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Guest Editors: J. Javaraiah, J. P. Rozelot, and Luca Bertello The Solar Cycle Advances in Astronomy

The Solar Cycle

This is a special issue published in “Advances in Astronomy.” All articles are open access articles distributed under the Creative Com- mons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Editorial Board

Cesare Barbieri, Italy Martin Hardcastle, UK Valery Nakariakov, UK Joshua S. Bloom, USA Dean Hines, USA Jerome Orosz, USA Michael Brotherton, USA Dieter Horns, Germany George Pavlov, USA Giovanni Carraro, Italy Ivan Hubeny, USA Juri Poutanen, Finland Alberto J. Castro-Tirado, Spain John Hughes, USA Somak Raychaudhury, UK Michael Disney, UK Wing Huen Ip, Taiwan William Reach, USA Elmetwally Elabbasy, Egypt Valentina Klochkova, Russia Peter Roming, USA Nye Evans, UK Gregory Laughlin, USA Ata Sarajedini, USA Maurizio Falanga, Switzerland Myung G. Lee, Republic of Korea Regina Schulte-Ladbeck, USA Duncan Forbes, Australia Karen Leighly, USA Ravi Sheth, USA Andrew Fruchter, USA Jeﬀrey Linsky, USA Roberto Turolla, Italy B. T. Gansicke,¨ UK Mario Mateo, USA Gary Wegner, USA Paul Goldsmith, USA Ronald Mennickent, Chile Glenn J. White, UK Jonathan Grindlay, USA Zdzislaw E. Musielak, USA Paul J. Wiita, USA Contents

The Solar Cycle,J.Javaraiah,J.P.Rozelot,andLucaBertello Volume 2012, Article ID 470631, 2 pages

The Faint Young Sun Paradox: A Simpliﬁed Thermodynamic Approach, F. Angulo-Brown, MarcoA.Rosales,andM.A.Barranco-Jimenez´ Volume 2012, Article ID 478957, 10 pages Tendency of Discreteness of the Solar Amplitude and Intercycle Relatedness, Akio Yoshida and Ryan Sayre Volume 2012, Article ID 519852, 7 pages

Rapid Disappearance of Penumbra-Like Features near a Flaring Polarity Inversion Line: The Hinode Observations, B. Ravindra and Sanjay Gosain Volume 2012, Article ID 735879, 9 pages

Kinematic Approach to the 24th Solar Cycle Prediction, Vladimir Kaftan Volume 2012, Article ID 854867, 7 pages

Probable Values of Current Solar Cycle Peak,V.M.Silbergleit Volume 2012, Article ID 167375, 6 pages

Sunspot Cycle 24 and the Advent of Dalton-Like Minimum,H.S.AhluwaliaandR.C.Ygbuhay Volume 2012, Article ID 126516, 5 pages

Preliminary Results on Irradiance Measurements from Lyra and Swap, S. T. Kumara, R. Kariyappa, M. Dominique, D. Berghmans, L. Dame,´ J. F. Hochedez, V. H. Doddamani, and Lakshmi Pradeep Chitta Volume 2012, Article ID 623709, 5 pages

Observations of Correlated Behavior of Two Light Torsion Balances and a Paraconical Pendulum in Separate Locations during the Solar Eclipse of January 26th, 2009, A. F. Pugach and D. Olenici Volume 2012, Article ID 263818, 6 pages Hindawi Publishing Corporation Advances in Astronomy Volume 2012, Article ID 470631, 2 pages doi:10.1155/2012/470631

Editorial The Solar Cycle

J. Javaraiah,1 J. P. Rozelot,2 and Luca Bertello3

1 Sun and Solar System Group, Indian Institute of Astrophysics, II Block, Koramangala, Bangalore 560034, India 2 Nice Sophia-Antipolis University, OCA-Lagrange, CNRS UMR 7293, Boulevard de l’Observatoire, BP 4229, 06304 Nice Cedex 4, France 3 National Solar Observatory, 950 N. Cherry Avenue, Tucson, AZ 85719, USA

Correspondence should be addressed to J. Javaraiah, [email protected]

Received 28 June 2012; Accepted 28 June 2012

Copyright © 2012 J. Javaraiah et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The Sun provides variable energetic and magnetic field input solar flares and coronal mass ejections pose a serious hazard to the conditions in the heliosphere which directly affect the to astronauts, satellites, polar air traffic, electric power magnetosphere. In particular, the Sun’s variable magnetic grids, and telecommunications facilities on short time-scales fields constitute a rich source for processes that influence ranging from hours to days, the solar radiative output the Earth’s upper atmosphere and geomagnetism. The Sun affects planetary and global climate on much longer time- follows a periodic cycle of activity. This cycle, called the solar scales (from decades to stellar evolutionary time-scales). We cycle, has its evident manifestation by the periodic recurrence refer the readers to the recent review by David H. Hath- of sunspots, or darker, relatively cool and strong magnetic away (solarphysics. livingreviews.org/Articles/lrsp-2010-1/) regions at the Sun surface. This periodicity was discovered for more information on the solar cycle. first by Samuel Heinrich Schwabe in 1844 when he observed During the last few decades, technological advances have the variation of the number of sunspots over a seventeen- led to the acquisition of a huge amount of high-quality data year period. The solar cycle usually lasts about eleven years on solar magnetic field and solar activity. The development on the average, and there is little doubt that it is magnetic in of helioseismology, the technique of studying solar interior nature and produced by dynamo processes within the Sun. It through the study of its global oscillations, has led to is believed that the 11-year solar cycle results from generation spectacular success in determining Sun’s internal structure of strong toroidal magnetic fields in the Sun, with a main and rotation with increasing accuracy. period of about 22-years, by combined effects of convection We invited authors to contribute this special issue of the and differential rotation in the Sun. journal original research articles as well as review articles that Although most of the characteristics of the solar cycle can stimulate the continuing efforts to understand the solar have been investigated for many years, we still do not cycle and its impact on space weather and global climate. know exactly what causes the 11-year solar cycle. This is Eleven original research articles were received. All these were one of the most important unsolved problems in solar peer-reviewed by a minimum of two referees. Eight of them physics today. Because of the long record of observations, accepted for publications in this special issue. In three of sunspot measurements still constitute a primary source of the papers the predictions for the amplitude and duration of information to better understand the level and nature of solar cycle 24 were presented, mainly from the statistical analyzes activity. Statistical and morphological studies of sunspots of the sunspot data, and in five papers research on basic have significantly improved our knowledge of this field. property of solar cycle and related topics were presented. Other solar activity indicators including the 10.7 cm radio We hope that students and researchers will find this flux, the total and spectral solar irradiance, the magnetic special issue useful. Since the Advance in Astronomy is an field, flares and coronal mass ejections, geomagnetic activity, open-access journal, all of the papers of this special issue are and galactic cosmic ray fluxes have also shown temporal accessible free of charge to anyone with a computer and an properties related to the solar magnetic activity cycle. While Internet connection. 2 Advances in Astronomy

Acknowledgments We sincerely thank the authors and referees of the articles submitted to this special issue. We are also thankful to the members of the editorial board of Advances in Astronomy, Hindawi publisher. Without their support and hard work, this special issue would not have come into being. J. Javaraiah J. P. Rozelot Luca Bertello Hindawi Publishing Corporation Advances in Astronomy Volume 2012, Article ID 478957, 10 pages doi:10.1155/2012/478957

Research Article The Faint Young Sun Paradox: A Simpliﬁed Thermodynamic Approach

F. Angulo-Brown,1 Marco A. Rosales,1 and M. A. Barranco-Jimenez´ 2

1 Departamento de F´ısica, Escuela Superior de F´ısica y Matematicas,´ Instituto Polit´ecnico Nacional, UP Zacatenco, 07738 Mexico, DF, Mexico 2 Departamento de Formacion´ Basica,´ Escuela Superior de Computo,´ Instituto Polit´ecnico Nacional, Avenida Juan de Dios Batiz s/n. Esquina M. Othon´ de Mendizabal UP Adolfo Lopez´ Mateos, 07738 Mexico, DF, Mexico

Correspondence should be addressed to M. A. Barranco-Jimenez,´ [email protected]

Received 15 December 2011; Revised 16 March 2012; Accepted 15 May 2012

Academic Editor: J. P. Rozelot

Copyright © 2012 F. Angulo-Brown et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Classical models of the Sun suggest that the energy output in the early stage of its evolution was 30 percent less than today. In this context, radiative balance alone between The Sun and the Earth was not sufficient to explain the early presence of liquid water on Earth’s surface. This difficulty is called the faint young Sun paradox. Many proposals have been published to solve this paradox. In the present work, we propose an oversimplified finite-time thermodynamic approach that describes the air convective cells in the Earth atmosphere. This model introduces two atmospheric modes of thermodynamic performance: a first mode consisting in the maximization of the power output of the convective cells (maximum power regime) and a second mode that consists in maximizing a functional representing a good trade-off between power output and entropy production (the ecological regime). Within the assumptions of this oversimplified model, we present different scenarios of albedo and greenhouse effects that seem realistic to preserve liquid water on the Earth in the early stage of formation.

1. Introduction to reconcile these facts. Among the evidence for ancient liquid water temperatures at the Earth’s surface is the dating The so-called faint young Sun paradox [1]isakeydrawback of sedimentary rocks, that is, rocks laid down under water. in the understanding of the early conditions of the Earth These rocks date back to at least 4 Gyr before present (BP) as well as the Sun’s history itself [1, 2]. Such a paradox [5–8]. On the other hand, Cogley and Henderson-Sellers can be summarized as follows: the luminosity of the Sun, [9], based on fossil studies, assert that liquid water would approximately 4.5–3.8 Gyr ago, was about 70–80 percent of be necessary to explain the existence of diverse fossils in its present value [1–7], which accounts only for terrestrial rocks dated earlier than 3.5 Gyr BP. More recently, Watson temperatures below the freezing point of water. As is well and Harrison [10], by studying ancient zircons from Western known, the Earth’s surface temperature is mainly driven by Australia, suggest that their results substantiate the existence the ﬂux of solar radiation it receives and the interaction of wet, minimum melting conditions at 4.55 to 4.0 Gyr BP. of radiation with atmosphere gases. In fact, assuming a They further suggest that Earth had settled into a pattern black-body radiative balance between the young Sun and of crust formation, erosion, and sediment recycling at that Earth results in T = 255 K [1], lower enough to have epoch. kept large parts of the Earth’s surface frozen until 1-2 Gyr Several approaches have been proposed to try to solve ago [4]. However, evidence from several independent lines the faint young Sun paradox (FYSP) [1, 3–7, 11, 12]. Some of investigation suggests that for virtually its entire history solutions have usually involved higher amounts of green- Earth has maintained a surface temperature in the range house gases than the present in the modern-day atmosphere within which water is a liquid, raising question about how to compensate for the cooler Sun, for example, enhanced 2 Advances in Astronomy

amounts of CO2 [13, 14], ammonia (NH3)[15], or methane might have been overestimated by previous studies. They (CH4)[16]. In 2003 [4], Shaviv proposed another FYSP used a very detailed one-dimensional radiative-convective solution by considering the cooling effect that cosmic rays model based on several climate models to obtain CO2 are suspected to have on the global climate and that the concentrations compatible with the amount inferred from younger Sun must have had a stronger solar wind (associated sediment studies. with a modest mass loss), such that it was more effective at In summary, there exist a number of possible FYSP stopping cosmic rays from reaching Earth. However, Bada et solutions stemming from distinct approaches, that is, distinct al. [11] have emphasized that FYSP proposals must include a proposals that give liquid-water temperatures for the early scenario with a mechanism for melting a once frozen ocean. Earth’s surface. They proposed that bolide impacts between about 4.0 and In the present work, we also obtain liquid-water tem- 3.6 Gyr ago could have episodically melted an ice-covered peratures by means of an oversimplified finite-time ther- early ocean. modynamic model without the need of high concentrations Another kind of proposals have used alternative models of greenhouse gases. This approach is based on a highly of solar evolution (AMSE) originally constructed to explain idealized model that is not intended to provide a quanti- the anomalous depletion of lithium in the Sun and similar tatively accurate or physically complete description of the stars [5, 6, 17]. These AMSE incorporate early solar mass loss FYSP; that is, it is a toy model in the classification of Randall of 5–10 percent predicting higher early solar luminosities [5] and Wielicki for models in atmospheric sciences [21]. It is which have the potential to produce planetary temperatures necessary to emphasize that the convective cells of our model within the liquid water range without requiring very high (as in the GZ-model [22]) are only virtual cells attempting CO2 concentrations [5]. Very recently, Turck-Chieze` et al. to give a thermodynamically equivalent scheme of actual [18], based on the study of rotational internal profile of convection by means of taking into account the global the Sun, have shown that magnetic field has been probably thermodynamic restrictions over energy fluxes. However, present in the first stage with surface strong activity during we must mention that other oversimplified models can be the first million years and associated mass loss. These authors found in books of climate dynamics [23]. These approaches estimate the mass loss from the observations of young solar can be 0D models based on changing the opacity and the analogs which could reach up to 30 percent of the current number of effective layers of the atmosphere to compensate mass. Although that phase is insufficiently described, it is not even very large changes of the solar constant in order to excluded that the initial luminosity would have been greater keep the surface temperature constant. See for example, the than standard solar model (SSM) results [18]. Regarding take-home exercise 11.2 from the classical text by Hartmann AMSE proposals, although Gaidos et al. [6] by observing [23], where the FYSP is raised in terms of a greenhouse Π01 Ursa Majoris, a 300-million-year-old solar-mass star effect calculation, which leads to a very high normalized (probable analog of the early Sun) placed an upper limit greenhouse coefficient (around 0.7). This result corresponds on the mass loss rate that possibly rules out AMSE as a to a scenario that is not consistent with geological evidence solution of FYSP,the recent results by Turck-Chieze` et al. [18] [12, 24]. The present paper is organized as follows. In reinforce the feasibility of AMSE models. Section 2, we present a brief review of some basic concepts Most of the previous FYSP proposed solutions have faced of finite-time thermodynamics (FTT); in Section 3, a simple some form of contradictions or large uncertainties, either model for wind energy as a solar-driven heat engine is from geological data on atmospheric conditions or from discussed; in Section 4, an FTT-approach to the FYSP is atmospheric modeling [12]. For example, very high ancient proposed; finally in Section 5, we present some concluding CO2 concentrations may prove to be inconsistent with remarks. derived weathering rates. Thus, as Graedel et al. [5] assert, the imposition of high CO2 concentrations in Precambrian climate models is consistent with, but not required by, the 2. Finite-Time Thermodynamics temperature record. On the other hand, Hessler et al. [19] analyzed weathering rinds at river gravels dated back to During the last decades, finite-time thermodynamics has 3.2 Gyr suggesting a lower limit of CO2 partial pressure in extended its applications into many fields [26–32]. In the the atmosphere to only several times the present value, which same way that early classical thermodynamics in the 19th is two orders of magnitude below what is required to keep century, starting from the study of thermal engines, soon the surface temperature of Earth above freezing. In regard reached practically all macroscopic systems, FTT went on to high NH3 concentrations [3, 15], Shaviv [4] asserts that, to embrace many problems where entropy production of although not impossible, it is not easy to keep NH3 from global processes plays an unavoidable role. For example, in a irreversibly photolyzing into H2 and N2 [20]. Shaviv also typical FTT heat engine model the whole entropy production suggests that the CH4 solution requires a long residency time is ascribed only to the coupling between the working of methane in the atmosphere and probable dominance of substance and its surroundings, and it is permitted that methanogenic bacteria, concluding that this type of solutions the working fluid undergoes only reversible transformations. can neither be ruled out, nor proven at this point. This approach is called the endoreversibility hypothesis (EH) Recently von Paris et al. [12] reconsidered the role of [33]. By means of this hypothesis, it has been possible CO2 in warming the early Earth. They concluded that the to place realistic bounds on irreversible processes that amount of CO2 needed to warm the surface of the early Earth proceed in finite time. Usually, in FTT methodology one Advances in Astronomy 3

T1 ∑ ∑

α QH

P T1w P η P

T2w

β Q 0 L 0 ηC 1 η T 2 Figure 2: P versus η and Σ versus η for a CA cycle, (see [30, 38]).

Figure 1: Curzon and Ahlborn heat engine. Carnot cycle with both zero entropy and power productions. For the mentioned cycle model, CA maximized the power calculates an extremum or optimum of a thermodynamically output and found that the efficiency under maximum-power meaningful variable or functional [22]. Recently, Fischer and conditions is expressed by Hoffmann [34] showed that a simple endoreversible model (the so-called Novikov engine) can reproduce the complex T2 ηCA = 1 − . (2) engine behavior of a quantitative dynamical simulation T1 of an Otto engine including, but not limited to, effects from losses due to heat conduction, exhaust losses, and The same expression was previously obtained by other frictional losses. On the other hand, Curto-Risso et al. [35] authors [37]. Since the CA paper, many works have been have published an FTT model also for an irreversible Otto published in the FTT-field [22, 26–42]. In Figure 2,itcanbe P cycle suitable to reproduce performance results of a very observed the qualitative behavior of both the power and Σ ffi η elaborated dynamical model of a real spark ignition heat the entropy production in terms of the e ciency , for the engine including a turbulent flame propagation process, Curzon-Ahlborn cycle [30]. From this figure it can be seen valves overlapping, heat transfer across the cylindrical walls, that the function and a detailed analysis of the involved chemical reactions. In E = P − T2Σ (3) these two articles, the spirit of FTT is illustrated emphasizing the virtues and limitations of this methodology. However, is a convex curve with a maximum point. This function was in these articles, the usefulness of FTT models is shown proposed by Angulo-Brown [38] and it has the following E P ≈ beyond any doubt. In fact, we can assert that the FTT spirit is properties: at maximum , the power output satisfies Emax / P Σ ≈ / Σ concomitant with the spirit of a Carnotian thermodynamics (3 4) max; the entropy production is Emax (1 4) Pmax ; the ffi η ≈ / η η η in the sense of the search for certain kind of limits for e ciency is Emax (1 2)( C + CA), C being the Carnot thermodynamic variables and functionals. For example, in efficiency. Due to the previous properties, the function 1975, Curzon and Ahlborn (hereafter CA) [36] published given by (3) was named the ecological function, which an article where they proposed a kind of Carnot cycle that pertains to the class of compromise functions between gains produces entropy only due to an irreversible Newtonian and losses mentioned by Greenspan [43]. The so-called heat transfer between two thermal reservoirs at absolute ecological optimization has been applied in many areas. For temperatures T1 and T2 (T1 >T2) and the two isothermal instance, thermal engines [40], biochemical reactions [41, 42, branches of the working fluid at temperatures T1w and 44, 45], linear energy converters [41, 42], superconducting T2w (T1w >T2w), respectively (see Figure 1)givenby transition [46], thermoeconomical optimization [47, 48], and atmospheric convective cells [49–51]. The ecological Q = α T − T H ( 1 1w), function given by (3) was later slightly modified by means (1) of the inclusion of a parameter, , which takes into account QL = β(T w − T ), 2 2 the particular heat transfer law employed in the thermal where α and β are the thermal conductances of the materials engine model [52, 53]. However, the mentioned “ecological” that separate the reservoirs from the working substance and properties of the modified E do not appreciably change. QH and QL are the heat flows per unit time. In this way, ΔS > CA proposed an irreversible global model with tot 3. Wind Energy as a Solar-Driven Heat Engine 0 but internally reversible (EH). By integrating (1), CA obtained the cycle’s period Δt and therefore they had a The problem of thermal balance between the planets of cycle with nonzero power, in contrast to the reversible the solar system and the Sun under a FTT approach has 4 Advances in Astronomy been treated by several authors [22, 30, 49, 51, 54, 55]. In Reflection from Infrared radiation Solar radiation some of these articles, the question of conversion of the atmosphere 35% Solar constant into space (3 K) 2 solar energy into wind energy is also treated. As is well 342 W/m known [56], cosmic radiation, starlight, and moonlight can T2 be neglected for the thermal balance of any of the planets of the solar system and only the following quantities have an influence: the incident solar influx or solar constant S, the dimensionless planet’s albedo ρ, and the greenhouse effect of the planet’s atmosphere crudely evaluated by means of a Instantaneous coefficient γ.Thiscoefficient can be taken as the normalized adiabats greenhouse effect introduced by Raval and Ramanathan [57], which is defined as the infrared radiation energy trapped by the atmospheric gases and clouds. When only the global Cycle average thermal balance between the Sun and a planet is considered, solar input T 2 one can roughly obtain the planet’s surface temperature 1 223 W/m assumed to be a uniform temperature Tp. If the conversion of solar energy into wind energy Earth is to be modeled, it is necessary to involve at least two Figure 3: Schematic of a simplified solar-driven heat engine taken representative atmospheric temperatures for making the from [22]. creation of work possible, that is, to take the planet’s atmosphere as a working fluid that converts heat into mechanical work. This permits to introduce in a natural way the concept of atmospheric “heat engine” (recently, Lucarini [58] has remarked the importance of this kind of two- 3.1. The Gordon-Zarmi Model. In Figure 3, a schematic view temperature models for climate system analysis through an of a simplified Sun-Earth-Wind system as a heat engine cycle equivalent atmospheric Carnot engine). Within this context, is depicted (GZ-model). The cycle consists of four branches: process variables like work rate, heat fluxes, and efficiency, two isothermal branches, one in which the atmosphere for instance, find a simple theoretical framework, where absorbs solar radiation at low altitudes and the other in thermodynamical restrictions play a major role. This is in which the atmosphere rejects heat at high altitudes to the contrast with disciplines as nonequilibrium thermodynamics universe, and two intermediate instantaneous adiabats with and hydrodynamics based on local differential equations rising and falling air currents [22]. where the transition from local to global variables is not a According to GZ, this oversimplified Carnot-like engine trivial task [54]. corresponds very approximately to the global scale motion In 1989, Gordon and Zarmi (GZ) [22] introduced a FTT of wind in convective cells. In what follows, we use all of model taking the Sun-Earth-Wind system as a FTT cyclic GZ model assumptions. For instance, the work performed by the working fluid in one cycle W, the internal energy of heat engine where the heat input is the solar radiation, the the working fluid U, and the yearly average solar radiation working fluid is the Earth’s atmosphere, and the energy flux qs are expressed per unit area of Earth’s surface. The in the winds is the work produced. The cold reservoir temperatures of the four-branch cycle are taken as follows: to which the engine rejects heat is the 3 K surrounding T1 is the working fluid temperature in the isothermal branch universe. By means of this oversimplified model, Gordon at lowest altitude, where the working fluid absorbs solar and Zarmi were able to obtain reasonable values for the radiation for half of the cycle, during the second half of annual average power in Earth’s winds and for the average the cycle heat is rejected via black-body radiation from maximum and minimum temperatures of the atmosphere, the working fluid at temperature T2 (highest altitude of without resorting to detailed dynamic models of the Earth’s the cell) to the cold reservoir at temperature Tex (the 3 K atmosphere, and without considering any other effect (such surrounding universe). In the GZ-model the objective is to as Earth’s rotation, Earth’s translation around the Sun, and maximize the work per cycle (average power) subject to the ocean currents). We wish to remark that the oversimplifica- endoreversibility constraint [33], that is, tions of this atmospheric model do not consider horizontal thermal gradients which affect the midlatitude and high- latitude air circulation or the unstable motions. The only t 0 qs(t) − σ T4(t) − T4 (t) heat transfer mechanism taken into account in the GZ ΔS = ex dt = int T t 0, (4) model is the radiation. Other mechanisms such as latent heat 0 ( ) transport are also not considered. Later, De Vos and Flater [56] extended the GZ-model to take into account the wind energy dissipation. In [59] the previous model was extended where ΔSint is the change in entropy per unit area, t0 by including convective Hadley cells. is the time of one cycle, σ is Stefan-Boltzmann constant Advances in Astronomy 5

