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Sunspot dynamics

The goal of this research was the understanding of the various oscillatory, transient, and quasi-steady motions in sunspots and the basic structure of a sunspot. The research involved both theoretical modeling (based on thermohydrodynamic theory) and observations of dynamical phenomena in sunspots. The principal topics of the research were sunspot seismology (the interaction of solar p-modes with a sunspot as a probe of the subsurface structure of a sunspot); three minute umbral oscillations and their relation to the structure of the umbral atmosphere; siphon flows in isolated magnetic flux tubes and their relation to the photospheric Evershed flow and to intense magnetic elements outside of sunspots; and more general theoretical work on magneto-atmospheric waves. Here, a summary of results is given.

Thomas, John H.

Sunspot dynamics

This report describes recent results of our theoretical and observational work on dynamical phenomena in sunspots. The overall goal of this research has been a better understanding of the various oscillatory, transient, and steady motions in a sunspot and their relation to the basic structure of the sunspot. The principal topics of the research reported here are the following: (1) sunspot seismology, i.e., the study of the interaction of solar p-modes with a sunspot as a probe of the subsurface structure of a sunspot; (2) local sources of acoustic waves in the solar photosphere; and (3) siphon flows in isolated magnetic flux tubes and their relation to the photospheric Evershed flow and to intense magnetic elements outside of sunspots.

Thomas, John H.

On the Importance of Cycle Minimum in Sunspot Cycle Prediction

The characteristics of the minima between sunspot cycles are found to provide important information for predicting the amplitude and timing of the following cycle. For example, the time of the occurrence of sunspot minimum sets the length of the previous cycle, which is correlated by the amplitude-period effect to the amplitude of the next cycle, with cycles of shorter (longer) than average length usually being followed by cycles of larger (smaller) than average size (true for 16 of 21 sunspot cycles). Likewise, the size of the minimum at cycle onset is correlated with the size of the cycle's maximum amplitude, with cycles of larger (smaller) than average size minima usually being associated with larger (smaller) than average size maxima (true for 16 of 22 sunspot cycles). Also, it was found that the size of the previous cycle's minimum and maximum relates to the size of the following cycle's minimum and maximum with an even-odd cycle number dependency. The latter effect suggests that cycle 23 will have a minimum and maximum amplitude probably larger than average in size (in particular, minimum smoothed sunspot number Rm = 12.3 +/- 7.5 and maximum smoothed sunspot number RM = 198.8 +/- 36.5, at the 95-percent level of confidence), further suggesting (by the Waldmeier effect) that it will have a faster than average rise to maximum (fast-rising cycles have ascent durations of about 41 +/- 7 months). Thus, if, as expected, onset for cycle 23 will be December 1996 +/- 3 months, based on smoothed sunspot number, then the length of cycle 22 will be about 123 +/- 3 months, inferring that it is a short-period cycle and that cycle 23 maximum amplitude probably will be larger than average in size (from the amplitude-period effect), having an RM of about 133 +/- 39 (based on the usual +/- 30 percent spread that has been seen between observed and predicted values), with maximum amplitude occurrence likely sometime between July 1999 and October 2000.

Wilson, Robert M.

