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NASA NTRS1987

10.7-cm solar radio flux and the magnetic complexity of active regions

During sunspot cycles 20 and 21, the maximum in smoothed 10.7-cm solar radio flux occurred about 1.5 yr after the maximum smoothed sunspot number, whereas during cycles 18 and 19 no lag was observed. Thus, although 10.7-cm radio flux and Zurich sunspot number are highly correlated, they are not interchangeable, especially near solar maximum. The 10.7-cm flux more closely follows the number of sunspots visible on the solar disk, while the Zurich sunspot number more closely follows the number of sunspot groups. The number of sunspots in an active region is one measure of the complexity of the magnetic structure of the region, and the coincidence in the maxima of radio flux and number of sunspots apparently reflects higher radio emission from active regions of greater magnetic complexity. The presence of a lag between sunspot-number maximum and radio-flux maximum in some cycles but not in others argues that some aspect of the average magnetic complexity near solar maximum must vary from cycle to cycle. A speculative possibility is that the radio-flux lag discriminates between long-period and short-period cycles, being another indicator that the solar cycle switches between long-period and short-period modes.

Wilson, Robert M.↗
NASA NTRS2012

A Statistical Test of Uniformity in Solar Cycle Indices

Several indices are used to characterize the solar activity cycle. Key among these are: the International Sunspot Number, the Group Sunspot Number, Sunspot Area, and 10.7 cm Radio Flux. A valuable aspect of these indices is the length of the record -- many decades and many (different) 11-year cycles. However, this valuable length-of-record attribute has an inherent problem in that it requires many different observers and observing systems. This can lead to non-uniformity in the datasets and subsequent erroneous conclusions about solar cycle behavior. The sunspot numbers are obtained by counting sunspot groups and individual sunspots on a daily basis. This suggests that the day-to-day and month-to-month variations in these numbers should follow Poisson Statistics and be proportional to the square-root of the sunspot numbers themselves. Examining the historical records of these indices indicates that this is indeed the case - even with Sunspot Area and 10.7 cm Radio Flux. The ratios of the RMS variations to the square-root of the indices themselves are relatively constant with little variation over the phase of each solar cycle or from small to large solar cycles. There are, however, important step-like changes in these ratios associated with changes in observer and/or observer system. Here we show how these variations can be used to construct more uniform datasets.

Hathaway David H.↗
NASA NTRS2019

The Solar Clock

The Sun is powered by a very stable source of fusion energy in its core that radiates that energy outward in a constant flow. Yet it has a cycle of magnetic dynamo activity whose strength and duration are variable. This variability, which affects the Earth's ‘space climate', points to temporal changes in the convective and diffusive transport of magnetic flux above the tachocline, where the flux is generated. The longest record we have of this variability is the time series of Sunspot Numbers (SSN). This record suggests that the interior of the Sun follows a clocklike magnetic flux production cycle with a length of close to 11.05 yr. The variations in sunspot cycle duration, as well as the sunspot number rise and fall times, their hemispheric asymmetries, and the maximum sunspot numbers of the individual cycles, are likely produced in the process of the magnetic flux transport. Helioseismology continues to shed more light on the convection zone variabilities, including the ‘torsional oscillations' that seem to have a special connection to the emerging strong magnetic fluxes that produce the sunspots. These new observations may eventually lead to an explanation for the surprisingly good correlation between the rate of sunspot appearance and the maximum sunspot number, and to a better understanding of the relationship between the solar dynamo and the sunspot number cycle. Better understanding of the polar regions awaits long-term monitoring with a polar solar mission. Better predictions of nearterm space weather could be obtained from a permanent L5 monitor.