−8 2 4 (5.67 × 10 W/m K ), and qs, T,andTex are functions of a lumped nonendoreversibility parameter R which may time t,takenfrom[22] be considered as a measure of the departure from an ⎧ t endoreversible regime, due to internal losses [61, 62]. This ⎨⎪ 0 T1,0≤ t ≤ , parameter arises from Clausius’ inequality [63–65]. With this T t = 2 T T P ( ) ⎪ t approach, 1, 2,and also reach reasonable values. When ⎩T , 0 ≤ t ≤ t , R 2 2 0 the nonendoreversibility parameter and the greenhouse factor γ are considered, the integral constraint given by (4) T = ≤ t ≤ t ex 3K, 0 0, (5) must be modified, becoming ⎧ t 4 4 ⎪ t0 0 qs(t) − σ 1 − γ R T (t) − T (t) ⎨⎪0 ≤ t ≤ t , ΔS = ex dt = 0 R T t 0, qs(t) = 2 0 ( ) ⎪ S0 1 − ρ t ⎩ 0 ≤ t ≤ 0 , (9) 2 2 and the first law of thermodynamics applied over one cycle S / 2 with 0 the yearly average solar constant (1373 W m )and becomes ρ ≈ . ff 0 35 [22] are the e ective average albedo of the t0 ΔU =−W q t − σ − γ T4 t − T4 t dt = . earth’s atmosphere. The GZ model maximizes the work per + s( ) 1 ( ) ex( ) 0 cycle W (average power P), taken from the first law of 0 (10) thermodynamics for one cycle By substituting (5) into (10), by considering that the t 0 − γ ff ΔU =−W q t − σ T4 t − T4 t dt = factor (1 ) corresponding to the greenhouse e ect only + s( ) ( ) ex( ) 0 (6) 0 participates in the lower half of the cycle depicted in Figure 3, q σT4 and by integrating (10) with the approximation s ex, by means of the Euler-Lagrange formalism and denoting the expression for the average power output becomes average values as σ P = qs − 1 − γ T4 + T4 . (11) T + T 2 1 2 T = 1 2 , 2 With the same previous assumptions for the greenhouse Tn Tn effect, the integral constraint (9)turnsouttobe Tn = 1 + 2 , (7) qs σR 2 = 1 − γ T3 + T3 . (12) T 2 1 2 1 − ρ 1 qs = S . 0 4 Thus, for the maximization of the power output, we construct the following Lagrangian: From (6)and(7) and taking into account the constraint σ 4 4 L LR = qs − 1 − γ T + T given by (4), GZ construct the following Lagrangian ( ): 2 1 2 (13) q t qs σR 4 s( ) 3 − λ − − γ T3 T3 L = T (t) + λ − σT (t) ,(8) T 1 1 + 2 , T(t) 1 2 where λ is a Lagrange multiplier. From (13), by means of λ where is a Lagrange multiplier. By finding the extremum the Euler-Lagrange formalism, we obtain the following three L ∂L/∂T t = of by means of ( ) 0, GZ found for the Earth’s equations: T = T = atmosphere the following values: 1 277 K, 2 192 K q and P = W /t = 17.1W/m2. These numerical values T5 − 3RλT4 − s λ = max max 0 1 1 0, are not so far from the “actual” values, which are P ≈ 7W/m2 4 2σ 1 − γ T ≈ T ≈ [60], 1 290 K (at ground level), and 2 195 K (at 4 an altitude of around 75–90 km). However, as GZ assert, λ = T2, (14) 3R their power calculation must be taken as an upper bound 1 2qs due to several idealizations in their model. Later [49], the T4 − T T3 − = 0, GZ-model was used to maximize the ecological function 1 1 − γ 1 2 σR 1 − γ given by (3).Thiswasmadeforbothanendoreversible which, by the elimination of λ,reduceto and a nonendoreversible cases. For the endoreversible case 2qs (with a 3 K surrounding universe) the following values were T5 − T T4 − T = 0, 2 1 2 1 σR − γ 2 obtained: T1 = 294 K, T2 = 109.5K,andPmax = 6.89 W/m , 3 1 which are also good values, remarkably for T and P. Another (15) 1 1 2qs endoreversible case was proposed in [49], but using as cold T4 − T T3 − = 0. 1 1 − γ 1 2 σR 1 − γ reservoir the tropopause layer with Tex ≈ 200 K. In that case the numerical results were T1 = 293.3K,T2 = 239.2K, The numerical solutions of (15) give us the low altitude 2 and Pmax = 10.75 W/m , which are also reasonable values temperature T1 and the high altitude temperature T2 for for the troposphere characteristics. The nonendoreversible an atmospheric “heat engine” operating under maximum version of the GZ model was accomplished by means of power conditions. 6 Advances in Astronomy

3.2. The Maximum-Ecological Regime. If the objective is the MER). The altitude corresponding to T2 strongly depends maximization of the so-called ecological function given by onwhichlayerweuseascoldreservoir.Forthecasesof (3), ﬁrst, we need to calculate the mean entropy production atmospheres with a tropopause layer, T2 reaches very realistic per cycle of the thermodynamic universe, ΔSu/t0. Starting values within tropospheric characteristics [51]. from Figure 3,wehave t 0 −q t σ − γ R T4 t − T4 t 4. A FTT-Approach to the Faint s( ) + 1 ( ) ex( ) ΔSu = dt. (16) Young Sun Paradox 0 T(t)

If we consider the greenhouse effect only in the first half We take as the first hypothesis that solar radiation has of the cycle, by means of (5), we get increased over the main-sequence lifetime of the Sun due to the increase in the mean density of the solar core as hydrogen t / 0 2 S − ρ / σ − γ R T4 − T4 is converted into helium. In all the standard solar models ΔS = 0 1 2 + 1 1 ex dt u T (SSM) [25], the luminosity of the young Sun was estimated 0 1 30% less than the present value. According to Gough [3], the t 0 σR T4 − T4 rate of increase of luminosity with time, t, can be expressed 2 ex + dt, as t /2 Tex 0 (17) t −1 S t = . − S ( ) 1+04 1 t 0, (22) ΔS q σR T4 0 u =− s − γ T3 2 t T + 1 1 + T , (18) 0 1 2 ex where S0 is the present solar luminosity and t0 (≈ 4.56 Gyrs) is the present age of the Sun. Equations (15)and(21) where we have used the approximation, qs σT4 . ex necessary to calculate T1 and T2 under both MPR and MER Therefore, by the substitution of (11)and(18) into (3), the scenarios use the following as input data: the cold reservoir ecological function E becomes temperature Tex (the 3 K surrounding universe, which could σ T q be up to 9.5 K 12 Gyr ago [66]) the solar luminosity S(t) E = q − − γ T4 T4 ex s s 1 1 + 2 + and the effective average albedo ρ both combined through 2 T1 the yearly average solar radiation flux qs = S (1 − ρ)/2; the (19) 0 σRT T4 greenhouse coefficient γ; the nonendoreversibility parameter − ex − γ T3 2 . 1 1 + R. In principle, S(t) is taken as governed by Gough equation 2 Tex (22). Then, we propose the following Lagrangian, In Table 1, we show the numerical results for an atmosphere working under the MP-regime for several parameter σ T q L = q − − γ T4 T4 ex s values. The present-day values for average albedo and the E s 1 1 + 2 + 2 T1 greenhouse parameter are ρ ≈ 0.3andγ = 0.4, respectively. For the Earth, γ is a normalized greenhouse effect parameter σRT T4 − ex − γ T3 2 defined as γ = (Es − F)/Es [57], where Es is the surface 1 1 + T (20) 2 ex emission and F is the outgoing radiation. As we can see q σR for a low ρ and a low γ scenario (first row), we can obtain − λ s − − γ T3 T3 1 1 + 2 , liquid-watertemperaturesaround4.5–3.6Gyragoforsolar T1 2 constants within the interval [0.7S0,0.8S0]. In this case ρ = where λ is a Lagrange multiplier and the constraint given by 0.17 is a half of the present value and γ = 0.06 a seventh of (12) has been used. By solving the Euler-Lagrange equations the present value, that is, a scenario with small concentration for this Lagrangian, we obtain values of greenhouse gases. In Table 1, we also observe ρ several other possible scenarios for combinations of and 3T 2qs 1+R 1 γ values. For the first row in Table 1 weuseavalueof T5 + ex R − (1+R)T T4 − T 1 4 2 1 3σ R 1 − γ 2 R = 0.95, that is, an internally nonendoreversible convective cell model, taking into account in a lumped manner some T qs 1 internal dissipations [61, 62]. The sixth column corresponds + ex = 0, 2σ 1 − γ to surface temperatures estimated for S(t) values taken from Table 11 of [25]. As can be seen in sixth column, also 1 2qs 1 for this model we find liquid-water temperatures in early T4 + T T3 − = 0. 1 1 − γ 1 2 σR 1 − γ stages of Earth’s surface. In fact, these surface temperatures (21) are larger than those obtained with Gough’s curve (see Figure 4, for a comparison of both curves). In Table 2,we To summarize, by solving (15) for the maximum power present several possible scenarios of an Earth’s atmosphere regime (MPR) and (21) for the maximum ecological regime working under the ME regime. Here, we also obtain that for (MER), we can obtain the surface temperature T1 and the relatively small values of ρ and γ it is possible to find liquid- high altitude temperature T2 for both scenarios (MPR and water temperatures for the young Earth, by considering the Advances in Astronomy 7

Table 1: Possible scenarios of ancient surface temperatures under maximum power output regime. Input data: ρ, γ, R (one case). S/S0 is calculated according to Gough equation for a given age. The ﬁfth column corresponds to our calculated temperatures. For the ﬁrst row data R = 0.95 was considered. The sixth column shows the surface temperatures estimated from S(t) values reported in Table 11 of [25].

Solar constant S/S Albedo ρ Greenhouse coeﬃcient γ 0 Time BP (Gyr) Surface temperature, T (K) Surface temperature, T (K) (normalized) 1 1 0.17 0.06 0.7-0.8 4.5–3.6 273.7–283.04 280.1–283.01 0.25 0.15 0.72 4.47 273.7 280.33 0.30 0.20 0.74 4.04 273.1 279.74 0.35 0.30 0.72 4.47 273.8 280.01 0.40 0.35 0.73 4.25 273.1 280.03

Table 2: Possible scenarios of ancient surface temperatures under maximum ecological conditions. For the ﬁrst row data R = 0.95 was considered.

Albedo ρ Greenhouse coeﬃcient γ Solar constant S/S0 (normalized) Time BP (Gyr) Surface temperature, T1 (K) 0.17 0.06 0.7-0.8 4.5–3.6 293.6–303.6 0.0 0.81 2.297 273.1 0.40 0.1 0.73 4.253 273.0 0.0 0.88 1.568 273.1 0.1 0.80 2.875 273.2 0.45 0.15 0.76 3.631 273.4 0.20 0.71 4.697 273.7 0.1 0.88 1.568 273.2 0.15 0.83 2.355 273.3 0.50 0.20 0.79 3.056 373.5 0.25 0.74 4.045 273.1 way of thermodynamic performance of the atmosphere in 1 addition to the ρ and γ values. The FTT-approach here presented is mainly based on the role played by the global behavior of the Earth’s atmosphere and its mode of using the input of solar energy in order to propose the values 0.9 0

of both albedo and greenhouse parameters which produce /S ) t

T ( TCC surface temperatures, 1, above the freezing point of water. S In Table 3 (for MP regime) and Table 4 (for ME regime) we 0.8 show a similar calculation for Mars’ atmosphere by using several combinations of ρ and γ parameters. In this case, GC we also ﬁnd liquid-water temperatures corresponding to 0.7 early stages of the Sun, mainly for the ecological way of 4.5 4 3 2 1 0 thermodynamic performance. Time (Gyr BP)

5. Concluding Remarks Figure 4: Comparison between Gough curve ((22), GC) and Turck- Chieze` et al. curve (TCC) depicted with S(t)/S0 values taken from In Tables 1 and 2 for Earth and Tables 3 and 4 for Mars, we Table 11 of [25]. Both curves correspond to solar models without mass loss in the early stage of the Sun. present several possible scenarios for values of both albedo and greenhouse parameters (ρ and γ), which produce surface temperatures above the freezing point of water. For the case of the Earth, the temperatures for some ages are compatible the greenhouse (and albedo) effect is consistent with the with recent geological evidence of possible ancient existence second law of thermodynamics because a planet is not a of liquid water on Earth. Remarkably, in our approach only closed system. It exchanges heat with a high-temperature moderate and low values of greenhouse effect and albedo bath by absorbing radiation from the photosphere of its star are necessary to produce early liquid-water temperatures. and with a cold bath by emitting IR into the essentially zero- Our model is mainly based on the role played by the global temperature reservoir of space. The so-called “ecological” thermodynamical behavior of the atmosphere and on its scenarios offer a better range of greenhouse and albedo mode of using the input of solar energy. As asserted by combinations than the “maximum power” scenarios with Pierrehumbert [67], the planetary warming resulting from respect to a possible solution of the faint young Sun paradox. 8 Advances in Astronomy

Table 3: Possible scenarios of ancient surface temperatures for Mars under maximum power output regime.

Albedo ρ Greenhouse coeﬃcient γ Solar constant S/S0 (normalized) Time BP (Gyr) Surface temperature, T1 (K) 0.0 0.5 0.85 2.029 275.2 0.1 0.5 0.95 0.66 272.9

Table 4: Possible scenarios of ancient surface temperatures for Mars under maximum ecological function conditions.

Albedo ρ Greenhouse coeﬃcient γ Solar constant S/S0 (normalized) Time BP (Gyr) Surface temperature, T1 (K) 0.0 0.2 0.9 1.277 273.4 0.0 0.3 0.8 2.875 273.9 0.1 0.3 0.9 1.310 274.0 0.1 0.4 0.9 3.631 273.1 0.2 0.3 0.99 0.116 273.2 0.2 0.4 0.86 1.872 273.4 0.2 0.5 0.73 4.25 273.7 0.3 0.4 0.98 0.234 273.2 0.3 0.5 0.83 2.355 273.3 0.4 0.6 0.8 2.875 274.1

Although our model only uses average lumped parameters References and general thermodynamic restrictions, it leads to results qualitatively compatible with those recently published by von [1] C. Sagan and G. Mullen, “Earth and Mars: evolution of Paris et al [12], which were obtained by means of a very atmospheres and surface temperatures,” Science, vol. 177, no. 4043, pp. 52–56, 1972. detailed climate model. Very recently, Goldblatt et al. [68] [2] J. F. Kasting and D. H. Grinspoon, “The faint young Sun have published an outstanding proposal on the FYSP. They problem,” in The Sun in Time, pp. 447–462, The University suggest that a higher nitrogen level in the early atmosphere of Arizona, Tucson, Ariz, USA, 1991. probably helped warm the early Earth by means of an [3] D. O. Gough, “Solar interior structure and luminosity varia- increase in the atmosphere pressure stemming from N2, tions,” Solar Physics, vol. 74, no. 1, pp. 21–34, 1981. ff which would have augmented the warming e ect of existing [4] N. J. Shaviv, “Toward a solution to the early faint Sun paradox: greenhouse gases, by broadening their absorption lines. In a lower cosmic ray flux from a stronger solar wind,” Journal of 2010, Rosing et al. [24] have proposed that the mineralogy of Geophysical Research A, vol. 108, no. 12, article 1437, 8 pages, Archean (3.8to2.5 Gyr ago) sediments is inconsistent with 2003. high concentrations of greenhouse gases and the metabolic [5]T.Graedel,I.J.Sackmann,andA.Boothroyd,“Earlysolar constraints of extant methanogens. Prompted by this, they mass loss:a potential solution to the weak sun paradox,” hypothesize that a lower albedo on the Earth made an Geophysical Research Letters, vol. 18, pp. 1881–1884, 1991. important contribution to moderating surface temperature [6] E. J. Gaidos, M. Gudel,¨ and G. A. Blake, “The faint young sun in the Archean eon. In fact, they used albedos around 0.10 to paradox: an observational test of an alternative solar model,” 0.26, which are numbers consistent with those used in our Geophysical Research Letters, vol. 27, no. 4, pp. 501–503, 2000. calculations. In summary, our oversimplified model using [7] D. A. Minton and R. Malhotra, “Assessing the massive young the hypotheses of a faint young Sun does not face important SUN hypothesis to solve the warm young earth puzzle,” Astrophysical Journal, vol. 660, no. 2, pp. 1700–1706, 2007. contradictions with other solutions recently proposed. Of [8]S.A.Bowring,I.S.Williams,andW.Compston,“3.96Ga course we shall find even easier solutions for AMSE models gneisses from the Slave province, Northwest Territories, basedonmasslossobservedinyoungstarsandsuggestedby Canada,” Geology, vol. 17, no. 11, pp. 971–975, 1989. helioseismological data [18, 25, 69]. [9] J. G. Cogley and A. Henderson-Sellers, “The origin and earliest state of the earth’s hydrosphere,” Reviews of Geophysics & Space Physics, vol. 22, no. 2, pp. 131–175, 1984. Acknowledgments [10] E. B. Watson and T. M. Harrison, “Zircon thermometer reveals minimum melting conditions on earliest earth,” Science, vol. The authors gratefully acknowledge R. Hernandez-P´ erez´ and 308, no. 5723, pp. 841–844, 2005. T. E. Govindan for revising the paper. F. A. Brown and [11] J. L. Bada, C. Bigham, and S. L. Miller, “Impact melting of M. A. Barranco-Jimenez´ thank the financial support by frozen oceans on the early Earth: implications for the origin CONACYT, COFAA and EDI-IPN-Mexico.´ This paper is of life,” Proceedings of the National Academy of Sciences of the dedicated to the memory of Marco A. Rosales. United States of America, vol. 91, no. 4, pp. 1248–1250, 1994. Advances in Astronomy 9

