Evolution of Solar and Geomagnetic Activity Indices, and Their Relationship: 1960?�C?2001

We employ annually averaged solar and geomagnetic activity indices for the period 1960??C?2001 to analyze the relationship between different measures of solar activity as well as the relationship between solar activity and various aspects of geomagnetic activity. In particular, to quantify the solar activity we use the sunspot number R _s, group sunspot number R _g, cumulative sunspot area Cum, solar radio flux F10.7, and interplanetary magnetic field strength IMF. For the geomagnetic activity we employ global indices Ap, Dst and Dcx, as well as the regional geomagnetic index RES, specifically estimated for the European region. In the paper we present the relative evolution of these indices and quantify the correlations between them. Variations have been found in: i) time lag between the solar and geomagnetic indices; ii) relative amplitude of the geomagnetic and solar activity peaks; iii) dual-peak distribution in some of solar and geomagnetic indices. The behavior of geomagnetic indices is correlated the best with IMF variations. Interestingly, among geomagnetic indices, RES shows the highest degree of correlation with solar indices.     

The 27-Day and 22-Year Cycles in Solar and Geomagnetic Activity

We study the evolution of the longitudinal asymmetry in solar activity through the wave packet technique applied to the period domain of 25 – 31 days (centered at the 27-day solar rotation period) for the sunspot number and geomagnetic aa index. We observe the occurrence of alternating smaller and larger amplitudes of the 11-year cycle, resulting in a 22-year periodicity in the 27-day signal. The evolution of the 22-year cycle shows a change of regime around the year 1912 when the 22-year period disappears from the sunspot number series and appears in the aa index. Other changes, such as a change in the correlation between solar and geomagnetic activity, took place at the same time. Splitting the 27-day frequency domain of aa index shows an 11-year cycle for higher frequencies and a pure22-year cycle for lower frequencies, which we attribute to higher latitude coronal holes. This evidence is particularly clear after 1940, which is another benchmark in the evolution of the aa index. We discuss briefly the mechanisms that could account for the observed features of the 22-year cycle evolution.     

Grand Minima of Solar Activity and the Mean-Field Dynamo

We demonstrate that a simple solar dynamo model, in the form of a Parker migratory dynamo with random fluctuations of the dynamo governing parameters and algebraic saturation of dynamo action, can at least qualitatively reproduce all the basic features of solar Grand Minima as they are known from direct and indirect data. In particular, the model successfully reproduces such features as an abrupt transition into a Grand Minimum and the subsequent gradual recovery of solar activity, as well as mixed-parity butterfly diagrams during the epoch of the Grand Minimum. The model predicts that the cycle survives in some form during a Grand Minimum, as well as the relative stability of the cycle inside and outside of a Grand Minimum. The long-term statistics of simulated Grand Minima appears compatible with the phenomenology of the Grand Minima inferred from the cosmogenic isotope data. We demonstrate that such ability to reproduce the Grand Minima phenomenology is not a general feature of the dynamo models but requires some specific assumption, such as random fluctuations in dynamo governing parameters. In general, we conclude that a relatively simple and straightforward model is able to reproduce the Grand Minima phenomenology remarkably well, in principle providing us with a possibility of studying the physical nature of Grand Minima.     

Study of Coronal Jets During Solar Minimum Based on STEREO/SECCHI Observations

During the 2007 – 2008 minimum of solar activity, the internally occulted coronagraphs SECCHI-COR1 onboard the STEREO space mission recorded numerous jet-like ejections over a great range of latitudes. We have found more than 10000 white-light jets in the above-mentioned period. Sometimes they can be identified on the disk with bright points observed in ultraviolet images by EUVI. In this study we present a catalog consisting of jets observed by the SECCHI-COR1 instrument and their association with lower coronal activity (bright points, UV jets). Furthermore, their association with bright points in the context of previously proposed models is discussed. From the complete catalog we have selected 106 jets observed in both STEREO-A and STEREO-B images for which it is possible to derive their kinematics and point of origin.     

