Seismic tomography of the near solar surface

Surface gravity waves have been used to probe flows in the two megameters beneath the photosphere using the techniques of timedistance helioseismology. The results suggest that supergranule velocities are smaller than at the surface. The outward flow outside a sunspot penumbra (the moat) is observed, as is an inward flow in the region beyond the moat.     

Magnetic theories of solar flares

We have used the 512 channel diode array and vacuum telescope at KPNO to study the photospheric intensity distribution around sunspots, for comparison with isotherms predicted by convective blocking models of heat flow. Raster scan observations of 10 spots on 18 days were carried out in 1980 and 1981. Continuum passbands of 0.25 Å width were selected to avoid contamination by weak Fraunhofer lines, whose strength is sensitive to the presence of magnetic faculae often found near spots. Our observations show no evidence of extended bright rings around the spots at the level of 1–2%, as reported in one recent study using photographic photometry and much wider passbands. But 6 of the 10 spots we measured show marginally significant (2–3σ) bright rings of peak amplitude 0.1–0.3%. We are not able to explain these rings as a result of either residual facular signal, or instrumental effects. The excess radiative flux in these rings is small compared to the missing flux in the spot umbra and penumbra. We compare the brightness of the observed rings with peak brightnesses calculated from models of heat flow around spots of various depths and radii. Even if the spot is assumed to be unrealistically shallow, a detectable bright ring requires that the effective thermal conductivity (and/or its depth gradient) in layers surrounding the spot be significantly lower than the values indicated by mixing length models of the solar convection zone.     

Mass and energy flow near sunspots

New measurements of the velocities of moving magnetic features (MMFs) are made from spectroheliograms and filtergrams. The sample includes 200 MMFs found in the moats surrounding 7 different sunspots. Our data are compiled with the data from other authors to uncover common properties of moats. The moat radius is roughly twice the penumbral radius. No significant correlation between the average moat velocity or angular extent and any noted property of the spot or moat (size, age, stage of development) is found. Individual MMFs move radially outward with a constant speed, but nearby MMFs may have quite different speeds. The average moat speed is twice the supergranule flow speed. The speed of MMFs in moats is equal on average to the surface gas flow speed. A large bias is found in much of the existing observations of moat speeds from MMFs.     

High‐resolution observations of extremely bright penumbral grains

We observed a cluster of extremely bright penumbral grains located at the inner limb‐side penumbra of the leading sunspot in active region NOAA 10892. The penumbral grains in the cluster showed a typical peak intensity of 1.58 times the intensity I₀ of the granulation surrounding the sunspot. The brightest specimen even reached values of 1.8–2.0 I₀, thus, exceeding the temperatures of the brightest granules in the immediate surroundings of the sunspot. We find that the observed sample of extremely bright penumbral grains is an intermittent phenomenon, that disappears on time scales of hours. Horizontal flow maps indicating proper motions reveal that the cluster leaves a distinct imprint on the penumbral flow field. We find that the divergence line co‐located with the cluster is displaced from the middle penumbra closer towards the umbra and that the radial outflow velocities are significantly increased to speeds in excess of 2 km s^–1. The extremely bright penumbral grains, which are located at the inner limb‐side penumbra, are also discernible in offband Hα images down to Hα ± 0.045 nm. We interpret the observations in the context of the moving flux tube model arguing that hotter than normal material is rapidly ascending along the inner footpoint of the embedded flux tube, i.e., the ascending hot material is the cause of the extremely bright penumbral grains. This study is based on speckle‐reconstructed broad‐band images taken at 600 nm and chromospheric Hα observations obtained with two‐dimensional spectroscopy. All data were taken with adaptive optics under very good seeing conditions at the Dunn Solar Telescope, National Solar Observatory/Sacramento Peak, New Mexico on 2006 June 10. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Convection in a rotating deep compressible spherical shell: Application to the Sun

