network-scale features are predominantly rooted in the magnetic network lanes at the boundaries of the supergranules. The emission of the coronal network and bright points contribute only about 5% of the entire quiet solar coronal Fe MI emission. Here we investigate the large-scale corona, the supergranular and larger-scale structure that we had previously treated as a background, and that emits 95% of the total Fe XII emission. We compare the dim and bright halves of the large- scale corona and find that the bright half is 1.5 times brighter than the dim half, has an order of magnitude greater area of bright point coverage, has three times brighter coronal network, and has about 1.5 times more magnetic flux than the dim half These results suggest that the brightness of the large-scale corona is more closely related to the large- scale total magnetic flux than to bright point activity. We conclude that in the quiet sun: (1) Magnetic flux is modulated (concentrated/diluted) on size scales larger than supergranules. (2) The large-scale enhanced magnetic flux gives an enhanced, more active, magnetic network and an increased incidence of network bright point formation. (3) The heating of the large-scale corona is dominated by more widespread, but weaker, network activity than that which heats the bright points. This work was funded by the Solar Physics Branch of NASA's office of Space Science through the SR&T Program and the SEC Guest Investigator Program.

Falconer, David A.↗