Combined Analysis of Solar Neutrino and Solar Irradiance Data: Further Evidence for Variability of the Solar Neutrino Flux and Its Implications Concerning the Solar Core

A search for any particular feature in any single solar neutrino dataset is unlikely to establish variability of the solar neutrino flux since the count rates are very low. It helps to combine datasets, and in this article we examine data from both the Homestake and GALLEX experiments. These show evidence of modulation with a frequency of 11.85 year⁻¹, which could be indicative of rotational modulation originating in the solar core. We find that precisely the same frequency is prominent in power spectrum analyses of the ACRIM irradiance data for both the Homestake and GALLEX time intervals. These results suggest that the solar core is inhomogeneous and rotates with a sidereal frequency of 12.85 year⁻¹. From Monte Carlo calculations, it is found that the probability that the neutrino data would by chance match the irradiance data in this way is only 2 parts in 10 000. This rotation rate is significantly lower than that of the inner radiative zone (13.97 year⁻¹) as recently inferred from analysis of Super-Kamiokande data, suggesting that there may be a second, inner tachocline separating the core from the radiative zone. This opens up the possibility that there may be an inner dynamo that could produce a strong internal magnetic field and a second solar cycle.     

Brightness of the Coronal Green Line and Prediction for Activity Cycles 23 and 24

Cyclic variations of the mean semi-annual intensities I of the coronal green line 530.3 nm are compared with the mean semi-annual variations of the Wolf numbers W during the period of 1943–1999 (activity cycles 18–23). The values of I in the equatorial zone proved to correlate much better with the Wolf numbers in a following cycle than in a given one (the correlation coefficient r is 0.86 and 0.755, respectively). Such increase of the correlation coefficient with a shift by one cycle differs in different phases of the cycle, being the largest at the ascending branch. The regularities revealed make it possible to predict the behaviour of W in the following cycle on the basis of intensities of the coronal green line in the preceding cycle. We predict the maximum semi-annual W in cycle 23 to be 110–122 and the epoch of minimum between cycles 23 and 24 to take place at 2006–2007. A slow increase of I in the current cycle 23 permits us to forecast a low-Wolf-number cycle 24 with the maximum W50 at 2010–2011. A scheme is proposed on the permanent transformation of the coronal magnetic fields of different scales explaining the found phenomenon.     

Using Active Contours for Semi-Automated Tracking of UV and EUV Solar Flare Ribbons

Solar-flare UV and EUV images show elongated bright “ribbons” that move over time. If these ribbons are assumed to locate the footpoints of magnetic-field lines reconnecting in the corona, then it is clear that studying their evolution can provide important insight into the reconnection process. An image-processing method based on active contours (commonly referred to as “snakes”) is proposed as a method for tracking UV and EUV flare ribbons and is tested on images from the Transition Region and Coronal Explorer (TRACE). This paper introduces the basic concepts of such an approach with a brief overview of the history and theory behind active contours. It then details the specifics of the snake algorithm developed for this work and shows the results of running the algorithm on test images. The results from the application of the developed algorithm are reported for six different TRACE flares (five in UV and one in EUV). The discussion of these results uses the output from an expert tracking the same ribbons by eye as a benchmark, and against these the snake algorithm is shown to compare favourably in certain conditions, but less so in others. The applicability of the automated snake algorithm to the general problem of ribbon tracking is discussed and suggestions for ways to improve the snake algorithm are proposed.     

Solar Spicules: A Review of Recent Models and Targets for Future Observations – (Invited Review)