C T Russell↗
NASA NTRS1992

Search for evidence of a clock related to the solar 154 day complex of periodicities

Evidence that has recently been compiled (Bai and Sturrock 1991) indicates that the enigmatic 154-day periodicity in solar activity may be viewed as part of a complex of periodicities that are approximate multiples of 25.8 days, suggesting that the Sun contains a 'clock' with frequency in the range 440 to 463 nano Hz. The clock may comprise either an oscillator or a rotator, each of which may be either real or virtual. We have reconsidered a previous spectrum analysis of the Zurich sunspot-number sequence by Knight, Schatten, and Sturrock (1979) which revealed a sharp, persistent and significant periodicity with a period of 12.072 days, corresponding to a frequency of about 958.8 nano Hz. This periodicity may be regarded as the (second) upper sideband of the second harmonic (2nu(sub R) + 2nu(sub E)) of a fundamental frequency of 447.7 nano Hz that is clearly within the search band. In this expression, nu(sub R) is the sidereal frequency of the hypothetical rotator and nu(sub E) is the frequency (31.69 nano Hz) of the Earth in its orbital motion around the Sun. In analyzing sunspot area data derived from the Greenwich data set, and on noting that any frequency is defined only to within the Nyquist frequency, we find clear evidence not only for the upper sideband of the second harmonic, but also for the second harmonic (2nu(sub R)) and the lower sideband of the second harmonic (2nu(sub R) - 2nu(sub E)). There is no strong peak at the fundamental frequency in the Greenwich data, but there is in the Zurich sunspot data. The effect of a linear oscillator is, to the lowest order in the amplitude, the same as the combined effect of two rotators of opposite polarities. A rotator that has arbitrary orientation with respect to the ecliptic may influence the outer layers of the Sun and thereby modulate the occurrence of solar activity such as sunspots. By analyzing a simple model, we find that such a rotator would influence surface activity in such a way that the spectrum of a 'signal' (such as the record of sunspots), as seen from the Earth, would contain components with frequencies that are certain integral combinations of nu(sub R) and nu(sub E). The amplitudes of the various components depend sensitively on theta, the angle between the axis of the rotator and the axis of the Earth's orbital motion. This simple model therefore offers a kinematical (but not dynamical) interpretation of the sunspot spectrum. The present analysis, while offering support of our conjectures that the Sun contains a clock that regulates the 154-day complex of periodicities, cannot distinguish between an osillator or a rotator (that might be a traveling wave), nor between a real rotator or a virtual rotator (that might be an apparent traveling wave due to the aliasing effect of an oscillator in a rotating system). Further analysis of sunspot and other data sets will be required to confirm the existence of such clock and (if it is real) to determine its physical nature.

Sturrock, P. A.↗
NASA NTRS2003

Invited Talks at Naples and Coimbra

Prior to observations of the solar irradiance from space that began in 1979 there was no hope of obtaining even rough estimates of the solar irradiance variation over a solar cycle, since the space observations made since showed that the magnitude of the variation over a cycle to date is less than 0.1 %, a value too small to measure from the ground. At the same time, it would be useful to know the cycle-dependent variation over more than just the two recent cycles. Lacking a complete theory for the solar dynamo responsible for this variation, the current hope is to determine what proxy might yield the best values. Because there is an excellent database on sunspot umbral and penumbral areas from the Greenwich Observatory for the years 1874-1976 (but not beyond), the possibility exists that these data could be used. This talk will summarize results of a joint study in which satellite measurements of the solar irradiance variation are compared with ground-based measurements from the Coimbra Observatory of sunspot number, umbral area, and total sunspot area to determine which would serve as the best proxy for using the Greenwich observations back to 1874. From the near constancy of sunspot umbral magnetic fields upon which the useful parameter photometric sunspot index is based, we expected that umbral area would yield the beat proxy. To our surprise, after performing a statistical study of the observations over the period 1980-1990, preliminary indications are that sunspot number (a parameter available back into the 18th century) may be just as useful as the umbral area. As expected, both are quite superior as proxies to total sunspot area, which includes the penumbral area. This conclusion is consistent with earlier work of Hop and Schatten, who sought a proxy by studies of the umbral-penumbral area ratio. A second motivation for pursuing this work is the possibility that relatively small variations in the solar irradiance may induce larger responses in Earth's climate than would occur from simply introducing the corresponding heat differential into the terrestrial atmosphere. The talk will conclude with a description of why some climatologists are beginning to explore this possibility, which is suggest by some of the space observations used in the above search for a solar irradiance variation proxy.

