Author name code: petrovay ADS astronomy entries on 2022-09-14 author:"Petrovay, Kristof" ------------------------------------------------------------------------ Title: Role of observable nonlinearities in solar cycle modulation Authors: Talafha, M.; Nagy, M.; Lemerle, A.; Petrovay, K. Bibcode: 2022A&A...660A..92T Altcode: 2021arXiv211214465T Context. Two candidate mechanisms have recently been considered with regard to the nonlinear modulation of solar cycle amplitudes. Tilt quenching (TQ) comprises the negative feedback between the cycle amplitude and the mean tilt angle of bipolar active regions relative to the azimuthal direction. Latitude quenching (LQ) consists of a positive correlation between the cycle amplitude and average emergence latitude of active regions.
Aims: Here, we explore the relative importance and the determining factors behind the LQ and TQ effects.
Methods: We systematically probed the degree of nonlinearity induced by TQ and LQ, as well as a combination of both using a grid based on surface flux transport (SFT) models. The roles played by TQ and LQ are also explored in the successful 2×2D dynamo model, which has been optimized to reproduce the statistical behaviour of real solar cycles.
Results: The relative importance of LQ versus TQ is found to correlate with the ratio u0/η in the SFT model grid, where u0 is the meridional flow amplitude and η is the diffusivity. An analytical interpretation of this result is given, further demonstrating that the main underlying parameter is the dynamo effectivity range, λR, which is, in turn, determined by the ratio of equatorial flow divergence to diffusivity. The relative importance of LQ versus TQ is shown to scale as C_1+C_2/λ_R2 . The presence of a latitude quenching effect is seen in the 2×2D dynamo, contributing to the nonlinear modulation by an amount that is comparable to TQ. For other dynamo and SFT models considered in the literature, the contribution of LQ to the modulation covers a broad range - from entirely insignificant to serving as a dominant source of feedback. On the other hand, the contribution of a TQ effect (with the usually assumed amplitude) is never shown to be negligible. Title: The Polar Precursor Method for Solar Cycle Prediction: Comparison of Predictors and Their Temporal Range Authors: Kumar, Pawan; Nagy, Melinda; Lemerle, Alexandre; Karak, Bidya Binay; Petrovay, Kristof Bibcode: 2021ApJ...909...87K Altcode: 2021arXiv210105013K The polar precursor method is widely considered to be the most robust physically motivated method to predict the amplitude of an upcoming solar cycle. It uses indicators of the magnetic field concentrated near the poles around the sunspot minimum. Here, we present an extensive analysis of the performance of various such predictors, based on both observational data (Wilcox Solar Observatory (WSO) magnetograms, Mount Wilson Observatory polar faculae counts, and Pulkovo A(t) index) and outputs (polar cap magnetic flux and global dipole moment) of various existing flux transport dynamo models. We calculate Pearson correlation coefficients (r) of the predictors with the next cycle amplitude as a function of time measured from several solar cycle landmarks: setting r = 0.8 as a lower limit for acceptable predictions, we find that observations and models alike indicate that the earliest time when the polar predictor can be safely used is 4 yr after the polar field reversal. This is typically 2-3 yr before the solar minimum and about 7 yr before the predicted maximum, considerably extending the usual temporal scope of the polar precursor method. Reevaluating the predictors another 3 yr later, at the time of the solar minimum, further increases the correlation level to r ≳ 0.9. As an illustration of the result, we determine the predicted amplitude of Cycle 25 based on the value of the WSO polar field at the now official minimum date of 2019 December as 126 ± 3. A forecast based on the value in early 2017, 4 yr after the polar reversal would have only differed from this final prediction by 3.1 ± 14.7%. Title: Towards an algebraic method of solar cycle prediction. I. Calculating the ultimate dipole contributions of individual active regions Authors: Petrovay, Kristóf; Nagy, Melinda; Yeates, Anthony R. Bibcode: 2020JSWSC..10...50P Altcode: 2020arXiv200902299P We discuss the potential use of an algebraic method to compute the value of the solar axial dipole moment at solar minimum, widely considered to be the most reliable precursor of the activity level in the next solar cycle. The method consists of summing up the ultimate contributions of individual active regions to the solar axial dipole moment at the end of the cycle. A potential limitation of the approach is its dependence on the underlying surface flux transport (SFT) model details. We demonstrate by both analytical and numerical methods that the factor relating the initial and ultimate dipole moment contributions of an active region displays a Gaussian dependence on latitude with parameters that only depend on details of the SFT model through the parameter η/Δu where η is supergranular diffusivity and Δu is the divergence of the meridional flow on the equator. In a comparison with cycles simulated in the 2 × 2D dynamo model we further demonstrate that the inaccuracies associated with the algebraic method are minor and the method may be able to reproduce the dipole moment values in a large majority of cycles. Title: Towards an algebraic method of solar cycle prediction. II. Reducing the need for detailed input data with ARDoR Authors: Nagy, Melinda; Petrovay, Kristóf; Lemerle, Alexandre; Charbonneau, Paul Bibcode: 2020JSWSC..10...46N Altcode: 2020arXiv200902300N An algebraic method for the reconstruction and potentially prediction of the solar dipole moment value at sunspot minimum (known to be a good predictor of the amplitude of the next solar cycle) was suggested in the first paper in this series. The method sums up the ultimate dipole moment contributions of individual active regions in a solar cycle: for this, detailed and reliable input data would in principle be needed for thousands of active regions in a solar cycle. To reduce the need for detailed input data, here we propose a new active region descriptor called ARDoR (Active Region Degree of Rogueness). In a detailed statistical analysis of a large number of activity cycles simulated with the 2 × 2D dynamo model we demonstrate that ranking active regions by decreasing ARDoR, for a good reproduction of the solar dipole moment at the end of the cycle it is sufficient to consider the top N regions on this list explicitly, where N is a relatively low number, while for the other regions the ARDoR value may be set to zero. For example, with N = 5 the fraction of cycles where the dipole moment is reproduced with an error exceeding ±30% is only 12%, significantly reduced with respect to the case N = 0, i.e. ARDoR set to zero for all active regions, where this fraction is 26%. This indicates that stochastic effects on the intercycle variations of solar activity are dominated by the effect of a low number of large "rogue" active regions, rather than the combined effect of numerous small ARs. The method has a potential for future use in solar cycle prediction. Title: The determination of stellar temperatures from Baron B. Harkányi to the Gaia mission Authors: Petrovay, Kristof Bibcode: 2020arXiv200308092P Altcode: The first determination of the surface temperature of stars other than the Sun is due to the Hungarian astrophysicist Béla Harkányi. Prompted by the recent unprecedented increase in the availability of stellar temperature estimates from Gaia, coinciding with the 150th anniversary of Harkányi's birth, this article presents the life and work of this neglected, yet remarkable figure in the context of the history of stellar astrophysics. Title: Solar cycle prediction Authors: Petrovay, Kristóf Bibcode: 2020LRSP...17....2P Altcode: 2019arXiv190702107P A review of solar cycle prediction methods and their performance is given, including early forecasts for Cycle 25. The review focuses on those aspects of the solar cycle prediction problem that have a bearing on dynamo theory. The scope of the review is further restricted to the issue of predicting the amplitude (and optionally the epoch) of an upcoming solar maximum no later than right after the start of the given cycle. Prediction methods form three main groups. Precursor methods rely on the value of some measure of solar activity or magnetism at a specified time to predict the amplitude of the following solar maximum. The choice of a good precursor often implies considerable physical insight: indeed, it has become increasingly clear that the transition from purely empirical precursors to model-based methods is continuous. Model-based approaches can be further divided into two groups: predictions based on surface flux transport models and on consistent dynamo models. The implicit assumption of precursor methods is that each numbered solar cycle is a consistent unit in itself, while solar activity seems to consist of a series of much less tightly intercorrelated individual cycles. Extrapolation methods, in contrast, are based on the premise that the physical process giving rise to the sunspot number record is statistically homogeneous, i.e., the mathematical regularities underlying its variations are the same at any point of time, and therefore it lends itself to analysis and forecasting by time series methods. In their overall performance during the course of the last few solar cycles, precursor methods have clearly been superior to extrapolation methods. One method that has yielded predictions consistently in the right range during the past few solar cycles is the polar field precursor. Nevertheless, some extrapolation methods may still be worth further study. Model based forecasts are quickly coming into their own, and, despite not having a long proven record, their predictions are received with increasing confidence by the community. Title: Optimization of surface flux transport models for the solar polar magnetic field Authors: Petrovay, K.; Talafha, M. Bibcode: 2019A&A...632A..87P Altcode: 2019arXiv190906125P Context. The choice of free parameters in surface flux transport (SFT) models describing the evolution of the large-scale poloidal magnetic field of the Sun is critical for the correct reproduction of the polar magnetic flux built up during a solar cycle, which is known to be a good predictor of the amplitude of the upcoming cycle.
Aims: For an informed choice of parameters it is important to understand the effects of and interplay among the various parameters and to optimize the models for the polar magnetic field.
Methods: Here we present the results of a large-scale systematic study of the parameter space in an SFT model where the source term representing the net effect of tilted flux emergence was chosen to represent a typical, average solar cycle as described by observations.
Results: Comparing the results with observational constraints on the spatiotemporal variation of the polar magnetic field, as seen in magnetograms for the last four solar cycles, we mark allowed and excluded regions in the 3D parameter space defined by the flow amplitude u0, the magnetic diffusivity η and the decay time scale τ, for three different assumed meridional flow profiles.