[12] P.von Paris, H. Rauer, J. Lee Grenfell et al., “Warming the early [33] M. H. Rubin, “Optimal configuration of a class of irreversible earth-CO2 reconsidered,” Planetary and Space Science, vol. 56, heat engines. I,” Physical Review A, vol. 19, no. 3, pp. 1272– no. 9, pp. 1244–1259, 2008. 1276, 1979. [13] W. R. Kuhn and J. F. Kasting, “Effects of increased CO2 con- [34] A. Fischer and K. H. Hoffmann, “Can a quantitative simu- centrations on surface temperature of the early Earth,” Nature, lation of an Otto engine be accurately rendered by a simple vol. 301, no. 5895, pp. 53–55, 1983. Novikov model with heat leak?” Journal of Non-Equilibrium [14] J. F. Kasting, “Earth’s early atmosphere,” Science, vol. 259, pp. Thermodynamics, vol. 29, no. 1, pp. 9–28, 2004. 920–926, 1993. [35] P. L. Curto-Risso, A. Medina, and A. C. Hernandez,´ “Theo- [15] C. Sagan and C. Chyba, “The early faint sun paradox: organic retical and simulated models for an irreversible Otto cycle,” shielding of ultraviolet-labile greenhouse gases,” Science, vol. Journal of Applied Physics, vol. 104, no. 9, Article ID 094911, 276, no. 5316, pp. 1217–1221, 1997. 2008. [16]A.A.Pavlov,J.F.Kasting,L.L.Brown,K.A.Rages,andR. [36] F. Curzon and B. Ahlborn, “Efficiency of a carnot engine at Freedman, “Greenhouse warming by CH4 in the atmosphere maximum power output,” American Journal of Physics, vol. 43, of early Earth,” Journal of Geophysical Research E, vol. 105, no. pp. 22–24, 1975. 5, pp. 11981–11990, 2000. [37] M. Feidt, M. Costea, C. Petre, and S. Petrescu, “Optimization [17] H. D. Holland, B. Lazar, and M. McCaffrey, “Evolution of the of the direct Carnot cycle,” Applied Thermal Engineering, vol. atmosphere and oceans,” Nature, vol. 320, no. 6057, pp. 27–33, 27, no. 5-6, pp. 829–839, 2007. 1986. [38] F. Angulo-Brown, “An ecological optimization criterion for [18] S. Turck-Chieze,` L. Piau, and S. Couvidat, “The solar energetic finite-time heat engines,” Journal of Applied Physics, vol. 69, balance revisited by young solar analogs, helioseismology, and no. 11, pp. 7465–7469, 1991. neutrinos,” The Astrophysical Journal Letters, vol. 731, no. 2, [39] L. A. Arias-Hernandez,´ Algunas propiedades y aplicaciones article L29, 2011. del criterio de optimizacion´ ecologico´ en termodinamica´ fuera [19] A. M. Hessler, D. R. Lowe, R. L. Jones, and D. K. Bird, “A lower de equilibrio [Tesis Doctoral], Escuela Superior de F´ısica y limit for atmospheric carbon dioxide levels 3.2 billion years Matematicas´ del IPN, Pa´ıs, Mexico, 2000. ago,” Nature, vol. 428, no. 6984, pp. 736–738, 2004. [40] L. Chen, W. Zhang, and F. Sun, “Power, efficiency, entropy- [20] J. F. Kasting, “Stability of ammonia in the primitive terrestrial generation rate and ecological optimization for a class of atmosphere,” Geophysical Research Letters, vol. 87, pp. 3091– generalized irreversible universal heat-engine cycles,” Applied 3058, 1982. Energy, vol. 84, no. 5, pp. 512–525, 2007. [21] D. A. Randall and B. A. Wielicki, “Measurements, models, [41] F. Angulo-Brown, M. Santillan,´ and E. Calleja-Quevedo, and hypotheses in the atmospheric sciences,” Bulletin of the “Thermodynamic optimality in some biochemical reactions,” American Meteorological Society, vol. 78, no. 3, pp. 399–406, Il Nuovo Cimento D, vol. 17, no. 1, pp. 87–90, 1995. 1997. [42] M. Santillan,L.A.Arias-Hern´ andez,´ and F. Angulo-Brown, [22] M. Gordon and Y. Zarmi, “Wind energy as a solar-driven “Some optimization criteria for biological systems in linear heat engine: a thermodynamic approach,” American Journal of irreversible thermodynamics,” Nuovo Cimento della Societa Physics, vol. 57, pp. 995–998, 1989. Italiana di Fisica D, vol. 19, no. 1, pp. 99–109, 1997. [23] D. L. Hartmann, Global Physical Climatology, Academic Press, [43] N. S. Greenspan, “You can’t have it all,” Nature, vol. 409, article London, UK, 1994. 137, 2001. [24] M. T. Rosing, D. K. Bird, N. H. Sleep, and C. J. Bjerrum, “No [44] L. A. Arias-Hernandez, F. Angulo-Brown, and R. T. Paez-Her- climate paradox under the faint early Sun,” Nature, vol. 464, nandez, “First-order irreversible thermodynamic approach to no. 7289, pp. 744–747, 2010. a simple energy converter,” Physical Review E, vol. 77, no. 1, [25] S. Turck-Chieze,` W. Dappen,¨ E. Fossat, J. Provost, E. Schatz- Article ID 011123, 8 pages, 2008. man, and D. Vignaud, “The solar interior,” Physics Report, vol. [45] O. D´ıaz-Hernandez,´ R. Paez-Hern´ andez,´ and M. Santillan,´ 230, no. 2–4, pp. 57–235, 1993. “Thermodynamic performance vs. dynamic stability in an [26] A. Bejan, “Entropy generation minimization: the new ther- enzymatic reaction model,” Physica A, vol. 389, no. 17, pp. modynamics of finite-size devices and finite-time processes,” 3476–3483, 2010. Journal of Applied Physics, vol. 79, no. 3, pp. 1191–1218, 1996. [46] L. A. Arias-Hernandez, F. Angulo-Brown, and R. T. Paez- [27] W. Chih, L. Chen, and J. Chen, Recent Advances in Finite Time Hernandez, “First-order irreversible thermodynamic Thermodynamics, Nova Science, New York, NY, USA, 1999. approach to a simple energy converter,” Physical Review [28] A. Durmayaz, O. S. Sogut, B. Sahin, and H. Yavuz, “Optimiza- E, vol. 77, no. 1, Article ID 011123, 8 pages, 2008. tion of thermal systems based on finite-time thermodynamics [47] M. A. Barranco-Jimenez´ and F. Angulo-Brown, “Thermoe- and thermoeconomics,” Progress in Energy and Combustion conomic optimisation of Novikov power plant model under Science, vol. 30, no. 2, pp. 175–217, 2004. maximum ecological conditions,” JournaloftheEnergyInsti- [29] S. Sieniutycz and P. Salamon, Advances in Thermodynamics, tute, vol. 80, no. 2, pp. 96–104, 2007. vol. 4 of Finite-Time Thermodynamics and Thermoeconomics, [48] M. A. Barranco-Jimenez´ and F. Angulo-Brown, “Thermoe- CRC & Taylor & Francis, New York, NY, USA, 1990. conomic optimisation of endoreversible heat engine under [30] A. DeVos, Endoreversible Thermodynamics of Solar Energy maximum modified ecological criterion,” Journal of the Energy Conversion,OxfordUniversityPress,NewYork,NY,USA, Institute, vol. 80, no. 4, pp. 232–238, 2007. 1992. [49] M. A. Barranco-Jimenez´ and F. Angulo-Brown, “A nonendore- [31] L. Chen and F. Sun, Advances in Finite Time Thermodynamics, versible model for wind energy as a solar-driven heat engine,” Nova Science, New York, NY, USA, 2004. Journal of Applied Physics, vol. 80, no. 9, pp. 4872–4876, 1996. [32] K. H. Hoffmann, J. M. Burzler, and S. Schubert, “Endore- [50] M. A. Barranco-Jimenez,´ J. C. Chimal-Egu´ıa, and F. Angulo- versible thermodynamics,” Journal of Non-Equilibrium Ther- Brown, “The Gordon and Zarmi model for convective atmo- modynamics, vol. 22, no. 4, pp. 311–355, 1997. spheric cells under the ecological criterion applied to the 10 Advances in Astronomy

planets of the solar system,” Revista Mexicana de Fisica, vol. warming on early earth,” Nature Geoscience, vol. 2, no. 12, pp. 52, no. 3, pp. 205–212, 2006. 891–896, 2009. [51] M. A. Barranco-Jimenez´ and F. Angulo-Brown, “A simple [69] S. Turck-Chieze, S. Cahen, M. Casse,´ and C. Doom, “Revisit- model on the influence of the greenhouse effect on the ing the standar solar model,” The Astrophysical Journal Letters, efficiency of solar-to-wind energy conversion,” Nuovo Cimento vol. 335, pp. 415–424, 1988. della Societa Italiana di Fisica C, vol. 26, no. 5, pp. 535–552, 2003. [52] F. Angulo-Brown and L. A. Arias-Hernandez,´ “Reply to “comment on ’a general property of endoreversible thermal engines” [J. Appl. Phys. 89, 1518 (2001)],” Journal of Applied Physics, vol. 89, no. 2, pp. 1520–1521, 2001. [53] L. A. Arias-Hernandez,´ G. Ares De Parga, and F. Angulo- Brown, “A variational ecological-type optimization of some thermal-engine models,” Open Systems and Information Dynamics, vol. 11, no. 2, pp. 123–138, 2004. [54] G. Pollarolo and L. Sertorio, “Energy and entropy balance for a black piecewise homogeneous planet,” Il Nuovo Cimento C, vol. 2, no. 3, pp. 335–351, 1979. [55] A. De Vos and P.van der Wel, “The efficiency of the conversion of solar energy into wind energy by means of Hadley cells,” Theoretical and Applied Climatology, vol. 46, no. 4, pp. 193– 202, 1993. [56] A. DeVos and G. Flatter, “The maximum efficiency of the conversion of solar-energy into wind energy,” American Jour- nal of Physics, vol. 59, pp. 751–754, 1991. [57] A. Raval and V.Ramanathan, “Observational determination of the greenhouse effect,” Nature, vol. 342, no. 6251, pp. 758–761, 1989. [58] V. Lucarini, “Thermodynamic efficiency and entropy production in the climate system,” Physical Review E, vol. 80, no. 2, Article ID 021118, 5 pages, 2009. [59] A. DeVos and P. van der Well, “Endoreversible models for the conversion of solar energy into wind energy,” Journal of Non- Equilibrium Thermodynamics, vol. 17, pp. 79–89, 1992. [60] M. R. Gustavson, “Limits to wind power utilization,” Science, vol. 204, no. 4388, pp. 13–17, 1979. [61] S. Ozkaynak, S. Goktun, and H. Yavuz, “Finite-time thermodynamic analysis of a radiative heat engine with internal irreversibility,” Journal of Physics D, vol. 27, no. 6, pp. 1139– 1143, 1994. [62] J. Chen, “Maximum power output and maximum efficiency of an irreversible Carnot heat engine,” Journal of Physics D, vol. 27, no. 6, pp. 1144–1149, 1994. [63] S. Velasco, J. M. M. Roco, A. Medina, J. A. White, and A. Calvo Hernandez,´ “Optimization of heat engines including the saving of natural resources and the reduction of thermal pollution,” Journal of Physics D, vol. 33, no. 4, pp. 355–359, 2000. [64] L. Chen, C. Wu, and F. Sun, “Finite time thermodynamic optimization or entropy generation minimization of energy systems,” Journal of Non-Equilibrium Thermodynamics, vol. 24, no. 4, pp. 327–359, 1999. [65] G. Ares De Parga, F. Angulo-Brown, and T. D. Navarrete- Gonzalez,´ “A variational optimization of a finite-time thermal cycle with a nonlinear heat transfer law,” Energy, vol. 24, no. 12, pp. 997–1008, 1999. [66] R. Srianand, P. Petitjean, and C. Ledoux, “The microwave background temperature at the redshift of 2.33771,” Natur, vol. 408, pp. 931–934, 2000. [67] R. T. Pierrehumbert, “Infrared radiation and planetary temperature,” Physics Today, vol. 64, no. 1, pp. 33–38, 2011. [68] C. Goldblatt, M. W. Claire, T. M. Lenton, A. J. Matthews, A. J. Watson, and K. J. Zahnle, “Nitrogen-enhanced greenhouse Hindawi Publishing Corporation Advances in Astronomy Volume 2012, Article ID 519852, 7 pages doi:10.1155/2012/519852

Research Article Tendency of Discreteness of the Solar Amplitude and Intercycle Relatedness

Akio Yoshida1 and Ryan Sayre2

1 Center for Integrated Research and Education of Natural Hazards, Shizuoka University, 836 Ohya, Suruga-ku, Shizuoka 422-8529, Japan 2 Department of Anthropology, Yale University, P.O. Box 208105, New Haven, CT 06520, USA

Correspondence should be addressed to Akio Yoshida, [email protected]

Received 13 December 2011; Revised 21 January 2012; Accepted 17 February 2012

Academic Editor: J. P. Rozelot

Copyright © 2012 A. Yoshida and R. Sayre. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

We suggest that the average of the sunspot number (SSN) over a cycle oﬀers a more appropriate index than the maximum value of the SSN in the evaluation of the activity of solar cycles. We then show that the average SSN has a tendency to take discrete values, that is, integral multiples of 20. This remarkable ﬁnding is supported by the fact that SSNs around the maximum are likely to take some particular values. Further, it is shown that there exists a positive correlation in the amplitude between even-numbered cycles and succeeding odd-numbered cycles and an inverse correlation between (2n +1)cyclesand(2n +4)cycleswheren represents an integer. If these two correlations are combined, it turns out that there exist two mutually independent series of cycles which do not mix or merge.

1. Introduction highest when cycles are divided at a point three years before the minimum. These findings suggest that the SSN in the The solar cycle, that is, the waxing and waning of solar final several years of a cycle may include some critical activity over periods of roughly 11 years, is usually measured information about the amplitude of the following cycle. We by increases and decreases in the sunspot number (SSN). By consider this problem in Section 4 where some more relevant convention, the maximum SSN has been taken as represen- observational facts are presented. tative of a given cycle’s amplitude. The minimum, in turn, The main aim of this paper is to introduce two intriguing has been taken to serve as a cycle’s starting and ending points. and somewhat surprising behaviors made visible when one Here we show that the average SSN over a cycle is well corre- takes the average SSN as the amplitude of the solar cycle. We lated with the maximum SSN in the cycle and propose that first show that the amplitude tends to take discrete values. the former quantity offers a more appropriate index in the We then go on to discuss an interrelatedness of cycles which evaluation of the activity of solar cycles. we believe to have potential implications for the long-range In a previous study we showed that the correlation predictability of solar activity. between the monthly smoothed SSN and the maximum SSN of the succeeding cycle is highest for the SSN at a point three yearsbeforetheminimum[1] In this paper, it is shown that 2. Discreteness of the Amplitude of this proves also to be the case for the monthly smoothed Solar Cycles SSN and the average SSN. That is, the correlation coefficient between the average SSN over a cycle and the smoothed SSN The idea that the average SSN over a cycle may be more at a dividing point becomes largest when cycles are cut at appropriate than the maximum SSN in the evaluation of the a point three years before the minimum. The correlation activity of solar cycles occurred to us when we observed between the average SSN and the maximum SSN is also a diagram depicting monthly smoothed sunspot numbers 2 Advances in Astronomy

250 19 CC: 0.964 21 250 200 3 4 8 9 11 18 22 2 15 17 20 23 150 1 7 10 16 5 6 1213 14 200 Sunspot number 50 0 150 1750 1800 1850 1900 1950 2000 100 Year

Maximum SSN Maximum 50 Figure 1: Monthly smoothed sunspot number since 1750. Numer- als in the map indicate cycle number. 0 0 20406080100 Average sunspot number (a) ff since 1750, which showed significant di erence in the pattern CC: 0.972 of change around the maximum, with steep peaks in some 250 cycles, and more rounded peaks in others (Figure 1). Data 200 related to the monthly smoothed SSN was obtained from the Solar Influence Data Analysis Center (http://www.sidc.be/ 150 sunspot-data/). In this paper the maximum or the minimum 100 SSN means the maximum or minimum monthly smoothed Maximum SSN Maximum 50 SSN, and in cases in which the same value succeeds twice or 0 more, the last one is taken to specify the point where the solar 0 20 40 60 80 100 activity becomes a maximum or a minimum. Average sunspot number Figure 2(a) shows scatter plots between the maximum SSN and the average SSN over individual solar cycles when (b) the cycles are divided at the minimum. Figure 2(b) shows Figure 2: (a) Peak sunspot number versus average sunspot number that when the cycles are divided at a point three years before when solar cycle is divided at the minimum. (b) is the same as the minimum. Note that the correlation coefficient between (a); however the dividing point is set at three years before the the maximum SSN and the average SSN is larger in the latter minimum. CC on the top right-hand side of each map represents case. In fact, the correlation coefficient when solar cycles are the correlation coefficient. divided at the minimum and at points one, two, three, four, and five years before the minimum is 0.964 (0.916, 0.984), 0.966 (0.921, 0.985), 0.970 (0.929, 0.987), 0.972 (0.934, 0.988), 0.968 (0.923, 0.986), and 0.940 (0.862, 0.975), respec- CC: 0.935 tively, where numerals in parentheses indicate lower and 250 upper limits of the 95% confidence interval of the correlation 200 ffi ffi coe cient. Consequently, the largest correlation coe cient is 150 obtained when solar cycles are divided at a point three years before the minimum, though those values do not differ much 100 from each other. Figure 3 shows similar correlation between SSN Maximum 50 the sum of the SSN over a cycle and the maximum SSN. The 0 correlation coefficient when cycles are divided at the mini- 0 2000 4000 6000 8000 10000 12000 mum (Figure 3(a)) is 0.935 (0.851, 0.972) and the correlation Sum of sunspot number ffi coe cient when cycles are divided at a point three years (a) before the minimum (Figure 3(b)) is 0.919 (0.815, 0.965), CC: 0.919 respectively. Numerals in parentheses indicate lower and 250 upper limits of the 95% confidence interval of the correlation coefficient. It is interesting that the correlation when cycles 200 are divided at the minimum is better than the correlation 150 when cycles are divided at a point three years before the 100 minimum in this case. This notwithstanding, for every case of the dividing point, the correlation coefficient between SSN Maximum 50 the maximum SSN and the sum of the SSN is smaller com- 0 0 2000 4000 6000 8000 10000 12000 pared to that between the maximum SSN and the average SSN. This result demonstrates that the average SSN rather Sum of sunspot number than the sum of the SSN is a more appropriate quantity for (b) representing the amplitude of the solar cycle. Figure 3: (a) and (b) are the same as Figures 2(a) and 2(b) except Similar to the correlation between the average SSN and that sum of sunspot number over a cycle is taken instead of the the maximum SSN, the best correlation between the average average sunspot number. SSN and the SSN at the dividing point is obtained when solar cycles are divided at a point three years before the minimum. Advances in Astronomy 3

Figure 4(a) shows scatter plots between the minimum SSN CC: 0.783 and the average SSN over individual solar cycles when the 100 cycles are divided at the minimum. Figure 4(b) shows that 80 between the SSN at a point three years before the minimum 60 and the average SSN when the cycles are divided at the point. The correlation coefficient between the minimum 40 SSN and the average SSN divided at the minimum is 0.783 SSN Average 20 (0540, 0.906), while that between the SSN at a point three 0 years before the minimum and the average SSN over a cycle 02468101214 divided at the same point is 0.890 (0.749, 0.954), where SSN at the minimum numerals in the parentheses show lower and upper limits (a) of the 95% confidence interval of the correlation coefficient. CC: 0.890 The correlation coefficient when the dividing point is taken 100 at a point one year, two years, three years, four years, and 80 five years before the minimum is 0.706 (0.414, 0.866), 0.752 (0.493, 0.889), 0.890 (0.749, 0.954), 0.871 (0.715, 0.944), 60 and 0.829 (0.632, 0.925), respectively. Note that the best 40 correlation is again obtained when solar cycles are divided at SSN Average 20 a point three years before the minimum and that the value of 0 the correlation coefficient is nearly equal to the upper limit 0 1020304050607080 ffi of the 95% interval of the correlation coe cient obtained SSN at three-year prior to the minimum when cycles are divided at the minimum, suggesting that a (b) point three years before the minimum is more appropriate than the minimum as the cycle’s ending and starting points. Figure 4: (a) Average sunspot number divided at the minimum Here, we would like to add that, for each of the cases, the versus the minimum sunspot number. (b) Average sunspot number previously given correlation coefficient between the SSN at divided at a point three years before the minimum versus the the dividing point and the average SSN is larger than the sunspot number at the dividing point. CC on the top right-hand correlation coefficient that was obtained between the SSN at side of each map represents the correlation coefficient. Outliers the dividing point and the maximum SSN in the following plotted by white circles in the maps are omitted in the calculation ffi cycle [1]. of the correlation coe cient. We take all of these results to suggest that the average SSN over the course of a cycle is a proper quantity for representing the amplitude of a cycle and the point three years prior to activity can take a random continuous value, the statistical the minimum may be the most appropriate point at which probability of this occurring is calculated to be as small as 4.6 we define a cycle beginning/ending point. Although the latter × 10−3. This probability is so small that the hypothesis that maintenance does not accord with the conventional idea, we the amplitude takes a continuous value seems to be denied think that something meaningful should exist in the previous assuredly. However, it is to be noted that the deduction is results where the largest correlation coefficient is obtained dependent on the presupposition itself. If the assumption when a cycle is divided at a point three years before the is not correct, that is, in case the SSNs are liable to take minimum. We consider their implications in Section 4. some particular value and its multiples, the conclusion would Taking the average SSN as representative of the amplitude become a different one. We show next, however, that that is of a solar cycle, we now show that a number of intriguing most improbable. phenomena become visible. We use in the following analysis Figure 6 shows the number of months that enter in each the average SSN obtained by dividing cycles at a point three bin of SSN with an interval of 5, separating the cycle into years before the minimum. However, the overall results do three periods, around the maximum (two years before each not change if we use the average SSN calculated by taking the maximum to two years after the maximum), the rising phase, dividing point at the minimum. and the decaying phase. Note the intriguing distribution of Figure 5(a) illustrates the cumulative number of cycles in the number in Figure 6(a). The SSN at the period of the order of the amplitude over the 23 cycles since 1750. One can solar maximum swarms around several particular values, note a tendency of the average SSN to distribute around the centered at the bin of 60–65, 105–110, and 145–150. No values of 40 and 60, that is, multiples of 20 from the map. doubt this tendency should afford the basis for our finding This tendency is clearly visible when the cumulative number that the average SSN takes the value around multiples of of cycles is plotted in order of the difference of the average 20. It is to be noted that such a feature of swarming is not SSN from the nearest multiple of 20 (Figure 5(b)). Note that so clear for the SSN in other periods, that is, in the rising the clustering of the plotted points is hardly seen when the and decaying phases (Figures 6(b) and 6(c)), though small maximum SSN is taken as the representative of the amplitude bumps are observed around the bin of 45–50 for the rising (Figure 5(c)). We can see in Figure 5(b) that 12 of the total 23 phase and around the bins of 25–30 and 65–70 for the points fall in the range of −2.5 to 2.5 (i.e., one fourth of the decaying phase. For these phases, the fact that the ratio of potential range). If it is assumed that the amplitude of solar the SSN takes the value 5–10 or 10–15 is notable. We think 4 Advances in Astronomy