Jordan, Stuart↗
NASA NTRS1988

The solar origin of long-term variations of the interplanetary magnetic field strength

Using simple models for the coronal field structure, the spacecraft observations of the photospheric field during sunspot cycle 21 were extrapolated for the purpose of modeling quantitatively the long-term behavior of the IMF during the sunspot cycle 21. Results were compared with the measurements of the radial component of the IMF at earth. The results indicate that the solar source of the IMF can be represented to a first approximation by the dipole component of the photospheric field, whose axis is nearly perpendicular to the ecliptic plane around sunspot minimum, but tilts more strongly toward it around sunspot maximum. It was also found that the average radial IMF strength varies with heliographic latitude; around sunspot minimum, the radial IMF is expected to be roughly twice as strong above the sun's poles as near the ecliptic plane. The average strength of the photospheric field above latitude 55 deg is about 10 G around sunspot minimum.

Wang, Y.-M.↗
NASA NTRS1993

On the latitude and solar cycle dependence of the interplanetary magnetic field strength

Twenty years of solar magnetograph and in-ecliptic IMF measurements are used to verify that the radial IMF component (B sub r) can be approximated by a superposition of the sun's inclined magnetic dipole moment and a current sheet normal to the dipole axis. The net field is found to be about three times stronger along the dipole axis than near the current sheet. Over the sunspot cycle, the absolute value of B sub r should undergo the least modulation near the heliographic equator and the greatest modulation above the sun's poles, where, at 1 AU, it varies systematically between about 10 nT near sunspot minimum and about 1 nT near sunspot maximum. The latitudinal gradients in the absolute value of B sub r are expected to be steepest around sunspot minimum and flattest near sunspot maximum. It is predicted that Ulysses will encounter very strong fields when it flies over the solar poles during the declining phase of sunspot cycle 22.

Wang, Y.-M.↗
NASA NTRS1993

A discussion of plausible solar irradiance variations, 1700-1992

From satellite observations the solar total irradiance is known to vary. Sunspot blocking, facular emission, and network emission are three identified causes for the variations. In this paper we examine several different solar indices measured over the past century that are potential proxy measures for the Sun's irradiance. These indices are (1) the equatorial solar rotation rate, (2) the sunspot structure, the decay rate of individual sunspots, and the number of sunspots without umbrae, and (3) the length and decay rate of the sunspot cycle. Each index can be used to develop a model for the Sun's total irradiance as seen at the Earth. Three solar indices allow the irradiance to be modeled back to the mid-1700s. The indices are (1) the length of the solar cycle, (2) the normalized decay rate of the solar cycle, and (3) the mean level of solar activity. All the indices are well correlated, and one possible explanation for their nearly simultaneous variations is changes in the Sun's convective energy transport. Although changes in the Sun's convective energy transport are outside the realm of normal stellar structure theory (e.g., mixing length theory), one can imagine variations arising from even the simplest view of sunspots as vertical tubes of magnetic flux, which would serve as rigid pillas affecting the energy flow patterns by ensuring larger-scale eddies. A composite solar irradiance model, based upon these proxies, is compared to the northern hemisphere temperature depatures for 1700-1992. Approximately 71% of the decadal variance in the last century can be modeled with these solar indices, although this analysis does not include anthropogenic or other variations which would affect the results. Over the entire three centuries, approx. 50% of the variance is modeled. Both this analysis and previous similar analyses have correlations of model solar irradiances and measured Earth surface temperatures that are significant at better than the 95% confidence level. To understand our present climate variations, we must place the anthropogenic variations in the context of natural variability from solar, volcanic, oceanic, and other sources.

Hoyt, Douglas V.↗
NASA NTRS2016

Predictions of Solar Cycle 24: How are We Doing?

