Frequencies of low-degree solar acoustic oscillations and the phase of the solar cycle

A study of the solar total irradiance data of the Active Cavity Radiometer Irradiance Monitor (ACRIM) on the Solar Maximum Mission (SMM) satellite shows a small but formally significant shift in the frequencies of solar acoustic (p-mode) oscillations between the epochs of maximum and minimum solar activity. Specifically, the mean frequency of the strongest p-mode resonances of low spherical-harmonic degree (l = 0–2) is approximately 1.3 parts in 10⁴ higher in 1980, near the time of sunspot maximum, than in 1985, near sunspot minimum. The observed frequency shift may be an 11-yr effect but the precise mechanism is not clear.     

Variation of the solar constant during the solar cycle

Measurements of the Nimbus-7 and Solar Maximum Mission satellites reported temporary large decreases of the solar constant of the order of a few tenths of a percent on a time-scale from days to weeks. Our investigations show that these decreases were caused by active sunspot groups with fast development and complex structure. This connection between the solar constant variation and the appearance of the active groups seems to be more clear in the maximum of the solar activity. At the time of the solar minimum, mainly in the second part of 1984, there were not any active sunspot groups practically on the solar disk, the value of the solar constant only fluctuated around its mean without large variation. The results of time series analyses show that the periodicity of the solar constant values, of young and active spot areas was nearly 23.5 days in 1980, which increases to 28 days towards the minimum of the solar cycle till 1983. During this time interval the main periodicity of the old, passive spot areas was around 28 days. In 1984, at the time of the solar minimum, there were not any obvious periodicities practically in the projected areas of the different types of the sunspot groups.     

Activity of sunspots and solar constant variations during 1980

A strong inverse correlation is shown between the irradiance dips observed by the SMM/ACRIM radiometer and the projected areas of the active sunspots. This strong correlation and the results of a preliminary time series analysis indicate that the value of the solar constant decreased when quickly developing sunspot groups with complex structure occurred on the solar disk. On the other hand, when the old groups with simple structure were dominant the value of the solar constant increased slightly or these groups could reduce the effects of the active spots. On the basis of our investigations it seems that the formation of the sunspots and the new activity of the older ones as well as the decreases of the solar constant may be the common symptoms of such a physical process which takes place in deeper regions of the Sun through the interaction of magnetic fields with the convection.     

Periodicities of solar irradiance and solar activity indices,I

Using a standard FFT time series analysis, our results show an 8–11 months periodicity in the solar total and UV irradiances, 10.7 cm radio flux, Ca-K plage index, and sunspot blocking function. The physical origin of this period is not known, but the evidence in the results exclude the possibility that the observed period is a harmonic due to the FFT transform or detrending. Periods at 150–157 and 51 days are found in those solar data which are related to strong magnetic fields. The 51-day period is the dominant period in the projected areas of developing complex sunspot groups, but it is missing from the old decaying sunspot areas. This evidence suggests that the 51-day period is related to the emergence of new magnetic fields. A strong 13.5-day period is found in the total irradiance and projected areas of developing complex groups. This confirms those results (e.g., Donnelly et al., 1983, 1984; Bai, 1987, 1989) which show that active centers are located 180 deg apart from each other.Our study also shows that the modulation of various solar data due to the 27-day solar rotation is more pronounced during the declining portion of solar cycle than during the rising portion. This arises from that the active regions and their magnetic fields are better organized and more long-lived during the maximum and declining portion of solar cycle than during its rising portion.     

