Differential rotation,meridional and random motions of the solar Ca+ network

From high precision computer controlled tracings of bright Ca⁺-mottles we investigated differential rotation, meridional and random motions of these chromospheric fine structures. The equatorial angular velocity of the Ca⁺-mottles agrees well with that of sunspots (14°.50 per day, sidereal) and is 5 % higher than for the photosphere. The slowing down with increasing latitude is larger than for sunspots. Hence in higher latitudes Ca⁺-mottles rotate as fast as the photospheric plasma. A systematic meridional motion of about 0.1 km s^–1 for latitudes around 10° was found. The Ca⁺-mottles show horizontal random motions due to the supergranular flow pattern with an rms velocity of about 0.15 km s^–1. We finally investigated the correctness of the solar rotation elements i and derived by Carrington (1863).     

Meridional flow of small photospheric magnetic features

We study the meridional flow of small magnetic features, using high-resolution magnetograms taken from 1978 to 1990 with the NSO Vacuum Telescope on Kitt Peak. Latitudinal motions are determined by a two-dimensional crosscorrelation analysis of 514 pairs of consecutive daily observations from which active regions are excluded. We find a meridional flow of the order of 10 m s^–1, which is poleward in each hemisphere, increases in amplitude from 0 at the equator, reaches a maximum at mid-latitude, and slowly decreases poleward. The average observed meridional flow is fit adequately by an expansion of the formM () = 12.9(±0.6) sin(2) + 1.4(±0.6) sin(4), in m s^–1 where is the latitude and which reaches a maximum of 13.2 m s^–1 at 39°. We also find a solar-cycle dependence of the meridional flow. The flow remains poleward during the cycle, but the amplitude changes from smaller-than-average during cycle maximum to larger-than-average during cycle minimum for latitudes between about 15° and 45°. The difference in amplitude between the flows at cycle minimum and maximum depends on latitude and is about 25% of the grand average value. The change of the flow amplitude from cycle maximum to minimum occurs rapidly, in about one year, for the 15–45° latitude range. At the highest latitude range analyzed, centered at 52.5°, the flow is more poleward-than-average during minimumand maximum, and less at other times. These data show no equatorward migration of the meridional flow pattern during the solar cycle and no significant hemispheric asymmetry. Our results agree with the meridional flow and its temporal variation derived from Doppler data. They also agree on average with the meridional flow derived from the poleward migration of the weak large-scale magnetic field patterns but differ in the solar-cycle dependence. Our results, however, disagree with the meridional flow derived from sunspots or plages.Operated by the Association of Universities for Research in Astronomy, Inc. under cooperative agreement with the National Science Foundation.     

Dependence of the meridional motions of sunspot groups on life spans and age of the groups,and on the phase of the solar cycle

We have analyzed data on sunspot groups compiled during 1874–1981 and investigated the following: (i) dependence of the `initial' meridional motion (v <sub>ini</sub>()) of sunspot groups on the life span () of the groups in the range 2–12 days, (ii) dependence of the meridional motion (v(t)) of sunspot groups of life spans 10–12 days on the age (t) of the spot groups, and (iii) variations in the mean meridional motion of spot groups of life span 2–12 days during the solar cycle. In each of the latitude intervals 0°–10°, 10°–20° and 20°–30°, the values of both v <sub>ini</sub>() and v(t) often differ significantly from zero. In the latitude interval 20°–30°, the forms of v <sub>ini</sub>() and v(t) are largely systematic and mutually similar in both the north and south hemispheres. The form of v(t) suggests existence of periodic variation in the solar meridional motion with period of 4 days and amplitude 10–20 m s<sup>–1</sup>. Using the anchoring depths of magnetic structures for spot groups of different and testimated earlier, (Javaraiah and Gokhale, 1997), we suggest that the forms of v <sub>ini</sub>() and v(t) may represent radial variation of meridional flow in the Sun's convection zone, rather than temporal variation of the flow. The meridional flows (v <sub>e</sub>(t)) determined from the data during the last few days (i.e., age t: 10–12 days) of spot groups of life spans of 10–12 days are found to have magnitudes (10–20 m s<sup>–1</sup>) and directions (poleward) similar to the those of the surface meridional plasma flows determined from the Dopplergrams and magnetograms. The mean meridional velocity of sunspot groups living 2–12 days seems to vary during the solar cycle. The velocity is not significantly different from zero during the rising phase of the cycle and there is a suggestion of equatorward motion (a few m s<sup>–1</sup>at lower latitudes and 10 m s<sup>–1</sup>at higher latitudes) during the declining phase (last few years) of the cycle. The variation during the odd numbered cycles seems to anticorrelate with the variation during the even numbered cycles, suggesting existence of 22-year periodicity in the solar meridional flow. The amplitude of the anticorrelation seems to be depending on latitude and the cycle phase. In the latitude interval 20°–30° the `surface plasma meridional motion', v _e(t), is found to be poleward during maximum years (v _e(t) 20 m s^–1at 4th year) and equatorward during ending years of the cycle (v _e(t) –17 m s^–1at 10th year).     

