Statistics of the largest sunspot and facular areas per solar cycle

The statistics of extreme values is used to investigate the statistical properties of the largest areas of sunspots and photospheric faculae per solar cycle. The largest values of the synodic-solar-rotation mean areas of umbrae, whole spots and faculae, which have been recorded for nine solar cycles, are each shown to comply with the general form of the extreme value probability function. Empirical expressions are derived for the three extreme value populations from which the characteristic statistical parameters, namely the mode, median, mean and standard deviation, can be calculated for each population. These three extreme value populations are also used to find the expected ranges of the extreme areas in a group of solar cycles as a function of the number of cycles in the group. The extreme areas of umbrae and whole spots have a dispersion comparable to that found by Siscoe for the extreme values of sunspot number, whereas the extreme areas of faculae have a smaller dispersion which is comparable to that found by Siscoe for the largest geomagnetic storm per solar cycle. The expected range of the largest sunspot area per solar cycle for a group of one hundred cycles appears to be inconsistent with the existence of the prolonged periods of sunspot minima that have been inferred from the historical information on solar variability. This inconsistency supports the contention that there are temporal changes of solar-cycle statistics during protracted periods of sunspot minima (or maxima). Indeed, without such temporal changes, photospheric faculae should have been continually observable throughout the lifetime of the Sun.     

Latitude variations of photospheric activity areas with particular reference to solar faculae

Detailed studies of the development of photospheric activity centres for two solar cycles show that Spörer's Law holds in a very similar form to that applying to sunspots for the faculae which inhabit the sunspot zones. Similar differences between the two solar hemispheres can arise, and it seems to be confirmed that the average latitude of faculae tends to be a few degrees poleward of that of sunspots throughout a given cycle. It is shown that the normal averaging process involved in deriving Spörer's Law obscures a detail which is revealed in a breakdown into the variations within successive narrow latitude strips. These show the existence within a cycle of three separate maxima of activity occurring at different epochs and with different preferred latitudes. The main properties of these maxima are discussed.Now at NOAA, Environmental Data Service, NGSTDC, Boulder, Colo. 80302, U.S.A.     

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.     

Correlation Between the Sunspot Number,the Total Solar Irradiance,and the Terrestrial Insolation

Our study deals with the correlations between the solar activity on the one hand and the solar irradiance above the Earth’s atmosphere and at ground level on the other. We analyzed the combined ACRIM I+II time series of the total solar irradiance (TSI), the Mauna Loa time series of terrestrial insolation data, and data of terrestrial cosmic ray fluxes. We find that the correlation between the TSI and the sunspot number is strongly non-linear. We interpret this as the net balance between brightening by faculae and darkening by sunspots where faculae dominate at low activity and sunspots dominate at high activity. Such a behavior is hitherto known from stellar analogs of the Sun in a statistical manner. We perform the same analysis for the Mauna Loa data of terrestrial insolation. Here we find that the linear relation between sunspot number and insolation shows more than 1% rise in insolation by sunspot number variations which is much stronger than for the TSI. Our conclusion is that the Earth atmosphere acts as an amplifier between space and ground, and that the amplification is probably controlled by solar activity. We suspect the cosmic rays intensity as the link between solar activity and atmospheric transparency. A Fourier analysis of the time series of insolation shows three dominant peaks: 10.5, 20.4, and 14.0 years. As a matter of fact, the cosmic rays data show the same pattern of significant peaks: 10.7, 22.4, and 14.9 years. This analogy supports our idea that the cosmic rays variation has influence on the transparency of the Earth atmosphere.     

Periodicity of Total Solar Irradiance

We investigate the periodicity in the PMOD composite of the daily total solar irradiance (TSI) from 21 September 1978 to 9 June 2009. Besides the Schwabe cycle period (10.32 years), the quasi-rotation period is found to be statistically significant in TSI, whose value is about 32 days, longer than that in sunspot activity (27 days), and it intermittently appears around the sunspot maximum times. The quasi-rotation period in TSI is inferred to be mainly caused by sunspot activity, but to be modulated by bright features as well. It was previously found that variations of TSI over a Schwabe solar cycle mainly come from the combination of the sunspots’ blocking and the intensification due to bright faculae, plages, and network elements, with a slight dominance of the bright-feature effect during the maximum of the Schwabe cycle. For the sunspot-blocking and the bright-feature effect to contribute to TSI over a Schwabe solar cycle, the former is inferred to lead the latter by 29 days at least.     