Sunspots and Giant-Cell Convection

From analysis of Doppler velocity images from SOHO/MDI, Hathaway et al (2000, Solar Phys., in press) have found clear evidence for giant convection cells that fill the solar surface, have diameters 3 - 10 times that typical of supergranules, and have lifetimes approx. greater than 10 days. Analogous to the superposition of the granular convection on the supergranular convection, the approx. 30,000 km diameter supergranules are superposed on these still larger giant cells. Because the giant cells make up the large-scale end of a continuous power spectrum that peaks at the size scale of supergranules, it appears that the giant cells are made by the same mode of convection as the supergranules. This suggests that the giant cells are similar to supergranules, just longer-lived, larger in diameter, and deeper. Here we point out that the range of lengths of large bipolar sunspot groups is similar to the size range of giant cells. This, along with the long lives (weeks) of large sunspots, suggests that large sunspots sit in long-lived, deep downflows at the corners of giant cells, and that the distance from leader to follower sunspots in large bipolar groups is the distance from one giant-cell corner to the next. By this line of reasoning, an unusually large and strong downdraft might pull in both legs of a rising spot-group magnetic flux loop, resulting in the formation of a delta sunspot. This leads us to suggest that a large, strong giant-cell corner downdraft should be present at the birthplaces of large delta sunspots for some time (days to weeks) before the birth. Thus, early detection of such downdrafts by local helioscismology might provide an early warning for the formation of those active regions (large delta sunspot groups) that produce the Sun's most violent flares and coronal mass ejections. This work is supported by NASA's Office of Space Science through the Solar Physics Branch of its Sun-Earth Connection Program.

Moore, Ron L.

Updating of ADAPT predictions of sunspot activity

An eigenvector analysis procedure was used to analyze and develop algorithms for predicting sunspot numbers. The predictors in these algorithms consist of sunspot numbers from the preceding two solar cycles and magnetic index data from the preceding cycle. Predictions are presented for cycles 21 and 22. The sunspot activity for cycle 21 is predicted to remain below 100 until early 1980 when it will rapidly reach a peak of approximately 120. The two sigma accuracy on these estimates is approximately 20 sunspot numbers in the region of the peak and 10 sunspot numbers early and late in the cycle. Algorithms were also developed for predicting the period of future sunspot cycles using the same predictor vector.

Hunter, H. C.

Solar rotation and the sunspot cycle

Reexamination of the published sunspot rotation rates from Mount Wilson for the period from 1921 to 1982 suggests that the sun rotates more rapidly when there are fewer sunspots. This behavior is seen over the course of each cycle with the most rapid rotation usually observed at sunspot minimum. It is also seen in hemispheric differences with the southern hemisphere, having fewer spots, rotating more rapidly than the northern hemisphere. Furthermore, the rotation rate averaged over each cycle also shows that the sun rotates more rapidly during cycles with fewer sunspots and less sunspots area. This inverse correlation between sunspot area and rotation rate suggests that during the Maunder minimum the sun may have rotated slightly faster than is observed today.

Hathaway, David H.

Wave generation in a sunspot

In this paper we analyze the generation of waves in a sunspot by extending Stein's hydrodynamic approach to the turbulent medium permeated by a strong uniform magnetic field oriented parallel to the gravity. For wave sources appropriate to the sunspot, we consider magnetic perturbations and entropy changes as well as turbulent convection. To describe the anisotropy imposed by the sunspot, we use a one-dimensional correlation function relating the turbulent eddies separated along the symmetry axis of the spot. This treatment yields several interesting possibilities for wave generation in a sunspot. First, it is demonstrated that the entropy change and magnetic perturbation can lead to a relative enhancement of acoustic wave emission. Second, the energy flux of Alfven waves may be comparable to that of acoustic waves in sunspots. Third, the anisotropy of the sunspot dynamics can lead to wave energy spectrum in a form which may explain the origin of umbral atmospheric oscillations.

Lee, Jeongwoo W.

