Long-Term Variations in the Growth and Decay Rates of Sunspot Groups

Using the combined Greenwich (1874 – 1976) and Solar Optical Observatories Network (1977 – 2009) data on sunspot groups, we study the long-term variations in the mean daily rates of growth and decay of sunspot groups. We find that the minimum and the maximum values of the annually averaged daily mean growth rates are ≈ 52% day⁻¹ and ≈ 183% day⁻¹, respectively, whereas the corresponding values of the annually averaged daily mean decay rates are ≈ 21% day⁻¹ and ≈ 44% day⁻¹, respectively. The average value (over the period 1874 – 2009) of the growth rate is about 70% more than that of the decay rate. The growth and the decay rates vary by about 35% and 13%, respectively, on a 60-year time scale. From the beginning of Cycle 23 the growth rate is substantially decreased and near the end (2007 – 2008) the growth rate is lowest in the past about 100 years. In the extended part of the declining phase of this cycle, the decay rate steeply increased and it is largest in the beginning of the current Cycle 24. These unusual properties of the growth and the decay rates during Cycle 23 may be related to cause of the very long declining phase of this cycle with the unusually deep and prolonged current minimum. A ≈ 11-year periodicity in the growth and the decay rates is found to be highly latitude and time dependent and seems to exist mainly in the 0° – 10° latitude interval of the southern hemisphere. The strength of the known approximate 33 – 44-year modulation in the solar activity seems to be related to the north-south asymmetry in the growth rate. Decreasing and increasing trends in the growth and the decay rates indicate that the next 2 – 3 solar cycles will be relatively weak.     

Digitization of Sunspot Drawings by Staudacher in 1749 – 1796

Original drawings by J.C. Staudacher made in the period of 1749 – 1796 were digitized. The drawings provide information about the size of the sunspots and are therefore useful for analyses sensitive to sunspot area rather than Wolf numbers. The total sunspot area as a function of time is shown for the observing period. The sunspot areas measured do not support the proposition of a weak, “lost” cycle between cycles 4 and 5. We also evaluate the usefulness of the drawings for the determination of sunspot positions for future studies.     

The Observed Long- and Short-Term Phase Relation between the Toroidal and Poloidal Magnetic Fields in Cycle 23

The observed phase relations between the weak background solar magnetic (poloidal) field and strong magnetic field associated with sunspots (toroidal field) measured at different latitudes are presented. For measurements of the solar magnetic field (SMF) the low-resolution images obtained from Wilcox Solar Observatory are used and the sunspot magnetic field was taken from the Solar Feature Catalogues utilizing the SOHO/MDI full-disk magnetograms. The quasi-3D latitudinal distributions of sunspot areas and magnetic fields obtained for 30 latitudinal bands (15 in the northern hemisphere and 15 in the southern hemisphere) within fixed longitudinal strips are correlated with those of the background SMF. The sunspot areas in all latitudinal zones (averaged with a sliding one-year filter) reveal a strong positive correlation with the absolute SMF in the same zone appearing first with a zero time lag and repeating with a two- to three-year lag through the whole period of observations. The residuals of the sunspot areas averaged over one year and those over four years are also shown to have a well defined periodic structure visible in every two – three years close to one-quarter cycle with the maxima occurring at − 40° and + 40° and drifts during this period either toward the equator or the poles depending on the latitude of sunspot occurrence. This phase relation between poloidal and toroidal field throughout the whole cycle is discussed in association with both the symmetric and asymmetric components of the background SMF and relevant predictions by the solar dynamo models.     

Relationship between Rotating Sunspots and Flares

Active Region (AR) NOAA 10486 was a super AR in the declining phase of solar cycle 23. Dominated by the rapidly rotating positive polarity of an extensive δ sunspot, it produced several powerful flare-CMEs. We study the evolution and properties of the rotational motion of the major poles of positive polarities and estimate the accumulated helicity injected by them. We also present two homologous flares that occurred in the immediate periphery of the rotating sunspots. The main results are as follows: i) anticlockwise rotational motions are identified in the main poles of positive polarities in the AR; the fastest of them is about 220° for six days. ii) The helicity injection inferred from such rotational motion during the interval from October 25 to 30 is about − 3.0×10⁴³ Mx², which is comparable that calculated by the local correlation tracking (LCT) method (− 5.2×10⁴³ Mx²) in the whole AR. It is suggested that both methods reveal the essential topological properties of the AR, even if the former includes only the major poles and the fine features of the magnetic field are neglected. iii) It is found that there is a good spatial and temporal correspondence between the onset of two homologous CME-associated flares and the rotational motion of sunspots. This suggests that the rotational motions of sunspots not only relate to the transport of magnetic energy and complexity from the low atmosphere to the corona but may also play a key role in the onset of the homologous flares. Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users.     

