A new look at wolf sunspot numbers in the late 1700's

Long-term homogeneous observations of solar activity or many solar cycles are essential for investigating many problems in solar physics and climatology. The one key parameter used in most long-term studies is the Wolf sunspot number, which is susceptible to observer bias, particularly because it is highly sensitive to the observer's ability to see the smallest sunspots. In this paper we show how the Wolf sunspot number can be derived from the number of sunspot groups alone. We utilize this approach to obtain a Group Wolf number. This technique has advantages over the classical method of determining the Wolf number because corrections for observer differences are reduced and long-term self-consistent time series can be developed. The level of activity can be calculated to an accuracy of ± 5% using this method. Applying the technique to Christian Horrebow's observations of solar cycles 1, 2, and 3 (1761–1777), we find that the standard Wolf numbers are nearly homogeneous with sunspot numbers measured from 1875 to 1976 except the peak of solar cycle 2 is too low by 30%. This result suggests that further analyses of early sunspot observations could lead to significant improvements in the uniformity of the measurements of solar activity. Such improvements could have important impacts upon our understanding of long-term variations in solar activity, such as the Gleissberg cycle, or secular variations in the Earth's climate.     

Two Early Sunspots Observers: Teodoro de Almeida and José Antonio Alzate

We present the sunspot ideas and observations of the 18th century Portuguese scholar Teodoro de Almeida (1722 – 1804) and Mexican scientist José Antonio Alzate (1737 – 1799). We describe the implications of dating a single sunspot observation performed by Almeida in the early 1760s, during the maximum of cycle number 1. A possible solar cycle peak in 1760 (instead of 1761) is investigated. We present several observations of sunspots obtained by Alzate during 1769 (partially associated with the Venus and Mercury transits) and also on 20 July 1786. We estimate 100±34 as the Group Sunspot Number for this date. These records were unknown and, therefore, not included in the database compiled by Hoyt and Schatten (1998).     

Overlooked sunspot observations by Hevelius in the early Maunder Minimum, 1653–1684

In the bookMachina Coelestis (1679), Johannes Hevelius lists his daily solar observations from 1653 to 1679. He mentions 19 sunspot groups during this interval, of which 14 are unique to Hevelius and five are confirmed by other observers. There are an additional 9 sunspot groups during this interval that were not observed by Hevelius. In five cases he was not observing, but in the other four cases he did observe but failed to comment upon sunspots. The spots he missed or failed to observe tend to occur near the end of his career. This suggests Hevelius occasionally missed sunspots but usually was a reliable observer. These observations are important because they provide us the only known daily listing of solar observations during the early years of the Maunder Minimum. They are also important because they were overlooked by Wolf, Spoerer, Maunder, Eddy, and others in their study of solar activity in the seventeenth century. They provide us the best record of the sunspot maximum of 1660 when one sunspot lasted at least 86 days as it traversed the solar disk four times. The same region was active for seven solar rotations.     

The effects of sunspots on solar irradiance

Sunspots have an obvious direct effect upon the visible radiant energy falling upon the Earth. We show how to estimate this effect and compare it quantitatively with recent observations of the solar total irradiance (Willson et al., 1981). The sunspots explain about half of the total observed variance of one-day averages. Since the sunspot effect on irradiance produces an asymmetry of the solar radiation, rather than (necessarily) a variation of the total luminosity, we have also estimated the sunspot population on the invisible hemisphere. This extrapolation allows us to estimate the true luminosity deficit produced by sunspots, in a manner that tends toward the correct long-term average value. We find no evidence for instantaneous global re-emission to compensate for the sunspot flux deficit.     