25 120 20 100 80 15 60 10 40 of cycles 5 20 Number ofNumber months in maximum periodsin maximum Cumulative number Cumulative 0 0 5 20 35 50 65 80 95 110 125 140 155 170 185 200 0 20406080100 Sunspot number Average sunspot number (a) (a) 120 25 100 20 80 15 60 40 10 of cycles in rising phases 20 5 ofNumber months 0 Cumulative number Cumulative 0 5 20 35 50 65 80 95 110 125 140 155 170 185 200 −10 −7.5 −5 −2.5 0 2.5 5 7.5 10 Sunspot number Diﬀerence of average SSN from multiples of 20 (b) (b) 180 160 25 140 120 20 100 80 15 60 40

of cycles 10 in decaying phases in decaying

Number ofNumber months 20 5 0

Cumulative number Cumulative 5 20 35 50 65 80 95 110 125 140 155 170 185 200 0 Sunspot number 0 50 100 150 200 250 (c) Maximum sunspot number (c) Figure 6: Frequency distribution of monthly smoothed SSN during (a) periods at solar maximum (the period from two years before Figure 5: (a) Cumulative number of cycles in order of the average each of the maximums of the SSN to two years after the maximum), sunspot number over a cycle. (b) Cumulative number of cycles in (b) periods of rising phase (the period from the minimum SSN to order of the diﬀerence of the average sunspot number from the two years before the beginning of the solar maximum period), and nearest multiple of 20. (c) Cumulative number of cycles in order of (c) periods of decaying phase (the period from the end of each of the maximum sunspot number. In Figures 5, 7, 8,and9 the average the solar maximum periods to the minimum SSN), respectively. The sunspot number is obtained by dividing the solar cycle three years abscissa and the ordinate represent the monthly SSN and number of before the minimum. months, respectively.

that the aforementioned facts, especially the bumps in the observed for both cases, but the correlation in the former distribution seen in Figure 6(a), assure us that the tendency case is much better, carrying correlation coefficient of 0.985 of discreteness of solar amplitude does not stem from an (lower and upper limits of the 95% confidence interval are artificial cause such as the procedure to calculate the monthly 0.917 and 0.997, resp.), though included are a few outliers smoothed SSN, but is characteristic of the solar activity at its that are selected rather subjectively by an inspection. On the maximum period. other hand, the relationship between the average SSN of an even-numbered cycle and the average SSN of the preceding 3. Intercycle Relatedness of the Amplitude odd-numbered cycle is very weak, for which the correlation coefficient is 0.537 whose lower and upper limits of the The scatter plots in Figures 7(a) and 7(b) show the relation 95% confidence interval are −0.093 and 0.860, respectively between the average SSN of odd-numbered solar cycles and (Figure 7(b)). That is, the correlation is apparently observed that of their preceding even-numbered cycles (i.e., between in the even-odd pairs of cycles but is obscure in the odd-even the average SSN for (2n + 1) cycles and that for 2n cycles), pairs. The P value in the null hypothesis test is 6.57−7 for the and the relation between the average SSN of odd-numbered correlation of the even-odd pairs, while that for the odd-even cycles and that of their succeeding even-numbered cycles, pairs is 0.083. Therefore, the former correlation is accepted (i.e., between the average SSN for (2n + 1) cycles and that at a very high significance level, but the latter correlation is for (2n + 2) cycles), respectively. A positive correlation is rejected at the significance level of 5%. Advances in Astronomy 5

CC: 0.985 CC: 0.956 100 100 80 80 +1 n 60 60 40 40 Average SSN Average of cycle 2 Average SSN Average 20 of cycle even 20 0 0 0 20406080100 0 20406080 Average sunspot number of cycle 2n SNN at a point 3 years prior to the minimum before even cycle (a) CC: 0.537 (a) 100 CC: 0.738 80 100 +2

n 60 80 40 60 Average SSN Average of cycle 2 20 40 of odd cycle Average SSN Average 0 20 0 20406080100 0 Average sunspot number of cycle 2n +1 0 20406080 (b) SNN at a point 3 years prior to the minimum before odd cycle Figure 7: (a) Average sunspot number of odd-numbered solar (b) cycles versus that of the preceding even-numbered cycles showing correlation between average SSN of solar cycle 2n andthatofsolar Figure 8: (a) Average sunspot number divided at a point three years cycle (2n +1),wheren represents an integer. (b) is the same as before the minimum versus the sunspot number at the dividing (a) but showing average sunspot number of even-numbered solar point for even numbered cycles. (b) is the same as (a) but showing cycles (2n + 2) versus that of the preceding odd-numbered cycles for odd numbered cycles. (2n +1).

CC: −0.697 100 We note here an interesting finding that may indicate 80 intrinsic difference between even-numbered cycles and odd- +4 numbered cycles. Figures 8(a) and 8(b) show relationships n 60 between the SSN at a point three years before the minimum 40 Average SSN Average and the average SSN (see Figure 4) for even-numbered cycles of cycle 2 20 and for odd-numbered cycles, respectively. It is clear that 0 the relationship seen in Figure 8(a) is much stronger. The 0 20406080100 correlation coefficient for even-numbered cycles is 0.956 Average sunspot number of cycle 2n +1 (0.833, 0.989), while that for odd-numbered cycles is 0.738 (0284, 0.921), where numerals in parentheses show lower Figure 9: Scatter plot between the average sunspot number of and upper limits of the 95% confidence interval. It is to odd-numbered cycles (abscissa) and that of the succeeding even- be noted that no outliers that are observed in Figure 7(a) numbered cycle after the next cycle (ordinate), demonstrating an n exist in Figure 8(a).TheP value in the null hypothesis test inverse relationship between the average sunspot number for (2 + n is 9.76−7 for the correlation between the SSN at a point 4) cycles and that for (2 + 1) cycles. An outlier indicated by a white three years before the minimum and the average SSN of the circle is omitted when the least-regression line is drawn. succeeding even cycle, while that for the correlation between the SSN at a point three years before the minimum and the average SSN of the succeeding odd cycle is 0.0048. seen when the maximum SSN is taken instead of the average A still more intriguing relationship, shown in Figure 9, SSN. However, the correlations are not as strong as when the indicates that the average of the SSN for (2n + 1) cycles average SSN is taken. We also add that no other significant is related to those for (2n + 4) cycles, where n represents intercycle relatedness besides those two shown in Figures 7(a) an integer. Although the correlation is not very strong that and 9 has been found. the correlation coefficient is −0.697 (−0.062, −0.930), the When the positive correlation between the average SSN P value in the null hypothesis test is 0.030 indicating that for 2n cycles and that for (2n + 1) cycles and the negative existence of the correlation cannot be rejected at the signifi- correlation between the average SSN for (2n + 1) cycles and cance level of 5%. We note here that the previously described that for (2n + 4) cycles are combined, it turns out that the intercycle relatedness shown in Figures 7(a) and 9 can be cycles 1, 4, 5, 8, 9, 12, 13, 16, 17, 20, 21, and 24 are interrelated 6 Advances in Astronomy on the one hand and the cycles 2, 3, 6, 7, 10, 11, 14, 15, 18, significant which is indicative of the amplitude of the next 19, 22, and 23 reveal interrelatedness on the other. These two cycle comes out on the surface of the sun in the final stage of series of cycles do not mix or merge but, rather, constitute a solar cycle. two independent series. We shortly comment here that the intensity of the interplanetary magnetic field which is directly related to the geomagnetic activity decreased parallel with the SSN in the 4. Discussion last three years of solar cycle 23 [1]. Based on the finding they argued that the SSN in the last stage of the solar cycle The tendency of discreteness of the amplitude of solar cycle is is a good proxy of the poloidal magnetic field in the solar most astonishing. The fact that the SSNs are likely to swarm corona that should be the seed of the toroidal field of the sun near particular values around the peak of the solar cycle in the next solar cycle and that the physical ground of the indicates that the tendency is not an artifact produced by the empirically well-known relationship between the minimum formula to calculate the SSN. Although we cannot explain geomagnetic activity and the amplitude of the next solar the physical meaning of this remarkable finding at present, cycle (e.g., [4]) might be given by the supposition. we think that our result imposes an important and serious A simple and reasonable way to explain both these constraint on future theoretical studies. observations as well as our finding that the correlation Another notable finding is the intercycle relatedness of between the average SSN over a cycle and the SSN at a point the amplitude of solar cycles in which cycles are separated three years before the minimum is strongest is the hypothesis into two series that never mix nor merge. This remarkable that two cycles in the SSN overlap temporally with a phase result is derived from the positive correlation between the lag as suggested by Cameron and Schussler¨ [11]. Actually, average SSN for even cycles and that for the succeeding we see in the so-called butterfly diagram that high-latitude odd cycles and the negative correlation between the average sunspots of the new cycle begin to appear when the old cycle SSN for (2n + 1) cycles and that for (2n +4)cycles.Afew is still in progression in low latitudes, and we have known outliers observed in these correlations may not be due to the that stronger cycles rise more quickly toward their sunspot poor quality of early SSN. In fact, one of the outliers in the maximum [12]. Cameron and Schussler¨ [11], demonstrating correlation between the average SSN of even cycles and that that when the following cycle is strong, the point at the for the succeeding odd cycles is a pair at cycle 22 and cycle 23 minimum SSN actually moves to an earlier time making the (two other pairs are cycles 4-5 and cycles 8-9). At present, we length of the preceding cycle shorter, suggested that the faster do not have any idea about the appearance of outliers in the rise of a stronger following cycle which overlaps with the correlation. However, we would like to emphasize here that. preceding cycle leads to an earlier sunspot minimum than if those outlier pairs are excepted, the amplitude of odd cycles in the case of a weaker follower. The observational fact that tends to be larger than that of the preceding even cycles (see the maximum SSN is well correlated with the increasing rate also Figure 1) and the ratio between the amplitudes is nearly at the rising phase of the cycle [13] would seem to support the same (around 1.2). their postulation. We showed in this paper that the correlation between the maximum SSN and the average SSN as well as the correlation between the average SSN of the next cycle and the SSN at the 5. Summary dividing point becomes the best when solar cycles are divided at a point three years before the minimum. Why three years We have shown that the correlations between the average SSN before the minimum? and the maximum SSN of the cycle as well as between the It has been pointed out that the length of a solar cycle SSN at the dividing point of a solar cycle and the average is correlated with the maximum SSN in the succeeding cycle of the SSN over the following cycle are strongest when the which affords us an empirical means to predict the amplitude dividing point is set at three years before the minimum SSN. of the next solar cycle [2, 3]. Yoshida and Yamagishi [1] Following is our remarkable findings when the average of the disclosed that what is actually essential in the correlation is SSN is taken as representative of the solar amplitude. the time for the SSN to fall from a value of 50 to its minimum (1) The values of the average of the SSN show a tendency value, not the whole length of the period; that is, the really of discreteness to fall around multiples of 20. The tendency significant parameter for the predictability is the decreasing is supported by the observation that SSNs near the solar rate of the SSN in the last several years before the minimum. maximum are likely to take around some particular values. On the other hand, it has long been known empirically (2) A positive relationship is seen between the average that the magnitude of a global geomagnetic index during the of the SSN of even-numbered cycles and that of the declining phase of solar activity serves as a useful predictor succeeding odd-numbered cycles, but the relationship is of the succeeding solar cycle amplitude [4–7]. Further, it has obscure between the pair of odd-numbered cycles and the been discovered that the amplitude of the succeeding solar succeedingevennumberedcycles. cycle can be predicted based on (1) the polar magnetic field (3) On the other hand, an inverse relationship is seen on the sun during the three years prior to the minimum between the average of the SSN for (2n + 1) cycles and that SSN [8–10] and (2) the azimuthally averaged radial magnetic for (2n + 4) cycles. field at the surface of the sun in the late stages of a solar The aforementioned two relationships separate solar cycle [11]. All these observations suggest that something cycles into two mutually independent series. Advances in Astronomy 7

Acknowledgments The authors thank the SIDC-team, World Data Center for the Sunspot Index, Royal Observatory of Belgium, for the smoothed monthly mean SSNs. Critical reading by J. P. Rozelot and A. Kilcik improved the paper.

References

[1] A. Yoshida and H. Yamagishi, “Predicting amplitude of solar cycle 24 based on a new precursor method,” Annales Geophys- icae, vol. 28, no. 2, pp. 417–425, 2010. [2] S. Watari, “Forecasting solar cycle 24 using the relationship between cycle length and maximum sunspot number,” Space Weather, vol. 6, no. 12, Article ID S12003, 2008. [3] D. H. Hathaway, R. M. Wilson, and E. J. Reichmann, “Group sunspot numbers: sunspot cycle characteristics,” Solar Physics, vol. 211, no. 1-2, pp. 357–370, 2002. [4] A. I. Ohl, “Forecast of sunspot maximum number of cycle 20,” Solice Donie, vol. 9, p. 84, 1966. [5] D. H. Hathaway and R. M. Wilson, “Geomagnetic activity indicates large amplitude for sunspot cycle 24,” Geophysical Re- search Letters, vol. 33, no. 18, Article ID L18101, 2006. [6] R. P. Kane, “A preliminary estimate of the size of the coming solar cycle 24, based on Ohl’s precursor method,” Solar Physics, vol. 243, no. 2, pp. 205–217, 2007. [7] N. J. Bhatt, R. Jain, and M. Aggarwal, “Prediction of the maximum amplitude and timing of sunspot cycle 24,” Solar Physics, vol. 260, no. 1, pp. 225–232, 2009. [8]K.H.Schatten,P.H.Scherrer,L.Svalgaard,andJ.M.Wilcox, “Using dynamotheory to predict the sunspot number during solar cycle 21,” Geophysical Research Letters, vol. 5, p. 411, 1978. [9] K. Schatten, “Fair space weather for solar cycle 24,” Geophysical Research Letters, vol. 32, no. 21, Article ID L21106, pp. 1–4, 2005. [10] L. Svalgaard, E. W. Cliver, and Y. Kamide, “Sunspot cycle 24: smallest cycle in 100 years?” Geophysical Research Letters, vol. 32, no. 1, pp. 1–4, 2005. [11] R. Cameron and M. Schussler,¨ “Solar cycle prediction using precursors and ﬂux transport models,” Astrophysical Journal, vol. 659, no. 1, pp. 801–811, 2007. [12] M. Waldmeier, “Neue eigenshaften der sonnenﬂeckenkurve,” Astronomische Mitteilungen Zurich¨ , vol. 14, pp. 105–130, 1935. [13] R. J. Thompson, “The rise of solar Cycle number 22,” Solar Physics, vol. 117, no. 2, pp. 279–289, 1988. Hindawi Publishing Corporation Advances in Astronomy Volume 2012, Article ID 735879, 9 pages doi:10.1155/2012/735879

Research Article Rapid Disappearance of Penumbra-Like Features near a Flaring Polarity Inversion Line: The Hinode Observations

B. Ravindra1 and Sanjay Gosain2, 3

1 Indian Institute of Astrophysics, Koramangala, Bangalore 560034, India 2 Udaipur Solar Observatory, Dewali, Badi Road, Udaipur 313001, India 3 National Solar Observatory, 950 N Cherry Avenue, Tucson, AZ 85719, USA

Correspondence should be addressed to B. Ravindra, [email protected]

Received 13 January 2012; Revised 2 March 2012; Accepted 3 March 2012

Academic Editor: J. Javaraiah

Copyright © 2012 B. Ravindra and S. Gosain. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

We present the observations of penumbra-like features (PLFs) near a polarity inversion line (PIL) of flaring region. The PIL is located at the moat boundary of active region (NOAA 10960). The PLFs appear similar to sunspot penumbrae in morphology but occupy small area, about 6 × 107 km2, and are not associated with sunspot or pore. We observed a rapid disappearance of the PLFs after a C1.7 class flare, which occurred close to the PIL. The local correlation tracking (LCT) of these features shows presence of horizontal flows directed away from the end-points of the PLFs, similar to the radial outward flow found around regular sunspots, which is also known as the moat flow. Hard X-ray emission, coincident with the location of the PLFs, is found in RHESSI observations, suggesting a spatial correlation between the occurrence of the flare and decay of the PLFs. Vector magnetic field derived from the observations obtained by Hinode spectropolarimeter SOT/SP instrument, before and after the flare, shows a significant change in the horizontal as well as the vertical component of the field, after the flare. The weakening of both the components of the magnetic field in the flare interval suggests that rapid cancellation and/or submergence of the magnetic field in PLFs occurred during the flare interval.

1. Introduction found that a magnetic flux threshold above which penumbra forms is about 1–1.5 × 1020 Mx [3]. Well-developed sunspots have umbra surrounded by elon- Once the penumbra is formed it survives from hours to gated filamentary type of structures called penumbral fila- days exhibiting a variety of small-scale structures like dark ments. The magnetic field in the umbra is mostly vertical cores inside penumbral filaments, apparently propagating to the solar surface, while in the penumbra it is horizontally twisting structures, moving magnetic features to name a few. inclined. Further, the inclination of the penumbral magnetic Evershed flow [4], a mass flow directed radially outwards field shows an azimuthal variation, with channels of more from the sunspot along the penumbra, is observed in the horizontal field lying in between the channels of more photosphere, while inverse Evershed flow, directed towards vertical fields. This alternating inclination of penumbral field sunspot is observed in the chromosphere. The actual lifetime is also called “uncombed penumbra” and is well established of the penumbra depends upon the life of the sunspot, from the past observations [1]. The more horizontal compo- when the spot decays it gradually loses its penumbra, nent of the uncombed field is observed to harbor most of the becomes a “naked” sunspot, and finally fragments into pores. Evershed flow. Penumbrae form around pores abruptly with Moving Magnetic Features (MMFs [5]) are proposed as an increase in the magnetic field inclination at the boundary one of the candidates for the decay of sunspots. Once the [2]. Penumbral filament formation and Evershed flow occur sunspot decays, naturally the penumbra disappears. Decay of nearly simultaneously in pores [3], that is, as soon as the sunspots is studied in detail by Martinez Pillet [6]andfound penumbrae form the Evershed flow can be observed. It is that not all MMFs are related to the decay of sunspots. Bellot 2 Advances in Astronomy

Rubio et al. [7] have found that the absence of Evershed flow These magnetograms are used to study the magnetic field in penumbral field lines can raise the penumbral filaments parameters of the PLFs. to the chromosphere that can cause the disappearance of the penumbra at the photospheric level. Large flares can also cause the disappearance of the penumbra at the outer 3. Results boundary of the sunspots [8, 9]. It is believed that the field becomes more vertical at the outer edge of sunspot as the We focus our study on the small-scale penumbra-like feature overall active region field collapses towards the flaring PIL located at the moat boundary of the active region NOAA [10], which causes disappearance of penumbrae. 10960 observed from 6-7th June, 2007. The AR NOAA 10960 Inthispaper,wereportonanewtypeofpenumbra- consists of two large sunspots of negative polarity, a plage like features (PLFs) that are not associated with sunspot. region of positive polarity, and several pores of either polarity Further, we use LCT method to study the horizontal flow (http://www.solarmonitor.org/). Two sunspots were aligned patterns around these structures. We then study the evolu- along the East-West direction at a latitude of 6◦ in the tion of PLFs in the photosphere, chromosphere, and vector southern hemisphere. During our observations of event, the magnetograms using the space-based data obtained from active region was close to the disk center (S06E05). Active Hinode/SOT and find that the structure rapidly disappears Region NOAA 10960 produced several B and C class flares during flare. In the forthcoming sections, we present details with a very few M class flares, and the largest one was of the G-band, Ca II H, spectropolarimetric data, and its observed on June 04, 2007, which was of M8.9 class. A few analysis. This is followed by the observational results on the of these events were studied in detail by Srivastava et al. [19] disappearance of PLFs. Possible explanation for the flare- and Kumar et al. [20], where they have observed the sunspot related disappearance of PLFs is discussed in the last section. rotation and kink instability that lead to the initiation of the flare. During Hinode observations, there was one C1.7 class flare on June 06, 2007, at 23:31 UT, and it occurred 2. Data and Analysis close to the polarity inversion line (PIL marked in Figure 2). On June 07, 2007 between 00:00 to 05:00 UT there were The space-based telescope, Solar Optical Telescope (SOT two B-class flares and their magnitude was B7.6 and B6.6 [11]) onboard Hinode, obtains images of the Sun at an peaking at 00:45 and 01:40 UT, respectively. This event was unprecedented resolution of about 0.2 of the photo- well observed by the Hinode/SOT at high cadence (21 sec.) sphere and chromosphere. The broadband filter imager in Ca II H band with some small data gaps in-between. It was (BFI) instrument on the SOT produces images in several also observed in G-band at a slower cadence of about 100 sec. wavelengths with the 3–8 A˚ bandwidth filters. In this study, Figures 1(a) and 1(b) show the sunspot in the active we have used filtergrams observed at 4305 A˚ (G-band) and region at the photospheric and chromospheric level. 3968.5 A˚ (Ca II H). We have used the filtergrams observed Penumbra-like features (PLFs) are observed close to the in these wavelengths from June 06, 2007 at 15:00 UT to June sunspot and it is marked with a box. An enlarged portion 07, 2007 05:00 UT. The data are corrected for dark current, of boxed region is shown next to it. Close to the PLFs pixel-to-pixel gain variations, hot and dead pixels. The Ca II region, three pores are visible which are quite separated H data are corrected for the wavelength-dependent pixel size from the PLFs and are not like the pores which form with the G-band as a reference. These calibrated data sets are rudimentary penumbra. The same structure is also visible rigidly aligned with the first image in the time series using in the chromospheric image taken in Ca II H wavelength. a 2-dimensional cross-correlation algorithm. The alignment The region of interest that is shown in box is magnified and of the images is good to a subpixel accuracy. The aligned data displayed along side. Clearly, in the magnified image, one sets are passed through a subsonic filter with a cutoff value of can see a detailed view of the PLFs. They exhibit about 10 4kms−1 to remove the effect of acoustic oscillations [12]. linear size and appear very much like the sunspot penumbra. The spectro-polarimeter (SOT/SP [13]) instrument is The AR 10960 was a fast evolving region and started to one of the back-end instruments of SOT onboard Hinode disrupt from June 04, 2007 (see: http://solar-b.nao.ac.jp/QL- satellite, makes maps of the active region by spatial scanning movies/movie sirius/2007/06/04/hsc ql20070604 e.shtml). and obtains Stokes I, Q, U, and V spectra in Fe I 6301.5 The formation process of the PLFs could not be clearly and 6302.5 A˚ lines. A fast-mode raster scan with 980 steps identified as the cadence of the observations is intermit- atastepsizeof0.295 along the scanning direction and tent and the field-of-view of Hinode SOT is also limited. 0.317/pixel resolution along the slit direction made a raster However, here we concentrate more on two aspects (i) brief image with a field-of-view of about 290 × 162. The Stokes investigation of the properties of the new PLFs identified signals are calibrated using standard Solarsoft pipeline for in Hinode G-band observations and (ii) their evolution in SP. The magnetic fields are obtained by using an inversion relation to recurrent flares. The search for the origin or scheme based on the Milne-Eddington algorithm [14, 15]. formation of PLFs would require a fully dedicated high- The ambiguity in the azimuth is resolved based on the resolution observational campaign, which we plan to do in minimum energy algorithm [16, 17]. Later, the magnetic near future either with Hinode SOT or ground-based high- field vector has been transformed to the disk center [18]. resolution telescopes equipped with adaptive optics. The resulting vertical (Bz) and transverse (Bt)magnetic Interestingly, the PLFs are located next to the polarity fieldshavemeasurementerrorsof8Gand30G,respectively. inversion line (PIL) with PLFs filaments aligned nearly Advances in Astronomy 3