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。     

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.     

Do polar faculae on the sun predict a sunspot cycle?

The paper reports the results of the analysis of the data on polar faculae for three solar cycles (1960–1986) at the Kislovodsk Station of the Pulkovo Observatory and on polar bright points in Ca ii K line for two solar cycles (1940–1957) at the Kodaikanal Station of the Indian Institute of Astrophysics. We have noticed that the monthly numbers of polar faculae and polar bright points in Ca ii K line and monthly sunspot areas in each hemisphere of the following solar cycle have a correlation with each other. A new cycle of polar faculae and polar bright points in the Ca ii K line begins after the polar magnetic field reversal. We find that the smaller the period between the ending of the polar field reversal and the beginning of a new sunspot cycle is, the more intense is the cycle itself. The intensity of the forthcoming solar cycle (cycle 22) and the periods of strong fluctuations in activity expected in this cycle are also discussed.     

The Relative Phase Asynchronization between Sunspot Numbers and Polar Faculae

The monthly sunspot numbers compiled by Temmer et al. and the monthly polar faculae from observations of the National Astronomical Observatory of Japan, for the interval of March 1954 to March 1996, are used to investigate the phase relationship between polar faculae and sunspot activity for total solar disk and for both hemispheres in solar cycles 19, 20, 21 and 22. We found that (1) the polar faculae begin earlier than sunspot activity, and the phase difference exhibits a consistent behaviour for different hemispheres in each of the solar cycles, implying that this phenomenon should not be regarded as a stochastic fluctuation; (2) the inverse correlation between polar faculae and sunspot numbers is not only a long-term behaviour, but also exists in short time range; (3) the polar faculae show leads of about 50–71 months relative to sunspot numbers, and the phase difference between them varies with solar cycle; (4) the phase difference value in the northern hemisphere differs from that in the southern hemisphere in a solar cycle, which means that phase difference also existed between the two hemispheres. Moreover, the phase difference between the two hemispheres exhibits a periodical behaviour. Our results seem to support the finding of Hiremath (2010).     

A Comparison of Feature Classification Methods for Modeling Solar Irradiance Variation

Physical understanding of total and spectral solar irradiance variation depends upon establishing a connection between the temporal variability of spatially resolved solar structures and spacecraft observations of irradiance. One difficulty in comparing models derived from different data sets is that the many ways for identifying solar features such as faculae, sunspots, quiet Sun, and various types of “network” are not necessarily consistent. To learn more about classification differences and how they affect irradiance models, feature “masks” are compared as derived from five current methods: multidimensional histogram analysis of NASA/National Solar Observatory/Kitt Peak spectromagnetograph data, statistical pattern recognition applied to SOHO/Michelson Doppler Imager photograms and magnetograms, threshold masks allowing for influence of spatial surroundings applied to NSO magnetograms, and “one-trigger” and “three-trigger” algorithms applied to California State University at Northridge Cartesian Full Disk Telescope intensity observations. In general all of the methods point to the same areas of the Sun for labeling sunspots and active-region faculae, and available time series of area measurements from the methods correlate well with each other and with solar irradiance. However, some methods include larger label sets, and there are important differences in detail, with measurements of sunspot area differing by as much as a factor of two. The methods differ substantially regarding inclusion of fine spatial scale in the feature definitions. The implications of these differences for modeling solar irradiance variation are discussed. K.L. Harvey and S.R. Walton are deseased, to whom this paper is dedicated.     

Correlation of parameters characterizing the latitudinal distribution of sunspots

We attempt to establish a correlation between the solar activity level and some characteristics of the latitude distribution of sunspots by means of center-of-latitude (COL) of observed sunspots. We calculate the COL by taking the area weighted mean latitude of sunspots for each calendar month during a cycle, and adopt the cycle-integrated sunspot area as a measure of the strength of a cycle. We first determine the latitudinal distribution of COL of sunspots. We then compute three different statistical correlations between the cycle-integrated sunspot areas and the fitting parameters of all sunspot cycles from 1878 to 2009. Our main findings are as follows: (1) The distribution of COL is bimodal well represented by a double Gaussian function. (2) Ignoring cycle 19, the characteristic width of the distribution of COL shows a significant correlation with the cycle amplitude. (3) A correlation between the location of the maxima of the COL distribution (either centroid₁ or centroid₂) and the sum of sunspot area can be found, when the data point corresponding to the solar cycle 19 is omitted.     