Relative sunspot numbers in the first half of eighteenth century

We revised relative sunspot numbers in the time interval 1700–1748 for which Wolf derived their annual means. The frequency of daily observations, counting simultaneously the number of sunspots and the number of sunspot groups necessary for determinating Wolf's relative sunspot numbers, is in this time interval very low and covers, on average, 4.8% of the number of all days only. There also exist incomplete observations not convenient to determine relative sunspot numbers. To enlarge the number of daily relative sunspot numbers we used the nonlinear, two-step interpolation method derived earlier by Letfus (1996, 1999). After interpolation, the mean value increased to 13.8%. Waldmeier (1968) found that the scaling factor k can be derived directly from the observed number of spots f and from the number of sunspot groups g. From the observations made at Zürich (Wolf and his assistants, Wolfer), at Peckeloh, and at Moncalieri during the years 1861–1928, we derived a new, more correct empirical relation. The resulting annual relative sunspot numbers are given in Table II. However, only for 26 years (53.0%) from the total number of 49 years was it possible to derive annual relative sunspot numbers. The observations were missing for the other years. This corresponds with results of Wolf, which gives the annual relative sunspot numbers for all 49 years. For the years when the data were missing, he marked these values as interpolated or very uncertain ones. Most of the observations originate from two data series (Kirch, Plantade), for which Wolf derived a higher scaling factor (k=2.0) than followed from the newly derived relation (k=1.40). The investigated time interval covers four solar cycles. After our results, the height of the first cycle (No. –4), given by Wolf, should be lowered by about two-thirds, the following two cycles (Nos. –3 and –2) lowered by one-third, as given by Wolf, and only the height of the fourth one (No. –1) should be unchanged. The activity levels of the cycles, as represented by group sunspot numbers, are lower by about one-fourth and, in the case of the first one (No. –4) even by two-thirds of the levels derived by us. The group sunspot numbers, derived from a much greater number of observations, have also greater credibility than other estimates. The shapes of the cycles, as given by Wolf, can be considered only as their more or less idealized form.     

Meridional motions of sunspot groups during eleven activity cycles

Greenwich data (1874–1976) are used for a time-dependent analysis of meridional motions of sunspot groups. We obtain the latitude-dependence of meridional motions of sunspot groups with respect to a mean latitude determined for half-year intervals. The daily meridional motions of groups are also given separately for growing and decaying sunspot groups. The development is determined from changes of sunspot areas. Our results are compared with the reductions performed by Howard (1991b) using the Mt. Wilson sunspot data from 1917 until 1985: Although we have smaller errors, we do not find any significant drift. We also do not find different trends in the meridional motions of growing as compared to decreasing sunspots.     

The extreme solar activity during october–november 2003

The positional measurements of sunspots from the Kodaikanal Observatory and Solar Geophysical data are used to study the association between occurrence of the abnormal activities of big sunspot groups that were observed during the period of October–November 2003 and occurrence of the flares. During the evolution of the sunspot groups, we have investigated the temporal variations in (i) areas; (ii) rotation rates; (iii) longitudinal extents; and (iv) number of small spots produced in a sunspot group. Among all these activity variations, we find that the spot groups that experience abnormal rotation rates during their evolutionary phases eventually trigger the flares.     

Magnetic fields of sunspots based on combined optical and radio observations

In the present paper we present the results of measurement of magnetic fields in some sunspots at different heights in the solar atmosphere, based on simultaneous optical and radio measurements. The optical measurements were made by traditional photographic spectral observations of Zeeman splitting in a number of spectral lines originating at different heights in the solar photosphere and chromosphere. Radio observations of the spectra and polarization of the sunspot - associated sources were made in the wavelength range of 2–4 cm using large reflector-type radio telescope RATAN-600. The magnetic field penetrating the hot regions of the solar atmosphere were found from the shortest wavelength of generation of thermal cyclotron emission (presumably in the third harmonic of electron gyrofrequency). For all the eight cases under consideration we have found that magnetic field first drops with height, increases from the photosphere to lower chromosphere, and then decreases again as we proceed to higher chromosphere and chromosphere-corona transition region. Radio measurements were found to be well correlated with optical measurements of magnetic fields for the same sunspot. An alternative interpretation implies that different lines used for magnetic field measurements refer to different locations on the solar surface. If this is the case, then the inversion in vertical gradients of magnetic fields may not exist above the sunspots. Possible sources of systematic and random errors are also discussed.     