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Figure 1: (a) A sample image is obtained from Hinode/SOT using G-band ﬁlter. The boxed region shows the region of interest. A magniﬁed view of the region of interest is shown on the right side of it. (b) Same as left side image but obtained in the wavelength of 3968 AofCaIIH.˚ The scales are in unit of pixel.

parallel to the PIL (Figure 2). Figures 2(a) and 2(b) shows the 500 500 N PLFs in line-of-sight magnetogram and continuum images respectively. Both the images are obtained from SOT/SP. A W thin dark line in between the positive and negative polarity 400 400 is shown to represent the position of the PIL. Close to this PIL, numerous B and C-class flares were observed over a couple of days. The PLFs (location “L”, shown by an arrow in Figure 2) have positive polarity and is located close to the 300 300 PIL. Here, the magnetic field in the lower part of PLFs (close to the arrow-head) is more inclined leading to smaller signal in line-of-sight component of the magnetic fields. In the 200 N 200 magnetogram, it is very clear that the region PLFs is located N in the moat boundary of the negative polarity sunspot. P P 100 100 L 3.1. Evolution of the PLFs. The evolution of the PLFs at L the photospheric and chromospheric level is depicted in Figure 3. The PLFs in G-band and Ca II H images are shown 0 0 alternatively for near simultaneous time intervals. On June 0 50 100 150 200 0 50 100 150 200 06, at 16:00 UT the PLFs is clearly visible in the photospheric (a) (b) as well as in the chromospheric images. The PLFs appears to have very small pore at one end and, however, compared to the size of PLFs it is very tiny, so the origin of PLFs cannot Figure 2: A map of line-of-sight component of the magnetic field (a) and the corresponding continuum image (b) obtained from be this tiny pore. Later, at 00:30 UT on June 07, 2007, it spectropolarimeter onboard Hinode on June 06, 2007 at 22:57 reduced its size drastically, and at 01:30 UT a small remnant UT. The arrow indicates the position of PLFs. P and N represent of it is visible in the photospheric images. A similar type of the positive and negative polarity regions. A dark line between evolution is observed in the chromospheric images, except negative and positive polarity represents the position of the polarity that some brightening can also be seen close to the PIL on inversion line. The scales are in unit of pixel. June 7, 2007.

3.2. Temporal Correlation. We then measured the area of the quiet sun intensity in the photosphere. This criterion is same PLFs quantitatively starting from 15:00 UT of June 06, 2007. for all the images. This method clearly picks the dark regions The area of the PLFs is measured from the G-band images. that contain not only the PLFs but also the pore regions. We adopted the following methodology to measure the area To select only the PLFs region, we then labeled the regions of the PLFs. We first smooth the image by 0.9 × 0.9 pixel which assign a unique number to the individually detected box to remove any small-scale intensity variations in the subregions. We use “label region.pro” function of IDL data time sequence of images. This small-scale variations in the analysis platform to do the labeling. Using this technique, intensity of images could occur due to residual oscillations we isolated the PLFs from rest of the region. Once the PLFs after filtering and residual flat-fielding errors. We then pick region has been isolated, by counting the number of pixels the pixels whose values smaller than 0.6 times the value of the we estimated the area of the PLFs. The variation of PLF’s 4 Advances in Astronomy

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Figure 3: The temporal evolution of the PLFs is shown in sequence of G-band and Ca II H images alternatively. The date and time of the image acquisition is shown on the top of each image. The numbers on the axes represent the pixel. area as a function of time is shown in Figure 4.Wehave is, between 22:13 and 23:31 UT on June 06, 2007. (ii) The also plotted the GOES X-ray flux below the areal plot for PLFs area started to decrease during the C1.7-class flare, and easy comparison. In the plot, we have drawn the vertical it reduced to almost 3/4th of its original size during the B7.6 lines to show the peak time of the three flares, which are class flare (second flare). (iii) After the B6.6-class flare (third observed close to the PIL. We notice the following features in flare), the size of the PLFs reduced drastically and eventually the evolutionary trend: (i) the PLFs area is almost constant, the entire PLFs disappeared. Thus, from these observations it about 6 × 107 km2 before the C1.7-class flare (first flare), that is clear that the decrease of PLFs area is cotemporal with the Advances in Astronomy 5

disappeared, we can observe a supergranular like outward ) 6 2 5 flow pattern, which is roughly of the same size as that of the km 7 4 PLFs. 10 In order to compare the flow fields in the PLFs with the × 3 2 penumbral filaments, we selected one region on the PLF and

Area ( Area 1 another on the sunspot penumbra, as shown in Figure 6(a) 16:00 18:00 20:00 22:00 00:00 02:00 with a white line. The LCT velocities are compared for June 06, 2007 both the regions and is shown in Figure 6(b). The velocity in the penumbra which is directed towards the umbra is (a) small, about 0.2 km s−1, and after the mid penumbra towards 10 the outer penumbra the velocity increases. This result is 2

− 8 similar to the observations of Sobotka, Brandt, and Simon (1999). The velocity is large near the outer penumbra, about 6 ) Wm −1 6 0.8 km s . On the other hand, the velocity in PLFs increases − 4 10 on either side of mid portion of the PLF and it is at minimum

× − 2 of about 0.2 km s 1 in the mid portion of the PLF. This (1 0 suggests that there are diverging flows from the middle 16:00 18:00 20:00 22:00 00:00 02:00 portion of PLFs. Clearly then there is a difference in the June 06, 2007 transverse field flow patterns in the PLF with respect to (b) penumbra associated with sunspot.

Figure 4: (a) The area of the PLFs is plotted as a function of time. (b) The GOES X-ray flux is plotted as a function of time. The dotted 3.4. Spatial Correlation. Hard X-ray flux is the indicator vertical lines from left to right side represent the peak time of C1.7, of the footpoint of the source of flare ribbons in the B7.6, and B6.6 class flares, respectively. chromosphere [24]. It also represents the thermal and nonthermal footpoints of the loops during microflares [25]. We overlaid the contours of hard X-ray fluxes in the energy duration of three recurrent flares, which are closely spaced in range from 6 to 12 and 12–25 keV from RHESSI on to time and located along the same PIL. The PLFs disappeared the G-band images. As the pointing is known to be good in about 2 hours after it starts to decay. There are data gaps for the MDI, the G-band images were coaligned with the in between the observations; however, a decreasing trend in MDI intensity images by overlying the contours of MDI PLFs area can be easily recognized. In Section 3.4, we also intensity image on the G-band image. The contours of hard study the spatial correlation between the flare brightening X-ray from RHESSI is overlaid on the coaligned HINODE and the location of PLFs using coaligned RHESSI X-ray G-band images (Figure 7). This kind of low resolution images. These observations suggest cospatiality between RHESSI contours overlaid upon the hi-resolution G-band these PLFs and the flare emission in X-ray. We discuss the and SOT/NFI images has been successfully used to locate possible relation in Section 4. the footpoints of the reconnecting loops in the corona (e.g., [26, 27]). Figure 7(a) shows the contour maps for the 6– 12 keV energy range, and Figure 7(b) is for 12–25 keV range. 3.3. Flow Fields in the PLFs. The penumbrae associated with These contours were plotted for the 40, 50, 60, 70, 80, and the sunspots exhibit an outflow and inflow that appear to 90% of the maximum counts in the corresponding hard X- originate from the mid portion of the penumbra [21]. In ray images. An observation of these contour maps shows that general, there is a radial outflow pattern around sunspots the contours are mainly concentrated near the region of PLFs which is also known as the moat flow. From high-resolution suggesting the spatial correlation between the flare location observations, it was found that these radial outflows in the and the PLFs. moat region appear only when penumbrae are present and are not seen in those parts of irregular sunspots where penumbrae are missing [22]. In order to examine the flows in 3.5. Vector Field Maps. Figures 8(a) and 8(b) show the vector and around the PLFs, we computed the horizontal flow fields magnetic fields before and after the flares, respectively. The using the local correlation tracking (LCT: [23]) technique. vector maps show an overlay of the horizontal component Figure 5 shows the flow fields in the PLFs region. Figure 5(a) of the magnetic field (represented by arrows, where the shows the flow field on June 06, before the C1.7 class flare length of the arrow is proportional to the magnitude of (first flare), and Figure 5(b) is obtained after the B6.6 class the horizontal field and the direction tells the direction flare (third flare). In Figure 5(a), the PLFs exhibit an outward of the horizontal field) upon the vertical magnetic fields flow, which appears to be originating in the mid portion of (represented as gray-scale image with overlaid contours). the PLFs. The flow is in general, directed away from the PLFs, In the map, the boxed region shows the PLFs location and a little similar to what one finds around sunspots. However, the contours are drawn at ±50 and 100 G levels of the Bz here the PLFs are not in a radial symmetry-like sunspots component of the magnetic fields. Comparison shows that and hence the associated flows are also nonsymmetric. On the Bz and Bt component of the magnetic field in the PLFs Figure 5(b), we notice that at the location where the PLFs location decreased substantially after the flare. 6 Advances in Astronomy

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Figure 9 shows the histogram representing the distribu- its tail up to 1200 G. After the flare, its strength has been tion of Bz and Bt components of the magnetic fields in the reduced to less than half of its value. This suggests that the region of PLFs. Figures 9(a) and 9(b) show the distributions magnetic field itself has decreased in this region. before and after the flare. The plot shows that a large amount B of t component is present in PLFs before the flare, and 4. Discussion it decreased substantially after the flare. A similar result is found for the Bz component of the magnetic fields. Before the We have focused on a new type of magnetic features in flare, the Bz and Bt components of the field in PLFs extended the photosphere near the PIL of a flaring active region, Advances in Astronomy 7

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Figure 8: Transverse field vectors overlaid upon the vertical component of the magnetic field. (a) Images are obtained before the C1.7 class flare, and (b) images are obtained after the PLFs decay. which we call as penumbra-like features (PLFs). These PLFs eventually develop as full sunspot penumbrae if the magnetic could be observed due to high spatial resolution of Hinode flux in the pore continues to grow. More detailed study of SOT. These features are interesting in the sense that they these features utilizing high-resolution imaging as well as are not associated with a pore or sunspot. It is generally spectro-polarimetry would shed more light on the formation seen that as pores grow larger they develop penumbrae and evolution of these features along with the magnetic abruptly, sometimes called rudimentary penumbrae, which and thermodynamic properties of these features. Also, it is 8 Advances in Astronomy

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Figure 9: (a) Histogram of the vertical component (Bz) and transverse component of the magnetic fields (Bt) are plotted for the PLFs obtained an hour before the flare. (b) Same as the (a) plot, but for the data obtained about two hours after the flare. The thick line corresponds to the histogram of transverse field strength and the dash dotted line corresponds to the histogram of vertical magnetic field strength. important to know what is the vertical structure of these ing of highly inclined fields near the PIL. Generally the PILs features, are these shallow or deep rooted, do they harbor are observed to have strong horizontal fields and often har- similar Evershed flows and show similar uncombed magnetic bor twisted fields (as evidenced in twisted filament structures structure as in sunspot penumbrae. Such a study is currently lying along PIL. The twisted morphology becomes obvious underway using Hinode SOT/SP and FG instruments and we when they erupt as helical structures). At present we cannot plan to present the detailed observational characteristics of confirm or rule out either of these possibilities, however, we these features in a separate paper. hope future high-resolution observations would help us to Here we focused on the disappearance of the PLFs in gain more knowledge about the formation of the PLFs. association with the occurrence of three recurrent flares near The decay of PLFs after the flare could be due to two the PIL where PLFs were located. The PLFs area was about 6 main reasons: (i) change in field inclination from horizontal × 107 km2 initially and reduced rapidly during the interval of to vertical and (ii) flux cancellation and/or submergence. three flares suggesting a correlation between the occurrence In the former case, we expect the vertical magnetic flux of the flare and the decay of the closely located PLFs. The to increase after the flare, which is not observed in the location of the hard X-ray flux obtained from the RHESSI vector magnetograms. Also, if PLFs field becomes vertical, coincides with the location of the PLFs suggesting that the then we should see appearance of pores at the location of footpoints of the reconnecting loops in the corona are rooted PLFs, which is not seen in the images. Thus, we can rule in or close to the PLFs. The vector magnetic field associated out this possibility. The vector magnetic field observations with PLFs shows that these are largely transverse magnetic by Hinode SOT/SP, however, show a substantial decrease in fields. A comparison of vector magnetic field retrieved by the the magnetic field in the PLFs area, which suggests that the Stokes inversion of SP data before and after the flares shows decay of PLFs could be due to the flux cancellation and/or that there is a substantial decrease in the transverse as well as submergence. Since we do not have a continuous vector vertical field component at the location of the PLFs. magnetic field measurement, it is very difficult to conclude Due to the lack of long time sequence of observations firmly upon this. A future continuous high-resolution data it is difficult to tell exactly how the PLFs were formed. We is, therefore, required. can think of two possibilities: (i) since PLFs are found in In the past, the disappearance of penumbra has been the location of decaying sunspot, it could be the remnant of observed in large X and M-class flares. The high-resolution the sunspot wherein the sunspot got disrupted and a cluster Hinode images gave us opportunity of observing the changes of penumbra got separated from the decaying sunspot. in the photosphere even for the small flares with small However, this picture does not conform to the typical obser- penumbra-like regions (PLFs). We could detect the changes vations of sunspot decay, where the sunspot looses it penum- in the area of the decaying PLFs during flare interval, bral area gradually becoming so-called naked sunspot and but there is still a lack of vector magnetic field data at resembling a pore, while the penumbrae are lost completely high-temporal cadence to make more detailed study of the that is, they do not form PLFs in general; (ii) it could also evolution of magnetic field in PLFs. Vector magnetograms happen that these are formed independently due to cluster- from recently launched Solar Dynamic Observatory hold Advances in Astronomy 9 promise to the studies of vector magnetic field evolution of [15] B. W. Lites and A. Skumanich, “Stokes profile analysis and such small features. vector magnetic fields. V. The magnetic field structure of large sunspots observed with stokes II,” Astrophysical Journal Letters, vol. 348, no. 2, pp. 747–760, 1990. Acknowledgments [16] T. R. Metcalf, “Resolving the 180-degree ambiguity in vector magnetic field measurements: the minimum energy solution,” The authors thank the anonymous referee for constructive Solar Physics, vol. 155, no. 2, pp. 235–242, 1994. suggestions and comments on the paper. Hinode is a Japa- [17] K. D. Leka, G. Barnes, and A. Crouch, “An Automated Ambig- nese mission developed and launched by ISAS/JAXA, col- uity-Resolution Code for Hinode/SP Vector Magnetic Field laborating with NAOJ as a domestic partner, NASA and Data,” in 2nd Hinode Science Meeting: Beyond Discovery-To- STFC (UK) as international partners. Scientific operation ward Understanding, B. Lites, M. Cheung, T. Magara, J. of the Hinode mission is conducted by the Hinode science Mariska, and K. Reeves, Eds., ASP Conf. Ser. 415, p. 365, 2009. team organized at ISAS/JAXA. This team mainly consists of [18] P.Venkatakrishnan, M. J. Hagyard, and D. H. Hathaway, “Eval- ff scientists from institutes in the partner countries. Support uation of magnetic shear in o -disk center active regions,” for the postlaunch operation is provided by JAXA and NAOJ Solar Physics, vol. 122, no. 2, pp. 215–226, 1989. (Japan), STFC (UK), NASA, ESA, and NSC (Norway). [19] A. K. Srivastava, T. V. Zaqarashvili, P. Kumar, and M. L. Khodachenko, “Observation of kink instability during small B5.0 solar flare on 2007 June 4,” Astrophysical Journal Letters, References vol. 715, no. 1, pp. 292–299, 2010. [20] P. Kumar, A. K. Srivastava, B. Filippov, and W. Uddin, “Multi- [1] S. K. Solanki and C. A. P. Montavon, “Uncombed fields as the wavelength Study of the M8.9/3B Solar Flare from AR NOAA source of the broad-band circular polarization of sunspots,” 10960,” Solar Physics, vol. 266, no. 1, pp. 39–58, 2010. Astronomy and Astrophysics, vol. 275, p. 283, 1993. [21] B. Ravindra, “Moving magnetic features in and out of penum- [2] M. J. Tildesley and N. O. Weiss, “On the origin of filamentary bral filaments,” Solar Physics, vol. 237, no. 2, pp. 297–319, structure in sunspot penumbrae: non-linear results,” Monthly 2006. Notices of the Royal Astronomical Society, vol. 350, no. 2, pp. [22] S. Vargas Dom´ınguez, J. A. Bonet, V. Mart´ınez Pillet, Y. Katsu- 657–670, 2004. kawa, Y. Kitakoshi, and L. Rouppe Van Der Voort, “On the [3] K. D. Leka and A. Skumanich, “The evolution of pores and the moat-penumbra relation,” Astrophysical Journal Letters, vol. development of penumbrae,” Astrophysical Journal Letters, vol. 660, no. 2, pp. L165–L168, 2007. 507, no. 1, pp. 454–469, 1998. [23] L. J. November and G. W. Simon, “Precise proper-motion [4] J. Evershed, “Radial movement in sun-spots,” Monthly Notices measurement of solar granulation,” Astrophysical Journal, vol. of the Royal Astronomical Society, vol. 69, p. 454, 1909. 333, pp. 427–442, 1988. [5] K. Harvey and J. Harvey, “Observations of moving magnetic [24] S. Masuda, T. Kosugi, and H. S. Hudson, “A hard X-ray two- features near sunspots,” Solar Physics, vol. 28, no. 1, pp. 61–71, ribbon flare observed with YOHKOH/HXT,” Solar Physics, vol. 1973. 204, no. 1-2, pp. 57–69, 2001. [6] V. Martinez Pillet, “Decay of sunspots,” Astronomische Nachri- [25] I. G. Hannah, S. Krucker, H. S. Hudson, S. Christe, and R. P. chten, vol. 323, no. 3-4, pp. 342–348, 2002. Lin, “An intriguing solar microflare observed with RHESSI, [7]L.R.BellotRubio,A.Tritschler,andV.Mart´ınez Pillet, “Spec- Hinode, and TRACE,” Astronomy and Astrophysics, vol. 481, tropolarimetry of a decaying sunspot penumbra,” Astrophysi- no. 1, pp. L45–L48, 2008. cal Journal Letters, vol. 676, no. 1, pp. 698–703, 2008. [26] S. A. Matthews, S. Zharkov, and V. V. Zharkova, “Anatomy of [8] H. Wang, C. Liu, J. Qiu, N. Deng, P. R. Goode, and C. Denker, a solar flare: measurements of the 2006 December 14 X-class “Rapid penumbral decay following three X-class solar flares,” Flare with GONG, Hinode, and RHESSI,” The Astrophysical Astrophysical Journal, vol. 601, no. 2, pp. L195–L198, 2004. Journal, vol. 739, no. 2, p. 71, 2011. [9] J. J. Sudol and J. W. Harvey, “Longitudinal magnetic field [27] K. Watanabe, S. Krucker, H. Hudson, T. Shimizu, S. Masuda, changes accompanying solar flares,” Astrophysical Journal, vol. and K. Ichimoto, “G-band and hard x-ray emissions of the 635, no. 1, pp. 647–658, 2005. 2006 December 14 flare observed by hinode/sot and Rhessi,” [10] S. Gosain, ‘Evidence for Collapsing Fields in the Corona and Astrophysical Journal Letters, vol. 715, no. 1, pp. 651–655, 2010. Photosphere during the 2011 February 15 X2.2 Flare: SDO/ AIA and HMI Observations,” Astrophysical Journal, vol. 749, no. 1, pp. 85–94, 2012. [11] K. Tanaka, “Measurement and analysis of magnetic field variation during a class 2b flare,” Solar Physics, vol. 58, pp. 149–163, 1978. [12] A. M. Title, T. D. Tarbell, K. P.Topka, S. H. Ferguson, and R. A. Shine, “Statistical properties of solar granulation derived from the SOUP instrument on Spacelab 2,” Astrophysical Journal, vol. 336, pp. 475–494, 1989. [13] K. Ichimoto, B. Lites, D. Elmore et al., “Polarization calibration of the solar optical telescope onboard hinode,” Solar Physics, vol. 249, no. 2, pp. 233–261, 2008. [14] A. Skumanich and B. W. Lites, “Stokes profile analysis and vector magnetic-fields .1. Inversion of photospheric lines,” The Astrophysical Journal, vol. 322, no. 1, pp. 473–482, 1987. Hindawi Publishing Corporation Advances in Astronomy Volume 2012, Article ID 854867, 7 pages doi:10.1155/2012/854867

Research Article Kinematic Approach to the 24th Solar Cycle Prediction

Vladimir Kaftan

Geophysical Center of the Russian Academy of Sciences, Molodezhnaya Street 3, 119296 Moscow, Russia

Correspondence should be addressed to Vladimir Kaftan, [email protected]

Received 14 November 2011; Revised 20 January 2012; Accepted 10 February 2012

Academic Editor: J. Javaraiah

Copyright © 2012 Vladimir Kaftan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The results of kinematic modeling of the 24th solar cycle (SC) are discussed. Time series of solar and cosmic ray monthly mean indices were received from web resources of international data centers. The previous prediction of the solar cycle shape using kinematic modeling technique demonstrated rather close agreement with the ﬁnal phase of the SC23 and relatively large magnitude of SC24. The forecast of 2005 is updated with respect to the modern observation of monthly mean data. The study allows concluding that the SC24 magnitude will probably near the previous cycle. Predicted moments of the maximum monthly mean values are expected in July–September 2012. The uncertainty of this interval is about ±1-2 months. The maximum monthly mean estimation can reach 130 ± 20 relative sunspot number units. The mean amplitude of the generalized cycle shape is expected to be close to the 23rd maximum mean height. The SC24 form can be relatively narrow, and the cycle will probably be shorter than 10 years.