Large-scale motions in the sun

Large-scale solar motions comprise differential rotation (with latitudinal, and perhaps radial gradients), axially symmetric meridional motions, and possible asymmetric motions (giant convective cells or Rossby-type waves or both). These motions must be basic in any satisfactory theory of the changing pattern of solar magnetic fields and of the 22-yr cycle. In the present paper available data are discussed and, as far as possible, evaluated and explained.Rotational measurements are based on the changing positions of discrete features such as sunspots, on Doppler shifts, on geophysical changes and on statistical evaluation of the motions of diffuse objects. The first mentioned, comprising faculae, sunspots, K-corona (to latitudes 45°) and filaments, show agreement better than 0.7 %. A new formula for surface rotation _s , based on faculae and sunspot data, is _s = 14.52 – 2.48 sin² b – 2.51 sin⁶ b deg day^–1, where b is latitude, and validity may extend to about 70°. Errors in Doppler shift measurements and statistical treatments are discussed. There is evidence of a much slower coronal rate at high latitudes, and of a slower sub-surface rate at lower latitudes.Ordered meridional motions have been revealed by statistical investigations of the positions of spot groups, of spots and of filaments. All these results seem explicable in terms of an oscillating hydro-magnetic circulation in each hemisphere. These have both 11-yr and 22-yr components, and these periods are provided by a general dipole field of about one gauss, together with a pair of toroidal fields centred at latitudes ±16° and of average strength of order 10 G.Evidence of large-scale (perhaps 3 × 10⁵ km), irregular surface motions is provided by the distribution of surface magnetic flux, the motions of sunspots, and Doppler-shift observations; it is supported by Ward's theory of the equatorial acceleration. The possibility is suggested that these asymmetric motions also drive the oscillatory meridional motions.     

Large-scale convection cells in the solar atmosphere

The directions and velocities of meridional plasma motions are investigated using Doppler shifts of the magnetically non-split line Fe 557.6 nm. Possible drifts of the spectrograph were controlled by measuring nearly iodine lines from a laboratory source. The scattered light was kept low by using the Capri Coudé refractor mainly around local noon.There is a general scatter of about ±20 to ±50 m s^–1 in the yearly mean results. The scatter is up to –200 m s^–1 for the year 1985. The results are compared with published data. Although some systematic meridional plasma motions could be detected from the average of the meridional flows within the whole observing period 1982 until 1986, the final analysis suggests, that all meridional motions averaged over half a solar cycle are below ±10 m s^–1.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.This paper has also been presented at the IAU Colloquium No. 121Inside the Sun andAstronomy and Astrophysics 229, 224 (1990).     

The relationship between meridional drift and rotation of the large-scale solar magnetic field

The pattern of torsional oscillations was detected in the rotation of the large-scale magnetic field using the method of two-dimensional correlation functions. The position of areas of fast and slow rotation agrees with the Doppler picture obtained by Ulrich et al. (1988). The torsional wave amplitude is 20–40 ms^–1 and increases with latitude. A strong correlation of the pattern of residual E-W rate with the meridional drift pattern, obtained from the same data, was determined. The sign of correlation is consistent with the results reported by Ward (1965).     