In this paper we study the interaction of rotation with convection in a deep compressible spherical shell as the Sun's convection zone. We examine how the energy transport and the large scale motions can be affected by rotation. In particular we study how a large scale meridional circulation can give rise to variations of angular velocity with latitude and depth.It is assumed that the energy transport is only due to convection and that the mixing-length theory gives an adequate representation of it. Furthermore we assume that rotation acts as a perturbation of the turbulent convective flux through its transport coefficient.The equations involved in the model are integrated numerically in the limit of large viscosity and slow rotation. After having expanded all physical quantities to the first order in terms of Legendre polynomials, the fitting with the observed solar differential rotation gives the expansion parameter, which represents the coupling constant between rotation and convection.The results show a three-cell circulation extending from the poles to the equator. The first one is located in the lower half of the convection zone with the fluid rising at the equator and sinking at the poles. In the second one the direction of the motion is reversed while the third one, located in a thin upper layer, shows the same characteristics of the first one. The meridional velocities at the surface are directed towards the poles and are about 20 cm s^-1. In the other cells the meridional velocities are typically of a few cm s^-1 while the radial velocities are of the order of a few tenths of cm s^-1.The heat flux relative variation at the surface is about 10^-4 (3 × 10^-3 at the bottom) with a polar excess. The temperature variation at the surface is of the same order, with an equatorial excess however. The convection seems to be stabilized stronger at the equator. The angular velocity increases inwards and varies about 6% between the surface and the bottom of the convection zone.An attempt is made for explaining the picture which emerges. In particular the negligible flux and temperature variations at the surface are explained in terms of equalization by the particular structure of the latitudinal flow. This configuration of large scale circulation is attributed to the high stratification of the convection zone with depth.     

A continuum bright point at the penumbral edge

A small continuum bright point, observed at the outer edge of the penumbra of a small spot in a large complex spot group, is related to an occurrence beneath the Sun's surface. The characteristics of the point appear to be unique, and the name penumbra-periphery bright point is proposed.     

The crossover effect in sunspots and the fine structure of penumbra

The peculiarities of magnetosensitive lines in the penumbral spectrum and the abnormal distribution of circular polarization in them are explained satisfactorily in terms of superposition of radiation originating in different elements of penumbral fine structure. Complicated asymmetric rv ^– contours can be represented as a sum of two components related to bright (BR) and dark (DR) penumbral regions. Crossover effect in sunspot penumbra appears, when there is considerable relative radial mass velocity in BR and DR, having the magnetic field of different polarities in them. Such conditions are supposed to exist in the penumbra of some sunspots, situated close to the solar limb.     

Moving Magnetic Features in and out of Penumbral Filaments

A time sequence of high-resolution SOHO/MDI magnetograms, Dopplergrams, and continuum images is used to study the moving magnetic features (MMFs) in and out of penumbral filaments. Precursors of MMFs have been observed inside the penumbral filaments. One hundred and fifteen out of 127 well-observed individual MMFs in the moat of two sunspots have been identified to have precursors at an average distance of 4″ inside the penumbral filaments. The velocity of these precursors is small inside the penumbral filaments and becomes large once the MMFs cross the outer penumbra. The paths followed by the MMFs exhibit large fluctuations in their magnetic field strength values, with an additional hike in the fluctuations near the outer penumbra. It is also observed that the path followed by the MMFs appear as a cluster of fibrils which could be traced back inside the penumbra. The appearance of MMFs and their azimuthal velocity is position and time dependent. Electronic Supplementary Material Electronic Supplementary Material is available for this article at     