Conclusions: Without a significant decay term in the SFT equation (i.e., for τ > 10 yr) the global dipole moment reverses too late in the cycle for all flow profiles and parameters, providing independent supporting evidence for the need of a decay term, even in the case of identical cycles. An allowed domain is found to exist for τ values in the 5-10 yr range for all flow profiles considered. Generally higher values of η (500-800 km2 s-1) are preferred though some solutions with lower η are still allowed. Title: Precursors of an upcoming solar cycle at high latitudes from coronal green line data Authors: Petrovay, K.; Nagy, M.; Gerják, T.; Juhász, L. Bibcode: 2018JASTP.176...15P Altcode: 2018arXiv180205628P After reviewing potential early indicators of an upcoming solar cycle at high latitudes, we focus attention on the rush-to-the-poles (RTTP) phenomenon in coronal green line emission. Considering various correlations between properties of the RTTP with the upcoming solar cycle we find a correlation between the rate of the RTTP and the time delay until the maximum of the next solar cycle. On the basis of this correlation and the known internal regularities of the sunspot number series we predict that, following a minimum in 2019, cycle 25 will peak in late 2024 at an amplitude of about 130 (in terms of smoothed monthly revised sunspot numbers). This slightly exceeds the amplitude of cycle 24 but it would still make cycle 25 a fairly weak cycle. Title: Rogue Active Regions and the Inherent Unpredictability of the Solar Dynamo Authors: Petrovay, Kristóf; Nagy, Melinda Bibcode: 2018IAUS..340..307P Altcode: 2018arXiv180403427P New developments in surface flux transport modeling and theory of flux transport dynamos have given rise to the notion that certain large active regions with anomalous properties (location, tilt angle and/or Hale/non-Hale character) may have a major impact on the course of solar activity in subsequent years, impacting also on the amplitude of the following solar cycles. Here we discuss our current understanding of the role of such ``rogue'' active regions in cycle-to-cycle variations of solar activity. Title: The Effect of "Rogue" Active Regions on the Solar Cycle Authors: Nagy, Melinda; Lemerle, Alexandre; Labonville, François; Petrovay, Kristóf; Charbonneau, Paul Bibcode: 2017SoPh..292..167N Altcode: 2017arXiv171202185N The origin of cycle-to-cycle variations in solar activity is currently the focus of much interest. It has recently been pointed out that large individual active regions with atypical properties can have a significant impact on the long-term behavior of solar activity. We investigate this possibility in more detail using a recently developed 2 ×2 D dynamo model of the solar magnetic cycle. We find that even a single "rogue" bipolar magnetic region (BMR) in the simulations can have a major effect on the further development of solar activity cycles, boosting or suppressing the amplitude of subsequent cycles. In extreme cases, an individual BMR can completely halt the dynamo, triggering a grand minimum. Rogue BMRs also have the potential to induce significant hemispheric asymmetries in the solar cycle. To study the effect of rogue BMRs in a more systematic manner, a series of dynamo simulations were conducted, in which a large test BMR was manually introduced in the model at various phases of cycles of different amplitudes. BMRs emerging in the rising phase of a cycle can modify the amplitude of the ongoing cycle, while BMRs emerging in later phases will only affect subsequent cycles. In this model, the strongest effect on the subsequent cycle occurs when the rogue BMR emerges around cycle maximum at low latitudes, but the BMR does not need to be strictly cross-equatorial. Active regions emerging as far as 20∘ from the equator can still have a significant effect. We demonstrate that the combined effect of the magnetic flux, tilt angle, and polarity separation of the BMR on the dynamo is via their contribution to the dipole moment, δ DBMR. Our results indicate that prediction of the amplitude, starting epoch, and duration of a cycle requires an accurate accounting of a broad range of active regions emerging in the previous cycle. Title: Magnetic cycles at different ages of stars Authors: Oláh, K.; Kővári, Zs.; Petrovay, K.; Soon, W.; Baliunas, S.; Kolláth, Z.; Vida, K. Bibcode: 2016A&A...590A.133O Altcode: 2016arXiv160406701O
Aims: We study the different patterns of interannual magnetic variability in stars on or near the lower main sequence, approximately solar-type (G-K dwarf) stars in time series of 36 yr from the Mount Wilson Observatory Ca II H&K survey. Our main aim is to search for correlations between cycles, activity measures, and ages.
Methods: Time-frequency analysis has been used to discern and reveal patterns and morphology of stellar activity cycles, including multiple and changing cycles, in the datasets. Both the results from short-term Fourier transform and its refinement using the Choi-Williams distribution, with better frequency resolution, are presented in this study. Rotational periods of the stars were derived using multifrequency Fourier analysis.
Results: We found at least one activity cycle on 28 of the 29 stars we studied. Twelve stars, with longer rotational periods (39.7 ± 6.0 days), have simple smooth cycles, and the remaining stars, with much faster rotation (18.1 ± 12.2 days) on average, show complex and sometimes vigorously changing multiple cycles. The cycles are longer and quite uniform in the first group (9.7 ± 1.9 yr), while they are generally shorter and vary more strongly in the second group (7.6 ± 4.9). The clear age division between stars with smooth and complex cycles follows the known separation between the older and younger stars at around 2 to 3 Gyr of age. Title: Introduction to the Solar Activity Cycle: Overview of Causes and Consequences Authors: Balogh, A.; Hudson, H. S.; Petrovay, K.; von Steiger, R. Bibcode: 2015sac..book....1B Altcode: No abstract at ADS Title: The Solar Activity Cycle Authors: Balogh, André; Hudson, Hugh; Petrovay, Kristóf; von Steiger, Rudolf Bibcode: 2015sac..book.....B Altcode: No abstract at ADS Title: Oscillator Models of the Solar Cycle Authors: Lopes, Ilídio; Passos, Dário; Nagy, Melinda; Petrovay, Kristof Bibcode: 2015sac..book..535L Altcode: No abstract at ADS Title: Solar Polar Fields and the 22-Year Activity Cycle: Observations and Models Authors: Petrie, G. J. D.; Petrovay, K.; Schatten, K. Bibcode: 2015sac..book..325P Altcode: No abstract at ADS Title: Introduction to the Solar Activity Cycle: Overview of Causes and Consequences Authors: Balogh, A.; Hudson, H. S.; Petrovay, K.; von Steiger, R. Bibcode: 2014SSRv..186....1B Altcode: 2014SSRv..tmp...60B The 11-year activity cycle is a dominant characteristic of the Sun. It is the result of the evolution in time the solar dynamo that generates the solar magnetic field. The nearly periodic variation in the sunspot number has been known since the mid-1800s; as the observations of the Sun broadened to cover an increasing number of phenomena, the same 11-year periodicity was noted in most of them. The discovery of solar magnetic fields introduced a 22-year periodicity, as the magnetic polarities of the polar regions change sign every 11 years. Correlations have been identified and quantified among all the measured parameters, but in most cases such correlations remain empirical rather than grounded in physical processes. This introductory paper and the reviews in the volume describe and discuss the current state of understanding of the causal chains that lead from the variable nature of the solar magnetic fields to the variability of solar phenomena. The solar activity cycle is poorly understood: predictions made for the current Cycle 24 have proved to be generally wrong. However, the re-evaluation of the relationships in the light of unexpected shortcomings is likely to lead to a better physical understanding of solar physics. This will help in the systematic reassessment of solar activity indices and their usefulness in describing and predicting the solar activity cycle. Title: Oscillator Models of the Solar Cycle. Towards the Development of Inversion Methods Authors: Lopes, Ilídio; Passos, Dário; Nagy, Melinda; Petrovay, Kristof Bibcode: 2014SSRv..186..535L Altcode: 2014arXiv1407.4918L; 2014SSRv..tmp...32L This article reviews some of the leading results obtained in solar dynamo physics by using temporal oscillator models as a tool to interpret observational data and dynamo model predictions. We discuss how solar observational data such as the sunspot number is used to infer the leading quantities responsible for the solar variability during the last few centuries. Moreover, we discuss the advantages and difficulties of using inversion methods (or backward methods) over forward methods to interpret the solar dynamo data. We argue that this approach could help us to have a better insight about the leading physical processes responsible for solar dynamo, in a similar manner as helioseismology has helped to achieve a better insight on the thermodynamic structure and flow dynamics in the Sun's interior. Title: Solar Polar Fields and the 22-Year Activity Cycle: Observations and Models Authors: Petrie, G. J. D.; Petrovay, K.; Schatten, K. Bibcode: 2014SSRv..186..325P Altcode: 2014SSRv..tmp...28P We explore observations and models of the interacting, cyclical behavior of the active regions and the polar magnetic fields of the Sun. We focus on observational evidence of these fields interacting across the corridor between active and polar latitudes. We present observations of diverse magnetic signatures on, above and beneath the solar surface, and find much evidence of phenomena migrating in both directions across this corridor in each hemisphere, including photospheric fields, ephemeral bipoles, interior torsional oscillations, high-latitude filaments, and coronal green line intensity. Together these observations produce a complex physical picture of high-latitude solar magnetic field evolution in the photosphere, atmosphere and interior, and demonstrate their essential role in the solar cycle. The picture presented by these collected observations is consistent with the Babcock-Leighton phenomenological model for the cycle, and we discuss related efforts to predict cycle amplitudes based on polar field strengths and on combining activity and polar-field information in a single phase-independent, slowly-evolving index. We also briefly review related work on magnetic flux transport models for the solar cycle, with particular reference to the interaction between flux emergence patterns and meridional flows. Title: Turbulent magnetic energy spectrum and the cancellation function of solar photospheric magnetic fields Authors: Marschalkó, G.; Petrovay, K.; Petrovay, K. Bibcode: 2013AN....334..952M Altcode: 2014arXiv1404.1772M A simple analytical relation of form α=2κ-1 between the magnetic energy spectral exponent α of the turbulent magnetic field in the solar photosphere and its magnetic flux cancellation exponent κ, valid under certain restrictive assumptions, is tested and extended outside its range of validity in a series of Monte Carlo simulations. In these numerical tests artificial ``magnetograms'' are constructed in 1D and 2D by superposing a discrete set of Fourier modes of the magnetic field distribution with amplitudes following a power law spectrum and measuring the cancellation function on these simulated magnetograms. Our results confirm the validity of the analytical relation and extend it to the domain α<-1 where κ-> 0 as α-> -∞. The observationally derived upper limit of 0.38 on κ implies α<-0.24 in the granular size range, apparently at odds with a small scale dynamo driven in the inertial range. Title: Oscillator models of the solar cycle and the Waldmeier effect Authors: Nagy, M.; Petrovay, K. Bibcode: 2013AN....334..964N Altcode: 2014arXiv1404.3668N We study the behaviour of the van der Pol oscillator when either its damping parameter μ or its nonlinearity parameter ξ is subject to additive or multiplicative random noise. Assuming various power law exponents for the relation between the oscillating variable and the sunspot number, for each case we map the parameter plane defined by the amplitude and the correlation time of the perturbation and mark the parameter regime where the sunspot number displays solar-like behaviour. Solar-like behaviour is defined here as a good correlation between the rise rate and cycle amplitude and the lack of a good correlation between the decay rate and amplitude, together with significant ({⪆ 10} %) r.m.s. variation in cycle lengths and cycle amplitudes. It is found that perturbing μ alone the perturbed van der Pol oscillator does not show solar-like behaviour. When the perturbed variable is ξ, solar-like behaviour is displayed for perturbations with a correlation time of about 3-4 years and significant amplitude. Such studies may provide useful constraints on solar dynamo models and their parameters. Title: Flux transport dynamo coupled with a fast tachocline scenario Authors: Karak, Bidya Binay; Petrovay, Kristof Bibcode: 2013IAUS..294..427K Altcode: 2012arXiv1211.0140K The tachocline is important in the solar dynamo for the generation and the storage of the magnetic fields. A most plausible explanation for the confinement of the tachocline is given by the fast tachocline model in which the tachocline is confined by the anisotropic momentum transfer by the Maxwell stress of the dynamo generated magnetic fields. We employ a flux transport dynamo model coupled with the simple feedback formula of this fast tachocline model which basically relates the thickness of the tachocline to the Maxwell stress. We find that this nonlinear coupling not only produces a stable solar-like dynamo solution but also a significant latitudinal variation in the tachocline thickness which is in agreement with the observations. Title: Structures in compressible magnetoconvection and the nature of umbral dots Authors: Tian, C.; Petrovay, K. Bibcode: 2013A&A...551A..92T Altcode: 2011arXiv1105.5590T Context. Structures seen in idealized numerical experiments on compressible magnetoconvection in an imposed strong vertical magnetic field show important differences from those detected in observations or realistic numerical simulations of sunspot umbrae.