Since their discovery over 100 years ago, there have been many suggestions for the origin and development of solar spicules. Because the velocities of spicules are comparable to the sound and Alfvén speeds of the low chromosphere, linear theory cannot fully describe them. Consequently, detailed tests of theoretical ideas had to await the development of computing power that only became available during the 1970s. This work reviews theories for spicules and spicule-like features over approximately the past 25 years, with an emphasis on the models based on nonlinear numerical simulations. These models have given us physical insight into wave propagation in the solar atmosphere, and have helped elucidate how such waves, and associated shock waves, may be capable of creating motions and structures on magnetic flux tubes in the lower solar atmosphere. So far, however, it has been difficult to reproduce the most-commonly-quoted parameters for spicules with these models, using what appears to be the most suitable input parameters. A key impediment to developing satisfactory models has been the lack of reliable observational information, which is a consequence of the small angular size and transient lifetime of spicules. I close with a list of key observational questions to be addressed with space-based satellites, such as the currently operating TRACE satellite, and especially the upcoming Solar-B mission. Answers to these questions will help determine which, if any, of the current models correctly explains spicules.     

North and South Hemispheric Solar Activity for Cycles 21 – 23: Asymmetry and Conditional Volatility of Plage Region Areas

We study the dynamic evolution of the time series describing the plage regions areas observed daily at the Observatório Astronómico da Universidade de Coimbra, in each one of the solar hemispheres during solar cycles 21?–?23. The classical ARMA model has proven to be insufficient to describe the time variations seen in the data because of the strong conditional variability. We found that the data are well fitted by ARMA mixed with power-δ TGARCH error models. The power index δ is non-integer; this property has recently been introduced in the literature on time-series analyses and indicates the presence of strong volatility and long memory in the data series. We also detected dynamic asymmetry in the plage region areas observed in the two hemispheres when two different temporal models were obtained to fit them. The finding of a dynamic asymmetry is also supported by the dynamic evolution of the daily difference (north–south) time series, which is significantly different from white noise. This statistical modeling of time series, taking into account new and different characteristics of the solar activity, will be very useful in subsequent forecast developments.     

Investigation of the Differential Rotation by H�� Filaments and Long-Lived Magnetic Features for Solar Activity Cycles 20 and 21

For solar activity Cycles 20 and 21 (1966??C?1985) the solar differential rotation has been investigated using H?? filaments and relatively small-scale long-lived magnetic features with negative and positive polarities. We used annual averaged angular velocities of quiescent H?? filaments from H?? photoheliograms of the Abastumani Astrophysical Observatory film collection and selected long-lived magnetic features from the McIntosh atlas (McIntosh, Willock, and Thompson, Atlas of Stackplots, NGDC, 1991). We have determined coefficients of Faye??s formulas for H?? filaments as well as for long-lived magnetic features and have found that for Solar Cycles 20 and 21 the H?? filaments have lower rotation rates and rotated more differentially than the long-lived magnetic features.     

Effects of Random Flows on the Solar f Mode: II. Horizontal and Vertical Flow

We study the influence of horizontal and vertical random flows on the solar f mode in a plane-parallel, incompressible model that includes a static atmosphere. The incompressible limit is an adequate approximation for f-mode type of surface waves that are highly incompressible. The paper revisits and extends the problem investigated earlier by Murawski and Roberts (Astron. Astrophys. 272, 601, 1993). We show that the consideration of the proposed velocity profile requires several restrictive assumptions to be made. These constraints were not recognised in previous studies. The impact of the inconsistencies in earlier modelling is analysed in detail. Corrections to the dispersion relation are derived and the relevance of these corrections is analysed. Finally, the importance of the obtained results is investigated in the context of recent helioseismological data. Detailed comparison with our complementary studies on random horizontal flows (Mole, Kerekes, and Erdélyi, Solar Phys., accepted, 2008) and the random magnetic model of Erdélyi, Kerekes, and Mole (Astron. Astrophys. 431, 1083, 2005) is also given. In particular, for realistic solar parameters we find significant frequency reduction and wave damping, both of which increase with the characteristic thickness of the random layer.     

