Long-term persistence of solar activity

The solar irradiante has been found to change by 0.1% over the recent solar cycle. A change of irradiante of about 0.5% is required to effect the Earth's climate. How frequently can a variation of this size be expected? We examine the question of the persistence of non-periodic variations in solar activity. The Hürst exponent, which characterizes the persistence of a time series (Mandelbrot and Wallis, 1969), is evaluated for the series of¹⁴ C data for the time interval from about 6000 BC to 1950 AD (Stuiver and Pearson, 1986). We find a constant Hürst exponent, suggesting that solar activity in the frequency range of from 100 to 3000 years includes an important continuum component in addition to the well-known periodic variations. The value we calculate,H ≈ 0.8, is significantly larger than the value of 0.5 that would correspond to variations produced by a white-noise process. This value is in good agreement with the results for the monthly sunspot data reported elsewhere, indicating that the physics that produces the continuum is a correlated random process (Ruzmaikin et al., 1992), and that it is the same type of process over a wide range of time interval lengths. We conclude that the time period over which an irradiance change of 0.5% can be expected to occur is significantly shorter than that which would be expected for variations produced by a white-noise process. The full paper has been submitted to Solar Physics. Part of the research decribed here was carried out by JPL, Caltech under a contract with NASA.     

Hurst analysis of Mt. Wilson rotation measurements

I study the temporal variation of the solar rotation on time scales shorter than the 11-year cycle by analyzing the daily Mt. Wilson Doppler measurements from 1967 to 1992. The differential rotation is represented by the three coefficients,A, B, andC, of the following expansion: =A +B sin²() +C sin⁴(). TheA, B, andC time series show clearly the 11-year solar cycle and they also show high-frequency fluctuations. The Hurst analysis of these time series shows that a Gaussian random process such as observational noise can only account for fluctuations on time scales shorter than 20 days. For time scales from 20 days to 11 years, the variations of A give rise to a Hurst exponent ofH = 0.83, i.e., the variations ofA are persistent. The temporal variations ofB show the same behavior asC, which is different fromA. From one to 11 years, theB andC variations are dominated by the 11-year cycle, while for time lags shorter than about 250 days, theB andC fluctuations give rise to a Hurst exponent ofH = 0.66, which lies betweenH = 1/2, of a Gaussian random process, and the exponent of the persistent process shown byA. An analysis of the equivalent coefficients of the first three even Legendre polynomials, computed usingA, B, andC, provides additional information. For time scales between 100 and 1000 days, the ranges,R/S, of Legendre polynomial coefficients decrease with increasing order of the polynomials which suggests that the persistent process operates mainly on large spatial scales. The Hurst exponent ofH = 0.83 for variations inA is the same asH for monthly sunspot numbers with time scales between 6 months and 200 years and for¹⁴C radiocarbon data with time scales between 120 years and 3000 years, previously analyzed by other authors. The combined results imply that the underlying solar process shows the same persistent behavior for time scales as short as about 20 days up to time scales of a few thousand years.Operated by the Association of Universities for Research in Astronomy, Inc. under cooperative agreement with the National Science Foundation.     

Rescaled range analysis of the asymmetry of solar activity

Previous studies of the north-south asymmetry of solar activity (e.g., Carbonell, Oliver, and Ballester, 1993; Oliver and Ballester, 1994) suggest that the asymmetry time series can be represented by means of a multicomponent model made up of a long-term trend, a weak sinusoidal component (with a period close to 12.1 years) and a dominant random process. Here, we have used the rescaled range analysis to study the valuation of the stochastic component of the asymmetry. To avoid the influence of the trend and the sinusoidal component on the result, we have removed both from the original time series. The value obtained for the Hurst exponent (0.717 ± 0.002) suggests that the non-periodic component is a correlated random process.     

