We explore the latitudinal distribution of sunspots and pursue to establish a correlation between the statistical parameters of the latitudinal distribution of sunspots and characteristics of solar activity. For this purpose, we have statistically analyzed the daily sunspot areas and latitudes observed from May in 1874 to September in 2016. As results, we confirm that the maximum of the monthly averaged International Sunspot Number (ISN) strongly correlates with the mean number of sunspots per day, while the maximum ISN strongly anti-correlates with the number of spotless days. We find that both the maximum ISN and the mean number of sunspots per day strongly correlate with the the average latitude, the standard deviation, the skewness of the the latitudinal distribution of sunspots, while they appears to marginally correlate with the kurtosis. It is also found that the northern and southern hemispheres seem to show a correlated behavior in a different way when sunspots appearing in the northern and southern hemispheres are examined separately.

We study an association between the duration of solar activity and characteristics of the latitude distribution of sunspots by means of center-of-latitude (COL) of sunspots observed during the period from 1878 to 2008 spanning solar cycles 12 to 23. We first calculate COL by taking the area- weighted mean latitude of sunspots for each calendar month to determine the latitudinal distribution of COL of sunspots appearing in the long and short cycles separately. The data set for the long solar cycles consists of the solar cycles 12, 13, 14, 20, and 23. The short solar cycles include the solar cycles 15, 16, 17, 18, 19, 21, and 22. We then fit a double Gaussian function to compare properties of the latitudinal distribution resulting from the two data sets. Our main findings are as follows: (1) The main component of the double Gaussian function does not show any significant change in the central position and in the full-width-at-half-maximum (FWHM), except in the amplitude. They are all centered at  11◦ with FWHM of  5◦. (2) The secondary component of the double Gaussian function at higher latitudes seems to differ in that even though their width remains fixed at  4◦, their central position peaks at  22.1◦ for the short cycles and at  20.7◦ for the long cycles with quite small errors. (3) No significant correlation could be established between the duration of an individual cycle and the parameters of the double Gaussian. Finally, we conclude by briefly discussing the implications of these findings on the issue of the cycle 4 concerning a lost cycle.

The basic objective of helioseismology is to determine the structure and the dynamics of the Sun by analysing the frequency spectrum of the solar oscillations. Accurate frequency measurements provide information that enables us to probe the solar interior structure and the dynamics. Therefore the frequency of the solar oscillation is the most fundamental and important information to be extracted from the solar oscillation observation. This is why many efforts have been put into the development of accurate data analysis techniques, as well as observational efforts. To test one's data analysis method, a realistic artificial data set is essential because the newly suggested method is calibrated with a set of artificial data with predetermined parameters. Therefore, unless test data sets reflect the real solar oscillation data correctly, such a calibration is likely incomplete and a unwanted systematic bias may result in. Unfortunately, however, commonly used artificial data generation algorithms insufficiently accommodate physical properties of the stochastic excitation mechanism. One of reason for this is that it is computaionally very expensive to solve the governing equation directly. In this paper we discuss the nature of solar oscillation excitation and suggest an efficient algorithm to generate the artificial solar oscillation data. We also briefly discuss how the results of this work can be applied in the future studies.

Utilizing a new version of the sunspot number and group sunspot number dataset available since 2015, we have statistically studied the relationship between solar activity parameters describing solar cycles and the slope of the linear relationship between the monthly sunspot numbers and the monthly number of active days in percentage (AD). As an effort of evaluating possibilities in use of the number of active days to predict solar activity, it is worthwhile to revisit and extend the analysis performed earlier. In calculating the Pearson’s linear correlation coefficient r, the Spearman’s rank-order correlation coefficient rs, and the Kendall’s τ coefficient with the rejection probability, we have calculated the slope for a given solar cycle in three different ways, namely, by counting the spotless day that occurred during the ascending phase and the descending phase of the solar cycle separately, and during the period corresponding to solar minimum ± 2 years as well. We have found that the maximum solar sunspot number of a given solar cycle and the duration of the ascending phase are hardly correlated with the slope of a linear function of the monthly sunspot numbers and AD. On the other hand, the duration of a solar cycle is found to be marginally correlated with the slope with the rejection probabilities less than a couple of percent. We have also attempted to compare the relation of the monthly sunspot numbers with AD for the even and odd solar cycles. It is inconclusive, however, that the slopes of the linear relationship between the monthly group numbers and AD are subject to the even and odd solar cycles.