Aims: To elucidate the origin of these discrepancies, we present a series of idealized 3D compressible magnetoconvection experiments that differ from previous such experiments in several details, bringing them closer to realistic solar conditions.
Methods: An initially vertical magnetic field B0 is imposed on a time snapshot of fully developed solar-like turbulent convection in a layer bounded by a stable layer from above. Upon relaxation to a statistically steady state, the structure of the flow field and magnetic field is examined.
Results: Instead of the vigorous granular convection (GRC) well known to take place in magnetized or weakly magnetized convection, for high values of B0 heat is transported by small-scale convection (SSC) in the form of narrow, persistent convective columns consisting of slender upflows accompanied by adjacent downflow patches, which are reminiscent of the "convectons" identified in earlier semianalytic models. For moderate field strengths, flux separation (FXS) is observed: isolated field-free inclusions of GRC are embedded in a strongly magnetized plasma with SSC. Between the SSC and FXS regimes, a transitional regime (F/S) is identified where convectons dynamically evolve into multiply segmented granular inclusions and back.
Conclusions: Our results agree in some aspects more closely with observed umbral structures than earlier idealized models, because they do reproduce the strong localized, patchy downflows immediately adjacent to the narrow convective columns. Based on recent observations of umbral dots, we suggest that in some cases the conditions in sunspot umbræ correspond to the newly identified F/S transitional regime. Title: On the Compatibility of a Flux Transport Dynamo with a Fast Tachocline Scenario Authors: Karak, Bidya Binay; Petrovay, Kristof Bibcode: 2013SoPh..282..321K Altcode: 2012arXiv1209.0319K The compatibility of the fast-tachocline scenario with a flux-transport dynamo model is explored. We employ a flux-transport dynamo model coupled with simple feedback formulae relating the thickness of the tachocline to the amplitude of the magnetic field or to the Maxwell stress. The dynamo model is found to be robust against the nonlinearity introduced by this simplified fast-tachocline mechanism. Solar-like butterfly diagrams are found to persist and, even without any parameter fitting, the overall thickness of the tachocline is well within the range admitted by helioseismic constraints. In the most realistic case of a time- and latitude-dependent tachocline thickness linked to the value of the Maxwell stress, both the thickness and its latitudinal dependence are in excellent agreement with seismic results. In nonparametric models, cycle-related temporal variations in tachocline thickness are somewhat larger than admitted by helioseismic constraints; we find, however, that introducing a further parameter into our feedback formula readily allows further fine tuning of the thickness variations. Title: Solar Cycle Prediction Authors: Petrovay, Kristóf Bibcode: 2010LRSP....7....6P Altcode: 2010arXiv1012.5513P A review of solar cycle prediction methods and their performance is given, including forecasts for cycle 24. The review focuses on those aspects of the solar cycle prediction problem that have a bearing on dynamo theory. The scope of the review is further restricted to the issue of predicting the amplitude (and optionally the epoch) of an upcoming solar maximum no later than right after the start of the given cycle. Title: Turbulence in the Solar Atmosphere and Solar Wind Authors: Petrosyan, A.; Balogh, A.; Goldstein, M. L.; Léorat, J.; Marsch, E.; Petrovay, K.; Roberts, B.; von Steiger, R.; Vial, J. C. Bibcode: 2010SSRv..156..135P Altcode: 2010SSRv..tmp..117P The objective of this review article is to critically analyze turbulence and its role in the solar atmosphere and solar wind, as well as to provide a tutorial overview of topics worth clarification. Although turbulence is a ubiquitous phenomenon in the sun and its heliosphere, many open questions exist concerning the physical mechanisms of turbulence generation in solar environment. Also, the spatial and temporal evolution of the turbulence in the solar atmosphere and solar wind are still poorly understood. We limit the scope of this paper (leaving out the solar interior and convection zone) to the magnetized plasma that reaches from the photosphere and chromosphere upwards to the corona and inner heliosphere, and place particular emphasis on the magnetic field structures and fluctuations and their role in the dynamics and radiation of the coronal plasma. To attract the attention of scientists from both the fluid-dynamics and space-science communities we give in the first two sections a phenomenological overview of turbulence-related processes, in the context of solar and heliospheric physics and with emphasis on the photosphere-corona connection and the coupling between the solar corona and solar wind. We also discuss the basic tools and standard concepts for the empirical analysis and theoretical description of turbulence. The last two sections of this paper give a concise review of selected aspects of oscillations and waves in the solar atmosphere and related fluctuations in the solar wind. We conclude with some recommendations and suggest topics for future research. Title: An analytic interface dynamo over a shear layer of finite depth Authors: Petrovay, K.; Kerekes, A.; Erdelyi, R. Bibcode: 2010GApFD.104..619P Altcode: 2010arXiv1007.1634P Parker's analytic Cartesian interface dynamo is generalized to the case of a shear layer of finite thickness and low resistivity ("tachocline"), bounded by a perfect conductor ("radiative zone") on the one side, and by a highly diffusive medium ("convective zone") supporting an α-effect on the other side. In the limit of high diffusivity contrast between the shear layer and the diffusive medium, thought to be relevant for the Sun, a pair of exact dispersion relations for the growth rate and frequency of dynamo modes is analytically derived. Graphic solution of the dispersion relations displays a somewhat unexpected, non-monotonic behavior, the mathematical origin of which is elucidated. The dependence of the results on the parameter values (dynamo number and shear layer thickness) is investigated. The implications of this result for the solar dynamo problem are discussed. Title: The Magnetic Sun: Reversals and Long-Term Variations Authors: Petrovay, K.; Christensen, U. R. Bibcode: 2010SSRv..155..371P Altcode: 2010SSRv..tmp...64P; 2010arXiv1004.5102P A didactic introduction to current thinking on some aspects of the solar dynamo is given for geophysicists and planetary scientists. Title: Harmonic analysis approach to solar cycle prediction and the Waldmeier effect Authors: Petrovay, K. Bibcode: 2010IAUS..264..150P Altcode: It is demonstrated that, in addition to the precursor method, harmonic analysis approach to solar cycle prediction is also strongly conditioned by the Waldmeier effect. Title: The Magnetic Sun: Reversals and Long-Term Variations Authors: Petrovay, K.; Christensen, U. R. Bibcode: 2010tema.book..371P Altcode: No abstract at ADS Title: The importance of facular and plage data for the understanding of the solar cycle Authors: Petrovay, Kristof Bibcode: 2010cosp...38.2885P Altcode: 2010cosp.meet.2885P Most global analyses of the solar activity cycle are based on sunspot data as other indicators such as F10.8 or flare data only cover the last few solar cycles. The only solar activity param-eter covering a historically significant time span is the facular area data set in the Greenwich catalogue. In this poster we first demonstrate the use of such data for the study of the solar cycle by considering similarities and differences in the Waldmeier effect in faculae as opposed to sunspots. The Greenwich catalogue was discontinued in 1976, so the extension of such studies to more recent times relies on "proxy" data such as plage areas; however, due to the short overlap in time, cross-calibration of these data has not been consistently made. We discuss the possibilities offered by SDO to cross-correlate facular areas with their proxies and to set up a new systematic data set of these activity indices. Title: Solar and planetary dynamos: comparison and recent developments Authors: Petrovay, K. Bibcode: 2009IAUS..257...71P Altcode: 2009arXiv0901.0839P While obviously having a common root, solar and planetary dynamo theory have taken increasingly divergent routes in the last two or three decades, and there are probably few experts now who can claim to be equally versed in both. Characteristically, even in the fine and comprehensive book “The magnetic Universe” (Rudiger & Hollerbach 2004), the chapters on planets and on the Sun were written by different authors. Separate reviews written on the two topics include Petrovay (2000), Charbonneau (2005), Choudhuri (2008) on the solar dynamo and Glatzmaier (2002), Stevenson (2003) on the planetary dynamo. In the following I will try to make a systematic comparison between solar and planetary dynamos, presenting analogies and differences, and highlighting some interesting recent results. Title: ``Black Star'' or Astrophysical Black Hole? Authors: Petrovay, K. Bibcode: 2008AIPC..968..426P Altcode: 2007arXiv0707.2450P Recently wide publicity has been given to a claim by T. Vachaspati that ``black holes do not exist'', that the objects known as black holes in astrophysics should rather be called ``black stars'' and they not only do not have event horizons but actually can be the source of spectacular gamma ray bursts. In this short essay (no flimsier than the original preprint where these extravagant claims appeared) I demonstrate that these ill-considered claims are clearly wrong. Yet they present a good occasion to reflect on some well known but little discussed conceptual difficulties which arise when applying relativistic terminology in an astrophysical context. Title: A theoretical model for the magnetic helicity of solar active regions Authors: Chatterjee, Piyali; Choudhuri, Arnab