Persistence of solar activity on small scales: Hurst analysis of time series coming from Hα flares

We calculated the Hurst exponent H for the daily averaged intensity Q of optical flares, an index which describes the solar activity. We found that H0.74±0.02 in the range of scales from about 20 days up to 450 days. This value is well beyond H= , expected for a stochastic Brownian process, thus indicating that the solar cycle could show persistence on small scales, in agreement with what has been found using other indices of the solar cycle.     

Multi-technique Analysis of the Solar 10.7 cm Radio Flux Time-Series in Relation to Predictability

We studied the predictability of the 10.7 cm solar radio flux by using stationary and non-stationary time-series analysis techniques of fractal theory to find the correlation exponent, the spectral exponent, the Hurst exponent, and the fluctuation exponent of the time series. The Hurst exponent was determined, from which the fractal dimension and consequently the predictability was evaluated. The results suggest that stationary methods of analysis yield inconsistent result, that is, amongst the four techniques used, the values of the exponents show great disparity. While two of the techniques, namely the auto-correlation function analysis and the spectral analysis, indicate long-term positive correlation, the other two methods, specifically the Hurst rescaled range-analysis and the fluctuation analysis, clearly exhibit the anti-correlated nature of the time series. The two non-stationary methods, that is, the discrete wavelet transform and the centered moving-average analysis, yielded values of the Hurst exponent that are indicative of positive correlation, of persistent behavior, and also showed that the time series is predictable to a certain extent.     

Characteristics of soft solar X-ray bursts

The burst component of the solar X-ray flux in the soft wavelength range 2 < < 12 Å observed from Explorer 33 and Explorer 35 from July 1966 to September 1968 was analyzed. In this period 4028 burst peaks were identified.The differential distributions of the temporal and intensity parameters of the bursts revealed no separation into more than one class of bursts. The most frequently observed value for rise time was 4 min and for decay time was 12 min. The distribution of the ratio of rise to decay time can be represented by an exponential with exponent -2.31 from a ratio of 0.3 to 2.7; the maximum in this distribution occurred at a ratio of 0.3. The values of the total observed flux, divided by the background flux at burst maximum, can be represented by a power law with exponent -2.62 for ratios between 1.5 and 32. The distribution of peak burst fluxes can be represented by a power law with exponent - 1.75 over the range 1–100 milli-erg (cm² sec)^–1. The flux time integral values are given by a power law with exponent -1.44 over the range 1–50 erg cm^–2.The distribution of peak burst flux as a function of H importance revealed a general tendency for larger peak X-ray fluxes to occur with both larger H flare areas and with brighter H flares. There is no significant dependence of X-ray burst occurrence on heliographic longitude; the emission thus lacks directivity.The theory of free-free emission by a thermal electron distribution was applied to a composite quantitative discussion of hard X-ray fluxes (data from Arnoldy et al., 1968; Kane and Winckler, 1969; and Hudson et al., 1969) and soft X-ray fluxes during solar X-ray bursts. Using bursts yielding measured X-ray intensities in three different energy intervals, covering a total range of 1–50 keV, temperatures and emission measures were derived. The emission measure was found to vary from event to event. The peak time of hard X-ray events was found to occur an average of 3 min before the peak time of the corresponding soft X-ray bursts. Thus a changing emission measure during the event is also required. A free-free emission process with temperatures of 12–39 × 10⁶K and with an emission measure in the range 3.6 × 10⁴⁷ to 2.1 × 10⁵⁰ cm^–3 which varies both from event to event and within an individual event is required by the data examined.Now at Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey.     

Nonlinear Time Series Analysis of Sunspot Data

This article deals with the analysis of sunspot number time series using the Hurst exponent. We use the rescaled range (R/S) analysis to estimate the Hurst exponent for 259-year and 11 360-year sunspot data. The results show a varying degree of persistence over shorter and longer time scales corresponding to distinct values of the Hurst exponent. We explain the presence of these multiple Hurst exponents by their resemblance to the deterministic chaotic attractors having multiple centers of rotation.     