Evolution of magnetic fields and mass flow in a decaying active region

Five days of coordinated observation were carried out from 24–29 September, 1987 at Big Bear and Huairou Solar Observatories. Longitudinal magnetic fields of an p sunspot active region were observed almost continuously by the two observatories. In addition, vector magnetic fields, photospheric and chromospheric Doppler velocity fields of the active region were also observed at Huairou Solar Observatory. We studied the evolution of magnetic fields and mass motions of the active region and obtained the following results: (1) There are two kinds of Moving Magnetic Features (MMFs). (a) MMFs with the same magnetic polarity as the center sunspot. These MMFs carry net flux from the spot, move through the moat, and accumulate at the moat's outer boundary. (b) MMFs in pairs of mixed polarity. These MMFs are not responsible for the decay of the spot since they do not carry away the net flux. MMFs in category (b) move faster than those of (a). (2) The speed of the mixed polarity MMFs is larger than the outflow measured by photospheric Dopplergrams. The uni-polar MMFs are moving at about the same speed as the Doppler outflow. (3) The chromospheric velocity is in approximately the opposite direction from the photospheric velocity. The photospheric Doppler flow is outward; chromospheric flow is inward. We also found evidence that downward flow appears in the photospheric umbra; in the chromosphere there is an upflow.     

Periodic and non-periodic phenomena in a sunspot region

We have studied running penumbral waves, the homogeneous Evershed effect, and the spatial relation between intensity and Doppler velocity penumbral features of a chromospheric sunspot. The observations were obtained with the multichannel subtractive double-pass spectrograph (MSDP) operating in H at the Vacuum Tower Telescope (VTT) installed at Tenerife (Canary Islands). We derived intensity and Doppler velocity maps at H ± 0.3 Å over a two-dimensional field of view. We have computed the components of the velocity vector (radial, azimuthal, vertical) as a function of distance from the center of the spot under the assumption of axial symmetry. The results show the well-known, from previous observations, general large-scale characteristics of the chromospheric Evershed flow. Our measurements show that the axes along the discrete structures, where the Evershed flow is confined, are not spatially related to the axes along H ± 0.3 Å intensity features, and we suggest that either the flow is confined in flow channels or that it takes place along sheared magnetic field lines. We also detected, for the first time in velocity images, running penumbral waves, which started in the outer 0.3 of the umbral radius and propagated through the penumbra with propagation velocities 13–24 km s^–1. The propagation velocity, as well as the velocity amplitude, is greater for the waves closer to the center of the spot and diminishes as one moves outward.     

Faculae and east-west asymmetry of sunspot area

Asymmetry of sunspot area with respect to the central meridian is found to depend strongly on the location of the spot group in its chromospheric facula or plage. The usual area excess for spots in the eastern half of the disk is reversed for the relatively rare spot groups situated in the following part of the plage. Qualitatively, the observed asymmetries can be explained by supposing that the apparent area of the spot is decreased by overlying bright facula, especially west of central meridian where the spot (in the usual preceding position) is viewed through the relatively bright and extensive follower part of the plage. However, the variation with central meridian distance of the mean area of spots and of faculae demands a more complex model, in which the spatial distribution of facula and plage also depends on the location of the spot group. Since both facula and spot effects are seen along the same line of sight, optical depth must change slowly with geometric depth, that is, in the active region the atmosphere is relatively transparent.     

On the chromospheric velocity field in sunspot regions

The wavelength shifts of approximately 8000 absorption elements in the H-line from spectra of 66 different sunspot regions have been measured.The average velocity field in the chromosphere close to sunspots is determined. Inside 15000 km from the spot's penumbral rim the average velocity vector is directed towards the spot and downwards in the chromosphere; the angle with the horizontal direction is on the average equal to 20°. The magnitude of the average velocity vector shows a maximum of 6.8 ± 1.2 km/sec just outside the penumbral rim and decreases quickly with increasing distance from the spot. Outside 15000 km from the penumbral rim the average velocity vector is small (-0.7 km/sec) and directed nearly vertically outwards from the sun. No significant tangential component of the average velocity field is found.The deviations of the individual elements from the average velocity field are on the average larger than the value of the average velocity. The total rms deviation in the line of sight velocity is equal to 6.8 km/sec. Thus, a large number of elements, as used in this investigation, is required to give significant values of the average velocity vector.We have also observed velocities in the penumbra. The average velocity vector is here probably small and its direction uncertain. The rms deviation in the line of sight velocities observed in the penumbra is equal to 7.5 km/sec.     