Meridional motions of magnetic features in the solar photosphere

We cross-correlate pairs of Mt. Wilson magnetograms spaced at intervals of 24–38 days to investigate the meridional motions of small magnetic features in the photosphere. Our study spans the 26-yr period July 1967–August 1993, and the correlations determine longitude averages of these motions, as functions of latitude and time. The time-average of our results over the entire 26-yr period is, as expected, antisymmetric about the equator. It is poleward between 10° and 60°, with a maximum rate of 13 m s^–1, but for latitudes below ±10° it is markedly equatorward, and it is weakly equatorward for latitudes above 60°. A running 1-yr average shows that this complex latitude dependence of the long-term time average comes from a pattern of motions that changes dramatically during the course of the activity cycle. At low latitudes the motion is equatorward during the active phase of the cycle. It tends to increase as the zones of activity move toward the equator, but it reverses briefly to become poleward at solar minimum. On the poleward sides of the activity zones the motion is most strongly poleward when the activity is greatest. At high latitudes, where the results are more uncertain, the motion seems to be equatorward except around the times of polar field reversal. The difference-from-average meridional motions pattern is remarkably similar to the pattern of the magnetic rotation torsional oscillations. The correspondence is such that the zones in which the difference-from-average motion is poleward are the zones where the magnetic rotation is slower than average, and the zones in which it is equatorward are the zones where the rotation is faster.Our results suggest the following characterization: there is a constant and generally prevailing motion which is perhaps everywhere poleward and varies smoothly with latitude. On this is superimposed a cycle-dependent pattern of similar amplitude in which the meridional motions of the small magnetic features are directed away from regions of magnetic flux concentration. This is suggestive of simple diffusion, and of the models of Leighton (1964) and Sheeley, Nash, and Wang (1987). The correspondence between the meridional motions pattern and the torsional oscillations pattern in the magnetic rotation suggests that the latter may be an artifact of the combination of meridional motion and differential rotation.     

Meridional drift in the large-scale solar magnetic field pattern

A method of two-dimensional correlation functions has been applied to a sequence of synoptic maps of the large-scale magnetic field to obtain the meridional drift pattern of field structures. The meridional drift profile obtained is antisymmetric about the equator. The meridional drift is directed from the equator to the poles at latitudes below 45°. A maximum drift velocity of 11–13 m s^–1 is attained in the latitude range 30°. A picture of the space-time distribution of meridional drift is also obtained, which may be interpreted as resulting from the effect of azimuthal convective rolls (3 rolls per hemisphere) on the large-scale magnetic field. Rolls originate at high latitudes following the cycle maximum, and migrate equatorwards until the minimum of the next cycle. The picture in the equatorial region can correspond to convective rolls with lifetimes of about two years, or to the process of interaction of rolls from two hemispheres.     

E-W motions of large-scale magnetic field structures of the sun

By applying a new method of processing daily full-disk magnetograms obtained at the Wilcox Solar Observatory at Stanford University, it has become possible to reveal the pattern of global E-W motions of field structures which appears to reflect large-scale convective plasma motions beneath the photosphere.Structures of E-W velocity of different sign extend from north to south, traversing the equator. The extent of the structures in longitude is 25°–45°, and the velocity amplitude reaches 0°.4–0°.5 day^-1 (60–70 m s^-1 at the equator). Boundaries of E-W flows of different sign correlate with strong, large-scale magnetic field hills. The lifetime of the velocity structures is comparable with that of magnetic field structures.     

The concentration of the large-scale solar magnetic field by a meridional surface flow

We calculate analytical and numerical solutions to the magnetic flux transport equation in the absence of new bipolar sources of flux, for several meridional flow profiles and a range of peak flow speeds. We find that a poleward flow with a broad profile and a nominal 10 m s^–1 maximum speed concentrates the large-scale field into very small caps of less than 15° half-angle, with average field strengths of several tens of gauss, contrary to observations. A flow which reaches its peak speed at a relatively low latitude and then decreases rapidly to zero at higher latitudes leads to a large-scale field pattern which is consistent with observations. For such a flow, only lower latitude sunspot groups can contribute to interhemispheric flux annihilation and the resulting decay and reversal of the polar magnetic fields.     