Solar Cycle Predictions Near Sunspot Minimum

Observations of solar magnetic activity and the dynamics of the solar convection zone have produced severe constraints on models of the Sun's magnetic dynamo. These constraints are so severe that, at present, we do not have numerical models that can accept the current conditions and then march forward in time to predict future activity. Given this state of solar dynamo theory we are forced to examine previous behavior to discover patterns and trends that afford us some measure of predictability. Here we examine the behavior of several indicators of solar activity near solar minimum that are well correlated with the amplitude of the following solar maximum to predict the level of solar activity over cycle 23. Sunspot numbers, areas, and positions are useful for characterizing solar cycle behavior due to the extent of the data (12 cycles or more). These data exhibit several patterns that relate future activity to past behavior. With the Odd-Even effect the odd numbered cycles have been larger than their even numbered predecessors for each of the last six cycle pairs. With the Amplitude-Period effect short period cycles have been followed by large amplitude cycles and long period cycles have been followed by small amplitude cycles for 10 of the last 13 cycles. With the Maximum-Minimum effect the sunspot number at minimum is directly correlated with the sunspot number at maximum for a given cycle. The geomagnetic indices aa and Ap are also related to solar activity by the connections between disturbances in the solar wind and variations in the Earth's magnetic field. Like the Maximum-Minimum effect for sunspots, the size of the aa and Ap indices at minimum are directly related to the amplitude of the following maximum. The number of geomagnetically disturbed days (days with Ap >= 25) over the course of a cycle is another indicator for the size of the next cycle. The aa and Ap indices can each be separated into a component in phase with the current sunspot cycle and an "extended cycle" component that is directly related to the following cycle. Individually each of these indicators provides some measure of predictive ability for the amplitudes of previous cycles. Taken in combination we find that the predictions are much more accurate. Our multi-variate analysis indicates that a maximum sunspot number of 160 +/- 20 should occur near the end of 1999 for cycle 23.

Hathaway, David H.

Asymmetric Stokes-V Profiles at the Penumbral Boundary of a Sunspot

We present the spectropolarimetric measurements of a sunspot in the active region NOAA 6958 (15S03W), situated near the central meridian disk passage. The follower polarity sunspot was somewhat symmetrically round shaped with an elongated penumbra. There were several opposite polarity magnetic elements at, and beyond the penumbral boundary. The H-alpha images of the sunspot show the bright emission regions near the penumbral boundary towards the sun-center, which was of opposite polarity with respect to the main spot. The net-circular polarization (NCP) map shows that NCP is negative in the inner part of the spot and positive at the penumbral boundary and near the H-alpha plage. The Doppler velocities were determined by measuring the center-of-gravity (COG) of the Stokes-I profile and zero-crossing (ZC) wavelength of the Stokes-V profiles. The COG velocity map in general agrees with the Evershed flow. In addition, it shows the up flow in the penumbral region. The ZC velocities show the strong down flow at the penumbral boundary. Double-lobed Stokes-V profiles are observed at the locations, where the penumbral fibrils terminate coinciding the H-alpha plage. The Double lobed profiles had an unshifted component similar to the Stokes-V profiles of the sunspot penumbra and a shifted component with a velocity of about 5 km/s. The amplitude of the second component increases along the penumbral fibril as a function of the distance from the center of the sunspot. In this paper we discuss the role of emerging flux in generating the observed double lobed profiles. Based on our present observations, we propose to observe with the Solar-B Spectropolarimeter for understanding the nature of emerging flux near the sunspots.

Choudhary, Debi Prasad

On the Relationship Between Spotless Days and the Sunspot Cycle: A Supplement

This study provides supplemental material to an earlier study concerning the relationship between spotless days and the sunspot cycle. Our previous study, Technical Publication (TP)-2005-213608 determined the timing and size of sunspot minimum and maximum for the new sunspot cycle, relative to the occurrence of the first spotless day during the declining phase of the old sunspot cycle and the last spotless day during the rising portion of the new cycle. Because the number of spotless days (NSD) rapidly increases as the cycle nears sunspot minimum and rapidly decreases thereafter, the size and timing of sunspot minimum and maximum might be more accurately determined using a higher threshold for comparison, rather than using the first and last spotless day occurrences. It is this aspect that is investigated more thoroughly in this TP.

Wilson, Robert M.