On spatial characteristics of five-minute oscillations in the sunspot umbra

Using a differential method we have carried out observations of oscillations in six sunspots. Spectral lines Fe i 5434 Å and Fe i 5576 Å were used. Horizontal waves are not observed in the sunspot umbra photosphere. Results obtained indicate that, at least, the sunspot umbra oscillates as a single whole.     

On the sunspot transition region

The EUV line emission and relative line-of-sight velocity in the transition region between the chromosphere and corona of 36 sunspot regions are investigated, based on observations with the Coronal Diagnostic Spectrometer – CDS and the Solar Ultraviolet Measurements of Emitted Radiation – SUMER on the Solar and Heliospheric Observatory – SOHO. The most prominent features in the transition-region intensity maps are the sunspot plumes. In the temperature range between log T=5.2 and log T=5.6 we find that 29 of the 36 sunspots contain one or two sunspot plumes. The relative line-of-sight velocity in sunspot plumes is high and directed into the Sun in the transition region, for 19 of the sunspots the maximum velocity exceeds 25 km s^?1. The velocity increases with increasing temperature, reaches a maximum close to log T=5.5 and then decreases abruptly.

Attention is given to the properties of oscillations with a period of 3 min in the sunspot transition region, based on observations of six sunspots. Comparing loci with the same phase we find that the 3-min oscillations affect the entire umbral transition region and part of the penumbral transition region. Above the umbra the observed relation between the oscillations in peak line intensity and line-of-sight velocity is compatible with the hypothesis that the oscillations are caused by upward-propagating acoustic waves. Information about intensity oscillations in the low corona is obtained from observations of one sunspot in the 171 Å channel with the Transition Region And Coronal Explorer – TRACE. We conclude that we observe the 3-min sunspot oscillations in the chromosphere, the transition region and the low corona. The oscillations are observable over a wider temperature range than the sunspot plumes, and show a different spatial distribution than that of the plumes.

     

Absorption of acoustic waves by sunspots

Observations of the scattering of acoustic waves by sunspots show a substantial deficit in scattered power relative to incident power. A number of calculations have attempted to model this process in terms of absorption at the magnetohydrodynamic Alfvén resonance. The results presented here extend these calculations to the case of a highly structured axisymmetric translationally invariant flux-tube embedded in a uniform atmosphere. The fractional energy absorbed is calculated for models corresponding to flux-tubes of varying radius, mean flux-density and location below the photosphere. The effects of twist are also included.It is found that absorption can be very efficient even in models with low mean magnetic flux density, provided the flux is concentrated into intense slender annuli. Twist is found to increase the range of wave numbers over which absorption is efficient, but it does not remove the low absorption at low azimuthal orders which is a feature of resonance absorption calculations in axisymmetric geometry, and which is in conflict with observation.These results suggest that resonance absorption could be an efficient mechanism in plage fields and fibril sunspots as well as in monolithic sunspots. At present it is too early to make any definite deductions about sunspot structure from the observations, but the possible future use of sunspot seismology to resolve open questions in the theory of sunspots is briefly discussed.     

Equilibrium and decay of sunspots

We suggest a quantitative sunspot model developed in terms of mean-field magnetohydrodynamics (MHD). The model consistently describes the distributions of magnetic field, fluid velocity, and thermodynamic parameters in a sunspot and the surrounding matter. Two versions of the model allow the MHD equilibrium in sunspots and their slow decay to be analyzed. The baroclinic flow converging to the sunspot plays an important role in the equilibrium. Several calculated characteristics—almost uniform distributions of brightness and magnetic field inside sunspots, their abrupt changes at the boundary, and nearly linear decreases in the area and magnetic flux of decaying sunspots with time—qualitatively agree with the observations.     