Predictions of solar activity are an essential part of our Space Weather forecast capability. Users are requiring usable predictions of an upcoming solar cycle to be delivered several years before solar minimum. A set of predictions of the amplitude of Solar Cycle 24 accumulated in 2008 ranged from zero to unprecedented levels of solar activity. The predictions formed an almost normal distribution, centered on the average amplitude of all preceding solar cycles. The average of the current compilation of 105 predictions of the annual-average sunspot number is 106 +/- 31, slightly lower than earlier compilations but still with a wide distribution. Solar Cycle 24 is on track to have a below-average amplitude, peaking at an annual sunspot number of about 80. Our need for solar activity predictions and our desire for those predictions to be made ever earlier in the preceding solar cycle will be discussed. Solar Cycle 24 has been a below-average sunspot cycle. There were peaks in the daily and monthly averaged sunspot number in the Northern Hemisphere in 2011 and in the Southern Hemisphere in 2014. With the rapid increase in solar data and capability of numerical models of the solar convection zone we are developing the ability to forecast the level of the next sunspot cycle. But predictions based only on the statistics of the sunspot number are not adequate for predicting the next solar maximum. I will describe how we did in predicting the amplitude of Solar Cycle 24 and describe how solar polar field predictions could be made more accurate in the future.

Pesnell, William D.↗
NASA NTRS1975

Observations at 6 cm of the solar active region

Preliminary results are reported for the synthesis of a solar active region from observations with a synthesis radio telescope at a wavelength of 6 cm. Several individual sources are observed in the total-intensity and circular-polarization maps. These are shown to correspond to two large sunspots, two groups of small sunspots, and a plage. A magnetogram indicates that this active region had a bipolar structure with positive polarity concentrated on the main sunspots and negative polarity scattered over the plage and some of the small sunspots. It is noted that several radio bursts were recorded during the observation period and that one corresponded to a H-alpha flare near one of the sunspot groups.

Kundu, M. R.↗
NASA NTRS1980

Variations in the solar constant due to solar active regions

Solar activity is expected to affect the solar constant at some level. Recent observations and data analysis show the amount of variation to be expected for active regions, faculae, and sunspots on the apparent solar brightness. It is concluded that the maximum effect is about 20 times greater for sunspots than for faculae per unit area. Because facular areas are 25-30 times those for sunspots, the effect on the solar constant of faculae and sunspots is approximately equal and opposite, being typically in the neighborhood of 40-100 parts per million (ppm), but on occasion able to reach over 200 ppm. The issue of energy balance is not discussed here, for it requires further data analysis as well as information on the facular and sunspot limb darkening.

Chapman, G. A.↗
NASA NTRS1981

Short and long term variations in the solar constant

Short and long term variations in the solar constant are examined theoretically. The variations observed by the Solar Maximum Mission, lasting several days and associated with the passage of sunspot groups, strikingly demonstrates the well known lack of a bright ring effect around sunspots. This suggests that sunspot magnetic fields do not simply block the heat flowing upward into the photosphere. Rather, it is suggested that gravitational draining occurs; this cools sunspots and transports downward the heat that would otherwise flow into the photosphere. A model of sunspot temperature with depth shows modest support when compared with the empirical model of Van't Veer. Secular trends in the solar constant may occur and be associated with the influence of the convection zone magnetic field upon convective heat transport. As a start to understanding this problem, the Schwarzschild criterion has been modified to include the effects of magnetic field.

Schatten, K. H.↗
NASA NTRS1986

Solar irradiance variations from photometry of active regions

The Extreme Limb Photometer (ELP) has been used to measure the irradiance fluctuation of the sun due to selected active regions. Forty-five active regions that were completely scanned at various disk positions are included in the analysis. The contribution of these active regions to a global solar irradiance fluctuation has been correlated with photometric sunspot and facular indices (PSI and PFI) using published values of sunspot and calcium plage areas. The measured ELP fluctuations are converted to a global brightness fluctuation, Delta B/B. The sunspot component of Delta B/B correlates with PSI with r = 0.95. The facular component of Delta B/B correlates with PFI with r = 0.72. The expression for PFI is important to the question of energy balance between sunspots and faculae and the results presented here are not incompatible with energy balance between the two phenomena; that is the energy deficit of sunspots may be balanced by the energy excess of faculae.

Chapman, G. A.↗