Changed Relation between Solar 10.7-cm Radio Flux and some Activity Indices which describe the Radiation at Different Altitudes of Atmosphere during Cycles 21–23

The correlation coefficients of the linear regression of six solar indices versus 10.7 cm radio flux F _10.7 were analysed in solar cycles 21, 22 and 23. We also analysed the interconnection between these indices and F _10.7 with help of approximation by polynomials of second order. The indices we have studied in this paper are: the relative sunspot numbers – SSN, 530.3 nm coronal line flux – F ₅₃₀, the total solar irradiance – TSI, Mg II 280 nm core-to-wing ratio UV-index, the Flare Index – FI and the counts of flares. In most cases the regressions of these solar indices vs. F _10.7 are close to the linear regression except the moments of time near the minimums and maximums of the 11-year activity. For the linear regressions, we found that correlation coefficients K _corr(t) for the solar indices vs. F _10.7 and SSN dropped to their minimum values twice during each 11-year cycle.     

Applying an Expansion of the Second Derivatives of the Earth’s Gravitational Potential in Modified Spherical Harmonics for Constructing and Estimating Its Models

Second-order derivatives of the Earth’s potential in a local north-oriented coordinate system are expanded in series of modified spherical harmonics. Linear relations are derived between the spectral coefficients of these series and the spectrum of the geopotential. Based on these relations, recurrent procedures are developed for estimating the geopotential coefficients from the spectrum of each derivative and, conversely, for simulating the spectrum from a known geopotential model. The very simple structure of the expressions for the derivatives is convenient for estimating the coefficients of the geopotential by the least squares method at a certain step of processing satellite gradiometry data. Since the new series are orthogonal, the method with a quadrature formula can be applied, which helps avoid aliasing errors caused by the truncation of the series. The spectral coefficients of the derivatives are estimated using the derived relations for different models on an average orbital sphere of the GOCE satellite and at other altitudes above the Earth’s surface.

     

Comments on “Effects of Strong Regular Refraction in the Solar Radio Pulse Structure in Spike Events” by Afanasiev and Altyntsev and “Mathematical Modeling of the Formation of Type IIId Solar Decameter Radio Bursts with Echo Components” by Afanasiev

Presented are some comments on the papers by Afanasiev and Altyntsev (Solar Phys. 234, 151, 2006) and by Afanasiev (Solar Phys. 238, 87, 2006) devoted to the study of the influence of solar corona inhomogeneities on the form of radio bursts. It is pointed out that in these papers incorrect use is made of methods used previously in investigations into radio wave propagation through a randomly inhomogeneous ionosphere.     

Model of the W3(OH) Environment Based on Data for Both Maser and “Quasi-Thermal” Methanol Lines

In studies of the environment of massive young stellar objects, recent progress in both observations and theory allows a unified treatment of data for maser and quasi-thermal lines. Interferometric maser images provide information on the distribution and kinematics of masing gas on small spatial scales. Observations of multiple masing transitions provide constraints on the physical parameters.Interferometric data on quasi-thermal molecular lines permits an investigation of the overall distribution and kinematics of the molecular gas in the vicinity of young stellar objects, including those which are deeply embedded. Using multiple transitions of different molecules, one can obtain good constraints on the physical and chemical parameters. Combining these data enables the construction of unified models, which take into account spatial scales differing by orders of magnitude.Here, we present such a combined analysis of the environment around the ultracompact HII region in W3(OH). This includes the structure of the methanol masing region, physical structure of the near vicinity of W3(OH), detection of new masers in the large-scale shock front and embedded sources in the vicinity of the TW young stellar object.     

Analytic forms of the perpendicular cosmic ray diffusion coefficient for an arbitrary turbulence spectrum and applications on transport of Galactic protons and acceleration at interplanetary shocks

We investigate cosmic ray scattering in the direction perpendicular to a mean magnetic field. Unlike in previous articles we employ a general form of the turbulence wave spectrum with arbitrary behavior in the energy range. By employing an improved version of the nonlinear guiding center theory we compute analytically the perpendicular mean free path. As shown, the energy range spectral index, has a strong influence on the perpendicular diffusion coefficient. If this parameter is larger than one we find for some cases a perpendicular diffusion coefficient that is independent of the parallel mean free path and particle energy. Two applications are considered, namely transport of Galactic protons in the solar system and diffusive particle acceleration at highly perpendicular interplanetary shock waves.