1. Introduction the 23rd cycle and high amplitude of the 24th one (http:// journals.cambridge.org/action/displayAbstract?fromPage= As it was concluded by the special solar cycle prediction pan- online&aid=288312). As a matter of fact, the final stage el, the sample of different forecasts was separated in two of SC was predicted accurately using this technique in a con- main predictions of reasonably large or small SC24 magni- trast of many other predictions. The experience of the kine- tudes at 2007 (http://www.swpc.noaa.gov/SolarCycle/SC24/ matic technique usage made the author think that it could index.html). The first consensus proposed two rather differ- provide more or less precise predictions only for the ∼5year ent amplitudes of 140 and 90 sunspot number units as the forecasting interval in the case of about 50 year length most probable estimations, but later it was reduced to the monthly mean data processing. The last prediction of the lowest variant of 90. Another information on different SC current solar cycle shape was performed in 2005 and pub- prediction comparison can be seen at the Jan Janssens web lished in 2006. It is demonstrated relatively large monthly resource http://users.telenet.be/j.janssens/SC24.html/.Some mean sunspot index closed to 160 sunspot number units [9]. additional high magnitude forecasts can be found in [1–5]. Nowadays, this prediction is tested and updated taking into Another low prediction is published in [6]. Comparison an- account the up to date monthly data. alyses of different approaches to SC24 prediction are presented in papers [7, 8]. 2. Observation Data and Modeling Technique All the predictions were classified according to the used The time series of the monthly mean values of solar indi- technique as physical, statistical, and mixed. It is remarkable ces were used in the analyses. The international sunspot that the physical predictions have lower magnitudes than sta- numbers (Ri) were received from the website (http://sidc.oma tistical and mixed ones, with the exception of Dikpati re- .be/index.php3). The data of the 10.7 cm solar radio flux were searches [1–5]. The most of the used forecasting techniques obtained from the website (http://www.spaceweather.ca/ are statistical. sx-eng.php). The time series of monthly mean sunspot One of the statistical techniques called as kinematical ap- areas (S) was taken from the Internet site (http://solarsci- proach previously allowed to predict the long final stage of ence.msfc.nasa.gov/greenwch/sunspot area.txt). The cosmic 2 Advances in Astronomy ray time series of observation with monthly intervals Then, the least squares solution of (4)willbegivenas from the Moscow observation station was used in the re- T −1 T search as additional indirect data on solar variability (ftp:// xl =− Al PAl Al Pll. (7) cr0.izmiran.rssi.ru/COSRAY!/FTP DDMM/Data/). The time span of every series was varied between different analyses as At the second step, removing the modeled linear compo- described below. nent from the initial time-series, subtracting (3)from(2), we The observation data were processed using the numerical will search for dominating harmonic components. technique called as the sequential analysis of dominated har- The model for the residual time series will be presented monics method. The method was used firstly for the Caspian as Sea level change prediction [10] but fully described and pub- k lished in the thesis [11]. It is briefly described as follows. y = M A ω t φ . The results of repeated observation y of irregular time se- j + j sin j + j (8) j= ries are expressed in terms of k unknown parameters x and a 1 temporal argument t as Its unknown parameters will be searching consequently for every harmonic component yi = f (x1, x2, ..., xk, t). (1) This function has to be consisted of the number of periodical y = Mj + Aj sin ωj t + φj . (9) (sinusoidal) components which can be superposed to unidi- rectional trend changes. Thereafter, the connection equation Assigning by rough model parameters can be written as x = M A ω ϕ T n 0 [ 0, 0, 0, 0] (10) yt = b0 + b1t + Mj + Aj sin ωj t + φj ,(2) j=1 of the harmonic (9), after the linearization by first terms of Taylor series, we will receive a correction equation matrix B: where b0 is the value of the linear trend function at the initial v = B l moment, b1 is the linear coefficient of the first order (linear x + , (11) velocity), Mj is the ordinate of an oscillation axis of the jth harmonic, and Aj , ωj ,andϕj denote the amplitude, the an- and represent it as gular frequency, and angular phase of the jth harmonic, ⎡ ⎤ 1sinωot1 + φ0 Aot1 cosω0t1 + φ0 Ao cosω0t1 + φ0 ⎢ ⎥ respectively. ⎢ 1sinωot + φ Aot cos ω t + φ Ao cos ω t + φ ⎥ B = ⎣ 2 0 2 0 2 0 0 2 0 ⎦. In the absence of a priory information about a number 0 ··· ··· ··· ··· ω t φ A t ω t φ A ω t φ and a contribution level of periodical harmonics in the whole 1sino n + 0 o n cos 0 n + 0 o cos 0 n + 0 character of variations, the iteration step by step procedure (12) seems to be efficient in the analysis. Free terms of correction equations will be received as At the first stage, it is natural to determine and remove a ⎡ ⎤ trend component from the series using the equation y − M + A sin ω t + φ ⎢ 1 0 0 0 1 0⎥ y = b b t. ⎢y2 − M0 + A0 sin ω0t2 + φ0 ⎥ 0 + 1 (3) l0 = ⎢ ⎥. (13) ⎣ ··· ⎦ Correspondent correction equation system will be presented yi − M0 + A0 sin ω0ti + φ0 as ⎡ ⎤ ⎡ ⎤ As the initial model (9) is nonlinear, we will search for the 1 t −y ⎢ 1 ⎥ ⎢ 1⎥ unknown parameters x numerically by the iteration proce- ⎢ t ⎥ ⎢−y ⎥ v = ⎢ 1 2 ⎥ · b b − ⎢ 2⎥ = A x l l ⎣··· ···⎦ 0 1 ⎣···⎦ l l + l,(4)dure. Theiterationprocesswillbewrittenas 1 tn −yn xr = xr + f (xr ), (r = 0, 1, 2, ...), (14) where vl denotes a residual random noise term, l index +1 n reflects a linear part of variation, and is the number of va- where r is an iteration number. lues in the analyzed time series. Estimation of the vector-function f (xr )willbegivenby This task can be solved under condition of − T T 1 T vl Pvl = min, (5) f (xr ) =− Br PBr Br Plr . (15) P n n where is an × weight matrix. Then, the iteration process (14) will take the form For the common case, we can have a priory inverse weight −1 matrix x = x − BT PB BT Pl . ⎡ ⎤ r+1 r r r r r (16) q11 q12 ··· q1n ⎢ ⎥ ff Δ − ⎢ q21 q22 ··· q2n⎥ Signing by some neglecting di erence x,wecontinueiter- Ql = P 1 = ⎢ ⎥. (6) ⎣··· ··· ··· ⎦ ations for the moment when [xr +1− xr ] will be less than or Δ qn1 qn2 ··· qnn equal to x. Advances in Astronomy 3

Hence, the results of the last iteration will be accepted as 250 final estimations of the model (9) parameters T x = MAωφ . (17) 200 In order to estimate a statistical confidence of the resulted characteristics, we use the estimation of the unit weight 150 standard vT Pv μ = , (18) 100 n − 4 where v is an n×1 vector of residuals (11) computed with the use of (17). 50 Empirical standards S of harmonic parameter estimations will be determined as ⎡ ⎤ 0 sM 1985 1990 1995 2000 2005 2010 2015 ⎢ ⎥ ⎢s ⎥ ⎢ A ⎥ = μ Q = μ BT PB −1 Figure 1: Model, prediction, and epignosis of the monthly mean ⎣s ⎦ ii r r ii , (19) ω Ri pattern. Dotted line demonstrates the real data. Dashes show the sφ one sigma intervals. Blue dots are principal epignosis control marks. T −1 Abscissa axis fix years of the last modeled and predicted intervals. where Qii=(Br PBr )ii are diagonal elements of the inversed Ordinate axis shows international sunspot number values. weight matrix of parameters. Then, we will compute normalized parameter estimations ⎡ ⎤ M/sM radio flux data [13]. The prediction was appeared to be ⎢ ⎥ ⎢ A/sA ⎥ rather close to the real SC23 outline. Predicted monthly Z = ⎢ ⎥. (20) ffi ⎣ ω/sω ⎦ mean maximum was coincide with the o cial maximal φ/sφ smoothed value but monthly indices themselves had relative standard error of 10–15%. Moreover, several retrospective t ≥ Z Assigning a confidence limit q%, we determine a SC predictions using the technique showed rather accurate confidence level of received estimations. Depending on a sol- association with reality at least for the 5-year predicting t ving task, a confidence limit is assigned using a normal dis- intervals after the 50-year observation of the monthly mean tribution. In most of research, we can consider solved par- indices. Z ≥ ameters as statistically confident when 2. The practice proved that the best predicting results were Having a reason to consider a harmonic to be statistically received in a case of relatively short solar time series usage. confident, we receive an approximation function (9)which Predictions usually became confidently lower than reality in has to be subtracted from the previous residual time series. the use of hundreds years long-time series of monthly mean We follow the stepwise process of dominate harmonic de- indices. This feature can be explained by the less accurate termination (11)–(20)beforewewillbesureoftheabsence ancient observation and a possible miss of some cycles as it of confident components in the residual time series. The crit- was discussed in publications. erion of finishing an iteration procedure is a level of a close- It is necessary to remark that a quantity of a sample ness of unit weight standards of last harmonics. of determined periodically components is normally about The technique considered in this work is used in a statis- several tenses for a 50-year monthly mean solar time series. tical modeling of time variations in observed characteristics. In these cases, a statistical degree of freedom is more than This method can be considered among the periodogram an- 400, that demonstrates a level of an effectiveness of the used alysis methods the general theory of which was described, for approximation method. The time spans of series of relative example, in [12]. In a contrast to the majority of the known sunspot numbers and sunspot areas were spread from methods, the technique used in the present work does not 1950.0. Used series of 10.7 cm solar radio flux and cosmic require regularity of observations. The specific feature of this ray indices had begun from 1947.0 and 1958, respectively. technique consists also in an organized order of determining The final moments of all-time series were limited by the dominating sinusoidal components with decreasing ampli- beginning date for the last and the current predictions. tudes. The technique appears to be possible to individually The last SC predictions using the sequential analysis of estimate the accuracy of determination of required dominat- dominated harmonics were made in 2004-2005 (see Figures ing harmonics. 1–3)[9]. Three types of the solar indices were processed, and the 24th SC pattern was forecasted using about 50-year 3. Former Results of the 24th time series of the monthly mean values. Today, it is possible Solar Cycle Prediction to check the accuracy and reliability of these forecasts. The original curves of the predictions and control marks are The above-described method was used in the modeling and showed Figures 1–3. Blue marks are added on the published prediction of the 23rd solar cycle form using Ri and 10.7 cm figures to show the forecast effectiveness. 4 Advances in Astronomy

300 Actual solar indices are systematically lower than the forecasted positions for the Ri and 10.7 radio flux variations (see Figures 1 and 2). The character of the discrepancies is slightly 250 different for the sunspot areas (see Figure 3). All predictions demonstrate the visible phase shift between the predicted and 200 real data after the 5-year prognostic interval. The general conclusions of the former SC behavior forecast were the next [9, 14]. 150 (1) The minimal monthly mean indices were expected for the 2006.5–2008. 100 (2) The final stage of the 23rd solar cycle was expected to be reasonable long and have some local maxima.

50 (3) The 24th solar cycle monthly mean index was expec- 1985 1990 1995 2000 2005 2010 2015 ted to be near 150 ± 35 Ri. Figure 2: Model, prediction, and epignosis of the monthly mean in- The final phase was estimated especially for the main dices of 10.7 cm radio flux (S.F.U) pattern. Dotted line demonstrates solar indices together with galactic cosmic ray data [15]. We the real data. Dashes show the one sigma intervals. Blue dots are have to remark that the general features of the SC23 final principal epignosis control marks. Abscissa axis fix years of the last stage were predicted rather accurately. Especially the about modeled and predicted intervals. Ordinate axis shows S.F.U. values. 12.6-year abnormal length of the 23rd cycle [16] is closely coincided with prediction described. In a reference to the intercycle minimum phase, we have 4000 to give a passing mention to some principal studies. The nature of the minimal phase between 23rd and 24th solar cycles 3500 was carefully analyzed using 10.7 cm solar radio flux indices 3000 in the paper [17]. The interval between contiguous main solar cycle maxima is thoroughly studied in [18]. 2500 Today, it is a propitious moment for updating the published previous prediction because the amplitude and the 2000 time of maximum activity are not obvious yet. 1500 4. 24th Solar Cycle Prediction Update 1000 The same data type sets updated by the modern observed va- 500 lues were used for the correction of the former SC24 predi- 0 ction. Analyzed time series were consisted of monthly mean 1985 1990 1995 2000 2005 2010 2015 indices. Data archive addresses are denoted above. The main Figure 3: Model, prediction, and epignosis of the monthly mean task for the moment is improving the estimations of the sunspot areas pattern. Dotted line demonstrates the real data. amplitude and the length of the SC24. Dashes show the one sigma intervals. Blue dots are principal New data processing using the sequential analysis of epignosis control marks. Abscissa axis fix years of the last modeled dominated harmonics method was performed for the sun- and predicted intervals. Ordinate axis shows sunspot area values in spot numbers, 10.7 cm radio flux indices, and sunspot area units of millionths of a hemisphere. time series. Cosmic ray observations from the Moscow station were used too. The results of new SC24 predictions are illustrated in Figures 4, 7, 5,and6. As we can see from the Figures 4–6, new modeling of the It is necessary to explain that the one sigma tendencies four difference solar and cosmic processes demonstrates their were previously determined like mean square values of true probable future behavior closed each other. The amplitude of errors in five retrospective forecasts of the way of behavior of the SC24 is expected to be near to the previous cycle mean Ri indices. height. The International Sunspot Number prediction curve The analysis of the correlation between the different pair shows even larger modeled magnitude 130 ± 20 Ri. The of indices was allowed to determine the correspondent linear maximal phase interval can probably begin from the middle regression formulas which were used in one sigma interval to the end of 2012. determination for the S.F.U and sunspot area values. The interesting fact is that the previous high magnit- The tests of the previous SC forecasts demonstrate that ude SC24 forecast of the SC prediction panel coincides the best prediction is present in the 5-year interval as it was with the presented prediction in general in a reference to the expected from the earliest experiments. One can see that the magnitude and relatively narrow shape. It can be seen true errors of the forecast are near to one sigma margins. in comparison with Figure 8 taken from the original Advances in Astronomy 5

Observed data used from 1950 to October 2011 Observed data used from 1950 to October 2011 180 400

160 350 140 300 120

100 250

80 200 60 150 40

International sunspots numbers Ri sunspots numbers International 100 20 station) variation ray (Moscow Cosmic

0 50 1995 2000 2005 2010 2015 2020 1995 2000 2005 2010 2015 2020 Years Years Figure 4: SC24 shape prediction for monthly mean sunspot num- Figure 6: SC24 shape prediction for cosmic ray monthly index ber variation. Dotted line demonstrates the real data. Dashes show variation. Dotted line demonstrates the real data. Dashes show the the one sigma intervals. Solid is the modeled curve. one sigma intervals. Solid is the modeled curve.

Observed data used from 1950 to October 2011 Observed data used from 1950 to October 2011 2400 3500 2200 3000 2000 1800 2500 1600 2000 1400 1200 1500 Sunspot areas Sunspot 1000

10.7 cm radio ﬂux (sfu) 10.7 1000 800 500 600

400 0 1995 2000 2005 2010 2015 2020 1995 2000 2005 2010 2015 2020 Years Years Figure 5: SC24 shape prediction of monthly mean indices for Figure 7: SC24 shape prediction for monthly mean sunspot areas 10.7 cm radio ﬂux variation. Dotted line demonstrates the real data. variation. Dotted line demonstrates the real data. Dashes show the Dashes show the one sigma intervals. Solid is the modeled curve. one sigma intervals. Solid is the modeled curve.

web resource (http://www.swpc.noaa.gov/SolarCycle/SC24/ into July–September 2012. The uncertainty of this interval is index.html). But later, the panel researchers changed their about +1-2 months. The mean amplitude of the general cycle opinion to the lowest variant which is better coinciding with shape is expected to be close to the 23rd maximum as it is the presented predictions in relation to the time of a maxi- seen from Figures 7, 5,and6. The SC24 will continue not mum from the middle of 2012 to the beginning of 2013 long. It will be probably shorter than 10 years. The beginning (Figure 9). of the next minimum stage is preliminary predicted in 2017. The maximal monthly mean value of sunspot number Ri 5. Conclusions is forecasted as 130 ± 20. More than 2000 ± 350 units of millions of hemisphere are predicted for the maximal mon- Three types of solar data were used in the kinematic mod- thly mean sunspot area index. The 10.7 cm radio ﬂux maxi- eling for the previous prediction [9] updating. All new pre- mal monthly value is expected at the level of 200 ± 20 sfu. dictions demonstrate that 24th cycle maximum stage will Cosmic ray variation at the Moscow station is modeled too as probably occur at the middle of 2012 or a bit later. Predicted additional source of data. Its reversed magnitude is processed moments of the maximum monthly mean values are fallen to be slightly lower than the level of the last solar cycle shape. 6 Advances in Astronomy

ISES solar cycle sunspot number progression sunspot maximum will occur and experts have an opportu- data through March 31, 2008 nity to check and update current SC forecasts. 175 The results obtained from the simulation described above 150 support the relatively high (about 130 Ri) or moderate magnitude variants of the 24th SC predictions for the monthly 125 mean value case. Forecast capabilities of the modeling me- 100 thod were veriﬁed by several retrospective simulations. In the case of the forecast coming true, the entry into a super cen- 75 turial solar minimum would be shifted in decades to come.

