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.     

Average properties of bipolar magnetic regions during sunspot cycle 21

We examine the statistical properties of some 2700 bipolar magnetic regions (BMRs) with magnetic fluxes 3 × 10²⁰ Mx which erupted during 1976–1986. Empirical rules were used to estimate the fluxes visually from daily magnetograms obtained at the National Solar Observatory/Kitt Peak. Our analysis shows the following: (i) the average flux per BMR declined between 1977 and 1985; (ii) the average tilts of BMRs relative to the east-west line increase toward higher latitudes; (iii) weaker BMRs had larger root-mean-square tilt angles than stronger BMRs at all latitudes; (iv) over the interval 1976–1986, BMRs with their leading poles equatorward of their trailing poles contributed a total of 4 times as much flux as BMRs with inverted tilts, but the relative amount of flux contributed by BMRs with inverted or zero tilts increased as the sunspot cycle progressed; (v) only 4% of BMRs had reversed east-west polarity orientations; (vi) although the northern hemisphere produced far more flux during the rising phase of the sunspot cycle, the southern hemisphere largely compensated for this imbalance during the declining phase; (vii) southern-hemisphere BMRs erupted at systematically higher latitudes than northern-hemisphere ones through most of sunspot cycle 21.     

Connection of coronal holes with active regions

We have determined two qualitative parameters for 643 coronal holes (CHs). Parameter A characterizes the magnetic-field variation in CHs depending on the height. Parameter B characterizes the connection between the magnetic field in a CH and the polar field at the photosphere level. A comparison of these parameters corresponding to CH with and without active regions (ARs) has led to the following conclusions: the formation of AR in CH is a frequent phenomenon, since the former exist in every other CH for at least 1 day; unlike the case of a CH without an AR, the configuration of the magnetic field above the CH with an AR often changes with the height: two out of three CHs have the opposite sign of the magnetic field in photosphere, as compared to the sign of the polar magnetic field; the areas of ARs in CHs do not differ from those for many other ARs outside of CHs.     

Evolution of polar coronal holes and sunspots during cycles 21 and 22

A very good correlation between the evolution of polar coronal hole size and sunspot number half a solar cycle later was found by Bravo and Otaola for solar cycle 21. In this paper we use a more complete set of data to reanalyse the relationship for solar cycle 21 and investigate the same relationship for solar cycle 22. We find that the complete set of data for cycle 21 yields a slightly different time shift for the best correlation between sunspots and holes and that the time shift for cycle 22 is different from that of cycle 21. However, because of limited availability of data of cycle 22, we consider it necessary to wait until the end of this cycle in order to decide if the difference is statistically significant or not. We also found that the time between successive peaks of smoothed polar hole area and smoothed sunspot number is the same in both cycles. This may provide a useful tool for the forecasting of future sunspot maxima. The constant of proportionality between polar coronal hole area and sunspot number can be seen to be different in both cycles. We discuss this difference and interpret it in terms of a different magnitude of the polar field strength in the two cycles.     

The probable behaviour of sunspot Cycle 21

After an explanation of the method of forecasting based upon the 80-yr sunspot cycle, reasons are given for assuming that the maximum of the present 80-yr cycle now has passed. Starting from this assumption the following predictions can be made: (1) Cycle 21 will be so weak that the highest value of the smoothed monthly means of the sunspot-relative-numbers will lie between 56 and 96; (2) The minimum at the beginning of Cycle 21 will occur during the first half of 1975; (3) Cycle 21 will attain its maximum between 1979.5 and 1980.5; (4) The minimum terminating Cycle 21 will take place during the first half of 1986. A comparison with other predictions shows that they differ considerably from one another; nevertheless, several of them yield results similar to the predictions stated here.     

Area of polar coronal holes and sunspot activity: Years 1939–1993

The correlation between the size of polar coronal holes and sunspot numbers has been investigated for the last five solar cycles. The area of polar coronal holes over the period from 1939 to 1993 was derived from ground-based observations of the green coronal line at 530.3 nm (Fe xiv). Correlation analysis revealed that there is no general shift in the maxima of the curves of these two solar indices. The analysis showed the same shift in months in cycles 21 and 22 when the best correlation between the indices is reached; the time shift found in cycle 20 is slightly different from that in cycle 18; in cycle 19, there is found a shift with a value between the values in cycles 18, 20 and 21, 22. The time between succesive peaks of smoothed polar hole size and smoothed sunspot number is different in each cycle.     

