MHD simulations of sunspot rotation and the coronal consequences

A simplified magnetic configuration is used to model some aspects of observations of a rotating sunspot and its overlying coronal loops. In the observations a large sunspot rotates over a few days and two smaller pores spiral into it. The coronal loops become sigmoidal in shape and flares are seen in Yohkoh/SXT and GOES. We have modeled the sunspot, one of the pores and the loops connecting these to a diffuse region of plasma of the opposite polarity. Two sets of MHD simulations are considered: (i) rotation of the sunspot and pore alone and (ii) rotation of the sunspot with inflow of the pore. Rotation alone can trigger the ideal kink instability in the loops but only for a rotation that is much greater than the observed value. There is no build-up of current which is needed for magnetic reconnection to occur. However, when inflow is included a strong build-up of current is seen as the pore merges with the sunspot. Comparing these results from the simulations with the observations, we find that the observed merging of the pores coincides with the timing of the flare. Therefore, we suggest that the merging of the pores with the large sunspot may be responsible for the flaring.     

Pulsation,rotation and sunspot cycle

A suggestion is made that the periods for solar pulsation, solar rotation, and sunspot cycle may be closely related one to another.     

Polar coronal holes and the sunspot cycle. A new method to predict sunspot numbers

Twenty years ago, Ohl (1966, 1968) found a correlation between geomagnetic activity around the minimum of the solar cycle and the Wolf sunspot number in the maximum of the following solar cycle. In this paper we shall show that such a relation means indeed a relation between the polar coronal holes area around the minimum of the solar cycle and the sunspot number in the maximum of the next. In fact, a very high positive correlation exists between the temporal evolution of the size of polar coronal holes and the Wolf sunspot number 6.3. years later.     

A survey of coronal holes and their solar wind associations throughout sunspot cycle 20

To gain insight into the relationships between solar activity, the occurrence and variability of coronal holes, and the association of such holes with solar wind features such as high-velocity streams, a study of the period 1963–1974 was made. This period corresponds approximately with sunspot cycle 20. The primary data used for this work consisted of X-ray and XUV solar images obtained from rockets. The investigation revealed that:

1. The polar coronal holes prominent at solar minimum, decreased in area as solar activity increased and were small or absent at maximum phase. This evolution exhibited the same phase difference between the two hemispheres that was observed in other indicators of activity.
2. During maximum, coronal holes occurred poleward of the sunspot belts and in the equatorial region between them. The observed equatorial holes were small and persisted for one or two solar rotations only; some high latitude holes had lifetimes exceeding two solar rotations.
3. During 1963–74 whenever XUV or X-ray images were available, nearly all recurrent solar wind streams of speed ?500 km s^?1 were found associated with coronal holes at less than 40° latitude; however some coronal holes appeared to have no associated wind streams at the Earth.

     

An observational examination of models for sunspot magnetic field configurations

The magnetic field configuration for an isolated, nearly circular sunspot has been obtained from measurements at some 100 points in the spot. The observations are compared with theoretical models for the field configuration of an isolated, axially-symmetric sunspot. The results support the Schlüter, Temesváry model with no return flux and a limiting field line inclination of ~70°.     

Relation of the coronal green line intensity to magnetic fields and sunspot areas in the solar cycle

The intensity of the green coronal Fe XIV λ530.3-nm line is correlated with sunspot areas and the magnetic field strength calculated for a distance of 1.1R _⊙. The relation of the green line emission to large-scale and local magnetic fields is shown to change differently with cycle phase. Large-scale coronal magnetic fields play a decisive role at the ascending phase, while a slightly higher correlation of the green line intensity with the local magnetic fields of sunspots is observed at the descending phase. Our results can be used to construct and test various solar coronal heating models.     

On the rotation rates of sunspot groups

The analysis of Greenwich sunspot data for cycle No. 18 shows: (1) higher rotation rates for the southern sunspot belt than for the northern belt, (2) lower rotation rates and a tendency to a more rigid rotation for greater sunspot groups, (3) lower rotation rates and a tendency to a more rigid rotation for older sunspot groups, (4) no dependence of rotation rates on the life-time of sunspot groups, (5) a tendency to a more rigid rotation at the activity minimum. Results Nos. 2, 3, and 5 could be interpreted in terms of the evolution and interplay of the active regions, as the regions age. If we assume that the sunspot group life-time is a function of their depth in the solar atmosphere, result No. 4 shows that rotation rates do not depend on the depth.     