Meridional circulation and turbulence in surface layers of the stars

The meridional circulation is considered in the surface layers of the stars where the optical depth τ?1. It is shown that the radial component of circulation velocity reaches its maximum value at τ≈1 and decreases at τ→0. The tangential velocity reverses its sign at τ≈1 — i.e., the meridional flows are closed in stellar atmospheres. The tangential velocities can be of the order of 10⁶–10⁷ cm s^?1 in atmospheres of O-B-A stars. Such hydrodynamical motions can result in the generation of turbulence in the surface layers. Characteristic turbulent velocities are of the order of 10⁵–10⁶ cm s^?1 in early-type stars. The small-scale turbulent motions generate the acoustic waves and the flux of such waves may be the source of energy to heat coronae in O and B stars.     

Étude morphologique et cinématique des structures fines d'une tache solaire

A sequence of 34 photographs of the main spot of the group H 26 (Daily Maps of the Sun, Freiburg 1970, Rome number 5847) has been obtained with the 38 cm refractor of the Pic-du-Midi Observatory, showing throughout a resolution very close or equal to 0′'.3. An interval of 3 hr is covered. The pictures taken at intervals of 6 min approximately permit to study the fine structure of the penumbra and associated phenomena:

1. The penumbra appears to consist of bright grains, generally lined up in the form of filaments, showing up against a dark background (see Figure 1).
2. The bright grains form all over the penumbra (see Figure 5).
3. They move toward the umbra of the spot. Their horizontal velocity is zero at the border penumbra-photosphere and maximum at the umbral border (0.5 km s^?1) (see Figures 3,4 and 8). Therefore, the grains never originate in the photosphere nor do they enter it.
4. They disappear in the penumbra proper or, if they form near enough to the umbra and live long enough, they can enter the umbra and their appearance becomes similar to that of umbral dots.
5. The life time of the grains is a function of their place of origin within the penumbra: It is maximum and of the order of 3 hr or more for those forming in the middle part of the penumbra, and 50 and 40 min respectively for the points formed in the inner and outer part of the penumbra.

     

Oscillatory motions in sunspots

We observe vertical velocity oscillations in some sunspot umbrae with periods of about 180 s and peak to peak amplitudes up to 1 km s^–1. These oscillations are not visible in either the line depth, line width or the continuum intensity. No correlation seems to exist between the occurence of these oscillations and the presence of the chromospheric umbral flashes (Solar Phys. 7, 351, 1069). In the spot penumbra there is an indication of a long period oscillation, the period increasing from about 300 s in the inner penumbra to nearly 1000 s at the penumbra-photosphere boundary. An attempt has been made to interpret these oscillations in terms of gravity or acoustic waves, travelling along the magnetic field lines, taking into account the variation of scale height and magnetic field direction across the sunspot.     

Properties of spherical galaxies and clusters with an NFW density profile

Using the standard dynamical theory of spherical systems, we calculate the properties of spherical galaxies and clusters whose density profiles obey the universal form first obtained in high-resolution cosmological N -body simulations by Navarro, Frenk & White (NFW). We adopt three models for the internal kinematics: isotropic velocities, constant anisotropy and increasingly radial OsipkovMerritt anisotropy. Analytical solutions are found for the radial dependence of the mass, gravitational potential, velocity dispersion, energy and virial ratio and we test their variability with the concentration parameter describing the density profile and amount of velocity anisotropy. We also compute structural parameters, such as half-mass radius, effective radius and various measures of concentration. Finally, we derive projected quantities, the surface mass density and line-of-sight as well as aperture-velocity dispersion, all of which can be directly applied in observational tests of current scenarios of structure formation. On the mass scales of galaxies, if constant mass-to-light is assumed, the NFW surface density profile is found to fit HubbleReynolds laws well. It is also well fitted by Sérsic R ^{1/ m} laws, for     but in a much narrower range of m and with much larger effective radii than are observed. Assuming in turn reasonable values of the effective radius, the mass density profiles imply a mass-to-light ratio that increases outwards at all radii.     