We explore the associations between the total sunspot area, solar north-south asymmetry, and Southern Oscillation Index and the physical characteristics of clouds by calculating normalized cross-correlations, motivated by the idea that the galactic cosmic ray influx modulated by solar activity may cause changes in cloud coverage, and in turn the Earth’s climate. Unlike previous studies based on the relative difference, we have employed cloud data as a whole time-series without detrending. We found that the coverage of high-level and low-level cloud is at a maximum when the solar north-south asymmetry is close to the minimum, and one or two years after the solar north-south asymmetry is at a maximum, respectively. The global surface air temperature is at a maximum five years after the solar north-south asymmetry is at a maximum, and the optical depth is at a minimum when the solar north-south asymmetry is at a maximum. We also found that during the descending period of solar activity, the coverage of low-level cloud is at a maximum, and global surface air temperature and cloud optical depth are at a minimum, and that the total column water vapor is at a maximum one or two years after the solar maximum.

The solar magnetic field plays a central role in the field of solar research, both theoretically and practically. Sunspots are an important observational constraint since they are considered a discernable tracer of emerged magnetic flux tubes, providing the longest running records of solar magnetic activity. In this presentation, we first review the statistical properties of the latitudinal distribution of sunspots and discuss their implications. The phase difference between paired wings of the butterfly diagram has been revealed. Sunspots seem to emerge with the exponential distribution on top of slowly varying trends by periods of ~11 years, which is considered multiplicative rather than additive. We also present a concept for the center-oflatitude (COL) and its use. With this, one may sort out a traditional butterfly diagram and find new features. It is found that the centroid of the COL does not migrate monotonically toward the equator, appearing to form an ‘active latitude’. Furthermore, distributions of the COL as a function of latitude depend on solar activity and the solar North-South asymmetry. We believe that these findings serve as crucial diagnostic tools for any potential model of the solar dynamo. Finally, we find that as the Sun modulates the amount of observed galactic cosmic ray influx, the solar North-South asymmetry seems to contribute to the relationship between the solar variability and terrestrial climate change.

Parameters associated with solar minimum have been studied to relate them to solar activity at solar maximum so that one could possibly predict behaviors of an upcoming solar cycle. The number of active days has been known as a reliable indicator of solar activity around solar minimum. Active days are days with sunspots reported on the solar disk. In this work, we have explored the relationship between the sunspot numbers at solar maximum and the characteristics of the monthly number of active days. Specifically, we have statistically examined how the maximum monthly sunspot number of a given solar cycle is correlated with the slope of the linear relationship between monthly sunspot numbers and the monthly number of active days for the corresponding solar cycle. We have calculated the linear correlation coefficient r and the Spearman rank-order correlation coefficient rs for data sets prepared under various conditions. Even though marginal correlations are found, they turn out to be insufficiently significant (r ~ 0.3). Nonetheless, we have confirmed that the slope of the linear relationship between monthly sunspot numbers and the monthly number of active days is less steep when solar cycles belonging to the "Modern Maximum" are considered compared with rests of solar cycles. We conclude, therefore, that the slope of the linear relationship between monthly sunspot numbers and the monthly number of active days is indeed dependent on the solar activity at its maxima, but that this simple relationship should be insufficient as a valid method to predict the following solar activity amplitude.

We revisit the relation between the peak luminosity Liso and the spectral time lag in the source frame. Since gamma-ray bursts (GRBs) are generally thought to be beamed, it is natural to expect that the collimation-corrected peak luminosity may well correlate with the spectral time lag in the source frame if the lag-luminosity relation in the GRB source frame exists. With 12 long GRBs detected by the Swift satellite, whose redshift and spectral lags in the source frame are known, we computed L0,H and L0,W using bulk Lorentz factors Γ0,H and Γ0,W archived in the published literature, where the subscripts H and W represent homogeneous and wind-like circumburst environments, respectively. We have confirmed that the isotropic peak luminosity correlates with the spectral time lag in the source frame. We have also confirmed that there is an anti-correlation between the source-frame spectral lag and the peak energy, Epeak (1 + z) in the source frame. We have found that the collimation-corrected luminosity correlates in a similar way with the spectral lag, except that the correlations are somewhat less tight. The correlation in the wind density profile seems to agree with the isotropic peak luminosity case better than in the homogeneous case. Finally we conclude by briefly discussing its implications.