Solar rotation measurements at Mount Wilson

The ears velocity pattern described in Paper I (Howard et al., 1980) had no physical explanation. A reanalysis shows that the large scale solar velocity patterns are better described by a nonmonotonic limbshift and a meridional flow. The results of the new analysis imply that the study of solar velocity pattern at the level of a few ms^–1 required that magnetic regions be treated separately from nonmagnetic regions.Now at: Institute for Astronomy, University of Hawaii, Honolulu, Hawaii 96822, U.S.A.     

Additional electron flux detection after magnetic perturbations

An additional electron flux at an energy above 100 MeV was observed in the experiments carried out with high-altitude balloons flown at geomagnetic latitudes 46° and 49°, in the upper layers of the atmosphere, on the days following magnetic perturbations.Its intensity, equal to 6 × 10^–2 cm^–2s^–1 sr^–1, decreased over 20–30 hours. The effect observed confirms the presence of high-energy electrons in the regions of the trapped radiation.     

Large-scale solar velocity fields

Daily observations of Doppler line shifts made with very low spatial resolution (3) with the Stanford magnetograph have been used to study the equatorial rotation rate, limb effect on the disk, and the mean meridonial circulation. The equatorial rotation rate was found to be approximately constant over the interval May 1976–January 1977 and to have the value 2.82 rad s^–1 (1.96 km s^–1). This average compares favorably with the results of Howard (1977) of 2.83 rad s^–1 for the same time period. The RMS deviation of the daily measurements about the mean value was 1% of the rate (20 m s^–1), much smaller than the fluctuations reported by Howard and Harvey (1970) of several per cent. These 1% fluctuations are uncorrelated from day-to-day and may be due to instrumental problems. The limb effect on the disk was studied in equatorial scans (after suppressing solar rotation). A redshift at the center of the disk relative to a position 0.60R from the center of 30 m s^–1 was found for the line Fe i 5250 Å. Central meridian scans were used (after correcting for the limb effect defined in the equatorial scans) to search for the component of mean meridonial circulation symmetric across the equator. A signal is found consistent with a polewards flow of 20 m s^–1 approximately constant over the latitude range 10–50°. Models of the solar differential rotation driven by an axisymmetric meridonial circulation and an anisotropic eddy viscosity (Kippenhahn, 1963; Cocke, 1967; Köhler, 1970) predict an equatorwards flow at the surface. However, giant cell convection models (Gilman, 1972, 1976, 1977) predict a mean polewards flow (at the surface). The poleward-directed meridonial flow is created as a by-product of the giant cell convection and tends to limit the differential rotation. The observation of a poleward-directed meridonial circulation lends strong support to the giant cell models over the anisotropic eddy viscosity models.Now at Kitt Peak National Observatory, Tucson, Ariz., U.S.A.     

Explosive events in the solar transition zone

The properties of explosive events in the solar transition zone are presented by means of detailed examples and statistical analyses. These events are observed as regions of exceptionally high velocity ( 100 km s^–1) in profiles of Civ, formed at 10⁵ K, observed with the High Resolution Telescope and Spectrograph (HRTS). The following average properties have been determined from observations obtained during the third rocket flight of the HRTS: full width at half maximum extent along the slit - 1.6 × 10³ km; maximum velocity - 110 km s^–1; peak emission measure - 4 × 10⁴¹ cm^–3; lifetime - 60 s; birthrate - 4 × 10^–21 cm^–2 s^–1 in a coronal hole and 1 × 10^–20 cm^–2 s^–1 in the quiet Sun; mass - 6 × 10⁸ g; and, kinetic energy - 6 × 10²² erg. The 6 examples show that there are considerable variations from these average parameters in individual events. Although small, the events show considerable spatial structure and are not point-like objects. A spatial separation is often detected between the positions of the red and blue shifted components and consequently the profile cannot be explained by turbulence alone. Mass motions in the events appear to be isotropic because the maximum observed velocity does not show any correlation with heliographic latitude. Apparent motions of the 100 km s^–1 plasmas during their 60 s lifetime should be detected but none are seen. The spatial frequency of occurrence shows a maximum near latitudes of 40–50°, but otherwise their sites seem to be randomly distributed. There is enough mass in the explosive events that they could make a substantial contribution to the solar wind. It is hard to explain the heating of typical quiet structures by the release of energy in explosive events.     