Sunspot number Sunspot 50 Acknowledgments 25 The author would like to thank his closest collaborator Mi- 0 0 123456789101112 13 14 15 16 chail Krainev for his significant impact on cosmic ray vari- January ation modeling and to express gratitude to heads of the ex- Updates April 7, 2008 NOAA/SWPC Boulder, Co, USA periments who placed the data in the Internet. Especial ack- nowledgment has to be expressed to the anonymous reviewer Smoothed monthly values for his valuable comments and recommendations. Monthly values Predicted values (smoothed) References Figure 8: The first international consensus in SC24 prediction dated April 7, 2008 (http://www.swpc.noaa.gov/SolarCycle/SC24/in- [1] M. Dikpati, G. de Toma, and P. A. Gilman, “Predicting the dex.html). strength of solar cycle 24 using a flux-transport dynamo-based tool,” Geophysical Research Letters, vol. 33, no. 5, Article ID L05102, 2006. ISES solar cycle sunspot number progression [2] M. Dikpati, G. De Toma, and P. A. Gilman, “Polar flux, cross- data through April 09 equatorial flux, and dynamo-generated tachocline toroidal 175 flux as predictors of solar cycles,” Astrophysical Journal Letters, vol. 675, no. 1, pp. 920–930, 2008. 150 [3] M. Dikpati, P. A. Gilman, and G. De Toma, “The waldmeier effect: an artifact of the definition of wolf sunspot number?” 125 Astrophysical Journal Letters, vol. 673, no. 1, pp. L99–L101, 100 2008. [4] M. Dikpati, “Predicting solar “climate“ by assimilating mag- 75 netic data into a flux-transport dynamo,” Astronomische Nachrichten, vol. 328, no. 10, pp. 1092–1095, 2007. Sunspot number Sunspot 50 [5] M. Dikpati and P. A. Gilman, “Simulating and predicting solar 25 cycles using a flux-transport dynamo,” Astrophysical Journal, vol. 649, no. 1 I, pp. 498–514, 2006. 0 [6] L. Svalgaard, E. W. Cliver, and Y. Kamide, “Sunspot cycle 24: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 smallest cycle in 100 years?” Geophysical Research Letters, vol. January 32, no. 1, pp. 1–4, 2005. Updates May 8, 2009 NOAA/SWPC Boulder, Co, USA [7] R. Brajsa,H.Wˇ ohl,¨ A. Hanslmeier et al., “On solar cycle predictions and reconstructions,” Astronomy and Astrophysics, Smoothed monthly values vol. 496, no. 3, pp. 855–861, 2009. Monthly values [8] K. Petrovay, “Solar cycle prediction,” Living Reviews in Solar Predicted values (smoothed) Physics, vol. 7, pp. 1–59, 2010. Figure 9: The updated international prediction of SC24 dated April [9] V.I. Kaftan, “Kinematic modeling of the solar activity. 24th 9, 2009 (http://www.swpc.noaa.gov/SolarCycle/SC24/index.html). solar cycle prediction,” in Proceedings of the Experimental and Theoretical Research of the Principles of Solar-Geophysical Activity Predicting, pp. 145–150, Troitsk, Moscow, Russia, 2006, (Russian). The cosmic ray next minimum is shifted about a year to [10] V. I. Kaftan, “Analysis of periodicities of cosmogeophysical future in a reference to predicted solar data maximum. The processes and Caspian Sea level changes,” in Book of Abstracts: last estimation of the shift between galactic cosmic ray and Caspian Region: Economics, Ecology, Mineral Resources. Inter- national Conference “Caspiy-95”, p. 14, Moscow, Russia, 1995, solar activity variations was 0.6 years [15]. (Russian). As it is shown by Jan Janssens, the medium 90–140 amp [11] V. I. Kaftan, Temporal Analysis of Spatial Data: Kinematic Mod- litude SC24 forecasts predominate for today. At present, els, Ph.D. thesis, Moscow State University of Transportation, some researchers conclude that the maximal SC phase has Moscow, Russia, 2003, (Russian). already started. Our modeling allows presuming that re- [12] A. Worthing and J. Geffner, Treatment of Experimental Data, searchers have at least a half of a year before monthly mean Wiley, New York, NY, USA, 1944. Advances in Astronomy 7

[13] G. V. Demianov, V. I. Kaftan, and V. I. Zubinsky, “Participation of the Central Research Institute of Geodesy, Aerial Surveying and Cartography in the third Baltic Sea Level GPS campaign,” in Final results of the Baltic Sea Level 1997 GPS campaign, Re- search Works of the SSC 8.1 of the International Association of Geodesy, M. Poutanen and J. Kakkuri, Eds., pp. 127–132, Finnish Geodetic Institute, Kirkkonummi, Finland, 1999. [14] V. I. Kaftan, “Kinematic modeling of the main solar cycle,” in Multi-Wavelength Investigations of Solar Activity,A.V.Step- anov, E. E. Benevolenskaya, and A. G. Kosovichev, Eds., pp. 111–112, Cambridge University Press, Cambridge, UK, 2004. [15] V. I. Kaftan and M. B. Krainev, “Estimation of the eﬀect of solar activity on the intensity of galactic cosmic rays,” Geo- magnetism and Aeronomy, vol. 47, no. 2, pp. 137–148, 2007. [16] B. Komitov, P. Duchlev, K. Stoychev, M. Dechev, and K. Kol- eva, “Determination of the sunspot minimum epoch between the cycles No 23 and 24 and prediction of the cycle No 24 magnitude on the base of the ‘Waldmeier’s Rule‘,” Bulgarian Astronomical Journal, vol. 16, pp. 44–49, 2011. [17] K. Tapping and J. Valdes,´ “Did the sun change its behaviour during the decline of cycle 23 and into cycle 24?” Solar Physics, vol. 272, no. 2, pp. 337–350, 2011. [18] K. L. Harvey, “What is solar cycle minimum?” Journal of Geo- physical Research A, vol. 104, no. 9, Article ID 1999JA900211, pp. 19759–19764, 1999. Hindawi Publishing Corporation Advances in Astronomy Volume 2012, Article ID 167375, 6 pages doi:10.1155/2012/167375

Research Article Probable Values of Current Solar Cycle Peak

V. M. Silbergleit1, 2

1 Consejo Nacional de Investigaciones Cient´ıﬁcas y T´ecnicas (CONICET), Buenos Aires, Argentina 2 Facultad de Ingenier´ıa, Universidad de Buenos Aires, Av. Las Heras 2214-Piso 3-C1127AAR, Buenos Aires, Argentina

Correspondence should be addressed to V. M. Silbergleit, [email protected]

Received 18 November 2011; Revised 27 December 2011; Accepted 3 January 2012

Academic Editor: J. P. Rozelot

Copyright © 2012 V. M. Silbergleit. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

An analysis of multiple linear regression method applied to solar cycles 4 to 23 using lagged values of smoothed monthly mean sunspot numbers as independent variables is presented. According to that, the amplitude of current solar cycle 24 is estimated providing a quantitative prediction result. Our adjustment shows that the current cycle would have a sunspot peak less than the biggest one observed during the cycle 19 giving an additional support to the declination in solar activity which is currently happening.

1. Introduction solar activity level have been published (e.g., [1–6]). The general trend observed in recent solar activity cycles is Good predictions of the intenseness of solar activity are toward larger amplitude sunspot cycles. Some articles use increasing by considering satellites information. Such satel- the analysis of the time series of historical spot numbers lites often provide determinative links in communications to obtain a power spectrum of periodicities. On the other as well as defense and are also often origin of impor- hand, there is evidence that shows some kind of regularity tant scientific information. The enlargement of ultraviolet in sunspot cycle modulation. The sunspot numbers present emission from the Sun at times of high solar activity periodicities of 11 years (Schwabe cycle), 22 years (Hale heats the Earth’s upper atmosphere, which in turn causes cycle), and 88 years (Gleissberg cycle). As it was published the spread and enlargement of the influence on these by [7] the duration of each cycle could be associated with a satellites. The predictions of solar activity are important variation in the solar energy output. for technology, including the goodness of the operations Reading the above-mentioned articles, we found several of low-Earth orbiting satellites, electric power transmission interesting topics related to the three main groups of grids, and high-frequency radio communications, among prediction methods. other problems. Long-term predictions of solar activity are therefore extremely important to auxiliary plan missions and (1) Precursor methods depend on the value of some to project satellites that will remain active for their available data of solar activity or magnetism at a definite lifetime. time to predict the amplitude of the following solar As we know, the solar magnetism is the route to maximum. They concluded that each numbered understanding the processes involved. The Sun’s differential solar cycle is a consistent unit in itself, while solar rotation, meridional circulation, and large-scale convective activity appears consist of a series of less compact motions all contribute to produce the cyclic magnetic intercorrelated particular cycles. development observed. So far we have not produced theories (2) Extrapolation methods are based on the previous that combine these mechanisms in a model, then we are history that the physical process giving rise to the necessitated to predict solar activity by statistical methods sunspot number register is statistically homogeneous; that depend on determining correlations between past and that is, the mathematical regularities underlying its future behavior. Numerous studies to predict the maximum changes are the same at any point of time, and, 2 Advances in Astronomy

Monthly mean sunspot mass ejection. This disturbed solar activity often occurs near sunspots. 250 Cycle 19 was the largest in recorded history (with 201.3 smoothed sunspot number at the maximum); cycles 21 and 18 22 200 22 both showed annual averages of geomagnetic activity that were large in comparison with most cycles in the 150 4 8 record of an indices. Cycles 21 and 22 were the second and 20 the third largest (with 164.5 and 158.5 smoothed sunspot 14 16 number maximum, resp.). The important variability from 10 12 100 one cycle to the next shows the difficulty in making empirical predictions of the Sun activity. 6 50 In this study, our goal is to describe a technique for predicting the amplitude of the solar cycles considering multiple regression method and using lagged values as 0 1786 1895 2004 independent variables. This technique will provide more (years) reliable estimations of the level of solar activity several years into the future. One fundamental problem associated with Figure 1: The sunspot cycle well documented over last 300 years solar cycle predictions is the small number of solar cycles that shows a 11-year pattern of solar activity. Data from cycle 4 to cycle are well observed. Therefore most of our efforts at predicting 23. solar cycle activity levels are obtained with the statistics of 10 or 20 cycles. therefore, it lends itself to analysis and forecasting by time series methods. 2. Data, Regression Technique, and Results (3) Finally, lieu of an analysis of measured data alone, model-based predictions use physically consistent Over 300 years, the average number of sunspots has regularly dynamo models to predict solar activity. increased and decreased in an approximately 11-year sunspot cycle. While some other aspects of the Sun vary distinctly During the last few solar cycles, precursor methods have over the years (e.g., coronal holes tend to be most numerous clearly been superior to extrapolation methods. Thompson’s following sunspot maximum), the differential rotation of method by the “precursor method” (see [3]) considers the Sun, southern circulation, and large-scale convective that the maximum amplitude of a cycle is proportional motions all play important roles in generating the cyclic to the number of geomagnetic disturbed days in the cycle magnetic behavior (see [9]). preceding it. It takes into consideration a solar dynamo For the present analysis we used monthly averages theory hypotesis, where the polar field in the declining phase of the international sunspot number available from the and at minimum is the origin of future toroidal field within National Geophysical Data Center (ftp://ftp.ngdc.noaa.gov/). the Sun that will cause solar activity. This method that has Although these data extend from 1749 to the present, the produced predictions according to the right range during the nature of the data is: (a) poor for during 1700–1748, (b) past few solar cycles was published by [8], whose approach doubtful during 1749–1817, (c) appropriate during 1818– is based on the polar field precursor. This method produces 1847, and certain from 1848 to the present (see [10]). Values the solar physical union between the polar field, coronal for years prior to 1849 are missing, thereby making that data holes, the interplanetary magnetic field, and the geomagnetic less reliable. Taking into account the sunspot cycles plotted in activity. The “precursor method” appears to be the best, but Figures 1 and 2a, we can observe that the pairs: 4-5, 8-9, and this is largely due to its accuracy in predicting the amplitude 22-23 do not verify the “even-odd” effect. Thus, the analysis of cycle 19. of the available solar data, including both statistical and The beginning cycle 24 will probably mark the end of the physical indices, make it possible to assume that the integral Sun switching to a state of less strong activity. It will be an even-odd effect and the rise rate-amplitude effect are the important proof for cycle prediction methods and for the most prominent and universal statistical features of the solar understanding of the solar dynamo. activity cycles. The differences between odd and even solar Physical processes contribute to producing the Sun’s 11- cycles are a consequence of the nonlinear interactions that year activity cycle as the occurrence of coronal holes. Many procure the stabilizing mechanism for the cycle’s amplitude. models of the solar dynamo exist but none are complete. If, for example, the magnetic field is larger than average for Part of the solution related to flows in the solar convection a given cycle (say odd), the nonlinear feedback machine can zone is studied by helioseismology and large-scale numerical generate a magnetic field that is smaller than average for the models. The sun shows a roughly 11-year cycle of activity, next cycle (even), then one that is larger than average for from stormy to quiet and back again. Solar storms begin with the following cycle (odd), and so forth. As a consequence complex magnetic fields generated by the sun’s disturbing the odd cycles have larger amplitudes than even cycles in the electrically charged gas. Solar magnetic fields can suddenly sunspot records; it is less pronounced before 1823, which break, rejecting extremely great energy as a flare or a coronal might be associated with lesser accuracy of the data [31]. Advances in Astronomy 3

Pn Rn

19 180 19 200 17

21 160 8 18 22 21 150 4 11 140 9 17 23 15 24 23 18 22 20 100 13 120 10 20 7 12 16 100 50 14 5 6 80 16 0 5 10 15 20 25 16 18 20 22 24 Solar cycles Solar cycles (a) (b)

Figure 2: (a) Solar cycle amplitudes from cycle 4 to cycle 23 used to calculate the Rn. The ﬁlled circles are the observed sunspots (Pn), and (b) Solar cycle peaks from cycles 16 to 24 as they are estimated. The ﬁlled triangles are the predicted sunspots (Rn).

Sunspots appear on the Sun in two bands on either side Table 1: Observed (Pn) and predicted (Rn)amplitudes. of the equator that drift toward lower latitudes as each nP R sunspot cycle progresses. The observation of the drift of n n the centroid of the sunspot area toward the equator in (1) 16 78.1 86.2 each hemisphere from 1874 to 2002 shows that the drift (2) 17 119.2 169.8 rate slows as the centroid approaches the equator. The (3) 18 151.8 133.1 comparison between the drift rate at sunspot cycle maximum (4) 19 201.3 177.3 and the period of each cycle for each hemisphere exhibits (5) 20 110.3 120.8 an extremely significant anticorrelation: hemispheres with (6) 21 164.5 150.5 faster drift rates have shorter periods. The drift rate at (7) 22 158.5 134.5 maximum is significantly correlated with the amplitude of (8) 23 120.8 133.2 the following cycle; a prediction of dynamo models that use a (9) 24 104a 136.3 ± 30.0 deep meridional flow toward the equator must be considered a [32]. As cycles 22 and 23 were determined with good data sunspot number observed on 11/12/30. quality, we inferred that processes into the Sun would be the most important reason for this behavior. Inspection cycle. Several changes have been considered to make this of Figure 1 reveals that each cycle shows a broad range of method more accurate and useful (e.g., the method can be temporal behavior, and the development of cycles 22-23 used recursively as it was adopted by the Space Environment could be explained by considering that the Geissberg cycle Service Center in Boulder, Colorado); the MSAFE (Marshall (with a period of 88 years) is in the declining phase giving Solar Activity Future Estimates) method described by [12] us an additional support to the declination in solar activity andusedby[13]. which is currently happening. A multiple linear regression (MLR) has the form: The sunspot cycle is a useful route to mark the changes in the Sun. Some cycles (like 5-6-7-10-12-14-16) are small in Sk = α0 + Yi αi,(1) amplitude (about half the size of cycle 19), while others are considerably larger (like 18-19-21 and 22). Most cycles show where the αi are constants (with i = 1, 2, ..., n and i =/ k)and asymmetries, with the rise to maximum being faster than the the independent variables Yi,arelaggedvaluesofSk. fall to minimum. To select the delayed values to be used in (1) the Reference [11] suggested a regression technique for autocorrelation analysis of each series was calculated, then predicting solar activity levels one year to the future. They the best combination was find. The parameters of the used an average sunspot cycle made up of smoothed sunspot multiple regression equation were estimated by using the numbers starting with cycle 8. The regression coefficients least squares method applied to the data observed from cycles are obtained by minimizing the sum of RMS differences 4–23. The final error was calculated as the sum of the square between predicted and observed variations from the mean difference between the observed value and the predicted one. 4 Advances in Astronomy

Table 2: Statistical results.

(a)

Multiple Regression: independent data Pn−12 and Pn−7; dependent data Pn Parameter Value Error t-value Prob > |t|

a0 283.89853 60.46631 4.69515 0.00536

a2 −0.59136 0.28610 −2.06696 0.09360

a1 −0.86801 0.44384 −1.95568 0.10788 (b) RR-Square (COD) Adj. R-Square Root- MSE (SD) 0.74548 0.55574 0.37803 30.28774 (c) ANOVA table. Item Degrees of freedom Sum of squares Mean square F statistic Prob >F Model 2 5711.72512 2855.86256 3.09568 0.13342 Error 5 4612.65363 922.53073 Total 7 10324.37875 At the 0.005 level, the means are not signiﬁcantly diﬀerent.

Table 3: Predicted maximum amplitude (PMA) for solar cycle 24 The constant resulted to be: a0 = 284 (± 60), a1 = as they were published. −0, 87 (± 0, 44) and a2 =−0, 59 (± 0, 28). The correlation coefficient obtained was R = 0.75 and a negligible probability Reference Year PMA values that it is due to chance. Finally, (2) can be rewritten with the . ± . (1) [5] 2003 (87 5 23 5) least error of prediction, as (2) [10] 2008 (94 ± 44) < (3) [15] 2001 ( 50) Rn, = 284 − 0.87 Pn−7, − 0.59 Pn−12. (3) (4) [16] 2002 (101.3 ± 18.1) (5) [17] 2003 (100 ± 30) The accuracy of the prediction based on (3)canbe (6) [18] 2003 (110 ± 15) verified by looking for the results shown in Table 1.The (7) [19] 2009 (145 ± 7) statistical test and partial and final results are shown in Table 2. (8) [20] 2011 (90 ± 20) Figures 2(a) and 2(b) show the Pn values for cycles 4 to 23 (9) [21] 2007 (142 ± 24) and the estimated Rn values for cycles 16 to 24, respectively. (10) [22] 2008 (90 ± 10) The plotted Rn values have a mean sequence of upward (11) [23] 2009 (78 ± 10%) (cycles 16 to 19) and downward (cycles 19 to 24) trends. (12) [24] 2009 (87 ± 5) The present technique is appropriate to solve the problem (13) [25] 2011 (113.3) of maximum amplitude prediction for solar cycles, and (14) [26] 2011 (65) we have estimated each of the last 8 cycles with typical (15) [27] 2010 (67 ± 8) differences between calculated and observed data less than (16) [28] 2010 (131 ± 20) 24 in terms of sunspot number (for all the cycles except cycle ff ff (17) [29] 2008 (87 ± 7) 17 which presents a di erence of 50.6). These di erences are in the same order as the ones obtained by [3] in which the (18) [30] 2010 (84.5 ± 23.9) author used the “precursor” method.

To predict the maximum activity of solar cycles (here 3. Discussion and Conclusions called Rn), the MLR is applied to the observed solar peaks (Pn). Rn is related to the amplitudes of two prior cycles Multiple linear regression method is used to estimate cycles (lagged values, identified by n1 and n2 with values equal to 16 to 24 amplitude maximum. From an analysis of solar 7 and 12, resp.). The expression to be considered is cycle peaks for cycles 4 to 23, a shorter recurrence trend of 7 or 12 cycles is observed. One is related to the Gleissberg R = a a P a P . n 0 + 1 n−n1 + 2 n−n2 (2) period, and the other agrees with one of the periodicities in the C14 time record, which is associated with solar activity 14 The constant values a0, a1,anda2 are obtained by variation because changes in the C activity result primarily applying the MLR method to the data series from cycles 4 to from varying degree of modulation of the galactic cosmic ray P P 23. We considered n−n1 and n−n2 as independent variables flux by the sun. Historical data show that during periods of and Rn as the dependent variable. depressed solar activity the atmospheric C14 was rising and Advances in Astronomy 5 at times when large sunspots were reported, C14 showed a [10] R. P. Kane, “Prediction of solar cycle maximum using solar tendency to decrease (see [14]). The estimated amplitudes cycle lengths,” Solar Physics, vol. 248, no. 1, pp. 203–209, 2008. of future solar cycles (as they are shown in Table 1)confirm [11] A. G. McNish and J. V. Lincoln, “Prediction of sunspot that the present cycle would have a sunspot peak less than the numbers,” Eos, Transactions, American Geophysical Union, vol. biggest one observed during the cycle 19. 30, p. 673, 1949. For maximum amplitude of solar cycle 24, some pub- [12] K. O. Neihuss, H. C. Euler Jr., W. W. Vaugan et al., “Statistical lished articles show differences in the results as they are technique for intermediate and long-range estimation of 13- shown in Table 3. month smoothed solar flux and geomagnetic index,” NASA Ourresultagreeswith[1] which indicates a decline in Technical Reports TM-4759, 81, 1996. solar activity since the recorded cycle 22 maximum. Also the [13] R. L. Holland and W. W. Vaughan, “Lagrangian least-squares “even-odd” effect was not verified for the pair, 22-23 giving prediction of solar flux (F-10.7),” Journal of Geophysical an additional support to the declination in solar activity Research, vol. 89, no. 1, pp. 11–16, 1984. which is currently happening. [14] M. Stuiver, “Variations in radiocarbon concentration and The method considered for the prediction of the max- sunspot activity,” Journal Geophysical Research, vol. 66, no. 1, imum amplitude of solar cycles enables us to work out a pp. 273–276, 1961. reliable estimation for the size of the following cycle 24 as [15] O. G. Badalyan, V. N. Obridko, and J. Sykora, “Brightness of 136.3 ± 30.0 smoothed monthly mean sunspot numbers, the coronal green line and prediction for activity cycles 23 and some months in advance. Our study confirms that maximum 24,” Solar Physics, vol. 199, no. 2, pp. 421–435, 2001. amplitude of current solar cycle would be lower than the first [16] J. L. Wang, J. C. Gong, S. Q. Liu, G. M. Le, and J. L. largest one. Sun, “The prediction of maximum amplitudes of solar cycles and maximum amplitude of solar cycle 24,” Chinese Journal Astronomy Astropysics, vol. 2, no. 6, pp. 557–562, 2002. Acknowledgments [17] K. H. Schatten, “Solar activity and the solar cycle,” Advances in Space Research, vol. 32, no. 4, pp. 451–460, 2003. The author is grateful to unknown referees for helpful com- [18] F. De Meyer, “A transfer function model for the sunspot cycle,” ments and suggestions. This work was partially supported by Solar Physics, vol. 217, no. 2, pp. 349–366, 2003. 20020100100227 (UBACYT) of Facultad de Ingenier´ıa, Uni- [19] I. J. Crosson and P. M. Binder, “Chaos-based forecast of versidad de Buenos Aires and 11420090100258 of CONICET sunspot cycle 24,” Journal of Geophysical Research A, vol. 114, of Argentina. no. 1, Article ID A01108, 2009. [20] R. P. Kane, “Prediction of the size of coming solar cycle 24 based on solar parameters during sunspot minimum between References cycles 23 and 24,” Indian Journal of Radio & Space Physics, vol. 40, pp. 72–75, 2011. [1] W. Gleissberg, “Probability laws of sunspot variations,” Astro- [21] R. P. Kane, “A preliminary estimate of the size of the coming physical Journal, vol. 96, p. 234, 1942. solar cycle 24, based on Ohl’s precursor method,” Solar Physics, [2]G.M.BrownandE.C.Butcher,“Theuseofabnormal vol. 243, no. 2, pp. 205–217, 2007. quiet days in Sq(H) for predicting the magnitude of sunspot maximum at the time of preceding sunspot minimum,” [22] W. D. Pesnell, “Predictions of solar cycle 24,” Solar Physics, vol. Planetary and Space Science, vol. 29, no. 1, pp. 73–77, 1981. 252, no. 1, pp. 209–220, 2008. [3] R. Thompson, “A technique for predicting the amplitude of [23] I. N. Kitashvili and A. G. Kosivichev, “Prediction of solar the solar cycle,” Solar Physics, vol. 148, no. 2, pp. 383–388, activity cycles by assimilating sunspot data into a dynamo 1993. model. Solar and stellar variability: impact on earth and planets,” in Proceedings of the International Astronomical [4] D. H. Hathaway, R. M. Wilson, and E. J. Reichmann, “A Union, no. 264, p. 202, IAU Symposium, 2009. synthesis of solar cycle prediction techniques,” Journal of Geophysical Research A, vol. 104, no. 10, pp. 22375–22388, [24]A.Kilcik,C.N.K.Anderson,J.P.Rozelot,H.Ye,G.Sugihara, 1999. and A. Ozguc, “Nonlinear prediction of solar cycle 24,” The [5] S. Duhau, “An early prediction of maximum sunspot number Astrophysical Journal, vol. 693, no. 2, p. 1173, 2009. in solar cycle 24,” Solar Physics, vol. 213, no. 1, pp. 203–212, [25] N. R. Rigozo, M. P. Souza Echer, H. Evangelista, D. J. R. 2003. Nordemann, and E. Echer, “Prediction of sunspot number [6] V. M. Silbergleit and P. A. Larocca, “Geomagnetic activity and amplitude and solar cycle length for cycles 24 and 25,” Journal solar cycles,” Advances in Space Research, vol. 36, no. 12, pp. of Atmospheric and Solar-Terrestrial Physics, vol. 73, no. 11-12, 2384–2387, 2005. pp. 1294–1299, 2010. [7] E. Friis-Christensen and K. Lassen, “Length of the solar cycle: [26] A. Ajabshirizadeh, N. M. Jouzdani, and S. Abbassi, “Neural an indicator of solar activity closely associated with climate,” network prediction of solar cycle 24,” Research in Astronomy Science, vol. 254, no. 5032, pp. 698–700, 1991. and Astrophysics, vol. 11, no. 4, pp. 491–496, 2011. [8] K. H. Schatten and W. D. Pesnell, “An early dynamo predic- [27] M. I. Pishkalo, “Prediciton of amplitude of solar cycle 24. tion: cycle 23 is approximately cycle 22,” Geophysical Research Based on polar magnetic field of the sun at cycle minimum,” Letters, vol. 20, no. 20, pp. 2275–2278, 1993. Sun and Geosphere, vol. 5, no. 2, pp. 47–51, 2010. [9] D. H. Hathaway, R. M. Wilson, and E. J. Reichmann, “A [28] R. S. Dabas and K. Sharma, “Prediction of solar cycle 24 using synthesis of solar cycle prediction techniques,” Journal of geomagnetic precursors: validation and update,” Solar Physics, Geophysical Research A, vol. 104, no. 10, pp. 375–388, 1999. vol. 266, no. 2, pp. 391–403, 2010. 6 Advances in Astronomy