An explanation of the observed differences between coronal holes and quiet coronal regions

The main differences between a coronal hole and quiet coronal regions are explained by a reduction of the thermal conduction coefficient by transverse components of the magnetic field in the transition region of quiet coronal regions.Calculations of minimum flux coronae show that if the flux of energy heating the corona is maintained constant while the thermal conductivity in the transition region is reduced, the coronal temperature, the pressure in the transition region and the corona, and the temperature gradient in the transition region all increase. At the same time the intensities of lines emitted from the transition region are almost unchanged. Thus all the main spectroscopically observed differences between coronal holes and quiet coronal regions are explained.The flux of energy heating the corona in both coronal holes and quiet coronal regions is 3.0 × 10⁵ erg cm^-2 s^-1.The energy lost from coronal holes by the high speed streams in the solar wind is not sufficient to explain the difference in the coronal temperature in coronal holes and quiet coronal regions. The most likely explanation of the high velocity streams in the solar wind associated with coronal holes is that of Durney and Hundhausen.     

Spatial and temporal variations of solar coronal loops

Skylab EUV observations of an active region near the solar limb were analyzed. Both cool (T < 10⁶ K) and hot (T > 10⁶ K) loops were observed in this region. For the hot loops the observed intensity variations were small, typically a few percent over a period of 30 min. The cool loops exhibited stronger variations, sometimes appearing and disappearing in 5 to 10 min. Most of the cool material observed in the loops appeared to be caused by the downward flow of coronal rain and by the upward ejection of chromospheric material in surges. The frequent EUV brightenings observed near the loop footpoints appear to have been produced by both in situ transient energy releases (e.g. subflares) and the infall/impact of coronal rain. The physical conditions in the loops (temperatures, densities, radiative and conducting cooling rates, cooling times) were determined. The mean energy required to balance the radiative and conductive cooling of the hot loops is approximately 3 × 10^–3 erg cm^–3 s^–1. One coronal heating mechanism that can account for the observed behavior of the EUV emission from McMath region 12634 is heating by the dissipation of fast mode MHD waves.     

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.

     

Spatial and temporal variations of EUV coronal bright points

This paper reports results of an analysis of Skylab observations of coronal bright points made in EUV spectral lines formed in the chromosphere, chromospheric-coronal transition region and corona. The most important result is that the observed bright points exhibited large variations in EUV emission over time scales as short as 5.5 min, the temporal resolution of the data. In most cases strong enhancements in the coronal line were accompanied by strong enhancements in the chromospheric and transition region lines. The intensity variations appear to take place within substructures of the bright points, which most likely consist of miniature loops evolving on time scales of a few minutes. Coronal cooling times derived from the data are consistent with an intermittent, impulsive coronal heating mechanism for bright points.     

Properties of the magnetic fields of coronal holes with active regions

We determine the structure of the magnetic fields of coronal holes (CHs) and investigate its change in connection with the emergence of active regions (ARs) in CHs. Based on our observations in the HeI 1083 nm line performed with the CrAO TST-2 telescope, we have selected CHs of two types: without (15 CHs) and with (28 CHs) ARs. Magnetograms obtained at the Kitt Peak National Solar Observatory have been used to calculate the magnetic fields of the same objects.     

Evidence for temporal variations of coronal emission line intensity and profile

The time sequence of line profiles of Fe xiv emission obtained at the 1965 solar eclipse is examined for temporal variations of intensity and profile. Although no variations are found in some regions examined, two regions with intensity and profile line width variations are found. A simple temperature wave is consistent with observations.Work performed under the auspices of the U.S. Energy Research and Development Administration.Work accomplished at the Department of Physics and Astronomy, University of Wyoming, Laramie, Wyoming.     

Magnetic measurements of coronal holes during 1975–1980

Photospheric magnetic fluxes and average field strengths have been measured beneath 33 coronal holes observed on 63 occasions during 1975–1980. The principal result is that low-latitude holes contained 3 times more flux near sunspot maximum than near minimum despite the fact that their sizes were essentially the same. Average magnetic field strengths ranged from 3–36 G near sunspot maximum compared to 1–7 G near minimum. Evidently the low-latitude coronal holes received a proportion of the extra flux that was available at low latitudes near sunspot maximum.Visiting Astronomer, KPNO.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Flow-tube dynamics and coronal holes

We reexamine the well-known polytropic flow-tube model of the expanding solar corona, and find that as the divergence of the flow tube increases the expansion speed increases throughout the flow, over a stated parameter range. Corresponding to a specified flow-tube geometry the terminal speed of the fluid may be far in excess of the value corresponding to purely spherically symmetric flow. The implications of the results for the modelling of high-speed streams emanating from coronal holes are discussed.     