The decay of the mean solar magnetic field

We have analyzed the effects that differential rotation and a hypothetical meridional flow would have on the evolution of the Sun's mean line-of-sight magnetic field as seen from Earth. By winding the large-scale field into strips of alternating positive and negative polarity, differential rotation causes the mean-field amplitude to decay and the mean-field rotation period to acquire the value corresponding to the latitude of the surviving unwound magnetic flux. For a latitudinally broad two-sector initial field such as a horizontal dipole, the decay is rapid for about 5 rotations and slow with a t ^–1/2 dependence thereafter. If a poleward meridional flow is present, it will accelerate the decay by carrying the residual flux to high latitudes where the line-of-sight components are small. The resulting decay is exponential with an e-folding time of 0.75 yr (10 rotations) for an assumed 15 m s^–1 peak meridional flow speed.E.O. Hulburt Center for Space Research.Laboratory for Computational Physics.     

An attempt to compare the differential rotation of the Ca+-network with that of the photospheric plasma

In this third paper of a series we report on results obtained from almost simultaneous observations of the differential rotation of the Ca⁺-chromosphere and the photospheric plasma. The observations (tracings of Ca⁺-mottles, Doppler-shift-measurements in a photospheric line) were performed at the Locarno station during two extended periods in 1976. Both data sets were used to search for a large scale circulation pattern. A regular long-lived pattern could not be detected, but a single cell with radial outflow (40 ms^-1) extending over more than 50° in longitude has been found. Statistically significant temporal changes of the differential rotation law of the Ca⁺-chromosphere correlated with changes of meridional motions and differences in the rotation of the two hemispheres were observed. The data of 1976 show no significant difference in the equatorial velocity of the Ca⁺-chromosphere and the photosphere. A comparison of temporal variations of the rotation velocity of the Ca⁺-mottles and the photospheric plasma yielded no significant correlation. Finally, we correlated the measurements of the photospheric rotation performed within the equatorial belts at Locarno with those obtained at Mt. Wilson by a different method during the same periods. The Locarno data show small temporal variations (±50 m^-1s) with no correlation between the two hemispheres, while from the Mt. Wilson data larger variations (±100 m s^-1) with a very high correlation between the two hemispheres have been found. A comparison of both sets of data yielded no correlation at all demonstrating the need for further coordinated observations and a drastic increase of internal accuracy.Mitteilung des Fraunhofer-Instituts Nr. 162.     

Properties of the large- and small-scale flow patterns in and around AR 19824

We trace the photospheric motions of 170 concentrations of magnetic flux tubes in and around the decaying active region No. 19824 (CMP 23 October 1986), using a series of magnetograms obtained at the Big Bear Solar Observatory. The magnetograms span an interval of just over five days and cover an area of about 4 × 5 arc min centered on the active region. We find a persistent large-scale flow pattern that is superposed on the small-scale random motions of both polarities. Correction for differential rotation unveils the systematic, large-scale flow surrounding the core region of the magnetic plage. The flow (with a mean velocity of 30 m s^–1) is faster and more pronounced around the southern side of the core region than around the northern side, and it accelerates towards the western side of the active region. The northern and southern branches of the large-scale flow converge westward of the core region, dragging along the westernmost sunspot and some of the magnetic flux near it. The overall pattern of the large-scale flow resembles the flow of a river around a sand bar. The long-term evolution of the active region suggests that the flow persists for several months. We discuss the possible association of the large-scale flow with the torsional oscillation.We correct the observed motions of concentrations of flux tubes for the large-scale flow in order to study their random motions. The small-scale random motions (with a mean speed of 150 m s^–1) can be characterized by a diffusion coefficient of 250 km² s^–1 for the area surrounding the core region of the magnetic plage. The diffusion coefficient characterizing the small-scale motions within the core region (mostly observed near its periphery and in areas of relatively low flux density) is only 110 km² s^–1. The lower diffusion coefficient in the core region appears to be caused mainly by a smaller step length rather than by a distinct difference in velocities.Visitor at the Lockheed Palo Alto Research Laboratories.     