The influence of faculae on sunspot heat blocking

We study the influence of faculae on sunspot heat blockage using a thermal model based on eddy heat diffusion through the convection zone. The facula is represented as a localized area of excess emission surrounding the sunspot, which is represented as a thermal plug. Our computations using a range of reasonable combinations of spot and facular depths show no significant influence of the facula on the long storage times of heat blocked by sunspots. However, the local cooling of surface layers produced by excess facular emission in this model propagates globally within the convection zone in a similar way to the heating produced by a spot. The net effect of spots and faculae on L over time scales longer than an active region lifetime should thus be determined by the global sum of sunspot flux deficits and facular excesses.     

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.     

The He I 10830 Å Line as an Indicator of Solar Activity

The behavior of the He I 10830 Å infrared triplet parameters in active and quiet solar regions was traced from 1976 until 2000. We analyze the correlation between the central depth of the main He I line component and other solar activity indices: the Wolf number, the radiation flux at a frequency of 2800 MHz, the mean number of flares in sunspot groups, and the mean solar magnetic field. We show that the strong correlation between the He I 10830 Å line depth and the phase of the 11-year solar cycle allows this depth to be effectively used as a new solar activity index both on long time scales (years) and on times scales of the order of a month or even days. The suggested new activity index is shown to have advantages over the universally accepted indices. The depth of the He I 10830 Å line in quiet regions was found to increase from the phase of minimum solar activity to the phase of maximum by a factor of about 2. In active regions, this increase is less than 30%. The differences between the cyclic variations of the chromospheric He I 10830 Å line radiation in active and quiet structures on the solar disk are indicative of the probable differences in the nature of cyclicity and its manifestations in magnetic fields of different spatial scales. The background magnetic fields appear to vary during the solar cycle more strongly than do the local fields associated with sunspots, faculae, and activity complexes. We suggest using regular observations in the He I 10830 Å line to predict solar activity.     

The 10-year time delay of the solar cycle luminosity modulation of the Sun behind the solar cycle magnetic oscillation

We found an evidence that the solar cycle luminosity modulation of the Sun deduced from the total irradiance modulation which was measured by the Earth Radiation Budget (ERB) experiment on board of Nimbus 7 from November 16, 1978 to December 13, 1993 was not in phase with the solar cycle magnetic oscillation when we used the sunspot relative number as its index. The modulation was delayed in time behind the solar cycle magnetic oscillation by an amount of about 10.3 years on the order of length of one solar cycle. In order to quantitatively evaluate the correlation between the two quantities, we devised a method to extract characteristics which were proper to a particular solar cycle by defining a new index of the correlation called multiplied correlation index (MCI). We found that the characteristics of the ERB data time profile between solar cycles 21 and 22 were more similar to those of the solar cycle magnetic oscillation between solar cycles 20 and 21 than those between solar cycles 21 and 22 and thus the time profile of the luminosity modulation from the maximum phase of solar cycle 21 to the declining phase of the solar cycle 22 corresponded to the solar cycle magnetic oscillation from the maximum phase of solar cycle 20 to the declining phase of solar cycle 21. We interpret this phenomenon as an evidence that main features of the modulation is not caused by dark sunspots and bright faculae and plages on the surface of the Sun that should instantaneously affect the luminosity modulation but is caused by time-delayed modulation of global convection by the Lorentz force of the magnetic field of the solar cycle. The delay time of about 10.3 years is the time needed for the force to modify the flows of the convection and to modulate heat flow. Thus the delay time is a function of the strength of the magnetic field oscillation of the solar cycle which is represented by amplitude of the solar cycle. Accordingly, the delay time for other time intervals of the solar cycle magnetic oscillation with different amplitudes can be different from 10.3 years for the interval of the present analysis.     

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).     

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.     

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.     

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.     

Zonal Velocity Bands and the Solar Activity Cycle

We compare the zonal-flow pattern in subsurface layers of the Sun with the distribution of surface magnetic features such as sunspots and polar faculae. We demonstrate that, in the activity belt, the butterfly pattern of sunspots coincides with the fast stream of zonal flows, although part of the sunspot distribution does spill over to the slow stream. At high latitudes, the polar faculae and zonal-flow bands have similar distributions in the spatial and temporal domains.