The shape of the sunspot cycle

The temporal behavior of a sunspot cycle, as described by the International sunspot numbers, can be represented by a simple function with four parameters: starting time, amplitude, rise time, and asymmetry. Of these, the parameter that governs the asymmetry between the rise to maximum and the fall to minimum is found to vary little from cycle to cycle and can be fixed at a single value for all cycles. A close relationship is found between rise time and amplitude which allows for a representation of each cycle by a function containing only two parameters: the starting time and the amplitude. These parameters are determined for the previous 22 sunspot cycles and examined for any predictable behavior. A weak correlation is found between the amplitude of a cycle and the length of the previous cycle. This allows for an estimate of the amplitude accurate to within about 30% right at the start of the cycle. As the cycle progresses, the amplitude can be better determined to within 20% at 30 months and to within 10% at 42 months into the cycle, thereby providing a good prediction both for the timing and size of sunspot maximum and for the behavior of the remaining 7–12 years of the cycle. The U.S. Government right to retain a non-exclusive, royalty free licence in and to any copyright is acknowledged.     

Mathematical modelling of the sunspot cycle

The sunspot record for the time interval 1749–1977 can be represented conveniently by an harmonic model comprising a relatively large number of lines. Solar activity can otherwise be considered as a sequence of partly overlapping events, triggered periodically at intervals of the order of 11 years. Each individual cycle is approximated by a function of the Maxwell distribution type; the resulting impulse model consists of the superposition of the independent pulses. Application of these two models for the prediction of annual values of the Wolf sunspot numbers leads to controversial results. Mathematical modelling of the sunspot time series does not give an unambiguous result.     

LASCO observations of the coronal rotation

The near-rigid rotation of the corona above the differential rotation of the photosphere has important implications for the form of the global coronal magnetic field. The magnetic reconfiguring associated with the shear region where the rigidly-rotating coronal field lines interface with the differentially-rotating photospheric field lines could provide an important energy source for coronal heating. We present data on coronal rotation as a function of altitude provided by the Large Angle Spectrometric Coronagraph (LASCO) instrument aboard the Solar and Heliospheric Observatory (SOHO) spacecraft. LASCO comprises of three coronagraphs (C1, C2, and C3) with nested fields-of-view spanning 1.1 R to 30 R. An asymmetry in brightness, both of the Fexiv emission line corona and of the broad-band electron scattered corona, has been observed to be stable over at least a one-year period spanning May 1996 to May 1997. This feature has presented a tracer for the coronal rotation and allowed period estimates to be made to beyond 15R, up to 5 times further than previously recorded for the white-light corona. The difficulty in determining the extent of differential motion in the outer corona is demonstrated and latitudinally averaged rates formed and determined as a function of distance from the Sun. The altitude extent of the low latitude closed coronal field region is inferred from the determined rotation periods which is important to the ability of the solar atmosphere to retain energetic particles. For the inner green line corona (<2 R) we determine a synodic rotation period of (27.4±0.1) days, whereas, for the outer white- light corona, (>2.5 R) we determine a rotation period of (27.7±0.1) days.     

Median ionospheric height variations over a sunspot cycle in the Australian-Japanese longitudinal sector

The monthly median virtual height (h′F) of the F-region was studied for a period of 6 years (1980–1985) from sunspot maximum to minimum, using data from 11 ionosonde stations in the Japanese-Australian longitudinal sector, in an invariant latitude range: 37°N to 54°S. The night-time maximum in the median height progressively decreases equatorwards, particularly in the local winter and spring, while a reverse weak tendency is observed in summer. The median height reaches peak in both hemispheres from 1 to 2 years after sunspot maximum then decreases towards sunspot minimum. A second diurnal maximum in h′F, preceded by a well-defined minimum, was consistently observed over the solar cycle close to the sunrise time at the F-region, mainly at low invariant latitudes (9–20°). The second maximum has a distinct seasonal variation, being most pronounced in winter and diminishing in summer. It is envisaged that the second peak in h′F is associated with the wave disturbance generated by the supersonic motion of the sunrise terminator. Possible effects of the background height variations on the propagation of the magnetic storm-induced travelling ionospheric disturbances are discussed.     

Additional measurements of the high-latitude sunspot rotation rate

We report measurements of the sunspot rotation rate at high sunspot latitutdes for the years 1966–1968. Ten spots at ¦latitude¦ 28 deg were found in our Mees Solar Observatory H patrol records for this period that are suitable for such a study. On the average we find a sidereal rotation rate of 13.70 ± 0.07 deg day^-1 at 31.05 ± 0.01 deg. This result is essentially the same as that obtained by Tang (1980) for the succeeding solar cycle, and significantly larger than Newton and Nunn's (1951) results for the 1934–1944 cycle. Taken together, the full set of measurements in this latitude regime yield a rotation rate in excellent agreement with the result =14^°.37₇–2^°.77 sin², derived by Newton and Nunn from recurrent spots predominatly at lower latitudes throughout the six cycles from 1878–1944.Summer Research Assistant.     