Characteristic size and diffusion of quiet sun magnetic patterns

We have previously studied large-scale motions using high-resolution magnetograms taken from 1978 to 1990 with the NSO Vacuum Telescope on Kitt Peak. Latitudinal and longitudinal motions were determined by a two-dimensional crosscorrelation analysis of pairs of consecutive daily observations using small magnetic features as tracers. Here we examine the shape and amplitude of the crosscorrelation functions. We find a characteristic length scale as indicated by the FWHM of the crosscorrelation functions of 16.6 ± 0.2 Mm. The length scale is constant within ±45° latitude and decreases by about 5% at 52.5° latitude; i.e., the characteristic size is almost latitude independent. The characteristic scale is within 3% of the average value during most times of the solar cycle, but it increases during cycle maximum at latitudes where active regions are present. For the time period 1978–1981 (solar cycle maximum), the length scale increases up to 1.7 Mm or 10% at 30° latitude. In addition, we derive the average amplitude of the crosscorrelation functions, which reflects the diffusion of magnetic elements and their evolutionary changes (including formation and decay). We find an average value of 0.091 ± 0.003 for the crosscorrelation amplitude at a time lag of one day, which we interpret as being caused by the combined effect of the lifetime of magnetic features and a diffusion process. Assuming a lifetime of one day, we find a value of 120 km² s^–1 for the diffusion constant, while a lifetime of two days leads to 230 km² s^–1.Operated by the Association of Universities for Research in Astronomy, Inc. under cooperative agreement with the National Science Foundation.     

Earth albedo and the orbit of Lageos

The long-period perturbations in the orbit of Lageos satellite due to the earth's albedo have been found using a new analytical formalism. The earth is assumed to be a sphere whose surface diffusely reflects sunlight according to Lambert's law. Specular reflection is not considered. The formalism is based on spherical harmonics; it produces equations which hold regardless of whether the terminator is seen by the satellite or not. Specializing in the case of a realistic zonal albedo shows that Lageos' orbital semimajor axis changes periodically by only about a centimeter and the eccentricity by two parts in 10⁵. The longitude of the node increases secularly by about 6×10^–4 arc sec yr^–1. The effect considered here can explain neither the secular decay of 1.1 mm day^–1 in the semimajor axis nor the observed along-track variations in acceleration of order 2×10^–12 ms^–2.     

Solar surface velocity fields determined from small magnetic features

We describe a method for the analysis of magnetic data taken daily at the Vacuum Telescope at Kitt Peak. In this technique, accurate position differences of very small magnetic features on the solar surface outside active regions are determined from one day to the next by a cross-correlation analysis. In order to minimize systematic errors, a number of corrections are applied to the data for effects originating in the instrument and in the Earth's atmosphere. The resulting maps of solar latitude vs central meridian distance are cross-correlated from one day to the next to determine daily motions in longitude and latitude. Some examples of rotation and meridional motion results are presented. For the months of May 1988 and October–November 1987, we find rotation coefficients A = 2.894 ± 0.011, B = - 0.428 ± 0.070, and C = -0.370 ± 0.077 in rad s^–1 from the expansion = A + B sin² + C sin⁴, where is the latitude. The differential rotation curve for this interval is essentially flat within 20 deg of the equator in these intervals. For the same intervals we find a poleward meridional motion a = 16.0 ± 2.8 m sec ^-1 from the relation v = a sin, where v is the line-of-sight velocity.Operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation.