Bimodal distribution of area-weighted latitude of sunspots and solar North-South asymmetry

We study the latitudinal distribution of sunspots observed from 1874 to 2009 using the center-of-latitude (COL). We calculate COL by taking the area-weighted mean latitude of sunspots for each calendar month. We then form the latitudinal distribution of COL for the sunspots appearing in the northern and southern hemispheres separately, and in both hemispheres with unsigned and signed latitudes, respectively. We repeat the analysis with subsets which are divided based on the criterion of which hemisphere is dominant for a given solar cycle. Our primary findings are as follows: (1) COL is not monotonically decreasing with time in each cycle. Small humps can be seen (or short plateaus) around every solar maxima. (2) The distribution of COL resulting from each hemisphere is bimodal, which can well be represented by the double Gaussian function. (3) As far as the primary component of the double Gaussian function is concerned, for a given data subset, the distributions due to the sunspots appearing in two different hemispheres are alike. Regardless of which hemisphere is magnetically dominant, the primary component of the double Gaussian function seems relatively unchanged. (4) When the northern (southern) hemisphere is dominant the width of the secondary component of the double Gaussian function in the northern (southern) hemisphere case is about twice as wide as that in the southern (northern) hemisphere. (5) For the distribution of the COL averaged with signed latitude, whose distribution is basically described by a single Gaussian function, it is shifted to the positive (negative) side when the northern (southern) hemisphere is dominant. Finally, we conclude by briefly discussing the implications of these findings on the variations in the solar activity.     

Statistical behavior of sunspot groups on the solar disk

In the present study we have produced a diagram of the latitude distribution of sunspot groups from the year 1874 through 1999 and examined statistical characteristics of the mean latitude of sunspot groups. The reliability of the observed data set prior to solar cycle 19 is found quite low as compared with that of the data set observed after cycle 19. A correlation is found between maximum latitude at which first sunspot groups of a new cycle appear and the maximum solar activity of the cycle. It is inferred that solar magnetic activity during the early part of an extended solar cycle may contain some information about the strength of forthcoming solar cycle. A formula is given to describe latitude change of sunspot groups with time during an extended solar cycle. The latitude-migration velocity is found to be largest at the beginning of solar cycle and decreases with time as the cycle progresses with a mean migration velocity of about 1.61° per year.     

Sunspot Group Decay

We examine daily records of sunspot group areas (measured in millionths of a solar hemisphere or μHem) for the last 130 years to determine the rate of decay of sunspot group areas. We exclude observations of groups when they are more than 60° in longitude from the central meridian and only include data when at least three days of observations are available following the date of maximum area for a group’s disk passage. This leaves data for over 18 000 measurements of sunspot group decay. We find that the decay rate increases linearly from 28 μHem day⁻¹ to about 140 μHem day⁻¹ for groups with areas increasing from 35 μHem to 1000 μHem. The decay rate tends to level off for groups with areas larger than 1000 μHem. This behavior is very similar to the increase in the number of sunspots per group as the area of the group increases. Calculating the decay rate per individual sunspot gives a decay rate of about 3.65 μHem day⁻¹ with little dependence upon the area of the group. This suggests that sunspots decay by a Fickian diffusion process with a diffusion coefficient of about 10 km² s⁻¹. Although the 18 000 decay rate measurements are lognormally distributed, this can be attributed to the lognormal distribution of sunspot group areas and the linear relationship between area and decay rate for the vast majority of groups. We find weak evidence for variations in decay rates from one solar cycle to another and for different phases of each sunspot cycle. However, the strongest evidence for variations is with latitude and the variations with cycle and phase of each cycle can be attributed to this variation. High latitude spots tend to decay faster than low latitude spots.     

Differential rotation of the sun determined tracing sunspots and oscillations of sunspot tilt angle

The time and spatial characteristics of 324 large sunspots (S50 millionths of the solar hemisphere) selected from the Abastumani Astrophysical Observatory photoheliogram collection (1950–1990) have been studied. The variations of sunspot angular rotation velocity residuals and oscillations of sunspot tilt angle were analyzed. It has been shown that the differential rotation rate of selected sunspots correlates on average with the solar cycle. The deceleration of differential rotation of large sunspots begins on the ascending arm of the activity curve and ends on the descending arm reaching minimum near the epochs of solar activity maxima. This behavior disappears during the 21st cycle. The amplitudes and periods of sunspot tilt-angle oscillations correlate well with the solar activity cycle. Near the epochs of activity maximum there appear sunspots with large amplitudes and periods showing a significant scatter while the scatter near the minimum is rather low. We also found evidence of phase difference between the sunspot angular rotation velocity and the amplitudes and periods of tilt-angle oscillations.     

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.     

Evolution of polar coronal holes and sunspots during cycles 21 and 22

A very good correlation between the evolution of polar coronal hole size and sunspot number half a solar cycle later was found by Bravo and Otaola for solar cycle 21. In this paper we use a more complete set of data to reanalyse the relationship for solar cycle 21 and investigate the same relationship for solar cycle 22. We find that the complete set of data for cycle 21 yields a slightly different time shift for the best correlation between sunspots and holes and that the time shift for cycle 22 is different from that of cycle 21. However, because of limited availability of data of cycle 22, we consider it necessary to wait until the end of this cycle in order to decide if the difference is statistically significant or not. We also found that the time between successive peaks of smoothed polar hole area and smoothed sunspot number is the same in both cycles. This may provide a useful tool for the forecasting of future sunspot maxima. The constant of proportionality between polar coronal hole area and sunspot number can be seen to be different in both cycles. We discuss this difference and interpret it in terms of a different magnitude of the polar field strength in the two cycles.     

Total Solar Irradiance Variation During Rapid Sunspot Growth

Large sunspot areas correspond to dips in the total solar irradiance (TSI), a phenomenon associated with the local suppression of convective energy transport in the spot region. This results in a strong correlation between sunspot area and TSI. During the growth phase of a sunspot other physics may affect this correlation; if the physical growth of the sunspot resulted in surface flows affecting the temperature, for example, we might expect to see an anomalous variation in TSI. In this paper we study NOAA active region 8179, in which large sunspots suddenly appeared near disk center, at a time (March 1998) when few competing sunspots or plage regions were present on the visible hemisphere. We find that the area/TSI correlation does not significantly differ from the expected pattern of correlation, a result consistent with a large thermal conductivity in solar convection zone. In addition we have searched for a smaller-scale effect by analyzing white-light images from MDI (the Michelson Doppler Imager) on SOHO. A representative upper-limit energy consistent with the images is on the order of 3×10³¹ ergs, assuming the time scale of the actual spot area growth. This is of the same order of magnitude as the buoyant energy of the spot emergence even if it is shallow. We suggest that detailed image analyses of sunspot growth may therefore show `transient bright rings' at a detectable level.     

Bimodal Distribution of Magnetic Fields and Areas of Sunspots

We applied automatic identification of sunspot umbrae and penumbrae to daily observations from the Helioseismic Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) to study their magnetic flux density (B) and area (A). The results confirm an already known logarithmic relationship between the area of sunspots and their maximum flux density. In addition, we find that the relation between average magnetic flux density ( $B_{\rm avg}$ ) and sunspot area shows a bimodal distribution: for small sunspots and pores (A≤20 millionth of solar hemisphere, MSH), $B_{\rm avg} \approx 800~\mbox{G}$ (gauss), and for large sunspots (A≥100 MSH), $B_{\rm avg}$ is about 600 G. For intermediate sunspots, average flux density linearly decreases from about 800 G to 600 G. A similar bimodal distribution was found in several other integral parameters of sunspots. We show that this bimodality can be related to different stages of sunspot penumbra formation and can be explained by the difference in average inclination of magnetic fields at the periphery of small and large sunspots.     

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).     

Solar Cycle Predictions based on Solar Activity at Different Solar Latitudes

Many methods of predictions of sunspot maximum number use data before or at the preceding sunspot minimum to correlate with the following sunspot maximum of the same cycle, which occurs a few years later. Kane and Trivedi (Solar Phys. 68, 135, 1980) found that correlations of R _z(max) (the maximum in the 12-month running means of sunspot number R _z) with R _z(min) (the minimum in the 12-month running means of sunspot number R _z) in the solar latitude belt 20° – 40°, particularly in the southern hemisphere, exceeded 0.6 and was still higher (0.86) for the narrower belt > 30° S. Recently, Javaraiah (Mon. Not. Roy. Astron. Soc. 377, L34, 2007) studied the relationship of sunspot areas at different solar latitudes and reported correlations 0.95 – 0.97 between minima and maxima of sunspot areas at low latitudes and sunspot maxima of the next cycle, and predictions could be made with an antecedence of more than 11 years. For the present study, we selected another parameter, namely, SGN, the sunspot group number (irrespective of their areas) and found that SGN(min) during a sunspot minimum year at latitudes > 30° S had a correlation +0.78±0.11 with the sunspot number R _z(max) of the same cycle. Also, the SGN during a sunspot minimum year in the latitude belt (10° – 30° N) had a correlation +0.87±0.07 with the sunspot number R _z(max) of the next cycle. We obtain an appropriate regression equation, from which our prediction for the coming cycle 24 is R _z(max )=129.7±16.3.     

Detection of the Long-Term Microwave `Darkening' Before the 14 July 2000 Flare

The latitudinal distribution of sunspot groups over a solar cycle is investigated. Although individual sunspot groups of a solar cycle emerge randomly at any middle and low latitude, the whole latitudinal distribution of sunspot groups of the cycle is not stochastic and, in fact, can be represented by a probability density function of the distribution having maximum probability at about 15.5°. The maximum amplitude of a solar cycle is found to be positively correlated against the number of sunspot groups at high latitude (35°) over the cycle, as well as the mean latitude. Also, the relation between the asymmetry of sunspot groups and its latitude is investigated, and a pattern of the N-S asymmetry in solar activity is suggested.     

Comparison of the Variations of CMEs and ICMEs with those of other Solar and Interplanetary Parameters During Solar Cycle 23

This paper examines the variations of coronal mass ejections (CMEs) and interplanetary CMEs (ICMEs) during solar cycle 23 and compares these with those of several other indices. During cycle 23, solar and interplanetary parameters had an increase from 1996 (sunspot minimum) to ∼2000, but the interval 1998–2002 had short-term fluctuations. Sunspot numbers had peaks in 1998, 1999, 2000 (largest), 2001 (second largest), and 2002. Other solar indices had matching peaks, but the peak in 2000 was larger than the peak in 2001 only for a few indices, and smaller or equal for other solar indices. The solar open magnetic flux had very different characteristics for different solar latitudes. The high solar latitudes (45^∘–90^∘) in both N and S hemispheres had flux evolutions anti-parallel to sunspot activity. Fluxes in low solar latitudes (0^∘–45^∘) evolved roughly parallel to sunspot activity, but the finer structures (peaks etc. during sunspot maximum years) did not match with sunspot peaks. Also, the low latitude fluxes had considerable N–S asymmetry. For CMEs and ICMEs, there were increases similar to sunspots during 1996–2000, and during 2000–2002, there was good matching of peaks. But the peaks in 2000 and 2001 for CMEs and ICMEs had similar sizes, in contrast to the 2000 peak being greater than the 2001 peak for sunspots. Whereas ICMEs started decreasing from 2001 onwards, CMEs continued to remain high in 2002, probably due to extra contribution from high-latitude prominences, which had no equivalent interplanetary ICMEs or shocks. Cosmic ray intensity had features matching with those of sunspots during 2000–2001, with the 2000 peak (on a reverse scale, actually a cosmic ray decrease or trough) larger than the 2001 peak. However, cosmic ray decreases started with a delay and ended with a delay with respect to sunspot activity.     

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).     

Study of Differences Between Sunspot and White Light Facular Area Data Determined from SDO/HMI and SOHO/MDI Observations

Sunspot and white light facular areas are important data for solar activity and are used, for example, in the study of the evolution of sunspots and their effect on solar irradiance. Solar Dynamic Observatory??s Helioseismic and Magnetic Imager (SDO/HMI) solar images have much higher resolution (??0.5????pixel^?1) than Solar and Heliospheric Observatory??s Michelson Doppler Imager (SOHO/MDI) solar images (??2????pixel^?1). This difference in image resolution has a significant impact on the sunspot and white light facular areas measured in the two datasets. We compare the area of sunspots and white light faculae derived from SDO/HMI and SOHO/MDI observations. This comparison helps the calibration of the SOHO sunspot and facular area to those in SDO observations. We also find a 0.22 degree difference between the North direction in SDO/HMI and SOHO/MDI images.     

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.     

Tilt of Sunspot Bipoles in Solar Cycles 15 to 24

We use recently digitized sunspot drawings from Mount Wilson Observatory to investigate the latitudinal dependence of tilt angles of active regions and its change with solar cycle. The drawings cover the period from 1917 to present and contain information as regards polarity and strength of magnetic field in sunspots. We identified clusters of sunspots of same polarity, and used these clusters to form “bipole pairs”. The orientation of these bipole pairs was used to measure their tilts. We find that the latitudinal profile of tilts does not monotonically increase with latitude as most previous studies assumed, but instead, it shows a clear maximum at about 25?–?30 degree latitudes. Functional dependence of tilt (\(\gamma\)) on latitude (\(\varphi\)) was found to be \(\gamma= (0.20\pm0.08) \sin(2.80 \varphi) + (-0.00\pm0.06)\). We also find that latitudinal dependence of tilts varies from one solar cycle to another, but larger tilts do not seem to result in stronger solar cycles. Finally, we find the presence of a systematic offset in tilt of active regions (non-zero tilts at the equator), with odd cycles exhibiting negative offset and even cycles showing the positive offset.     

大黑子群对太阳总辐照度的影响

本文用云南天文台在第２２周太阳活动峰年期间拍摄到的大太阳黑子群照相资料，太阳黑子目视描述资料，以及Ｎｉｍｂｕｓ—７卫星上辐射计测量的太阳总辐照度，分别计算了太阳总辐射照度与大黑子群的本影视面积，大黑子群全群视面积和日面上全部黑子的总视面积的相关系数。结果表明，太阳总辐射照度与这三种视面积均存在强的负相关。其中与大黑子群本影视面积的相关最强，其次是与全群视面积的相关，最后是与日面上全部黑子的总视面积的相关。并对以上结果和其它有关结果进行了分析和讨论。     

From Sunspot Area to Solar Variability: A Linear Transformation

The relationship between sunspot area and other observable solar parameters, such as spectral solar irradiance or total magnetic flux, is frequently sought by examining scatterplots of daily data, which generally show a non-linear distribution of points. We show that the scatterplots are consistent with our published result that these observable solar parameters are related to sunspot area by a transformation that is both linear and time invariant, namely by convolution with a finite impulse response function. Most solar parameters are affected by extended active regions, not just by sunspots. The fact that a complex active region evolves much more slowly than its associated sunspots provides a simple physical explanation of the observed non-linearities in scatterplots.     

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.     

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.