An Examination of Selected Geomagnetic Indices in Relation to the Sunspot Cycle

Previous studies have shown geomagnetic indices to be useful for providing early estimates for the size of the following sunspot cycle several years in advance. Examined this study are various precursor methods for predicting the minimum and maximum amplitude of the following sunspot cycle, these precursors based on the aa and Ap geomagnetic indices and the number of disturbed days (NDD), days when the daily Ap index equaled or exceeded 25. Also examined is the yearly peak of the daily Ap index (Apmax), the number of days when Ap greater than or equal to 100, cyclic averages of sunspot number R, aa, Ap, NDD, and the number of sudden storm commencements (NSSC), as well the cyclic sums of NDD and NSSC. The analysis yields 90-percent prediction intervals for both the minimum and maximum amplitudes for cycle 24, the next sunspot cycle. In terms of yearly averages, the best regressions give Rmin = 9.8+/-2.9 and Rmax = 153.8+/-24.7, equivalent to Rm = 8.8+/-2.8 and RM = 159+/-5.5, based on the 12-mo moving average (or smoothed monthly mean sunspot number). Hence, cycle 24 is expected to be above average in size, similar to cycles 21 and 22, producing more than 300 sudden storm commencements and more than 560 disturbed days, of which about 25 will be Ap greater than or equal to 100. On the basis of annual averages, the sunspot minimum year for cycle 24 will be either 2006 or 2007.

Wilson, Robert M.

Predicting the Sunspot Cycle

The 11-year sunspot cycle was discovered by an amateur astronomer in 1844. Visual and photographic observations of sunspots have been made by both amateurs and professionals over the last 400 years. These observations provide key statistical information about the sunspot cycle that do allow for predictions of future activity. However, sunspots and the sunspot cycle are magnetic in nature. For the last 100 years these magnetic measurements have been acquired and used exclusively by professional astronomers to gain new information about the nature of the solar activity cycle. Recently, magnetic dynamo models have evolved to the stage where they can assimilate past data and provide predictions. With the advent of the Internet and open data policies, amateurs now have equal access to the same data used by professionals and equal opportunities to contribute (but, alas, without pay). This talk will describe some of the more useful prediction techniques and reveal what they say about the intensity of the upcoming sunspot cycle.

Hathaway, David H.

An Estimate of the Size and Shape of Sunspot Cycle 24 Based on its Early Cycle Behavior using the Hathaway-Wilson-Reichmann Shape-Fitting Function

On the basis of 12-month moving averages (12-mma) of monthly mean sunspot number (R), sunspot cycle 24 had its minimum amplitude (Rm = 1.7) in December 2008. At 12 mo past minimum, R measured 8.3, and at 18 mo past minimum, it measured 16.4. Thus far, the maximum month-to-month rate of rise in 12-mma values of monthly mean sunspot number (AR(t) max) has been 1.7, having occurred at elapsed times past minimum amplitude (t) of 14 and 15 mo. Compared to other sunspot cycles of the modern era, cycle 24?s Rm and AR(t) max (as observed so far) are the smallest on record, suggesting that it likely will be a slow-rising, long-period sunspot cycle of below average maximum amplitude (RM). Supporting this view is the now observed relative strength of cycle 24?s geomagnetic minimum amplitude as measured using the 12-mma value of the aa-geomagnetic index (aam = 8.4), which also is the smallest on record, having occurred at t equals 8 and 9 mo. From the method of Ohl (the inferred preferential association between RM and aam), one predicts RM = 55 +/- 17 (the ?1 se prediction interval) for cycle 24. Furthermore, from the Waldmeier effect (the inferred preferential association between the ascent duration (ASC) and RM) one predicts an ASC longer than 48 mo for cycle 24; hence, maximum amplitude occurrence should be after December 2012. Application of the Hathaway-Wilson-Reichmann shape-fitting function, using an RM = 70 and ASC = 56 mo, is found to adequately fit the early sunspot number growth of cycle 24.

Wilson, Robert M.

