Leif Svalgaard

Revisiting the Sunspot Number

Our knowledge of the long-term evolution of solar activity and of its primary modulation, the 11-year cycle, largely depends on a single direct observational record: the visual sunspot counts that retrace the last 4 centuries, since the invention of the astronomical telescope. Currently, this activity index is available in two main forms: the International Sunspot Number initiated by R. Wolf in 1849 and the Group Number constructed more recently by Hoyt and Schatten (Sol. Phys. 179:189–219, 1998a, 181:491–512, 1998b). Unfortunately, those two series do not match by various aspects, inducing confusions and contradictions when used in crucial contemporary studies of the solar dynamo or of the solar forcing on the Earth climate. Recently, new efforts have been undertaken to diagnose and correct flaws and biases affecting both sunspot series, in the framework of a series of dedicated Sunspot Number Workshops. Here, we present a global overview of our current understanding of the sunspot number calibration.After retracing the construction of those two composite series, we present the new concepts and methods used to self-consistently re-calibrate the original sunspot series. While the early part of the sunspot record before 1800 is still characterized by large uncertainties due to poorly observed periods, the more recent sunspot numbers are mainly affected by three main inhomogeneities: in 1880–1915 for the Group Number and in 1947 and 1980–2014 for the Sunspot Number.After establishing those new corrections, we then consider the implications on our knowledge of solar activity over the last 400 years. The newly corrected series clearly indicates a progressive decline of solar activity before the onset of the Maunder Minimum, while the slowly rising trend of the activity after the Maunder Minimum is strongly reduced, suggesting that by the mid 18th century, solar activity had already returned to levels equivalent to those observed in recent solar cycles in the 20th century. We finally conclude with future prospects opened by this epochal revision of the Sunspot Number, the first one since Wolf himself, and its reconciliation with the Group Number, a long-awaited modernization that will feed solar cycle research into the 21st century.

The strength of the sun's polar fields

The magnetic field strength within the polar caps of the Sun is an important parameter for both the solar activity cycle and for our understanding of the interplanetary magnetic field. Measurements of the line-of-sight component of the magnetic field generally yield 0.1 to 0.2 mT near times of sunspot minimum. In this paper we report measurements of the polar fields made at the Stanford Solar Observatory using the Fe i line λ 525.02 nm. We find that the average flux density poleward of 55° latitude is about 0.6 mT peaking to more than 1 mT at the pole and decreasing to 0.2 mT at the polar cap boundary. The total open flux through either polar cap thus becomes about 3 × 1014 Wb. We also show that observed magnetic field strengths vary as the line-of-sight component of nearly radial fields.

Influence of solar magnetic sector structure on terrestrial atmospheric vorticity

Abstract The solar magnetic sector structure has a sizable and reproducible influence on tropospheric and lower stratospheric vorticity. The average vorticity during winter in the Northern Hemisphere north of 2ON latitude reaches a minimum approximately one day after the passing of a sector boundary, and then increases during the following two or three days. The effect is found at all heights within the troposphere, but is not prominent in the stratosphere, except at the lower levels. No single longitudinal interval appears to dominate the effect.

Long-term evolution of solar sector structure

The large-scale structure of the solar magnetic field during the past five sunspot cycles (representing by implication a much longer interval of time) has been investigated using the polarity (toward or away from the Sun) of the interplanetary magnetic field as inferred from polar geomagnetic observations. The polarity of the interplanetary magnetic field has previously been shown to be closely related to the polarity (into or out of the Sun) of the large-scale solar magnetic field. It appears that a solar structure with four sectors per rotation persisted through the past five sunspot cycles with a synodic rotation period near 27.0 days, and a small relative westward drift during the first half of each sunspot cycle and a relative eastward drift during the second half of each cycle. Superposed on this four-sector structure there is another structure with inward field polarity, a width in solar longitude of about 100° and a synodic rotation period of about 28 to 29 days. This 28.5 day structure is usually most prominent during a few years near sunspot maximum. Some preliminary comparisons of these observed solar structures with theoretical considerations are given.

The mean magnetic field of the Sun: Observations at Stanford

A solar telescope has been built at Stanford University to study the organization and evolution of large-scale solar magnetic fields and velocities. The observations are made using a Babcock-type magnetograph which is connected to a 22.9 m vertical Littrow spectrograph. Sun-as-a-star integrated light measurements of the mean solar magnetic field have been made daily since May 1975. The typical mean field magnitude has been about 0.15 G with typical measurement error less than 0.05 G. The mean field polarity pattern is essentially identical to the interplanetary magnetic field sector structure (see near the Earth with a 4 day lag). The differences in the observed structures can be understood in terms of a ‘warped current sheet’ model.