Rai; Petrovay, Kristof; Nandy, Dibyendu Bibcode: 2008AdSpR..41..893C Altcode: Active regions on the solar surface are known to possess magnetic helicity, which is predominantly negative in the northern hemisphere and positive in the southern hemisphere. Choudhuri et al. [Choudhuri, A.R. On the connection between mean field dynamo theory and flux tubes. Solar Phys. 215, 31 55, 2003] proposed that the magnetic helicity arises due to the wrapping up of the poloidal field of the convection zone around rising flux tubes which form active regions. Choudhuri [Choudhuri, A.R., Chatterjee, P., Nandy, D. Helicity of solar active regions from a dynamo model. ApJ 615, L57 L60, 2004] used this idea to calculate magnetic helicity from their solar dynamo model. Apart from getting broad agreements with observational data, they also predict that the hemispheric helicity rule may be violated at the beginning of a solar cycle. Chatterjee et al. [Chatterjee, P., Choudhuri, A.R., Petrovay, K. Development of twist in an emerging magnetic flux tube by poloidal field accretion. A&A 449, 781 789, 2006] study the penetration of the wrapped poloidal field into the rising flux tube due to turbulent diffusion using a simple 1-d model. They find that the extent of penetration of the wrapped field will depend on how weak the magnetic field inside the rising flux tube becomes before its emergence. They conclude that more detailed observational data will throw light on the physical conditions of flux tubes just before their emergence to the photosphere. Title: From solar cycle to solar cycle Authors: Petrovay, Kristof Bibcode: 2008cosp...37.2423P Altcode: 2008cosp.meet.2423P The start of the new solar cycle prompts us to wonder what it will be like? Strong or weak, long or short? There are sharply conflicting predictions concerning the behaviour of solar activity in the next few years, based on different models of the solar dynamo and on empirical relationships. To what extent is the long-term variation of solar activity characterized by regularities, chaotic or stochastic behaviour, and to what extent can it be predicted? The talk reviews this subject, focusing on model-based prediction methods and also presenting a possible new mechanism for the origin of grand minima of solar activity within the framework of the interface dynamo scenario. Title: On the possibility of a bimodal solar dynamo Authors: Petrovay, K. Bibcode: 2007AN....328..777P Altcode: 2007arXiv0708.2131P A simple way to couple an interface dynamo model to a fast tachocline model is presented, under the assumption that the dynamo saturation is due to a quadratic process and that the effect of finite shear layer thickness on the dynamo wave frequency is analogous to the effect of finite water depth on surface gravity waves. The model contains one free parameter which is fixed by the requirement that a solution should reproduce the helioseismically determined thickness of the tachocline. In this case it is found that, in addition to this solution, another steady solution exists, characterized by a four times thicker tachocline and 4-5 times weaker magnetic fields. It is tempting to relate the existence of this second solution to the occurrence of grand minima in solar activity. Title: Molecular cloud abundances and anomalous diffusion Authors: Marschalkó, G.; Forgács-Dajka, E.; Petrovay, K. Bibcode: 2007AN....328..871M Altcode: 2008arXiv0801.0510M The chemistry of molecular clouds has been studied for decades, with an increasingly general and sophisticated treatment of the reactions involved. Yet the treatment of turbulent diffusion has remained extremely sketchy, assuming simple Fickian diffusion with a scalar diffusivity D. However, turbulent flows similar to those in the interstellar medium are known to give rise to anomalous diffusion phenomena, more specifically superdiffusion (increase of the diffusivity with the spatial scales involved). This paper considers to what extent and in what sense superdiffusion modifies molecular abundances in interstellar clouds. For this first exploration of the subject we employ a very rough treatment of the chemistry and the effect of non-uniform cloud density on the diffusion equation is also treated in a simplified way. The results nevertheless clearly demonstrate that the effect of superdiffusion is quite significant, abundance values at a given radius being modified by order of unity factors. Title: The origin of magnetic helicity in solar active regions Authors: Petrovay, K. Bibcode: 2007AIPC..934....3P Altcode: The magnetic fields in solar active regions are known to be helical. The current helicity, as measured from magnetograms, is negative on the northern and positive in the southern hemisphere, its normalized mean value being αp≡B.(∇×B)/B2~10-8 m-1. Recent observations have convincingly demonstrated that the helicity originates in subsurface regions and the flux tubes emerge in an already helical form. One possible contribution to this helicity is the accretion of the weak general poloidal magnetic field of the Sun by the rising toroidal flux loop. For this process to work, the field lines of the background field first need to be wrapped around the rising flux tube, which assumes that freezing-in holds to a good degree of approximation. The wrapped-up field then has to diffuse into the flux tube, giving rise to a twisted magnetic field structure. The conflict between the requirements of freezing-in (for wrapup) and diffusion (for penetration into the tube) is only apparent. The role of diffusion is likely to be limited during most of the rise of the tube, allowing a significant amount of flux to be swept up; then, in the uppermost 20-30% of the tube's path through the convective zone diffusion prevails, allowing penetration of the wrapped up flux. Title: The Effect of Abnormal Granulation on Acoustic Wave Travel Times and Mode Frequencies Authors: Petrovay, K.; Erdélyi, R.; Thompson, M. J. Bibcode: 2007SoPh..240..197P Altcode: 2007astro.ph..2076P Observations indicate that in plage areas (i.e. in active regions outside sunspots) acoustic waves travel faster than in the quiet Sun, leading to shortened travel times and higher p-mode frequencies. Coupled with the 11-year variation of solar activity, this may also explain the solar cycle variation of oscillation frequencies. While it is clear that the ultimate cause of any difference between the quiet Sun and plage is the presence of magnetic fields of order 100 G in the latter, the mechanism by which the magnetic field exerts its influence has not yet been conclusively identified. One possible such mechanism is suggested by the observation that granular motions in plage areas tend to be slightly "abnormal", dampened compared to the quiet Sun. Title: Helical Magnetic Fields in Solar Active Regions: Theory vs. Observations Authors: Petrovay, K.; Chaterjee, P.; Choudhuri, A. Bibcode: 2007astro.ph..2073P Altcode: The mean value of the normalized current helicity in solar active regions is on the order of 1e-8 1/m, negative in the northern hemisphere, positive in the southern hemisphere. Observations indicate that this helicity has a subsurface origin. Possible mechanisms leading to a twist of this amplitude in magnetic flux tubes include the solar dynamo, convective buffeting of rising flux tubes, and the accretion of weak external poloidal flux by a rising toroidal flux tube. After briefly reviewing the observational and theoretical constraints on the origin of helicity, we present a recently developed detailed model for poloidal flux accretion. Title: Helical Magnetic Fields in Solar Active Regions: Theory vs. Observations Authors: Petrovay, K.; Chaterjee, P.; Choudhuri, A. Bibcode: 2006PADEU..17....5P Altcode: The mean value of the normalized current helicity α_p=čB\cdot(nabla×čB)/B^2 in solar active regions is on the order of 10^{-8} m^{-1}, negative in the northern hemisphere, positive in the southern hemisphere. Observations indicate that this helicity has a subsurface origin. Possible mechanisms leading to a twist of this amplitude in magnetic flux tubes include the solar dynamo, convective buffeting of rising flux tubes, and the accretion of weak external poloidal flux by a rising toroidal flux tube. After briefly reviewing the observational and theoretical constraints on the origin of helicity, we present a recently developed detailed model for poloidal flux accretion. Title: Sound Wave Travel Times in Plage Areas - The Effect of Abnormal Granulation Authors: Petrovay, K.; Erdélyi, R.; Thompson, M. J. Bibcode: 2006ESASP.617E..73P Altcode: 2006soho...17E..73P No abstract at ADS Title: On the Origin of Current Helicity in Active Regions Authors: Petrovay, K.; Chatterjee, P.; Choudhuri, A. Bibcode: 2006ESASP.617E..67P Altcode: 2006soho...17E..67P No abstract at ADS Title: Development of twist in an emerging magnetic flux tube by poloidal field accretion Authors: Chatterjee, P.; Choudhuri, A. R.; Petrovay, K. Bibcode: 2006A&A...449..781C Altcode: 2005astro.ph.12472C Aims.Following an earlier proposal for the origin of twist in the magnetic fields of solar active regions, we model the penetration of a wrapped up background poloidal field into a toroidal magnetic flux tube rising through the solar convective zone. Methods.The rise of the straight, cylindrical flux tube is followed by numerically solving the induction equation in a comoving Lagrangian frame, while an external poloidal magnetic field is assumed to be radially advected onto the tube with a speed corresponding to the rise velocity. Results.One prediction of our model is the existence of a ring of reverse current helicity on the periphery of active regions. On the other hand, the amplitude of the resulting twist depends sensitively on the assumed structure (diffuse vs. concentrated/intermittent) of the active region magnetic field right before its emergence, and on the assumed vertical profile of the poloidal field. Nevertheless, in the model with the most plausible choice of assumptions a mean twist comparable to the observations results. Conclusions.Our results indicate that the contribution of this mechanism to