The Effect of Missing Groups in the Calculation of the Solar Irradiance Deficit: Analysis of the Sunspot Areas from the SOON Network

Sunspot areas are one of the most important indices of solar activity. To obtain an extended time series covering multiple solar cycles one must combine data from different observatories after a proper comparison and calibration of the individual data sets. We compare the daily and group values of sunspot areas provided by the different stations from the Solar Optical Observing Network, SOON, which are determined using similar instruments and techniques. We investigate if there are systematic differences among the stations and whether the differences in the daily values can be attributed to missing groups in the records or errors in the measurements. We find significant differences among the stations of the SOON network in terms of sizes (average daily and group values), quality of observations and coverage (considering number of missing groups and data gaps). Our results indicate that calibration factors for daily values can be used with confidence to combine data sets from different stations. However, for some applications which require the location of the sunspot groups the same correction factors should not be used. We estimate the irradiance deficit due to sunspot through the Photometric Sunspot Index and compare the output from similar data sets to quantify the effect of missing groups. We find differences as high as 150 ppm during the maximum of solar cycle. The effect increases for sunspot groups near the center of the disk accounting for about 80% of the observed differences.

Luis Leuzzi

The nature of the sunspot phenomenon. I - Solutions of the heat transport equation

It is pointed out that sunspots represent a disruption in the uniform flow of heat through the convective zone. The basic sunspot structure is, therefore, determined by the energy transport equation. The solutions of this equation for the case of stochastic heat transport are examined. It is concluded that a sunspot is basically a region of enhanced, rather than inhibited, energy transport and emissivity. The heat flow equations are discussed and attention is given to the shallow depth of the sunspot phenomenon. The sunspot is seen as a heat engine of high efficiency which converts most of the heat flux into hydromagnetic waves.

Parker, E. N.

On long-term periodicities in the sunspot record

Sunspot records are systematically maintained, with the knowledge that an 11 year average period exists since about 1850. Thus, the sunspot record of highest quality and considered to be the most reliable is that of cycle eight through the present. On the basis of cycles 8 through 20, various combinations of sine curves were used to approximate the observed R sub MAX values (where R sub MAX is the smoothed sunspot number at cycle maximum). It is found that a three component sinusoidal function, having an 11 cycle and a 2 cycle variation on a 90 cycle periodicity, yields computed R sub MAX values which fit, reasonably well, observed R sub MAX values for the modern sunspot cycles. Extrapolation of the empirical functions forward in time allows for the projection of values of R sub MAX for cycles 21 and 22. For cycle 21, the function projects a value of 157.3, very close to the actually observed value of 164.5. For cycle 22, the function projects a value of about 107. Linear regressions applied to cycle 22 indicate a long-period cycle (cycle duration 132 months). An extensive bibliography on techniques used to estimate the time dependent behavior of sunspot cycles is provided.

Wilson, R. M.

Acoustic absorption by sunspots

The paper presents the initial results of a series of observations designed to probe the nature of sunspots by detecting their influence on high-degree p-mode oscillations in the surrounding photosphere. The analysis decomposes the observed oscillations into radially propagating waves described by Hankel functions in a cylindrical coordinate system centered on the sunspot. From measurements of the differences in power between waves traveling outward and inward, it is demonstrated that sunspots appear to absorb as much as 50 percent of the incoming acoustic waves. It is found that for all three sunspots observed, the amount of absorption increases linearly with horizontal wavenumber. The effect is present in p-mode oscillations with wavelengths both significantly larger and smaller than the diameter of the sunspot umbrae. Actual absorption of acoustic energy of the magnitude observed may produce measurable decreases in the power and lifetimes of high-degree p-mode oscillations during periods of high solar activity.

Braun, D. C.

Sunspot prediction using neural networks

The earliest systematic observance of sunspot activity is known to have been discovered by the Chinese in 1382 during the Ming Dynasty (1368 to 1644) when spots on the sun were noticed by looking at the sun through thick, forest fire smoke. Not until after the 18th century did sunspot levels become more than a source of wonderment and curiosity. Since 1834 reliable sunspot data has been collected by the National Oceanic and Atmospheric Administration (NOAA) and the U.S. Naval Observatory. Recently, considerable effort has been placed upon the study of the effects of sunspots on the ecosystem and the space environment. The efforts of the Artificial Intelligence Section of the Mission Planning and Analysis Division of the Johnson Space Center involving the prediction of sunspot activity using neural network technologies are described.

Villarreal, James