Modelling solar irradiance variations with an area dependent photometric sunspot index

The He 1083 nm line equivalent width and the 10.7 cm radio flux are employed to model the total solar irradiance corrected for sunspot deficit. A new area dependent photometric sunspot index (APSI) based on sunspot photometry by Steinegger et al. (1990) is used to correct the irradiance data for sunspot deficits. Two periods of time are investigated: firstly, the 1980–1989 period between the maxima of solar cycles 21 and 22; this period is covered by ACRIM I irradiance data. Secondly, the 1978–92 period which includes both maxima; here, the revised Nimbus-7 ERB data are used.For both He 1083 nm and 10.7 cm radio flux irradiance models as well as ACRIM I and ERB irradiance data, the APSI yields an improved fit compared to the one obtained with the standard Photometric Sunspot Index (PSI) which uses a constant bolometric spot contrast. With APSI, the standard deviation calculated from daily values is 0.461 Wm^–2 for the period 1980–89 modelling ACRIM I vs. He 1083 nm, as compared to 0.478 when PSI is used, and to 0.531 for the uncorrected ACRIM series. A similar improvement is obtained for the same period modelling ERB vs. He 1083 nm, while there is almost no improvement for the long period.As a general result the models provide a good fit with the spot-deficit.-corrected irradiance only during the period between the maxima. If both maxima are included (period 1978–92) the He 1083 nm and 10.7 cm radio flux models show appreciably larger discrepancies to the irradiances corrected for PSI or APSI.     

Time profiles of solar irradiance dips

ACRIM data have been analyzed to study the time profiles of simple irradiance dips caused by single active regions. Comparison of the average characteristics of the dips appearing in the minimum and maximum of the solar cycle shows that there are no significant differences. In both periods we disclosed the facular irradiance excess in the profile wings having typical duration of two to three days and an amplitude of about 20% of the dip amplitude. The profiles were asymmetric, with a stronger and longer excess in the trailing wing. We determined an average profile which was attributed to an idealized active region, and we calculated the luminosity perturbation caused by it. Excess radiation in the wings of the profile compensates about 1/3 of the deficit in the dip. In the most simple case from our sample we compared the profile based on ACRIM measurements and the proxy profile estimated using sunspot and plage areas published in Solar Geophysical Data catalogues. The comparison indicates that the facular excess was compensating instantaneously about 2/3 of the luminosity deficit caused by sunspots.     

Phase differences between irradiance and velocity low degree solar acoustic modes revisited

Since 1984, simultaneous observations of irradiance and velocity solar acoustic modes, have been carried out by several authors in order to measure the phase difference between irradiance and velocity modes. Following the earliest observations with stratospheric balloon (Frolich and van Der Raay, 1984), a two ground-based stations (Tenerife and Baja California) were established (Jimenez et al, 1990) obtaining coherence results in the frequency range from 2.5 mHz to 4.3 mHz. These phase differences between irradiance and velocity solar acoustic modes are interpreted in terms of the non-adiabatic behaviour of the solar atmosphere. In 1988 the IPHIR (Frolich et al, 1988) instrument flown on the PHOBOS-2 mission to Mars and measured the solar irradiance during 150 consecutive days. The best velocity observations obtained in Tenerife for this period were compared with IPHIR data to compute the phase differences (Schrijver et al, 1991). The final conclusion is that good agreement is attained between space quadsi-space and ground observations which yield a phase diffenrece of about -125 degrees in the frequency range 2.5 mHz to 4.2 mHz, with a slight increase suggested by the data running up to 4.6 mHz.     

Sunspot photometry and the total solar irradiance deficit measured in 1980 by ACRIM

Until now a simple Photometric Sunspot Index (PSI) model was used (e.g. Willsonet al., 1981) to describe the contribution of sunspots to the solar irradiance deficit measurement by ACRIM. In this work we replace this model by a photometry of sunspot pictures for the period of 19 August to 4 September, 1980 taking into account the individual features, like lightbridges or umbral dots, of each spot. The main results of this preliminary analysis are: (1) theA _u/A _p ratios and alsos the values vary in a wide range and are by no means constant as in the PSI model; (2) the general trend of the irradiance deficit from our analysis agrees well with the ACRIM measurements; (3) on some days there are differences of more than 50% between the deficits derived from our measurements and from the PSI model.Paper presented at the 11th Eurpean Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain     