The Balmer jump in astrophysical hydrogen plasmas

It is shown that, according to accepted theoretical concepts, there should be no intensity jump at the edge of the Balmer continuum, nor at that of other hydrogen series. We point out three reasons for a fairly smooth increase of the intensity to occur at the continuum edge. As a result, the jump sometimes spreads over hundreds of ångstroms, due mainly to the electron density inhomogeneity of solar plasma. Furthermore, the Doppler and Stark effects also give rise to a considerable spread of the series edge. We point out that excess continuum emission over a relatively narrow spectral interval before the continuum edge can result from overlapping of line wings.     

Energy Spectra of low-Flux Protons in the Inner Heliosphere under Quiet Solar Conditions

The energy spectra of protons at energies in the range of about 1–100 MeV are investigated during time periods of low solar activity using data sets from near Earth spacecraft. These populations pose a tough experimental and theoretical problem that remains unsolved up to now. We attempt to provide a consistent definition of low-flux quiet-time periods relevant to low solar activity as well as quasi-stationary periods useful at higher levels of solar activity. Using statistical methods, the possible instrumental contribution to the lowest observed proton fluxes for various detectors is estimated. We suggest and prove that there exists a low-flux population of charged particles in the energy range of about 1–10 MeV, which is present in the inner heliosphere even during the quietest conditions at lowest solar activity. The dynamics of the variations of proton spectra over the solar cycle is investigated. A series of low-flux periods is examined in detail and energy spectra of protons are approximated in the form of J(E)=AE ^–+CE. By determining the best fitting parameters to the energy spectra correlations are made among them as well as with monthly sunspot numbers characterizing solar activity. It has been demonstrated that the value of the energy minimum of proton spectrum E _min that `divides' the two populations – `solar/heliospheric' and `galactic' – is shifted towards higher values with increasing solar activity. Protons have been argued to be predominantly of solar origin up to several MeV near the solar cycle minimum and up to 20–30 MeV at maximum. The slope of the lower spectrum branch (parameter ) slightly decreases with increasing solar activity. The minimum fluxes observed during the last 3 minima of solar activity are compared; the lowest fluxes were those during the 1985–1987 period.     

Cosmic ray intensity variations and two types of high speed solar streams

This study deals with the short-term variations of cosmic ray intensity during the interval 1973–78. Daily means of high latitude neutron and meson monitors from the same station and those of a low latitude neutron monitor have been analysed using the Chree method of superposed epochs. The zero epoch for the Chree analyses corresponds to the day of a substantial increase (V 200 km s^–1) in the solar wind speed to values of 550 km s^–1 and which persists at such high values for an interval of at least three days. The investigation reveals the existence of two types of cosmic ray intensity variations with distinctly different spectral characteristics. During the interval 1973–76, relative changes in the neutron and meson monitor rates are nearly equal indicating an almost flat rigidity spectrum of variation. During 1977–78, however, the spectrum acquires a negative spectral character similar to that observed for Forbush decreases. We suggest that events of the interval 1973–76 are essentially due to high speed streams associated with solar coronal holes and that events of the interval 1977–78 are due to fast streams from solar active regions with flare activity.     

A Fractal Structure of the Time Series of Global Indices of Solar Activity

The structure of time series of daily global indices of solar activity is investigated: the sunspot numbers for the time interval between the years 1854 and 1996, the Greenwich total sunspot area for 1874–1983, the radio-flux at 10.7 cm (F10.7) for 1964–1996, and the Stanford mean solar magnetic field for 1975–1996. The fractal dimensions are determined by two fractal and spectral methods. The identified three time-scale ranges, 2 days–2 months, 2 months–2 years, 2 years–8 and more years, with the fractal dimensions 1.4–1.6, 2, 1.2–1.6, respectively, show perhaps some fractal structure of time series of global indices. The first time-scale range may correspond to ordinary brownian noise and the second to flicker noise. The solar rotation influence of the value of the fractal dimensions at the time range close to the rotational period is studied.     