Dynamics of coronal hole regions

The hydrodynamic properties of a steadily expanding corona are explored for situations in which departures from spherically symmetric outflow are large, in the sense that the geometrical cross section of a given flow tube increases outward from the Sun faster than r ² in some regions. Assuming polytropic flow, it is shown that in certain cases the flow may contain more than one critical point. We derive the criterion for determining which of these critical points is actually crossed by the transonic solution which begins at the Sun and extends continuously outward. Next, we apply the theory to geometries which exhibit rapid spreading of the flow tubes in the inner corona, followed by more-or-less radial divergence at large distances. This is believed to be the type of geometry found in coronal hole regions. The results show that, if this initial divergence is sufficiently large, the outflow becomes supersonic at a critical point encountered low in the corona in the region of high divergence, and it remains supersonic at all greater heights in the corona. This feature strongly suggests that coronal hole regions differ from other open-field regions of the corona in that they are in a fast, low density expansion state over much of their extent. Such a dynamical configuration makes it possible to reconcile the low values of electron density observed in coronal holes with the large particle fluxes in the associated high speed streams seen in the solar wind.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Differential rotation of coronal holes

Using KPNO helium 10830 Å synoptic charts of Carrington rotations 1716 through 1739, and by assembling a time sequence representing single latitude zone, rotational properties of coronal holes for five zones of latitudes (±10°, ±20° – ±40°, and ±40° – ±60°) have been examined. It seems that the rotation period of coronal holes is a function of latitude, thus reflecting differential rotation of coronal holes.     

Variation of the solar atmospheric rotation over the 11 year cycle

The synodic rotation period and power spectra of solar microwave sources are investigated using accurate data in the interval 1956 to 1970. The variation of the approximate 27 day period is obtained over a complete solar cycle and is thought to be a result of the latitude change over the solar cycle of the origins of the radio emissions. High resolution power spectra have also been obtained and revealed the existence of a double peaked line near 160 day period. This line is attributed to changes in either the Eartn's heliographic latitudes or the Earth's inclination to the Earth-Sun line.     

Cyclic variations of the polar coronal hole

The extension of the polar coronal holes has been studied for four cycles (1940–1978), using the observations of the corona line 530.3 nm. For about 7 years of each cycle, including sunspot minimum, the polar hole exists permanently and has a diameter of about 40° or even more. For about 3 years around sunspot maximum no polar hole does exist (Figure 5). The boundary of the hole is flanked at a distance of 10° by the polar zone of the corona and at one of 20° by that of the prominences. In the polar caps, so far they are occupied by the holes, polar photospheric faculae and the well-known plumes of the polar corona are found, and the polar crown of prominences, encircling the polar hole, is the belt where the reversal of the magnetic polarity takes place.     

Positions of sunspot groups and solar rotation

The question is studied whether the one-year solar oscillation found by V. F. Chistyakov for the years 1965–1973 can be traced in the observations of sunspots of 1874–1971 published by Greenwich Observatory. The result is negative. But the study leads to the following two conclusions: (1) The average observable centres of gravity of spot groups are variably displaced towards the central meridian or towards the limb, the time scale of this variability being of the order of 70 years. Thus the angular velocity should be determined from recurrent groups in transit of the central meridian only. (2) The angular velocity will be smaller when determined from older spots.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

On long-term periodicities in the sunspot cycle

Occurrences of interplanetary shock waves near the Earth after the powerful isolated flares of 1957–1978 are investigated. The close connection between the occurrences of shock waves and the positions of magnetic axes of bipolar groups of sunspots is suggested on the basis of a statistical study. The shock waves are principally observed when the Earth finds itself near the planes that are projected through the flares in parallel to the appropriate magnetic axes of the nearest bipolar groups. This regularity is interpreted as an indirect argument for a three-dimensional geometry for the interplanetary shock waves which, when projected on these flattened to corresponding planes, are traces of large circular arcs. The typical angular scales of isolated interplanetary shock waves are estimated as 150° and 30° parallel and perpendicular, respectively, to the magnetic axes correspondingly.     

Meterwave observations of a coronal hole

We present meterwave maps showing a coronal hole at 30.9, 50.0, and 73.8 MHz using the Clark Lake Radioheliograph in October 1984. The coronal hole seen against the disk at all three frequencies shows interesting similarities to, and significant differences from its optical signatures in He i l10830 spectroheliograms.Using the model of coronal holes by Dulk et al. (1977) we derive the electron density from the radio observations of the brightness temperature. The discrepancy between the density value derived from the Skylab EUV data and that computed from our radio data is even larger than in Dulk et al. 's comparison at similar and higher frequencies.     

Solar cycle variation of sunspot intensity

Broad band pinhole photometer intensity observations of 15 large sunspots covering the spectral region 0.387–2.35 m are presented. The data are based on measurements on approximately 500 days during the period June, 1967 to December, 1979.We have found real and significant intensity differences between large sunspots. These differences may be explained by a systematic variation in the umbral temperature throughout the solar cycle. A connection between umbra intensity and heliographic latitude is discussed.No center-limb variation in the umbra/photosphere intensity ratio is detected. We have searched for possible connections between umbra intensity and a number of other sunspot parameters, like the spot size, without detecting any significant correlation. We conclude that the umbra/photosphere intensity ratio seems to be a unique function of epoch for large sunspots.