the twist can be quite significant, and under favourable circumstances it can potentially account for most of the current helicity observed in active regions. Title: A History of the Department of Astronomy Authors: Petrovay, K. Bibcode: 2006PADEU..16...69P Altcode: The head of the observatory at Nagyszombat, founded in in 1755, already had the privileges of a full professor, so the foundation of the observatory can be regarded as the beginning of the Chair of Astronomy. Both the university and its department of astronomy have been moved and renamed on several occasions. Nevertheless, the institutional continuity can be traced down to the contemporary Department of Astronomy of Eötvös University. Title: A theoretical model for the magnetic helicity of solar active regions Authors: Choudhuri, A. R.; Chatterjee, P.; Petrovay, K.; Nandy, D. Bibcode: 2006cosp...36..714C Altcode: 2006cosp.meet..714C Active regions on the solar surface are known to possess magnetic helicity which is predominantly negative in the northern hemisphere and positive in the southern hemisphere Choudhuri 2003 Sol Phys 123 217 proposed that the magnetic helicity arises due to the wrapping up of the poloidal field of the convection zone around rising flux tubes which form active regions Choudhuri Chatterjee and Nandy 2004 ApJ 615 L57 used this idea to calculate magnetic helicity from their solar dynamo model and found broad agreements with observational data Chatterjee Choudhuri and Petrovay 2006 A A in press have studied the penetration of the wrapped poloidal field into the rising flux tube and concluded that more detailed observational data will throw light on the physical conditions of flux tubes just before their emergence to the photosphere Title: British-Romanian-Hungarian N+N+N Workshop for Young Researchers on Plasma- and Astrophysics: from laboratory to outer space Authors: Ballai, I.; Forgács-Dajka, E.; Marcu, A.; Petrovay, K. Bibcode: 2005PADEU..15.....B Altcode: The International Networking for Young Scientists (INYS), initiated and funded by the British Council, models itself on the N+N concept, where N+N refers to a workshop involving a number of researchers from the UK and an equal number of local researchers; ideally eight or more from each country. INYS is an initiative that supports the British Council's purpose of "nurturing mutually beneficial relationships with other countries", by encouraging and facilitating the mobility of, and direct contact between, young researchers (and their supervisors). It supports face-to-face meetings between young scientists and engineers from the UK and other countries, for the exchange of ideas, knowledge and information and the building of international connections that assist the innovation process. The meeting was an extended N+N workshop, where young scientist from UK, Romania and Hungary (N+N+N) got together to discuss their results, to initiate further real and virtual networking and to identy common research areas. It was the first time that Babes-Bolyai University (Cluj, Romania) has hosted such a meeting and the support by the University (Department of Physics, in particular) gives us hope that there will be other events to follow. The topic of the meeting was "Plasma- and astrophysics: from laboratory to outer space". Plasma is a gaseous state, commonly known as the fourth state of matter and it is made of electrically charged particles where the dynamics of particles is controlled by ambient magnetic fields. Plasmas make up almost 99 per cent of astrophysical objects such as galaxies, stars and supernovae. On Earth, plasmas exist naturally as lightning bolts and the bath of charged particles in the Earth's upper atmosphere. In the high-tech electronics industry, beams of artificially created plasmas engrave sophisticated patterns on computer chips. In an attempt to provide mankind with an abundant source of cheap clean energy, scientists work hard to make artificial suns: plasmas so hot and so dense that their particles fuse to release free energy. This pursuit of nuclear fusion, as a practical energy source, is another major branch of plasma physics research. The meeting was hosted by the Babes-Bolyai University and took place from 17th to 19th January, 2005. The Host provided all the technical support and the infrastructure needed for a smooth and successful meeting. The event was opened by Prof. Laszlo Nagy (Pro-Vice Chancellor) and Mrs Monica Marasescu (British Council). Title: The Sun as a laboratory for turbulence theory: the problem of anomalous diffusion Authors: Petrovay, K. Bibcode: 2005PADEU..15...53P Altcode: The solar atmosphere offers a unique possibility to study tuubulent motions under conditions presently unattainable in laboratory experiment or even numerical simulations. This short review will focus on one controversial issue in turbulence theory, on which some light can be shed by solar observations: anomalous turbulent diffusion. Title: The effect of a meridional flow on Parker's interface dynamo Authors: Petrovay, K.; Kerekes, A. Bibcode: 2004MNRAS.351L..59P Altcode: 2004astro.ph..4607P; 2004MNRAS.tmp..150P Parker's interface dynamo is generalized to the case when a homogeneous flow is present in the high-diffusivity (upper) layer in the lateral direction (i.e. perpendicular to the shear flow in the lower layer). This is probably a realistic first representation of the situation near the bottom of the solar convective zone, as the strongly subadiabatic stratification of the tachocline (lower layer in the interface dynamo) imposes a strong upper limit on the speed of any meridional flow there.

Analytic solutions to the eigenvalue problem are presented for the cases of vanishing diffusivity contrast and infinite diffusivity contrast. Unlike the trivial case of a homogeneous system, the ability of the meridional flow to reverse the propagation of the dynamo wave is strongly reduced in the interface dynamo. In particular, in the limit of high diffusivity contrast relevant to the solar case it is found that a meridional flow of realistic amplitude cannot reverse the direction of propagation of the dynamo wave. The implications of this result for the solar dynamo problem are discussed. Title: British-Hungarian N+N Workshop for Young Researchers On Computer processing and use of satellite data in astronomy and astrophysics and 3rd Workshop of Young Researchers in Astronomy & Astrophysics Authors: Forgács-Dajka, E.; Petrovay, K.; Erdélyi, R. Bibcode: 2004PADEU..14.....F Altcode: The N+N Young Researchers' Workshop scheme, initiated and funded by the British Council, aims to provide an opportunity for young researchers to exchange ideas, knowledge and information by coming together in the form of N+N workshops and meetings. Here the term N+N workshop refers to a workshop involving a number of researchers from the UK and an equal number of local researchers. The workshops are followed by real and virtual networking to sustain the contacts made with a view to produce a proposal for longer term externally funded collaboration or applications for further funding. As at the Department of Astronomy of the Eötvös University we have had a tradition of national workshops of young researchers in astronomy and astrophysics with similar characteristics, the call for meeting proposals by the British Council seemed an ideal way to extend the geographical scope of our meeting, while still maintaining its general format and spirit. Thus, this year's Hungarian Young Researchers' Workshop in Astronomy and Astrophysics was held in tandem with the British-Hungarian N+N workshop, and the contributions are also presented together in this volume. For the topic of this year's meeting we chose "Computer processing and use of satellite data in astronomy and astrophysics". The reason for this is that, thanks to a high number of space probes, in the past decades a vast amount data has been collected from the extraterrestrial world, from the magnetosphere to the most distant galaxies and beyond. We are now in a situation where the amount data grows much faster than the speed by which they can be processed and duly analyzed. The workshop was devoted to methods aimed at improving on this situation, as well as to scientific results born out of the use of space data. The workshop was open to post-doctoral scientists and engineers and those tenured for five years or less. PhD students in an advanced phase of their project were also admitted. The number of participants from the U.K. was nine, while a total of 13 applications were accepted from Hungary for the N+N workshop (with many more participants at the adjoining national workshop). It is to be noted that from the nine UK participants, only four were British citizens, the rest hailing from Armenia, Germany, Hungary, and Italy. Nevertheless, all have been residing in the UK for years, and this composition reflects well the international character and openness of current British academic research. Title: Past and future of scientific space missions: an overview Authors: Petrovay, K. Bibcode: 2004PADEU..14....5P Altcode: After briefly mentioning a few highlights of recent, current and future scientific space missions, an extensive list of all the most important such missions, together with web links, is given. Title: Turbulence, Waves and Instabilities in the Solar Plasma Authors: Erdélyi, R.; Petrovay, K.; Roberts, B.; Aschwanden, M. Bibcode: 2003twis.book.....E Altcode: Significant advances have been made recently in both the theoretical understanding and observation of small-scale turbulence in different layers of the Sun, and in the instabilities that give rise to them. The general development of solar physics, however, has led to such a degree of specialization as to hinder interaction between workers in the field. This book therefore presents studies of different layers and regions of the Sun, but from the same aspect, concentrating on the study of small-scale motions. The main emphasis is on the common theoretical roots of these phenomena, but the book also contains an extensive treatment of the observational aspects.