Analysis of a white-light flare spectrum

The continuum emission of an X₁ flare on 26 March, 1970 observed close to the solar limb (N 05 E 64) was analyzed by a photometric determination of the contrast I()/I ₀() in the wavelength range 3558–5920 Å. Two possible mechanisms for the emission were investigated, namely hydrogen Paschen and H^– continua. We show the unlikeness of the Paschen possibility and derive strong constraints on the temperature structure and energy deposition mechanism imposed by the H^– continuum process.We conclude that the emission must have originated in deep atmospheric layers. The relevance of this result with respect to flare energy release and transport processes is also discussed.     

Characteristics of enhanced and low-amplitude cosmic-ray diurnal variation

The occurrence of a large number of high- and low-amplitude cosmic-ray diurnal wave trains during the two solar cycles (20 and 21) over the years 1965–1990 has been examined as a function of solar activity. The high-amplitude days with the time of maximum in the 18:00 hr corotation direction do not indicate any significant correlation with solar activity. But, the low-amplitude days are inversely correlated with solar activity and the time of maximum shifts to earlier hours ( 15:00 hr direction). The slope of the power-specrum density roughly characterized by power spectral index n in the high-frequency range 3.5 x 10^–5 Hz to 8.3 x 10^–4 Hz (time scales of 20 min to 8 hr) is different for the two classes of events. A suggestion is made that the enhanced and low-amplitude cosmic-ray diurnal variations are produced by different types of interplanetary magnetic field distributions.     

On the variability timescales and magnetic field in OJ 287

The continuum spectrum of OJ 287, like most other BL Lac objects, is featureless- no emission or absorption lines are observed. However, OJ 287 shows variations at different timescales in flux and polarization at various wavelength bands. Using the available variability data one can estimate the sizes of the emission regions in the source from light travel time arguments. We assume the emission mechanism to be synchrotron radiation by high energy electrons with single power law energy distribution. Theoretical synchrotron spectrum in the frequency range 10¹¹–10¹⁷ H _z is compared with the observed spectral shape, obtained from new multifrequency quasi-simultaneous observations, to estimate the lower and upper cut off frequencies. These frequencies are used to obtain theoretical values of the variability timescales and magnetic field in the emission region. We obtain a value of 0.93 G for the magnetic field and 5.184×10⁴ sec for the cooling time from the quiescent continuum spectrum. The shock-in-jet model explains the spectrum where shocks accelerate the particles and amplify the magnetic field in the jet. This timescale is compared with the one obtained from observed short timescale variability (20 minutes) with proper beaming correction. The short timescale variations (200 minutes in the source frame), possibly caused by an additional, flaring, component of the source, are also used to calculate compressed magnetic field. The observed and theoretically estimated variability timescales and the shape of the spectrum suggest that there are more than one emission components in OJ 287.     

On the relationship between polar faculae and large-scale magnetic field

We investigate a latitude–time distribution of polar faculae observed at Ussuriysk Observatory in years 1966–1986. The distribution is compared with the longitude-averaged (zonal) magnetic field of the Sun calculated from the data obtained at Mount Wilson Observatory in the years 1966–1976, and at Kitt Peak National Observatory during the period from 1976 to 1985. We found that slow, poleward-directed migration of the polar faculae zones occurring during the course of the solar cycle is not a continuous process, but it contains several episodes of appearance and fast poleward drift of new zones of polar faculae. At the rising phase of the solar cycle, new zones of polar faculae appear at latitudes as low as 40°, but the ones observed during the declining phase of the solar cycle originate at higher latitudes of 50–55°. Such episodes of appearance and fast migration of the polar faculae zones are associated with the poleward-directed streams of magnetic field originated at low latitudes. Moreover, we found some evidence for existence of an additional component of the polar faculae activity that reveals an equatorward migration during the course of the solar cycle. We also investigated a relationship between the number of polar faculae, n, and absolute magnetic flux _z of the zonal mode of the solar magnetic field. We found that within the polar zones of the Sun, substantial correlation between temporal variations of n and _z takes place both on the time scale of the solar cycle and on a shorter time scale of 2–4 years. The relationship between the number of polar faculae and magnetic flux may be approximated by a linear dependence n=0.12_z (where _z is expressed in 10²¹ Mx), except for time interval 1977 through 1980 for which the factor of proportionality is found to have a systematically larger value of 0.20.     