Latitudinal Distribution of Polar Faculae

The distribution of polar faculae with respect to latitude is investigated, using data obtained at the Ussuriysk Observatory during the years 1963–1994. To correct the data for the effect of visibility, a visibility function of polar faculae is derived. Corrected surface density of polar faculae is calculated as a function of latitude and time. During most part of each solar cycle, polar faculae exhibit pronounced concentrations at high latitudes with maxima of the surface density located near the poles. Such concentrations of polar faculae (below referred to as `polar condensations') are formed after a lapse of 1–2 years from the polar magnetic field reversals, and then they persist for 7–9 years, until the high-latitude magnetic fields again start to reverse. During several years after the sunspot minima, the polar condensations co-exist with the new latitudinal belts of polar faculae which appear at middle latitudes and then migrate toward the poles. To describe the evolution of the polar condensations quantitatively, the polar faculae density n at latitudes above 60° has been approximated by means of the power law nn ₀ cos^m where is polar angle. The parameters n ₀ and m both are found to vary during the course of the solar cycle, reaching maximum values near or shortly after the minimum of sunspot activity. At the minimum phase of the solar cycle, on average, the surface density of polar faculae varies as cos¹⁴. In addition to the 11-yr variation, the latitude–time distribution of polar faculae exhibits short-term variations occurring on the time scale of 2–3 years.     

Variation of the solar constant connected with the coronal activity

A strong correlation was found between the dips in the total solar irradiance and the peaks in the active sunspot areas as well as in the 260 MHz coronal radio flux. This connection might indicate that Alfvén-waves, generated during the interaction of the magnetic fields of the active sunspot groups with the convection, are able to transport away part of the missing energy in the solar constant decreases. These waves can heat the solar corona above the sunspot groups. Another part of the missing energy could be re-radiated later, for example during the decay of the active regions.     

Extrema in Sunspot Cycle Linked to Sun's Motion

Partitions of 178.8-year intervals between instances of retrograde motion in the Sun's oscillation about the center of mass of the solar system seem to provide synchronization points for the timing of minima and maxima in the 11-year sunspot cycle. In the investigated period 1632–1990, the statistical significance of the relationship goes beyond the level P=0.001. The extrapolation of the observed pattern points to sunspot maxima around 2000.6 and 2011.8. If a further connection with long-range variations in sunspot intensity proves reliable, four to five weak sunspot cycles (R0) are to be expected after cycle 23 with medium strength (R100).     

Study of the distribution of daily fluctuations in observed solar irradiances and other full-disk indices of solar activity

Analyses based on irradiance observations from space within the last one and a half decades have discovered variations in the entire solar spectrum and at UV wavelengths on time scales of minutes to decades. In this paper we analyze the distribution of the measuring uncertainties and daily fluctuations in total solar irradiance measured by the Nimbus-7/ERB and SMM/ACRIM I radiometers as a function of solar cycle. Changes in solar total irradiance and its surrogates shorter than the solar rotation have also been considered as noise and have been removed from the data. Our results show that the noise (both instrumental and solar noise) changes as a function of the solar cycle, being higher during high solar activity conditions. The analysis of the scatter plot diagrams between the data and their standard deviation, the so-called dispersion diagrams, provides a useful tool to estimate and predict the time of solar maximum and minimum activity conditions.Deceased on October 13, 1994.     

Transformation of the absolute solar radiation data into the ‘International Practical Temperature Scale of 1968’

Corrections are given which transform the Tables of the solar radiation data (Labs and Neckel, 1968) into the International Practical Temperature Scale of 1968. Additionally, for the adjustment of the data of the true continuum and the corresponding line blanketing as well, the veiled line effect mentioned first by Carbon et al. (1968), but studied in more detail by Holweger (1970a), has been considered also.The corresponding corrections of the solar irradiance result in an improved value of the spectrophotometric solar constant: S = 1.947 cal cm^-2 min^-1 or 0.1358 W cm^-2. Two Tables presenting the highest (window-) intensities and the corrected irradiance data have been added.     