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).     

A Curious History of Sunspot Penumbrae

Daily records of sunspot group areas compiled by the Royal Observatory, Greenwich, from May of 1874 through 1976 indicate a curious history for the penumbral areas of the smaller sunspot groups. On average, the ratio of penumbral area to umbral area in a sunspot group increases from 5 to 6 as the total sunspot group area increases from 100 to 2000 μHem (a μHem is 10^?6 the area of a solar hemisphere). This relationship does not vary substantially with sunspot group latitude or with the phase of the sunspot cycle. However, for the sunspot groups with total areas <?100 μHem, this ratio changes dramatically and systematically through this historical record. The ratio for these smallest sunspots is near 5.5 from 1874 to 1900. After a rapid rise to more than 7 in 1905, it drops smoothly to less than 3 by 1930 and then rises smoothly back to more than 7 in 1961. It then returns to near 5.5 from 1965 to 1976. The smooth variation from 1905 to 1961 shows no indication of any step-like changes that might be attributed to changes in equipment or personnel. The overall level of solar activity was increasing monotonically during this time period when the penumbra-to-umbra area ratio dropped to less than half its peak value and then returned. If this history can be confirmed by other observations (e.g. Mt. Wilson or Kodaikanal), it may impact our understanding of penumbra formation, our dynamo models, and our estimates of historical changes in the solar irradiance.     

The growth and decay of sunspot groups

Digitized Mount Wilson sunspot data from 1917 to 1985 are analyzed to examine the growth and decay rates of sunspot group umbral areas. These rates are distributed roughly symmetrically about a median rate of decay of a few hemisphere day^-1. Percentage area change rates average 502% day^-1 for growing groups and -45% day^-1 for decaying groups. These values are significantly higher than the comparable rates for plage magnetic fields because spot groups have shorter lifetimes than do plages. The distribution of percentage decay rates also differs from that of plage magnetic fields. Small spot groups grow at faster rates on average than they decay, and large spot groups decay on average at faster rates than they grow. Near solar minimum there is a marked decrease in daily percentage spot area growth rates. This decrease is not related to group area, nor is it due to latitude effects. Sunspot groups with rotation rates close to the average (for each latitude) have markedly slower average rates of daily group growth and decay than do those groups with rotation rates faster or slower than the average. Similarly, sunspot groups with latitude drift rates near zero have markedly slower average rates of daily group growth and decay than do groups with significant latitude drifts in either direction. Both of these findings are similar to results for plage magnetic fields. These various correlations are discussed in the light of our views of the connection of the magnetic fields of spot groups to subsurface magnetic flux tubes. It is suggested that a factor in the rates of growth or decay of spot groups and plages may be the inclination angle to the vertical of the magnetic fields of the spots or plages. Larger inclination angles may result in faster growth and decay rates.Operated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.     

Solar Rotation During the Period 1847?–?1849

Solar rotation rate has been measured using the sunspot positions recorded by W.C. Bond during the period 1847 – 1849 at the Harvard College Observatory. From the drawings carried out by Bond we have selected the sunspots and groups of sunspots with more reliable positions presented in three or more drawings on successive days. We have calculated from the positions of the selected sunspots (41 in total) a synodic rotation rate of ω=[(12.92±0.08)−(1.5±1.0)sin ² φ] degrees/day, where φ is the heliographic latitude. This rate, although slightly lower, is similar to the actual solar rotation rate, confirming no important changes in the solar rotation during the last 160 years.     

Intensity and Magnetic Field Distribution of Sunspots

We study the relationship between the brightness (I) and magnetic field (B) distributions of sunspots using 272 samples observed at the San Fernando Observatory and the National Solar Observatory, Kitt Peak, whose characteristics varied widely. We find that the I – B relationship has a quadratic form for the spots with magnetic field less than about 2000 G. The slope of the linear part of the I – B curve varies by about a factor of three for different types of spots. In general the slope increases as the spot approaches disk center. The I – B slope does not have a clear dependency on the spot size but the lower limit appears to increase as a function of the ratio of umbra and penumbra area. The I – B slope changes as a function of age of the sunspots. We discuss various sunspot models using these results.     

Long-Term Variations in the Solar Differential Rotation

Using Greenwich data (1879–1976) and SOON/NOAA data (1977–2002) on sunspot groups we found the following results: (i) The Sun's mean (over all the concerned cycles during 1879–1975) equatorial rotation rate (A) is significantly larger (≈0.1%) in the odd-numbered sunspot cycles (ONSCs) than in the even-numbered sunspot cycles (ENSCs). The mean rotation is significantly (≈10%) more differential in the ONSCs than in the ENSCs. North–south difference in the mean equatorial rotation rate is larger in the ONSCs than in the ENSCs. North–south difference in the mean latitude gradient of the rotation is significant in the ENSCs and insignificant in the ONSCs. (ii) The known very large decrease in A from cycle 13 to cycle 14 is confirmed. The amount of this decrease in the mean A was about 0.017 μrad s⁻¹. Also, we find that A decreased from cycle 17 to cycle 18 by about 0.008 μrad s⁻¹ and from cycle 21 to cycle 22 by about 0.016 μrad s⁻¹. From cycle 13 to cycle 14 the decrease in A was more in the northern hemisphere than in the southern hemisphere, it is opposite in the later two epochs. The time gap between the consecutive drops in A is about 44 years, suggesting the existence of a `44-yr' cycle or `double Hale cycle' in A. The time gap between the two large drops, viz., from cycle 13 to cycle 14 and from cycle 21 to cycle 22, is about 90 years (Gleissberg cycle). We predict that the next drop (moderate) in A will be occurring from cycle 25 to cycle 26 and will be followed by a relatively large-amplitude `double Hale cycle' of sunspot activity. (iii) Existence of a 90-yr cycle is seen in the cycle-to-cycle variation of the latitude gradient (B). A weak 22-yr modulation in B seems to be superposed on the relatively strong 90-yr modulation. (iv) The coefficient A varies significantly only during ONSCs and the variation has maximum amplitude in the order of 0.01 μrad s<sup>−1</sup> around activity minima. (v) There exists a good anticorrelation between the mean variation of B during the ONSCs and that during the ENSCs, suggesting the existence of a `22-yr' periodicity in B. The maximum amplitude of the variation of B is of the order of 0.05 μrad s⁻¹ around the activity minima. (vi) It seems that the well-known Gnevyshev and Ohl rule of solar activity is applicable also to the cycle-to-cycle amplitude modulation of B from cycle 13 to cycle 20, but the cycles 12 (in the northern hemisphere, Greenwich data) and 21 (in both hemispheres, SOON/NOAA data) seem to violate this rule in B. And (vii) All the aforesaid statistically significant variations in A and B seem to be related to the approximate 179-yr cycle, 1811–1989, of variation in the Sun's motion about the center of mass of the solar system.     

The Behavior of Sunspot Contrast during Cycle 23

Results are presented from a study of various sunspot contrast parameters in broadband red (672.3 nm) Cartesian full-disk digital images taken at the San Fernando Observatory (SFO) over eight years, 1997 – 2004, of the twenty-third sunspot cycle. A subset of over 2700 red sunspots was analyzed and values of average and maximum sunspot contrast as well as maximum umbral contrast were compared to various sunspot parameters. Average and maximum sunspot contrasts were found to be significantly correlated with sunspot area (r _s=− 0.623 and r _s=− 0.714, respectively). Maximum umbral contrast was found to be significantly correlated with umbral area (r _s=− 0.535). These results are in agreement with the works of numerous other authors. No significant dependence was detected between average contrast, maximum contrast, or maximum umbral contrast during the rising phase of the solar cycle (r _s=0.024, r _s=0.033, and r _s=0.064, respectively). During the decay phase, no significant correlation was found between average contrast or maximum contrast and time (r _s=− 0.057 and r _s=0.009, respectively), with a weak dependence seen between maximum umbral contrast and cycle (r _s=0.102).     

Sunspot groups at high latitude

Data of sunspot groups at high latitude (35°), from the year 1874 to the present (2000 January), are collected to show their evolutional behaviour and to investigate features of the yearly number of sunspot groups at high latitude. Subsequently, an evolutional pattern of sunspot group number at high latitude is given in this paper. Results obtained show that the number of sunspot groups of a solar cycle at high latitude rises to a maximum value about 1 yr earlier than the time of the maximum of sunspot relative numbers of the solar cycle, and then falls to zero more rapidly. The results also show that, at the moment, solar activity described by the sunspot relative numbers has not yet reached its minimum. In general, sunspot groups at high latitude have not appeared on the solar disc during the last 3 yr of a Wolf solar cycle. The asymmetry of the high latitude sunspot group number of a Wolf solar cycle can reflect the asymmetry of solar activity in the Wolf solar cycle, and it is suggested that one could further use the high latitude sunspot group number during the rising time of a Wolf solar cycle, maximum year included, to judge the asymmetry of solar activity over the whole solar cycle.     

Digitization of sunspot drawings by Spörer made in 1861–1894

Most of our knowledge about the Sun's activity cycle arises from sunspot observations over the last centuries since telescopes have been used for astronomy. The German astronomer Gustav Spörer observed almost daily the Sun from 1861 until the beginning of 1894 and assembled a 33‐year collection of sunspot data covering a total of 445 solar rotation periods. These sunspot drawings were carefully placed on an equidistant grid of heliographic longitude and latitude for each rotation period, which were then copied to copper plates for a lithographic reproduction of the drawings in astronomical journals. In this article, we describe in detail the process of capturing these data as digital images, correcting for various effects of the aging print materials, and preparing the data for contemporary scientific analysis based on advanced image processing techniques. With the processed data we create a butterfly diagram aggregating sunspot areas, and we present methods to measure the size of sunspots (umbra and penumbra) and to determine tilt angles of active regions. A probability density function of the sunspot area is computed, which conforms to contemporary data after rescaling. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Deceleration of the rotational velocities of sunspot groups during their evolution

Using the Greenwich Photoheliographic Results for the years 1874–1976 the daily rotational velocities for 955 recurrent and 13169 non-recurrent sunspot groups from the first day of their appearance and during their evolution have been determined. The rotational velocities were divided in six latitude strips with a width of five degrees and grouped according to the age of the groups. It was established that the rotational velocities of recurrent and non-recurrent sunspot groups decrease with time in all studied latitude strips. At their birth the recurrent spot groups rotate faster by about 0.15° day⁻¹ than the non-recurrent ones and settle, within the errors of measurements, to an about 0.5° day⁻¹ slower velocity value during the second disc passage. A comparison of our results with helioseismology measurements indicates that in the frame of the anchoring hypothesis, the recurrent sunspot groups at their birth could be coupled to the fast rotating layer at about r=0.93 R _⊙.     

Differential Rotation of Strong Magnetic Flux During Solar Cycles 21 – 23

In the present investigation we measure the differential rotation of strong magnetic flux during solar cycles 21 – 23 with the method of wavelet transforms. We find that the cycle-averaged synodic rotation rate of strong magnetic flux can be written as ω=13.47−2.58sin ² θ or ω=13.45−2.06sin ² θ−1.37sin ⁴ θ, where θ is the latitude. They agree well with the results derived from sunspots. A north–south asymmetry of the rotation rate is found at high latitudes (28°<θ<40°). The strong flux in the southern hemisphere rotates faster than that in the northern hemisphere by 0.2 deg day⁻¹. The asymmetry continued for cycles 21 – 23 and may be a secular property.     

Statistical Properties Of Sunspots In 1996–2004: I. Detection, North–South Asymmetry And Area Distribution

The first statistical results in sunspot distributions in 1996–2004 obtained from the Solar Feature Catalogues (SFC) are presented. A novel robust technique is developed for automated identification of sunspots on SOHO/MDI white-light (WL) full-disk solar images. The technique applies image standardization procedures for elimination of the limb darkening and non-circular image shape, uses edge-detection methods to find the sunspot candidates and their edges and morphological operations to smooth the features and fill in gaps. The detected sunspots are verified with the SOHO/MDI magnetograms by strong magnetic fields being present in sunspots. A number of physical and geometrical parameters of the detected sunspot features are extracted and stored in the relational SFC database including umbra/penumbra masks in the form of run-length data encoding of sunspot bounding rectangles. The detection results are verified by comparison with the manual daily detection results in Meudon and Locarno Observatories in 2002 and by correlation (about 96%) with the 4 year sunspot areas produced manually at NOAA. Using the SFC data, sunspot area distributions are presented in different phases of the solar cycle and hemispheres which reveals a periodicity of the north–south asymmetry with a period of about 7–8 years. The number of sunspots increases exponentially with the area decrease with the index slightly increasing from −1.15 (1997) to −1.34 (2001).     

Making Sense of Sunspot Decay. I. Parabolic Decay Law and Gnevyshev–Waldmeier Relation

In a statistical study of the decay of individual sunspots based on DPR data we find that the mean instantaneous area decay rate is related to the spot radius r_o and the maximum radius r_o as D = C_D r/r_o, C_D = 32.0±0.26 MSH day ^-1. This implies that sunspots on the mean follow a parabolic decay law; the traditional linear decay law is excluded by the data. The validity of the Gnevyshev–Waldmeier relationship between the maximum area A ₀ and lifetime T of a spot group, A₀/T 10 MSH day^-1, is also demonstrated for individual sunspots. No evidence is found for a supposed supergranular quantization of sunspot areas. Our results strongly support the recent turbulent erosion model of sunspot decay while all other models are excluded.     

Spatial variations in parameters of quasi-hourly sunspot fragment oscillations and a singular penumbra oscillator

We obtained three-dimensional interpolated portraits for the radial and torsional oscillations of fragments of 12 sunspots in the form of deviations of their polar coordinates from drift as functions of the time and distance from the sunspot center. We performed a wavelet analysis of the two orthogonal components and determined the dominant oscillation modes; the period varies between 40 and 100 min for different sunspots. We revealed two types of dominant modes, one is associated with the sunspot and the other is associated with its surrounding pores: the central-mode frequency depends on the maximum field strength of the sunspot and decreases from its center toward the boundary, while the peripheral-mode frequency depends on the heliographic latitude and decreases toward the sunspot boundary from the far periphery. We revealed radial variations in frequency and amplitude with a spatial period of 0.8 sunspot radius. The types of dominant modes and the radial variations in oscillation parameters are linked with the subphotospheric structure of an active region—with two types of spiral waves and concentric magnetic-field waves. We estimated the mean pore oscillation energy to be ～10³⁰ erg and found a singular oscillator with a mean energy of ～10³¹ erg in the penumbra at a distance of 0.8 sunspot radius. We argue that the singular penumbra oscillator is the source of solar flares.     

Photospheric Plasma Flows Around a Solar Spot

We study photospheric plasma flows in an active region NOAA 8375, by using uninterrupted high-resolution SOHO/MDI observations (137 intensity images, 44 hours of observations). The active region consists of a stable large spot and many small spots and pores. Analyzing horizontal flow maps, obtained with local correlation tracking technique, we found a system of stable persistent plasma flows existing in the active region. The flows start on either side of the sunspot and extend over 100′′ to the east. Our measurements show that the speed of small sunspots and pores, averaged over 44 hours, was about 100 m s⁻¹, which corresponds to root-mean-square longitudinal drifts of sunspots of 0.67°–0.76° day⁻¹. We conclude that these large-scale flows are due to faster proper motion of the large sunspot relative to the ambient photospheric plasma. We suggest that the flows may be a good carrier to transport magnetic flux from eroding sunspots into the outer part of an active region.     

Predicting the Amplitude of a Solar Cycle Using the North – South Asymmetry in the Previous Cycle: II. An Improved Prediction for Solar Cycle 24

Recently, using Greenwich and Solar Optical Observing Network sunspot group data during the period 1874 – 2006, Javaraiah (Mon. Not. Roy. Astron. Soc. 377, L34, 2007: Paper I), has found that: (1) the sum of the areas of the sunspot groups in 0° – 10° latitude interval of the Sun’s northern hemisphere and in the time-interval of −1.35 year to +2.15 year from the time of the preceding minimum of a solar cycle n correlates well (corr. coeff. r=0.947) with the amplitude (maximum of the smoothed monthly sunspot number) of the next cycle n+1. (2) The sum of the areas of the spot groups in 0° – 10° latitude interval of the southern hemisphere and in the time-interval of 1.0 year to 1.75 year just after the time of the maximum of the cycle n correlates very well (r=0.966) with the amplitude of cycle n+1. Using these relations, (1) and (2), the values 112±13 and 74±10, respectively, were predicted in Paper I for the amplitude of the upcoming cycle 24. Here we found that the north – south asymmetries in the aforementioned area sums have a strong ≈44-year periodicity and from this we can infer that the upcoming cycle 24 will be weaker than cycle 23. In case of (1), the north – south asymmetry in the area sum of a cycle n also has a relationship, say (3), with the amplitude of cycle n+1, which is similar to (1) but more statistically significant (r=0.968) like (2). By using (3) it is possible to predict the amplitude of a cycle with a better accuracy by about 13 years in advance, and we get 103±10 for the amplitude of the upcoming cycle 24. However, we found a similar but a more statistically significant (r=0.983) relationship, say (4), by using the sum of the area sum used in (2) and the north – south difference used in (3). By using (4) it is possible to predict the amplitude of a cycle by about 9 years in advance with a high accuracy and we get 87±7 for the amplitude of cycle 24, which is about 28% less than the amplitude of cycle 23. Our results also indicate that cycle 25 will be stronger than cycle 24. The variations in the mean meridional motions of the spot groups during odd and even numbered cycles suggest that the solar meridional flows may transport magnetic flux across the solar equator and potentially responsible for all the above relationships. The author did a major part of this work at the Department of Physics and Astronomy, UCLA, 430 Portola Plaza, Los Angeles, CA 90095-1547, USA.