Link: http://www.springer.com/east/home?SGWID=5-102-22-3362=5696-0&changeHeader=true Title: A Consistent one-Dimensional Model for the Turbulent Tachocline Authors: Petrovay, K. Bibcode: 2003SoPh..215...17P Altcode: 2003astro.ph..3034P The first consistent model for the turbulent tachocline is presented, with the turbulent diffusivity computed within the model instead of being specified arbitrarily. For the origin of the 3D turbulence a new mechanism is proposed. Owing to the strongly stable stratification, the mean radial shear is stable, while the horizontal shear is expected to drive predominantly horizontal, quasi-2D motions in thin slabs. Here I suggest that a major source of 3D overturning turbulent motions in the tachocline is the secondary shear instability due to the strong, random vertical shear arising between the uncorrelated horizontal flows in neighboring slabs. A formula for the vertical diffusivity due to this turbulence, Equation (9), is derived and applied in a simplified 1D model of the tachocline. It is found that Maxwell stresses due to an oscillatory poloidal magnetic field of a few hundred gauss are able to confine the tachocline to a thickness less than 5 Mm. The integral scale of the 3D overturning turbulence is the buoyancy scale, on the order of 10 km, and its velocity amplitude is a few m s−1, yielding a vertical turbulent diffusivity on the order of 108 cm2 s−1. Title: Contributions to NATO Advanced Research Workshop Turbulence, Waves, and Instabilities in the Solar Plasma Authors: Forgács-Dajka, E.; Petrovay, K.; Erdélyi, R. Bibcode: 2003PADEU..13.....F Altcode: This volume contains focus reviews, oral contributions and poster papers presented at the NATO Advanced Research Workshop ``Turbulence, Waves, and Instabilities in the Solar Plasma'', held at Hotel Normafa, Budapest, 16-20 September, 2002. The more exensive invited reviews presented at the same meeting are published by Kluwer in a companion volume, with the same title as that of the meeting. The purpose of the workshop was to facilitate interchange and communication between diverse groups studying different layers and regions of the Sun but from the same aspect, concentrating on the study of small-scale motions. While the emphasis was on the common theoretical roots of these phenomena, observational aspects were not excluded either. The selection of invited speakers concentrated on the researchers currently most active in the field, mostly on a post-doctoral/tenure/fresh faculty position level. A number of senior experts and PhD students were also invited. Scientists from NATO partner countries were especially encouraged to apply. Altogether, 50 scientists from 11 different countries participated in the workshop. The relative isolation of the venue, as well as the fact that the participants all lived at the same place, where the conference was also held, contributed to the success of the meeting, offering plenty of opportunities to meet and exchange ideas. We are convinced that many of the papers in the present volume will prove to be a very useful reference for some rarely discussed chapters of solar physics. Title: A new model for the lower overshoot layer in the Sun Authors: Marik, D.; Petrovay, K. Bibcode: 2002A&A...396.1011M Altcode: 2003astro.ph..7534M We present a model for the lower overshoot layer of the Sun, based on the realistic solar stratification, without the use of a ``mixing-length'' parameter, by solving the system of Reynolds momentum equations using the closure formalism of Canuto & Dubovikov (\cite{Canuto+Dubov:1,Canuto+Dubov:2}). A fixed value of velocity anisotropy is assumed, and the local convection model is assumed to be valid for the convectively unstable layer. In accordance with seismic constraints, overshoot (defined as the amount by which the convectively mixed zone extends beyond its boundary in local theory) is found to be as low as about 6 percent of the pressure scale height, and it is not bounded by a discontinuity from below. Title: Dynamics of the fast solar tachocline. I. Dipolar field Authors: Forgács-Dajka, E.; Petrovay, K. Bibcode: 2002A&A...389..629F Altcode: 2002astro.ph..1241F One possible scenario for the origin of the solar tachocline, known as the ``fast tachocline'', assumes that the turbulent diffusivity exceeds eta >~ 109 cm2 s-1. In this case the dynamics will be governed by the dynamo-generated oscillatory magnetic field on relatively short timescales. Here, for the first time, we present detailed numerical models for the fast solar tachocline with all components of the magnetic field calculated explicitly, assuming axial symmetry and a constant turbulent diffusivity eta and viscosity nu . We find that a sufficiently strong oscillatory poloidal field with dipolar latitude dependence at the tachocline-convective zone boundary is able to confine the tachocline. Exploring the three-dimensional parameter space defined by the viscosity in the range log nu =9-11, the magnetic Prandtl number in the range Prm=0.1-10, and the meridional flow amplitude (-3 to +3 cm s-1), we also find that the confining field strength Bconf, necessary to reproduce the observed thickness of the tachocline, increases with viscosity nu , with magnetic Prandtl number nu /eta , and with equatorward meridional flow speed. Nevertheless, the resulting Bconf values remain quite reasonable, in the range 103-104 G, for all parameter combinations considered here. The thickness of the tachocline shows a marked dependence on both time and latitude. The latitude dependence is similar to that inferred by helioseismology, while the time dependence is within the observational errors. Title: How Turbulent is the Tachocline? Authors: Petrovay, Kristóf Bibcode: 2002smra.progE..20P Altcode: No abstract at ADS Title: The Role of Active Regions in the Generation of Torsional Oscillations Authors: Petrovay, K.; Forgács-dajka, E. Bibcode: 2002SoPh..205...39P Altcode: 2001astro.ph..8297P We present a model for torsional oscillations where the inhibiting effect of active region magnetic fields on turbulence locally reduces turbulent viscous torques, leading to a cycle- and latitude-dependent modulation of the differential rotation. The observed depth dependence of torsional oscillations as well as their phase relationship with the sunspot butterfly diagram are reproduced quite naturally in this model. The resulting oscillation amplitudes are significantly smaller than observed, though they depend rather sensitively on model details. Meridional circulation is found to have only a weak effect on the oscillation pattern. Title: Tachocline Confinement by an Oscillatory Magnetic Field Authors: Forgács-dajka, E.; Petrovay, K. Bibcode: 2001SoPh..203..195F Altcode: 2001astro.ph..6133F Helioseismic measurements indicate that the solar tachocline is very thin, its full thickness not exceeding 4% of the solar radius. The mechanism that inhibits differential rotation to propagate from the convective zone to deeper into the radiative zone is not known, though several propositions have been made. In this paper we demonstrate by numerical models and analytic estimates that the tachocline can be confined to its observed thickness by a poloidal magnetic field Bp of about one kilogauss, penetrating below the convective zone and oscillating with a period of 22 years, if the tachocline region is turbulent with a diffusivity of η∼1010 cm2 s−1 (for a turbulent magnetic Prandtl number of unity). We also show that a similar confinement may be produced for other pairs of the parameter values (Bp, η). The assumption of the dynamo field penetrating into the tachocline is consistent whenever η≳109 cm2 s−1. Title: Can an inverse Λ-effect explain the thin tachocline? Authors: Forgács-Dajka, E.; Petrovay, K. Bibcode: 2001ESASP.464..301F Altcode: 2001soho...10..301F Helioseismic measurements indicate the existence of a transition layer (the tachocline) between the differentially rotating convection zone and the rigidly rotating radiative interior. According to the theoretical models, the differential rotation should penetrate into the deep layers of the radiative interior, but, based on helioseismic measurements, the tachocline is thin. This is known as the "Thin Tachocline Problem". In this paper we examine the influence of an assumed inverse Λ-effect on the radial spreading of the differential rotation. This effect may contribute to horizontal angular momentum transport below the convection zone. Our results indicate that an inverse Λ-effect can only reduce the thickness of the tachocline to the observed value if an unrealistically high amplitude is assumed. Thus, our results practically exclude the possibility that the thin tachocline is a consequence of a Λ-effect. Title: Numerical solutions of the momentum equations for the lower overshoot layer Authors: Marik, D.; Petrovay, K. Bibcode: 2001ESASP.464..657M Altcode: 2001soho...10..657M The lower overshooting layer, which plays an important role in the dynamo mechanism, is one of the least known regions of the Sun. The most promising way to model this region is the Reynolds-stress method. In this paper we determine the radial distribution of the turbulent kinetic energy k, the mean square relative temperature fluctuation q, the normalized energy flux J, and the energy dissipation rate ɛ. We present solutions in the case of a simple k-ɛ model and in the case of solving all four differential equations using various Δ∇ distributions (temperature stratifications). We use a diffusive approximation for the nonlocal fluxes ("Xiong's closure"), considering the case of both strong and weak nonlocality. The resulting profiles of k and ɛ are found to be approximately linear and the profiles of the turbulent lengths and time scales l and τ are also similar for different cases. The shapes of these profiles thus seem to be robust properties of the solution, with little sensitivity to the particular parameter values and background stratification assumed. In contrast, we find that the penetration depth depends rather sensitively on the slope of the Δ∇ curve and on the strength of nonlocality assumed. Title: Turbulence in the Solar Photosphere Authors: Petrovay, K. Bibcode: 2001SSRv...95....9P Altcode: 2000astro.ph..5409P The precise nature of photospheric flows, and of the transport effects they give rise to, has been the subject of intense debate in the last decade. Here we attempt to give a brief review of the subject emphasizing interdisciplinary (solar physics-turbulence theory) aspects, key open questions, and recent developments. Title: What Makes the Sun Tick? The Origin of the Solar Cycle Authors: Petrovay, K. Bibcode: 2000ESASP.463....3P Altcode: 2000sctc.proc....3P; 2000astro.ph.10096P In contrast to the situation with the geodynamo, no breakthrough has been made in the solar dynamo problem for decades. Since the appearance of mean-field electrodynamics in the 1960's, the only really significant advance was in the field of flux tube theory and flux emergence calculations. These new results, together with helioseismic evidence, have led to the realization that the toroidal magnetic flux giving rise to activity phenomena must be stored and presumably generated below the convection zone proper, in what I will call the DOT (Dynamo-Overshoot-Tachoclyne) layer. The only segment of the problem we can claim to basically understand is the transport of flux from this layer to the surface. On the other hand, as reliable models for the DOT layer do not exist we are clueless concerning the precise mechanisms responsible for toroidal/poloidal flux conversion and for characteristic migration patterns (extended butterfly diagram) and periodicities. Even the most basic result of mean-field theory, the interpretation of the butterfly diagram as an alpha-omega dynamo wave, has been questioned. This review therefore will necessarily ask more questions than give answers. Some of these key questions are - Structure of the DOT layer - alpha-quenching and distributed dynamo - High-latitude migration patterns and their interpretation - The ultimate fate of emerged flux Title: Making sense of sunspot decay - II. Deviations from the Mean Law and Plage Effects Authors: Petrovay, K.; Martínez Pillet, V.; van Driel-Gesztelyi, L. Bibcode: 1999SoPh..188..315P Altcode: 1999astro.ph..6258P In a statistical analysis of Debrecen Photoheliographic Results sunspot area data we find that the logarithmic deviation (log D)' of the area decay rate D from the parabolic mean decay law (derived in the first paper in this series) follows a Gaussian probability distribution. As a consequence, the actual decay rate D and the time-averaged decay rate are also characterized by approximately lognormal distributions, as