Rotation of Plasma in Sunspots

In this paper we present the results of a sunspot rotation study using Abastumani Astrophysical Observatory photoheliogram data for 324 sunspots. The rotation amplitudes vary in theinebreak 2–64° range (with maximum at 12–14°), and the periods around 0–20 days (with maximum atinebreak 4–6 days). It could be concluded that sunspot rotations are rather inhomogeneous and asymmetric, but several types of sunspots are distinguished by their rotational parameters.During solar activity maximum, sunspot average rotation periods and amplitudes slightly increase. This can be affected by the increase of sunspot magnetic flux tube depth. So we can suppose that sunspot formation during solar activity is connected to a rise of magnetic tubes from deeper layers of the solar photosphere, strengthening the processes within the tube and causing variations in rotation.There is a linear relation between tilt-angle oscillation periods and amplitudes, showing higher amplitudes for large periods. The variations of those periods and especially amplitudes have a periodical shape for all types of sunspots and correlate well with the solar activity maxima with a phase delay of about 1–2 years.     

Solar irradiance variations from photometry of active regions

The Extreme Limb Photometer (ELP) has been used to measure the irradiance fluctuation of the Sun due to selected active regions. Forty-five active regions that were completely scanned at various disk positions are included in the analysis. The contribution of these active regions to a global solar irradiance fluctuation has been correlated with photometric sunspot and facular indices (PSI and PFI) using published values of sunspot and calcium plage areas. The measured ELP fluctuations are converted to a global brightness fluctuation, B/B. The sunspot component of B/B correlates with PSI with r = 0.95. The facular component of B/B correlates with PFI with r - 0.72. The expression for PFI is important to the question of energy balance between sunspots and faculae and the results presented here are not incompatible with energy balance between the two phenomena; that is the energy deficit of sunspots may be balanced by the energy excess of faculae.     

Predictions of the maximum amplitude for solar cycle 23 and its subsequent behavior using nonlinear methods

Two nonlinear methods are employed for the prediction of the maximum amplitude for solar cycle 23 and its declining behavior. First, a new heuristic method based on the second derivative of the (conveniently smoothed) sunspot data is proposed. The curvature of the smoothed sunspot data at cycle minimum appears to correlate (R 0.92) with the cycle's later-occurring maximum amplitude. Secondly, in order to predict the near-maximum and declining activity of solar cycle 23, a neural network analysis of the annual mean sunspot time series is also performed. The results of the present study are then compared with some other recent predictions.     

Sunspots Observed to Physically Weaken in 2000–2001

The strength of a sunspot depends on its magnetic field and umbral darkness, factors which go together. The strongest field in an umbra is always found at the darkest position. We use this relationship, B=f(1/T), to demonstrate that at the maximum of cycle 22 (1990–1991) sunspots were statistically stronger than at the same phase of cycle 23 (2000–2001). Within our sample of 195 spots, cycle 23 exhibits an excess of small bright spots, and possibly, a dearth of large dark spots. This could alter the total solar irradiance (TSI)–sunspot number relationship.     

Short periodicities in solar activity

Several indices of solar activity are subjected to a high pass filter and power spectral analysis to verify the existance of shorter periodicities in solar activity. Though all these indices show the presence of short periodicities, above 95% confidence level, the common indices like sunspot number, fail to show these periodicities when a stringest statistical test is applied based on a percentage of the ²/v distribution that is appropriately higher than the 95% point (Mitchell et al., 1966). The basic parameters given by Kopecký (1967), however, reveal the presence of 5.6- and 3.5-yr periodicities even when this stringent statistical test is applied.     

Fractal dimensions of solar activity

Solar activity changes in amplitude and long-term behavior irregularly. Fractal theory is used to examine the variation of solar activity, using daily solar indices (i.e., sunspot number, 10.7 cm radio flux, the SME L, Fexiv coronal emission, and the total solar irradiance measured by the ERB (Earth Radiation Budget) on the NIMBUS-7. It can handle irregular variations quantitatively. The fractal dimension of 10.7 cm radio fluxes in cycle 21 for periods of 7 days or less was 1.28, 1.3 for periods longer than 272 days, and 1.86 for periods between them, for example. Fractal dimensions for other solar indices show similar tendencies. These results suggest that solar activity varies more irregularly for time scales that are longer than several days and shorter than several months. Yearly values of fractal dimensions and bending points do not change in concert with the solar cycle.