Characteristics of Two-Way Cosmic-Ray Diurnal Anisotropy

We examine the deviation of the solar diurnal anisotropy vector from the 18 LT direction during the positive state of the solar cycle by assuming two anisotropies in free space. We use two detectors characterized by two linearly independent coupling functions. The median primary rigidity of response of these detectors covers the range 16 GV R _m 331 GV. Amplitude, direction, spectrum exponent, and the upper cut-off rigidity of each anisotropy have been calculated using the least-squares method over the time interval 1968–1988. This period covers a complete solar magnetic cycle. Only one anisotropy is dominant during each magnetic state of the solar cycle. The upper cut-off rigidity at which the dominant anisotropy vanishes varies between 50–250 GV. The direction of the dominant anisotropy vector points toward the 18 LT direction during the negative state of the solar cycle and toward earlier hours than 18 LT during the positive state. The non-dominant anisotropy is characterized by very high upper cut-off rigidity and sharper energy spectral.     

Variable solar wind

The solar wind in the heliosphere is a variable phenomenon on all spatial and time scales. It has been shown that there are two basic types of solar wind by the Strouhal number S = L/VT, which characterizes relative variations in the main parameters of the solar wind on the given time interval T and linear scale L for velocity V, which is never zero. The first type is transient (S > 1), which is usually the basic type for sufficiently small values of T and large values of L. The second type is quasi-stationary, when 1 > S > 0. The constant solar wind is nonexistent. The extreme case of S = 0 is physically impossible, as is the case of S = ∞. It is always necessary to indicate and justify the range of applicability for a special quasi-stationary case 1 ? S > 0. Otherwise, to consider the case of S = 0 is incorrect. Regarding this, the widely-spread views on the stationary state of the solar wind are very conditional. They either lack physical sense, or have a very limited range of applicability for time T and scale L.     

Cross-correlation of solar wind parameters with sunspots (‘Long-term variations’) at 1 AU during cycles 21 and 22

Long-term variations of solar wind parameters at 1 AU are correlated with sunspots for the time interval 1973 to 1993 (solar cycles 21, 22). Using theNear-Earth Heliosphere Data OMNI the plasma density, the magnitude of the interplanetary magnetic field, the solar wind velocity and the solar wind temperature show consistent long-term variations in each cycle (21 and 22) — pointing to specifictime-lags in the coupling between sunspots (and the underlying convection zone), the solar corona and the solar wind parameters at 1 AU (ecliptic).     

The spectrum of the inner corona observed during the total solar eclipse of 30 May 1965

A series of spectrograms of the inner solar corona were obtained at the total solar eclipse of 30 May 1965 using a fast spectrograph with a circular slit that recorded the spectrum from 3000 to 9000 at all position angles around the limb simultaneously. In this paper absolute intensity is given as a function of position angle for the stronger lines and the continuum. In the coronal enhancement or condensation centered at heliocentric position angle 293°, absolute intensity is given for 34 forbidden emission lines and the continuum.     

Series of classical solar activity indices: Kislovodsk data

We present data on the series of solar activity indices, Wolf sunspot numbers W and total sunspot areas S, obtained at the Kislovodsk high-altitude station of the Pulkovo Observatory. The problem of properly extending the 133-year-long Zürich series of W and the 102-year-long Greenwich series of S, which were discontinued in 1980 and 1976, respectively, is emphasized. We stress that the Kislovodsk data have retained mutual homogeneity with the classical series until now and that they are preferred for extension. The question under consideration is of fundamental importance in studying the solar activity variations on long time scales and related processes in the Sun-Earth system.