found in an earlier work. The correlation time of (log D)' is about 3 days. We find a significant physical anticorrelation between (log D)' and the amount of plage magnetic flux of the same polarity in an annulus around the spot on Kitt Peak magnetograms. The anticorrelation is interpreted in terms of a generalization of the turbulent erosion model of sunspot decay to the case when the flux tube is embedded in a preexisting homogeneous `plage' field. The decay rate is found to depend inversely on the value of this plage field, the relation being very close to logarithmic, i.e., the plage field acts as multiplicative noise in the decay process. A Gaussian probability distribution of the field strength in the surrounding plage will then naturally lead to a lognormal distribution of the decay rates, as observed. It is thus suggested that, beside other multiplicative noise sources, the environmental effect of surrounding plage fields is a major factor in the origin of lognormally distributed large random deviations from the mean law in the sunspot decay rates. Title: Transport Effects in the Evolution of the Global Solar Magnetic Field Authors: Petrovay, K.; Szakály, G. Bibcode: 1999SoPh..185....1P Altcode: 1998astro.ph.12464P The axisymmetric component of the large-scale solar magnetic fields has a pronounced poleward branch at higher latitudes. In order to clarify the origin of this branch we construct an axisymmetric model of the passive transport of the mean poloidal magnetic field in the convective zone, including meridional circulation, anisotropic diffusivity, turbulent pumping and density pumping. For realistic values of the transport coefficients we find that diffusivity is prevalent, and the latitudinal distribution of the field at the surface simply reflects the conditions at the bottom of the convective zone. Pumping effects concentrate the field to the bottom of the convective zone; a significant part of this pumping occurs in a shallow subsurface layer, normally not resolved in dynamo models. The phase delay of the surface poloidal field relative to the bottom poloidal field is found to be small. These results support the double dynamo wave models, may be compatible with some form of a mixed transport scenario, and exclude the passive transport theory for the origin of the polar branch. Title: Science and Astronomy Education in Hungary: A Personal View Authors: Petrovay, K. Bibcode: 1999arse.conf...67P Altcode: No abstract at ADS Title: Close Encounters of the Fourth Kind: Getting Astrophysics to the People of the Canary Islands Authors: Petrovay, K. Bibcode: 1999arse.conf...72P Altcode: No abstract at ADS Title: Origin and Propagation of Fluctuations of Turbulent Magnetic Fields Authors: Petrovay, K. Bibcode: 1999ASPC..183...70P Altcode: 1998astro.ph.12466P; 1999hrsp.conf...70P The degree of linear polarization has recently been found to show wide random variations over the solar disk. These variations are presumably at least partly due to fluctuations in the flux density of turbulent photospheric magnetic fields and associated variations in the degree of Hanle depolarization. In order to understand the origin of such large scale fluctuations of the turbulent magnetic flux density we develop a phenomenological model to calculate the spatial Fourier spectrum of the fluctuations of turbulent magnetic fields in the solar photosphere and convective zone. It is found that if the model parameters are fitted to turbulence closure models and numerical experiments the characteristic scale of the fluctuations is by about an order of magnitude larger than the turbulence scale (the scale of the granulation), owing to the more effective quenching of small-scale fluctuations by turbulent diffusion. Title: On the validity of quasi-linear kinematic mean-field electrodynamics in astrophysical flows Authors: Petrovay, K.; Zsargo, J. Bibcode: 1998MNRAS.296..245P Altcode: Mean-field theory in its kinematic form with the quasi-linear approximation is widely used for the modelling of the transport of weak magnetic fields in turbulent media. The validity of this approach to real astrophysical flows is discussed. Numerically evaluating the turbulent electromotive force using Lagrangian analysis for a set of simple, prescribed 2D flow patterns with a wide range of parameters, we find that quasi-linear expressions for the turbulent diffusivities and for the pumping velocities are correct within a factor of 2 for a wide variety of flow types with order of unity (or even higher) effective Strouhal numbers. The degree of the non-linear quenching of turbulent transport by a weak magnetic field is also discussed. We argue that, owing to the intermittency and small filling factors of magnetic fields in realistic astrophysical media, diffusivity and pumping effects are not quenched to order of magnitude, while a more moderate quenching of order 10 per cent is still present. Title: Limits on Anomalous Diffusion in the Solar Photosphere from Sunspot Decay Authors: Petrovay, K. Bibcode: 1998ESASP.417..273P Altcode: 1998cesh.conf..273P No abstract at ADS Title: K-epsilon models of the lower overshoot layer Authors: Petrovay, K. Bibcode: 1998IAUS..185..121P Altcode: Apart from the solar core, the overshoot layer below the convective zone is the layer where some discrepancies between the standard and seismic solar models continue to exist. Non-local mixing length models are in clear conflict with the seismic evidence. A major difficulty for the development of more sophisticated models is the large degree of arbitrariness in formulating expressions for input parameters like the length scale. We propose that the application of the k-epsilon modelling approach, widely used in physics and engineering, could help in alleviating these difficulties. We present some simple overshoot models calculated with this approach, and we point out that the resulting expression of the length scale naturally reduces to the usual mixing length expression (proportional to the pressure scale height) well inside the convectively unstable region. Implications for the solar Li problem and for dynamo theory will also be discussed. Title: Making Sense of Sunspot Decay. I. Parabolic Decay Law and Gnevyshev-Waldmeier Relation Authors: Petrovay, K.; van Driel-Gesztelyi, L. Bibcode: 1997SoPh..176..249P Altcode: 1997astro.ph..6029P In a statistical study of the decay of individual sunspots based on DPR data we find that the mean instantaneous area decay rate is related to the spot radius ro and the maximum radius ro as D = CD r/ro, CD = 32.0±0.26 MSH day -1. This implies that sunspots on the mean follow a parabolic decay law; the traditional linear decay law is excluded by the data. The validity of the Gnevyshev-Waldmeier relationship between the maximum area A 0 and lifetime T of a spot group, A0/T ≃10 MSH day-1, is also demonstrated for individual sunspots. No evidence is found for a supposed supergranular `quantization' of sunspot areas. Our results strongly support the recent turbulent erosion model of sunspot decay while all other models are excluded. Title: Turbulent Erosion of Magnetic Flux Tubes Authors: Petrovay, K.; Moreno-Insertis, F. Bibcode: 1997ApJ...485..398P Altcode: 1997astro.ph..3152P Results from a numerical and analytical investigation of the solution of a nonlinear axisymmetric diffusion equation for the magnetic field are presented for the case when the nonlinear dependence of the diffusivity ν(B) on the magnetic field satisfies basic physical requirements. We find that for sufficiently strong nonlinearity (i.e., for sufficiently strong reduction of ν inside the tube) a current sheet is spontaneously formed around the tube within one diffusion timescale. This sheet propagates inward with a velocity inversely proportional to the ratio of the field strength just inside the current sheet to the equipartition field strength B0/Be, so the lifetime of a tube with constant internal flux density is increased approximately by a factor not exceeding B0/Be, even for infinitely effective inhibition of turbulence inside the tube. Among the applications of these results, we point out that toroidal flux tubes in the solar convective zone are subject to significant flux loss owing to turbulent erosion on a timescale of ~1 month and that turbulent erosion may be responsible for the formation of a current sheet around a sunspot. It is further proposed that, despite the simplifying assumptions involved, our solutions correctly reflect the essential features of the sunspot decay process. Title: Theory of Passive Magnetic Field Transport Authors: Petrovay, Kristof Bibcode: 1997astro.ph..3154P Altcode: In recent years, our knowledge of photospheric magnetic fields went through a thorough transformation--nearly unnoticed by dynamo theorists. It is now practically certain that the overwhelming majority of the unsigned magnetic flux crossing the solar surface is in turbulent form (intranetwork and hidden fields). Furthermore, there are now observational indications (supported by theoretical arguments discussed in this paper) that the net polarity imbalance of the turbulent field may give a significant or even dominant contribution to the weak large-scale background magnetic fields outside unipolar network areas. This turbulent magnetic field consists of flux tubes with magnetic fluxes below 1e10 Wb (1e18 Mx). The motion of these thin tubes is dominated by the drag of the surrounding flows, so the transport of this component of the solar magnetic field must fully be determined by the kinematics of the turbulence (i.e. it is "passive"), and it can be described by a one-fluid model like mean-field theory (MFT). This paper reviews the theory of passive magnetic field transport using mostly first (and occasionally higher) order smoothing formalism; the most important transport effects are however also independently derived using Lagrangian analysis for a simple two-component flow model. Solar applications of the theory are also presented. Among some other novel findings it is proposed that the observed unsigned magnetic flux density in the photosphere requires a small-scale dynamo effect operating in the convective zone and that the net polarity imbalance in turbulent (and, in particular, hidden) fields may give a major contribution to the weak large-scale background magnetic fields on the Sun. Title: Sunspot Decay as Turbulent Erosion of a Magnetic Flux Tube Authors: Petrovay, K.; van Driel-Gesztelyi, L. Bibcode: 1997ASPC..118..145P Altcode: 1997fasp.conf..145P Decisive evidence is presented against the validity of the conventional linear decay law for sunspots. Preliminary results from a statistical analysis of Debrecen Photoheliographic Results data show that the decay rate of sunspots is significantly slower in late phases of the decay than in earlier phases. Our findings are compatible with the predictions of a recently developed turbulent erosion model for sunspot decay. Title: Turbulent magnetic fields in the solar photosphere: diagnostics and interpretation. Authors: Faurobert-Scholl, M.; Feautrier, N.; Machefert, F.; Petrovay, K.; Spielfiedel, A. Bibcode: 1995A&A...298..289F Altcode: Turbulent magnetic fields in the solar photosphere may be determined by their depolarizing Hanle effect on the linear polarization of some solar absorption lines formed outside active regions (Stenflo 1982). In Faurobert-Scholl (1993) the center-to-limb variation of the linear polarization in the SrI 4607 A line was analyzed. It was shown that it is affected by the Hanle effect due to a weak magnetic field with mixed polarity at small scales. The accurate determination of the turbulent magnetic field strength requires radiative transfer calculations taking into account the effect of collisions and magnetic fields on the frequency and angular redistribution of the light. Here we present the different steps in the theory of redistribution, together with the first precise quantum calculations of the collisional cross-sections between hydrogen and SrI and CaI atoms. These new results are then used to perform a more accurate determination of the turbulent magnetic field strength in the solar photosphere. It is shown that the center-to-limb variation of the linear polarization in the SrI line is mainly sensitive to the average value of the field strength between the altitudes 200 and 400km. According to the observations this average value is between 20 and 10G. A theoretical interpretation is given in terms of a one-dimensional passive magnetic field transport equilibrium model with first-order smoothing. The resulting <|B_x_|>(z) equilibrium distribution reproduces the observations rather well, but the uncertainty in the amplitude, height-dependence and