Morphology, dynamics and plasma parameters of plumes and inter-plume regions in solar coronal holes

Coronal plumes, which extend from solar coronal holes (CH) into the high corona and??possibly??into the solar wind (SW), can now continuously be studied with modern telescopes and spectrometers on spacecraft, in addition to investigations from the ground, in particular, during total eclipses. Despite the large amount of data available on these prominent features and related phenomena, many questions remained unanswered as to their generation and relative contributions to the high-speed streams emanating from CHs. An understanding of the processes of plume formation and evolution requires a better knowledge of the physical conditions at the base of CHs, in plumes and in the surrounding inter-plume regions. More specifically, information is needed on the magnetic field configuration, the electron densities and temperatures, effective ion temperatures, non-thermal motions, plume cross sections relative to the size of a CH, the plasma bulk speeds, as well as any plume signatures in the SW. In spring 2007, the authors proposed a study on ??Structure and dynamics of coronal plumes and inter-plume regions in solar coronal holes?? to the International Space Science Institute (ISSI) in Bern to clarify some of these aspects by considering relevant observations and the extensive literature. This review summarizes the results and conclusions of the study. Stereoscopic observations allowed us to include three-dimensional reconstructions of plumes. Multi-instrument investigations carried out during several campaigns led to progress in some areas, such as plasma densities, temperatures, plume structure and the relation to other solar phenomena, but not all questions could be answered concerning the details of plume generation process(es) and interaction with the SW.     

Extreme-ultraviolet observations of coronal holes

The disk boundaries of coronal holes have been systematically determined from XUV observations taken during the manned Skylab missions (June 1973–January 1974). The resulting Atlas was used to find the sizes, global distributions, differential rotation rates, growth/decay rates and lifetimes of holes during this period. The polar cap holes together covered 15% of the Sun's total surface area, a number which remained surprisingly constant throughout Skylab despite the fact that each pole was independently evolving in time. Lower latitude holes contributed another 2 to 5%. The anomalous differential rotation law derived for a large north-south hole by Timothy et al. (1975) has been confirmed. However, other Skylab holes were too low in latitude to demonstrate the generality of this result. The average growth/decay rate for holes was 1.5 × 10⁴ km² s^-1, in excellent agreement with the value used by Leighton (1964) for his successful treatment of the surface transport of solar magnetic fields. The lifetimes of lower-latitude holes are found to regularly exceed 5 solar rotations, in good agreement with the lifetimes of recurrent geomagnetic storms with which holes are now known to be associated.     

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.     

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.     

Solar mass ejections and coronal holes

In this paper we present observations of two types of solar mass ejections, which seem to be associated with the location of coronal, holes. In the first type, a filament eruption was observed near a coronal hole, which gave rise to a strong interplanetary scintillations. as detected by IPS observations. In the second type, several large scale soft X-ray blow-outs were observed in the YOHKOH SXT X-ray movies, in all the cases they erupted from or near the boundary of coronal holes and over the magnetic neutral line. It is proposed that the open magnetic field configuration of the coronal hole provides, the necessary field structure for reconnection to take place, which in turn is responsible for filament eruption, from relatively lower heights. While, in the case of X-ray blow-outs, the reconnection takes place at a greater height, resulting in high temperature soft X-ray emission visible as X-ray blow-outs.     

Polar coronal holes and solar cycles

The relationship between the geomagnetic activity of the three years preceding a sunspot minimum and the peak of the next sunspot maximum confirms the polar origin of the solar wind during one part of the solar cycle. Pointing out that the polar holes have a very small size or disappear at the time of the polar field reversal, we suggest a low latitude origin of the solar wind at sunspot maximum and we describe the cycle variation of solar wind and geomagnetic activity. In addition we note a close relationship between the maximum level of the geomagnetic activity reached few years before a solar minimum and its level at the next sunspot maximum. Studying separately the effects of both the low latitude holes and the solar activity, we point out the possibility of predicting both the level of geomagnetic activity and the sunspot number at the next sunspot maximum. As a conclusion we specify the different categories of phenomena contributing to a solar cycle.