Sunspot and Auroral Activity During Maunder Minimum

The extremely low sunspot activity during the period of the Maunder minimum 1645–1715 was confirmed by group sunspot numbers, a new sunspot index constructed by Hoyt and Schatten (1998a,b). Neither sunspots nor auroral data time behavior indicate the presence of 11-year solar cycles as stated by Eddy (1976). The evidence for solar cycles was found in the butterfly diagram, constructed from observations made at Observatoire de Paris. After Clivier, Boriakoff, and Bounar (1998) the solar cycles were reflected also in geomagnetic activity. Results are supported by the variation of cosmogenic isotopes ¹⁰Be and ¹⁴C. The majority of the observed 14 naked-eye sunspots occurred on days when telescopic observations were not available. A part of them appeared in the years when no spot was allegedly observed. Two-ribbon flares appear in plages with only very small or no sunspots. Some of these flares are geoactive. Most aurorae (90%), which were observed during the Maunder minimum, appeared in years when no spot was observed. Auroral events as a consequence of proton flares indicate that regions with enhanced magnetic field can occur on the Sun when these regions do not produce any sunspots.     

Erratum to: Width of Sunspot Generating Zone and Reconstruction of Butterfly Diagram

Based on the extended Greenwich – NOAA/USAF catalogue of sunspot groups, it is demonstrated that the parameters describing the latitudinal width of the sunspot generating zone (SGZ) are closely related to the current level of solar activity, and the growth of the activity leads to the expansion of the SGZ. The ratio of the sunspot number to the width of the SGZ shows saturation at a certain level of the sunspot number, and above this level the increase of the activity takes place mostly due to the expansion of the SGZ. It is shown that the mean latitudes of sunspots can be reconstructed from the amplitudes of solar activity. Using the obtained relations and the group sunspot numbers by Hoyt and Schatten (Solar Phys. 179, 189, 1998), the latitude distribution of sunspot groups (“the Maunder butterfly diagram”) for the eighteenth and the first half of the nineteenth centuries is reconstructed and compared with historical sunspot observations.     

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 Zürich suspot 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 Zürich 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.Operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation.     

Measurement of Kodaikanal White-Light Images – III. Rotation Rates and Activity Cycle Variations

The Kodaikanal sunspot data set covering the interval 1906–1987 is analyzed for differential rotation of sunspots of different sizes. As is known, smaller sunspots rotate faster than larger sunspots, and this result is verified in the analysis of this data set. These results agree well with the Mount Wilson sunspot results published earlier. The activity cycle dependence of sunspot rotation is studied. An increase in this rate at the minimum phase is seen, which has been reported earlier. It is demonstrated that this cycle variation is seen for sunspots in all size categories, which suggests that it is not a relative increase in the number of the faster-rotating small sunspots that causes the cycle dependence. These results are discussed as they may relate to subsurface dynamic properties of the Sun.     

Automatic Sunspots Detection on Full-Disk Solar Images using Mathematical Morphology

Sunspots are solar features located in active regions of the Sun, whose number is an indicator of the Sun’s magnetic activity. Therefore accurate detection and classification of sunspots are fundamental for the elaboration of solar activity indices such as the Wolf number. However, irregularities in the shape of the sunspots and their variable intensity and contrast with the surroundings, make their automated detection from digital images difficult. Here, we present a morphological tool that has allowed us to construct a simple and automatic procedure to treat digital photographs obtained from a solar telescope, and to extract the main features of sunspots. Comparing the solar indices computed with our algorithm against those obtained with the previous method exhibit an obvious improvement. A favorable comparison of the Wolf sunspot number time series obtained with our methodology and from other reference observatories is also presented. Finally, we compare our sunspot and group detection to that of other observatories.     

太阳黑子面积数与黑子数指标在大气预报中的应用对比分析

分别应用太阳黑子视面积数和太阳黑子相对数代表太阳活动水平与天津夏季降水总量进行相关分析,结果表明黑子面积指标明显优于黑子数.     

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.