A model combining the polar and the sector structured solar magnetic fields

A phenomenological model of the interplay between the polar magnetic fields of the Sun and the solar sector structure is discussed. Current sheets separate regions of opposite polarity and mark the sector boundaries in the corona. The sheets are visible as helmet streamers. The solar sector boundary is tilted with respect to central meridian, and boundaries with opposite polarity change are oppositely tilted. The tilt of a given type of boundary [(+, −) or (−, +)] changes systematically during the sunspot cycle as the polarity of the polar fields reverses. Similar reversals of the position of the streamers at the limbs takes place.If we consider (a) a sunspot cycle where the northern polar field is inward (−) during the early part of the cycle and (b) a (+, −) sector boundary at central meridian then the model predicts the following pattern; a streamer at high northern latitudes should be observed over the west limb together with a corresponding southern streamer over the east limb. The current sheet runs now NW-SE. At sunspot maximum the boundary is more in the N-S direction; later when the polar fields have completed their reversal the boundary runs NE-SW and the northern streamer should be observed over the east limb and the southern streamer over the west limb.Observational evidence in support of the model is presented, especially the findings of Hansen, Sawyer and Hansen and Koomen and Howard that the K-corona is highly structured and related to the solar sector structure.

Structure of the extended solar magnetic field and the sunspot cycle variation in cosmic ray intensity

THE interplanetary magnetic field within several astronomical units of the Sun appears to have one polarity in most of the hemisphere north of the solar equatorial plane and the opposite polarity in most of the hemisphere south of the equatorial plane1–7. The two hemispheres are separated by a curved current sheet that typically crosses the solar equatorial plane in either two or four places, thus dividing the equatorial region into either two or four sectors. Near sunspot minimum, at 1 AU the curved current sheet has a spread in latitude of typically ± 15°, so that the sector boundary (the current sheet separating the two hemispheres of opposed field polarity) is almost parallel to the solar equatorial plane. In the photosphere, on the other hand, the sector boundary makes an angle of ∼ 90° with the equatorial plane8. At 1.5 R\cirċ, in 1972 and 1973, the angle between the sector boundary and the equatorial plane was ∼ 45° (ref. 9), and at 3–10 R\cirċ the angle between boundary and plane was ∼ 25° (ref. 10). A schematic diagram of this structure for the case of four sectors is shown in Fig. 1. We here propose that a connection exists between the extent of these magnetic fields and the observed variations in cosmic ray intensity at the Earth.

Reconstruction of the Sunspot Group Number: The Backbone Method

We have reconstructed the sunspot-group count, not by comparisons with other reconstructions and correcting those where they were deemed to be deficient, but by a re-assessment of original sources. The resulting series is a pure solar index and does not rely on input from other proxies, e.g. radionuclides, auroral sightings, or geomagnetic records. “Backboning” the data sets, our chosen method, provides substance and rigidity by using long-time observers as a stiffness character. Solar activity, as defined by the Group Number, appears to reach and sustain for extended intervals of time the same level in each of the last three centuries since 1700 and the past several decades do not seem to have been exceptionally active, contrary to what is often claimed.

Asymmetric Solar Polar Field Reversals

The solar polar fields reverse because magnetic flux from decaying sunspots moves toward the poles, with a preponderance of flux from the trailing spots. If there is a strong asymmetry, in the sense that most activity is in the northern hemisphere, then that excess flux will move toward the north pole and reverse that pole first. If there is more activity in the south later on, then that flux will help to reverse the south pole. In this way, two humps in the solar activity and a corresponding difference in the time of reversals develop (in the ideal case). Such a difference was originally noted in the very first observation of polar field reversal just after the maximum of the strongly asymmetric solar cycle 19, when the southern hemisphere was most active before sunspot maximum and the south pole duly reversed first, followed by the northern hemisphere more than a year later, when that hemisphere became most active. Solar cycles since then have had the opposite asymmetry, with the northern hemisphere being most active before solar maximum. We show that polar field reversals for these cycles have all happened in the north first, as expected. This is especially noteworthy for the present solar cycle 24. We suggest that the association of two or more peaks of solar activity when separated by hemispheres with correspondingly different times of polar field reversals is a general feature of the cycle, and that asymmetric polar field reversals are simply a consequence of the asymmetry of solar activity.

DECREASING SUNSPOT MAGNETIC FIELDS EXPLAIN UNIQUE 10.7 cm RADIO FLUX

Infrared spectral observations of sunspots from 1998 to 2011 have shown that on average sunspots changed, the magnetic fields weakened, and the temperatures rose. The data also show that sunspots or dark pores can only form at the solar surface if the magnetic field strength exceeds about 1500 G. Sunspots appear at the solar surface with a variety of field strengths, and during the period from 1998 to 2002 a histogram of the sunspot magnetic fields shows a normal distribution with a mean of 2436 ± 26 G and a width of 323 ± 20 G. During this observing period the mean of the magnetic field distribution decreased by 46 ± 6 G per year, and we assume that as the 1500 G threshold was approached, magnetic fields appeared at the solar surface which could not form dark sunspots or pores. With this assumption we propose a quantity called the sunspot formation fraction and give an analytical form derived from the magnetic field distribution. We show that this fraction can quantitatively explain the changing relationship between sunspot number and solar radio flux measured at 10.7 cm wavelengths.