Coronal prominences on the disk observed on 29 October 1972

A group of coronal prominences appeared over a large sunspot group near the central meridian on October 29, 1972. The bright points, which were most clearly seen on the H-image taken at the line center, are interpreted as the points of inflow of the prominence matter into the penumbra. The amount of mass transported by the largest prominence among the group is found to share a considerable fraction of the total mass which may be contained in the permanent coronal condensation over the spot group. The observational data for the microwave emission from the spot group is discussed in relation to this phenomenon.     

Black hole at the center of the globular cluster M15: Estimation of the mass and specific angular momentum

Using the technique of determining the sum of the masses of double stars, we have estimated the mass of the central object in the globular cluster M15. The radial velocities of stars at distances up to 1″ from the cluster center have been used. The parameters of circular orbits and the space velocities of 11 selected field stars relative to the cluster center have been determined from the calculated velocity dispersions with respect to the mean radial velocity. Based on the mean space velocity V, 14 km s^?1, and using the energy integral, we have estimated the mass of the central object to be within the range (1?9) × 10³ M _⊙. We have estimated the kinetic power of the outflow of matter from the region surrounding the black hole in M15 and the specific angular momentum of the black hole.     

The effects of mutual irradiation on the observed radial velocity of the components of close binary systems

The aim of the present paper will be to investigate the effects, on the observed radial velocities of the components of close binary systems, of atmospheric motions caused by mutual irradiation of the two stars. Such motions can (and, in general, will) produce systematic differences between the observed radial velocity and that of the centre of mass of the respective star — differences varying with with the phase and thus giving rise to spurious deformations of the star's radial-velocity curves due to orbital motion. A failure to separate the two could (and in general, will) vitiate the physical elements deduced from these curves —such as the masses or absolute dimensions of the components and of the shape of their orbit; but in order to do so, an investigation of atmospheric motions invoked by irradiation becomes a necessary prerequisite.In the Introduction following this abstract, the problem at issue will be described in general terms, and phenomena outlined which should arise in this connection (together with the observations indicating their presence). In Section 2, general expressions for the radial velocity at any point of stellar surface arising from atmospheric motions will be formulated while Section 3 will isolate such velocities for components of close binary systems as are produced by mutual irradiation of their mates, in terms of hydrodynamical equations of radiative transfer describing the problem. In Sections 4 and 5, the effects of non-rotational motions on the observed radial velocities will be specified, and hydrodynamical equations formulated which specify atmospheric convection caused by irradiation of each component of a close binary by its mate. Linearized versions of such equations will be constructed in Section 6; while Section 7 contains an evaluation of the effects which such gas streams exert on the observed radial velocity of the stars.In the concluding Section 8 applications to practical cases are carried out. It will be shown that no reliable spectroscopic elements of close binary systems (including the masses and absolute dimensions of their components) can be obtained until the effects of atmospheric convection caused by mutual irradiation have been accounted for to permit us to convert the observed radial velocities (influenced as they are by the motion of as in which they originate) to those of the centre of mass of the respective stars.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

The evershed flow in the transition region chromosphere-photosphere

The Mgb₁ line profile is studied as a function of spatial position in the sunspot region. Comparing the wavelengths of the core and the wing, in and just outside the penumbra, a reversal in the shift is detected. The displacements of the core and the wing are interpreted as horizontal motions directed into the spot in the chromosphere and as a flow directed out of the spot in deeper layers.Systematic wavelength shifts are detected in the line core in some regions outside the penumbra. This is interpreted as a chromospheric velocity field usually directed horizontally away from the spot.