interpretation of microturbulence suggests that the present model could be brought to an even better agreement with the observations if a microturbulence different from the VAL3C model is used. It is finally pointed out that in the upper photosphere the turbulent field becomes force-free instead of being passively transported. It is found that this does not seriously modify our conclusions. Title: Numerical Tests of the Quasilinear Approximation of Mean-field Electrodynamics Authors: Zsargo, J.; Petrovay, K. Bibcode: 1995AAS...186.0209Z Altcode: 1995BAAS...27..814Z It is widely known that a sufficient condition for the applicability of quasilinear-type approximations (e.g. the second-order correlation approximation or SOCA) in mean-field electrodynamics is that Utau << min {l, H} where l, H, U and tau are characteristic horizontal and vertical scale lengths, velocity, and time, respectively. A necessary condition for their validity is however not known. In order to check the validity of the quasilinear results in cases where the above condition is not satisfied, as well as to study qualitative and quantitative differences between the quasilinear results and the actual solutions, we numerically solve the MHD induction equation for the kinematical case in a series of simplified "toy" model flows and then compare the results with the corresponding quasilinear solutions. Our model flows are two-dimensional two-component flows with simple (exponential or linear) stratifications. For conceptual clarity, in each model only one independent physical quantity (initial magnetic field, density, or velocity amplitude, respectively) has an inhomogeneous distribution. Solutions are computed for several widely differing values of the l/H horizontal/vertical scale length ratio. In all cases we find that the computed turbulent electromotive force does not differ from the quasilinear value by more than an order-of-unity factor, as long as Utau does not greatly exceed min {l, H}. Title: On the Existence of a Discontinuity at the Lower Boundary of the Solar Convective Zone Authors: Petrovay, K.; Marik, M. Bibcode: 1995ASPC...76..216P Altcode: 1995gong.conf..216P No abstract at ADS Title: Theory of passive magnetic field transport Authors: Petrovay, K. Bibcode: 1994ASIC..433..415P Altcode: No abstract at ADS Title: Density pumping of magnetic fields in the solar convective zone Authors: Petrovay, K. Bibcode: 1994smf..conf..146P Altcode: No abstract at ADS Title: The origin of intranetwork fields: a small-scale solar dynamo Authors: Petrovay, K.; Szakaly, G. Bibcode: 1993A&A...274..543P Altcode: The intranetwork magnetic fields observed on the solar surface consist of flux tubes that are thin enough for their motion to be fully determined by the drag forces exerted on them by turbulent motions. The equations governing such a passive transport of the mean magnetic flux density <B> and of the unsigned flux density <|B|> in the convective zone of the Sun (assuming a one-dimensional geometry) are derived and discussed: turbulent diffusion and turbulent pumping are found to be the main transport effects. As the timescale of the transport is much shorter than the solar cycle, the flux density at any instant is given by an equilibrium solution of the transport equations. These solutions are computed and presented. The main conclusions are the following. 1. If no source terms are included in its transport equation, the mean flux density increases by 4 orders of magnitude from the surface to the bottom of the convective zone, showing that turbulent pumping is one of the main mechanisms confining the global dynamo to the bottom of the convective zone. 2. The observed emergence rate of magnetic flux in active regions is not sufficient to sustain the observed mean magnetic fields which must therefore be sustained and continuously refreshed on a time scale of ∼20 days by the emergence of statistically aligned smaller bipolar flux concentrations (intranetwork fields or small ephemeral regions) from below. 3. The observed unsigned flux density of intranetwork fields is only consistent with the model if a small-scale dynamo mechanism is operating in the convective zone continuously producing unsigned flux; no other likely sources of flux of the correct order of magnitude are known. 4. Modelling the source term corresponding to the small-scale dynamo on the basis of numerical simulation results, the hidden magnetic flux density is predicted to lie between about 2.5 and 7.5 mT. This prediction may be tested by observations in the not too distant future. Title: Local and non-local contributions to horizontal motions in stellar convective zones Authors: Petrovay, K. Bibcode: 1993ASPC...40..293P Altcode: 1993IAUCo.137..293P; 1993ist..proc..293P No abstract at ADS Title: The Sizes of Active Regions and Convective Triggering of Buoyant Loop Instability Authors: Petrovay, K.; Szakaly, G. Bibcode: 1993ASPC...46..108P Altcode: 1993IAUCo.141..108P; 1993mvfs.conf..108P No abstract at ADS Title: Area-Weighting of Sunspot Group Positions and Proper Motion Artifacts Authors: Petrovay, K. Bibcode: 1993ASPC...46..123P Altcode: 1993mvfs.conf..123P; 1993IAUCo.141..123P No abstract at ADS Title: The Small-Scale Photospheric Magnetic Field as an Indicator of the Dynamo Authors: Petrovay, K.; Szakaly, G. Bibcode: 1993ASPC...46..143P Altcode: 1993mvfs.conf..143P; 1993IAUCo.141..143P No abstract at ADS Title: The anisotropy of low prandtl number turbulent convection Authors: Petrovay, K. Bibcode: 1992GApFD..65..183P Altcode: 1997astro.ph..3155P A model for homogeneous anisotropic incompressible turbulence is proposed. The model generalizes the GISS model of homogeneous isotropic turbulence; the generalization involves the solution of the GISS equations along a set of integration paths in wavenumber (k-) space. In order to make the problem tractable, these integration paths ("cascade lines") must be chosen in such a way that the behaviour of the energy spectral function along different cascade lines should be reasonably similar. In practice this is realized by defining the cascade lines as the streamlines of a cascade flow; in the simplest case the source of this flow may be identified with the source function of the turbulence. Owing to the different approximations involved, the resulting energy spectral function is not exact but is expected to give good approximative values for thebulk quantities characterising the turbulent medium, and for the measure of the anisotropy itself in particular. The model is then applied to the case of low Prandtl number thermal convection. The energy spectral function and the bulk quantities characterizing the flow are derived for different values of the parameter S = Rao. The most important new finding is that unlike the anisotropy of the most unstable mode in linear stability analysis the anisotropy of the turbulence doesnot grow indefinitely with increasingS but it rather saturates to a relatively moderate finite asymptotic value. Title: On the Properties of Toroidal Flux Tubes in the Solar Dynamo Authors: Petrovay, K. Bibcode: 1991SoPh..134..407P Altcode: Prompted by a recently revived debate concerning the structure of the toroidal magnetic field of the Sun, this letter points out that the observational evidence now suggests that the toroidal flux tubes have fluxes of 1014 Wb (1022 Mx) and flux densities of about 10 T (105 G). It is proposed that such high flux densities may be produced by the work done on the flux tubes by the drag force due to differential rotation. Title: Cluster analysis of the space-time distribution of sunspot groups during solar cycle no. 20 Authors: Petrovay, Kristof; Abuzeid, Bashir K. Bibcode: 1991SoPh..131..231P Altcode: Cluster analysis (a Bayesian iteration procedure) was used to study the space-time distribution of sunspot groups in the time interval from 1965 to 1977. (Data were taken from the Greenwich and Debrecen Heliographic Results.) The distribution proved to be significantly non-random for the 8-10 groups cluster−1 (gr cl−1) level of clustering. Convincing evidence also favours non-random behaviour for other levels of clustering from the lowest (3-4 gr cl−1) up to the highest (∼ 150 gr cl−1) level. The rotation rate of the non-random pattern is generally slightly lower than the Carrington rate. Title: Topological Pumping in the Lower Overshoot Layer Authors: Petrovay, Kristóf Bibcode: 1991LNP...380...67P Altcode: 1991sacs.coll...67P; 1991IAUCo.130...67P Problems associated with topological pumping in the lower overshoot layer suggest a strongly turbulent and strongly differentially rotating upper radiative zone as the seat of the dynamo and as flux reservoir. Title: Morphology of Convection and Mixing-Length Theory Authors: Petrovay, Kristof G. Bibcode: 1990ApJ...362..722P Altcode: It is pointed out that observations and numerical experiments are not the only way to determine the morphological characteristics of convection in different layer of stars. It is demonstrated that a sufficiently general formulation of mixing length theory (MLT) that incorporates the kinetic energy flux and the anisotropy of turbulence can be used to give reliable predictions concerning the morphology. Such an MLT, applied to a recent model of the solar convective zone (SCZ), shows that the morphology in the bulk of the SCZ is characterized by isolated fibrillar downflows. A topology reversal occurs a few hundred km below the photosphere, and the outer layers are characterized by isolated upflows and a cellular structure. If the SCZ has a thin lower boundary layer, then near it the structure becomes cellular again, but with isolated downflows. Unlike solar-type stars, convective stellar cores are probably not dominated by fibrillar isolated downflows, but rather by isolated upflows. Title: Asymmetric Flux Loops in Active Regions - Part Two Authors: Petrovay, K.; Brown, J. C.; van Driel-Gesztelyi, L.; Fletcher, L.; Marik, M.; Stewart, G. Bibcode: 1990SoPh..127...51P Altcode: We propose that magnetic flux loops in the subphotospheric layers of the Sun are seriously asymmetrical as a consequence of the drag force exerted on them because of the different rotational rate of the surrounding plasma. In numerical models of stationary slender flux loops in the plane parallel approximation we show that a serious tilt is both possible and probable. Observational facts (see van Driel-Gesztelyi and Petrovay, 1989; Paper I) strongly support the case for high asymmetry. The different stability of p and f spots may also be related to such an asymmetry. Title: Asymmetric flux loops in active regions, I Authors: van Driel-Gesztelyi, L.; Petrovay, K. Bibcode: 1990SoPh..126..285V Altcode: 1990SoPh..126..285G We investigate asymmetries of bipolar sunspot groups. We find that the magnetic field distribution of simple bipolar sunspot groups is significantly asymmetrical: the polarity inversion line is usually nearer to the main following polarity spot than to the main preceding one. This asymmetry grows with the age of the sunspot group. We suggest that this asymmetry has a causal link with two long-established asymmetries- the one in the proper motions of young sunspots, the other in the relative stability of p and f spots. Title: Asymmetry of Emerging Flux Loops Caused by Radial Differential Rotation Authors: Marik, M.; Petrovay, K. Bibcode: 1990IAUS..138..321M Altcode: No abstract at ADS Title: An Investigation of Sunspot Nests during Solar Cycle No.20 Authors: Abuzeid, B. K.; Petrovay, K. Bibcode: 1990PDHO....7...98A Altcode: 1990dysu.conf...98A; 1990ESPM....6...98A The space-time distribution of sunspot groups in the time interval 1965 - 1977 was studied using cluster analysis. Results for the 8 - 10 groups/cluster level of clustering are presented. Title: Properties of a Spherical Galaxy with Exponential Energy Distribution Authors: Petrovay, K. Bibcode: 1987Ap&SS.138..323P Altcode: Some analytical relations for the phase space functions of a self-consistent spherical stellar system are derived. The integral constraints on the distribution function by imposing a given ϱ(r) density distribution andN(E) fractional energy distribution are determined. For the case of radially-anisotropic velocity distribution in theE→0 limit the constraint by an exponentialN(E) implies thatf(E, J 2) tends to zero in the order (-E)3/2. This lends analytical support to the use of the Stiavelli and Bertin (1985) distribution function for modeling elliptical galaxies. Maximum phase space density constraint confirms the necessity of high collapse factors to produce such a distribution function. Limits on the steepness of an exponentialN(E) for the case when ϱ(r) resembles the emissivity law of ellipticals are also derived.