[29] J. Javaraiah, “Predicting the amplitude of a solar cycle using the north-south asymmetry in the previous cycle: II. An improved prediction for solar cycle 24,” Solar Physics, vol. 252, no. 2, pp. 419–439, 2008. [30] A. Yoshida and H. Yamagishi, “Predicting amplitude of solar cycle 24 based on a new precursor method,” Annales Geophysicae, vol. 28, no. 2, pp. 417–425, 2010. [31] B. R. Durney, “On the diﬀerences between odd and even solar cycles,” Solar Physics, vol. 196, no. 2, pp. 421–426, 2000. [32] D. H. Hathaway and L. Rightmire, “Variations in the Sun’s meridional ﬂow over a solar cycle,” Science, vol. 327, no. 5971, pp. 1350–1352, 2010. Hindawi Publishing Corporation Advances in Astronomy Volume 2012, Article ID 126516, 5 pages doi:10.1155/2012/126516

Research Article Sunspot Cycle 24 and the Advent of Dalton-Like Minimum

H. S. Ahluwalia and R. C. Ygbuhay

Department of Physics and Astronomy, University of New Mexico, MSC07 4220, Albuquerque, NM 87131, USA

Correspondence should be addressed to H. S. Ahluwalia, [email protected]

Received 12 October 2011; Revised 2 December 2011; Accepted 15 December 2011

Academic Editor: J. Javaraiah

Copyright © 2012 H. S. Ahluwalia and R. C. Ygbuhay. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Ahluwalia and Jackiewicz (2011) have predicted that sunspot cycle 24 will be only half as active as cycle 23, reaching its peak in May 2013 ± 6 months. Here, we discuss the timeline for cycle 24 since its onset in December, 2008 and compare it to the timelines for the last ten cycles (14 to 23) of the 20th century; cycle 24 is rising the slowest. We speculate that cycle 24 may herald the onset of a Dalton-like minimum in the 21st century. The implications of this outcome on global temperature change and ensuing socioeconomic and political scenarios are discussed, on the basis of the historical record.

1. Introduction 2. Sunspot Series 1700–2010

The topic of climate change is of great importance and im- Figure 1 shows a plot of the annual mean SSNs for 1700– mense interest to the peoples of the world from the socioe- 2010, it spans part-Maunder minimum (1645–1715), the conomic and political perspectives. The contribution of the Dalton (1800–1830), and the Gleissberg (1889–1902) min- variations in solar activity to the observed climate change is ima; every fourth cycle is boldly labeled. The Dalton mini- controversial, but past history indicates that at least a part of mum (DM) was preceded by a long cycle 4 (164 months); the observed change may be related to the solar activity and cycle 23 was 159 months long. The declining phases of cycles a part of the expected future change may therefore arise from 4 and 23 lasted for 123 and 104 months, respectively. Further, the solar variability as represented by the sunspot numbers one notes that beginning with cycle 10, there is a pattern (SSNs). where even cycles of the even-odd pairing are less active; it disappears after cycle 21. Also, every third cycle is less active The art of predicting the peak SSNs for a cycle and its rise (14, 17, 20, and 23). AJ11 [4] suggest that cycle 24 may lead time has made signiﬁcant advances since cycle 20 forecasts. to a Dalton-like minimum in the 21st century. We examine Petrovay [1] provides an excellent review of the solar cycle the developmental phase of cycle 24 to date and discuss some prediction methods and forecasts resulting from them. The implications of this outcome, drawing from the historical empirical methods inspired by the work of Ohl [2, 3]made evidence. remarkably accurate forecasts for the last two solar cycles. Ahluwalia and Jackiewicz [4]—AJ11 hereafter—describe the unusual decay phase of the sunspot cycle 23 and use a 3. Planetary Indices Ap and aa heuristic approach (which is not based on any model) to Planetary index Ap was designed by Bartels [5]tomeasure make a prediction for sunspot cycle 24 parameters, inferring the geoeﬀectiveness of the solar corpuscular emission (now that it will be only half as active as cycle 23, reaching its solar wind). The index has a linear scale with a range between peak in May 2013 ± 6 months. The smoothed SSNs for cycle 0 (quietest day) and 400 (most disturbed day); the maximum 24 have been rising steadily (albeit slowly) since its onset in valueofAphasneverbeenobservedtodate,thedatago December, 2008. back to 1932. The aa index bears a linear correlation to Ap 2 Advances in Astronomy

200 1700–2010 150 Maunder 4 8 minimum Gleissberg minimum 20 100 Dalton 0 minimum 16 12 50 Sunspot numbers Sunspot 0 1700 1750 1800 1850 1900 1950 2000 (year) Figure 1: SSNs are plotted for 1700–2010; every fourth cycle and the grand minima are labeled.

and covers a longer period to 1868. AJ11 [4] note that aa 1963 69 75 81 87 93 99 2005 25 index seems to be riding a line of positive slope after the mMmM m Mmm M 11.5 1901 minimum; no such trend is seen in SSN minima in Figure 1. After 1996 aa/Ap minimum, the trend line changes 20 Ap slope to a steeper negative value; the slope of the trend line 9.5 before 1901 is also negative. We infer that aa/Ap data may 15 have a period ∼200 years (de Vries/Suess cycle) embedded in 7.5 (nT)

them. These indices measure the amplitude of the solar wind B Ap (2 nT) (2 Ap 10 electric ﬁeld [6] at earth orbit, given by the product of the solar wind speed (V)andB; in situ measurements of B and 5 5.5 V started in October 1963. The data are readily available at B the National Geophysical Data Center website SPIDER of the 0 3.5 National Oceanic and Atmospheric Agency at Boulder, CO, 1963 67 71 75 79 83 87 91 95 99 3 7 USA. AJ11 [4] forecast uses aa/Ap data and the methodology (Year) developed by Ahluwalia [7]. This approach led to an accurate forecast for the amplitude of cycle 23 [1]. Figure 2: Annual mean values of Ap and B at earth orbit are plotted for 1963–2009; at the bottom of the graph, the 3-cycle trend is highlighted by dashed lines. See text for details. 4. Grand Minima

Eddy [8] notes that Maunder minimum (1645–1715), a (ii) A 3-cycle quasiperiodicity (TCQP) in the limited B period of extremely low solar activity in which sunspots data is highlighted in Figure 2 with dashes, with a similar became scarce, corresponds to the coldest excursion of the trend in the Ap data. The slope of the trend line changes from Little Ice Age (1450–1850) in Europe and North America. positive to a steeper negative value after 1996, as also is the Reid [9] shows that 11-yr running mean of SSNs bears a close case for aa data (not shown). Ahluwalia [11] discovered the resemblance to the 11-year running average of the measured TCQP in an extended shielded ion chamber (IC) data (1937– sea surface temperatures (SSTs) for 1860–1980. Cliver et 1994) and noted its correspondence to TCQP present in the al. [10] show that there is a correspondence between the solar and geophysical data over a much longer time interval. trend of the annual mean (aa)min values and SSTs for 1880– He points out that cosmic ray intensity (CRI) minimum in 2000. These analyses indicate that there may be a cause-and- 1939 (cycle 17) is distinctly shallower than CRI minima for ff B e ect relationship between the SSNs, (aa)min/Ap, ,and cycles 18 and 19 and CRI minimum for cycle 20 is shallower SSTs. More work is needed to clarify the precise relationship than for cycles 21 and 22. Further, Ahluwalia [12,and between these physical parameters. references therein] shows that CRI is inversely proportional Figure 2 shows a plot of the annual mean values of Ap to B. So, TCQP in CRI implies the presence of TCQP in B and B for 1963–2009. The positions of the SSN maxima (M) data string for the period when in situ measurements of B and minima (m) are marked. The vertical dashed lines are are not available, that is, prior to 1963. drawn through the intervals of the solar polar field reversals. None of the currently available solar dynamo theories are In addition to the Schwabe cycle in the two time series, some able to account for the TCQP observed in the annual mean B additional features are also seen. values. Furthermore, the annual mean value (3.9 nT) of B in (i) The annual mean value of B reached the highest value 2009 is similar to its value in 1912 [4], indicating that we may (9.1 nT) in 1991 (cycle 22); in 2009, it declined to ∼2/3 of its be returning to the geomagnetic and solar conditions near value in 1963, the lowest ever measured since the measure- the early part of the 20th century (Gleissberg minimum), ments in space began in 1963. The reader is reminded that in terms of the interplanetary electromagnetic state at earth data at the Wilcox Solar Observatory (WSO) indicate that orbit. In 2009, CRI reached the highest value [13]observed solar polar field strength for cycle 23 is significantly lower since the instrumental (IC) measurements began in 1935. (∼50%) than for the previous 3 cycles. AJ11 [4] infer that if TCQP endures in the latter half of the Advances in Astronomy 3

90 150 Slow rise cycles Rapid rise cycles 19 120 22 23 20 60 21 90 15 18 17 14 60 30

Smooth SSNs Smooth SSNs Smooth 16 24 30

0 0 048 1216202428 048 1216202428 Months from cycle onset Months from cycle onset (a) (b)

Figure 3: (a) Timelines for the slow rise cycle of the 20th century are plotted. (b) Timelines for the rapid rise cycles of the 20th century are plotted.

de Vries cycle in the aa/Ap index, we may see the next two 50 sunspot cycles (25 and 26) to be successively less active; at this time, we cannot predict whether they will be long or 40 short cycles. It follows that the change in the slope of B 14 24 30 for cycle 23 may portend a decreasing trend in SSTs. One is reminded of the prolonged descending phase of cycle 4 20 5 leading to DM when earth was cooler. A careful analysis SSNs Smooth is needed to estimate how the anticipated decrease in SST 10 may compare with an increase in global warming due to an 0 increase in the concentration of the greenhouse gases (such 048 1216202428 as CO2) in the atmosphere and other causes described in the Months from cycle onset IPCC report. Figure 4: Cycles 5, 14, and 24 compared. 5. Timeline Comparisons

We use smoothed SSNs (to suppress the transients) in de- even-odd symmetry in sunspot cycles broke down with cycle scribing the profiles of several sunspot cycles of the last cen- 22. Figure 2 shows that the annual mean value of B reached tury. Figures 3(a) and 3(b) show a comparison between the the highest value in cycle 22 and the lowest value in cycle timelines of cycle 24 activity and ten prior cycles (14–23) for 23. Furthermore, the data at the Wilcox Solar Observatory 29 months after the onset. The cycles are normalized at the indicate that the solar polar field strength for cycle 23 is lower origin by subtracting the smoothed SSN at the onset from (∼50%) than for the previous three cycles. The peculiar solar those for the subsequent months. The observed timelines fall behavior during cycles 22-23 is not understood at present. into two distinct groups. The cycles 14, 15, 17, 20, and 23 Figure 4 shows a comparison between the ascending are slow risers like cycle 24; they are depicted in Figure 3(a), phases of cycles 5, 14, and 24 for 29 months after the onset. and the slow rise cycles have <100 smooth SSNs at their peak. Clearly, cycle 5 is the slowest riser; at its peak, the smooth The cycles 16, 18, 19, 21, and 22 rise rapidly (compare scales SSN 49.2 may be compared to 56.4 predicted for cycle 24. on the left of Figures 3(a) and 3(b)); they have >100 smooth Also, cycle 24 seems to follow the timeline of cycle 14, and it SSNs at their peak. They are plotted in Figure 3(b); cycles 18, led to the onset of the Gleissberg minimum; at its peak, the 19, 21, 22 are very active cycles (see Figure 1 above), 19 being smooth SSN reached a value of 64.2. At this point in time, it the most active cycle ever observed. Additional points noted is not clear whether the timeline of cycle 24 will lie betweet areasfollows. those of cycles 5 and 14. We will follow differences between For the 29-month period shown in Figure 3(a), the time- the three timelines in the future as cycle 24 reaches its peak line for cycle 23 overlaps with that for cycle 20 since the onset in 2013. for 21 months (the profiles are barely distinguishable). Early on, cycle 24 follows cycle 17 timeline closely but deviates 6. Global Temperature Change significantly later on. After 27 months, cycle 24 became more active than cycle 14. An interesting question is whether cycle Feulner and Rahmstorf [14] use a coupled climate model 24 may end up being more like cycle 5 that led to the onset of to explore the future global temperatures. They expect a the DM. temperature offset of no more than −0.30◦C in 2100, much Figure 3(b) shows that cycle 22 started out to be more smaller than the published estimates for anthropogenic active than cycle 19, but became less so after 18 months. The global warming [IPCC, 2001]. 4 Advances in Astronomy

Akasofu [15] reviews the available data on sea-level century, the higher food prices (if they occur) may cause changes, glacier retreat, tree-ring observations, ice cores, and social and political upheaval in the overpopulated countries changes in CRI from the year 1000 to present. He concludes of Asia and Africa; people living in the towns of sub-Saharan that the Little Ice Age (LIA) occurred in Asia as well. He Africa spend a bigger share of their income on food than do infers that the global recovery from the LIA has proceeded urban residents almost anywhere else in the world. Laborers continuously (in about a linear manner) from 1800–1850 use up over half their wage just to eat. So, they will spend less to the present @∼0.5◦C/century. Akasofu predicts that the on school fees, sanitation, and health. temperature increase in 2100 will be 0.5◦C ± 0.2◦Cin The food, fuel, and climate crises are by themselves seri- contrast to 4◦C ± 2◦C predicted by the IPCC. An interesting ous issues, but taken together, their impact could be disas- possibility presents itself. If Akasofu and Fuelner and Rahm- trous for the world economy and intranational and interna- storf are both right, we may end up with little net long-term tional conflicts, threatening the security of individuals and temperature change in the year 2100. nations. Optimistically speaking, we may hope that advances Lean et al. [16] show that the total solar irradiance (TSI) in sciences and the agricultural technology in the 21st decreased significantly during the DM; the decrease was even century may meet the challenge of food shortage and mit- more remarkable for the Maunder minimum (MM) for an igate the adverse circumstances forecast by Thomas Robert extended time period (see Figure 2). Since these estimates Malthus FRS (1766–1834) nearly two centuries ago. In this are all proxy based, the relevant science is far from settled context, we note further that there were remarkable strides yet. For example, Schrijver et al. [17] suggest that TSI during in the scientific enterprise during DM, for example, advances that period may not have been as low as previously thought. in electromagnetism and thermodynamics. The University of They analyze direct measurements of solar magnetic activity Berlin was founded in 1810; it led to a new model for science during the recent 2008-2009 period of low sunspot activity, teaching, later copied worldwide. which they argue is similar to the activity level during the MM. They find that even when there are no sunspots, the sun has a baseline level of magnetic activity. This baseline 7. Summary has not been taken into account in previous estimates of TSI We have examined the progress of SSN cycle 24 activity during the MM, which are based solely on SSNs. The authors since its onset in December, 2008 and compared it with the suggest that earlier estimates of the TSI during the MM are timelines of the last ten solar cycles (14–23) of the 20th too low. They argue that MM probably had levels of magnetic century. We find that cycle 24 is the slowest riser. According activity and TSI similar to the 2008-2009 values. So, factors to Waldmeier [24], the rise time of a cycle is determined by a other than low TSI resulting from low sunspot activity must single parameter, namely, the SSN at its peak; he showed that have contributed to the LIA, inferring that drivers other than active cycles have a steeper rise and moderate cycles rise more TSI dominate the long-term climate change on earth. slowly. Ahluwalia [7] certified the validity of the Waldmeier Ahluwalia [18] argues that if solar wind existed during effect for seven cycles (17 to 23) of the 20th century, showing the MM, the value of B must have been ≥3.3 nT. In our that moderate cycles attain their maximum an average of opinion, the role of B in contributing to the global climate eight months later and have a tendency to linger near the change is neither fully appreciated nor understood. IPCC maximum. The physical cause of the Waldmeier effect and undervalues the forcing arising from changes in solar activity its relationship to the workings of the solar dynamo is not and B which may turn out to be much more important than known. Nevertheless, the observed trend to date of cycle 24 the forcing from CO . 2 timeline strongly suggests that AJ11 [4]forecastofverylow There is a great interest in understanding the relationship activity for cycle 24 is quite reasonable and likely to come between cosmic ray caused ionization in the atmosphere true. We have discussed the implications of this outcome on and the cloud cover [19–22, and references therein]. The the future earth climate change and the socioeconomic and underlying hypothesis (unverified experimentally) is that political scenarios drawing from the past history. cosmic rays, modulated by solar activity, influence cloud formation and therefore temperature. So, the natural versus anthropogenic causes of global warming debate is likely to Acknowledgments continue for a while, yet we still do not know as much as we think we know. The challenges posed by the climate change The authors are grateful to the providers of solar, interplan- can only be addressed by interdisciplinary efforts, using high- etary, and geomagnetic data used in this study. One referee quality data. Perhaps we stand at the crossroads. made useful suggestions. This research is supported by NASA Our heuristic analysis (which is not based on any model) EPSCoR Award NNX09AP76A-Q01378. cannot rule out the premise that cycle 24 may herald the onset of a DM-like minimum in the present century [4]. References

6.1. Probable Socioeconomic and Political Scenarios. It is in- [1] K. Petrovay, 7, 1-63, 2010, http://arxiv.org/PS cache/arxiv/pdf/ teresting to note that the interval of the DM coincided with 1012/1012.5513v2.pdf. a signiﬁcant rise in inﬂation in England, for example, the [2] A. I. Ohl, “Wolf’s number prediction for the maximum of the price of wheat rose by a factor ∼2[23]. Considering that cycle 20,” Solnechnye Dannye (solar data, in Russian) Bulletin, human population is projected to reach 10 billion in the 21st vol. 12, pp. 84–85, 1966. Advances in Astronomy 5

[3] A. I. Ohl, “A preliminary forecast of some parameters of 21 [24] M. Waldmeier, Ergebnisse und Probleme der Sonnenforschung, solar cycle activity,” Solnechnye Dannye Bulletin, vol. 9, pp. 73– Leipzig, Germany, 2nd edition, 1955. 75, 1976. [4] H. S. Ahluwalia and J. Jackiewicz, “Sunspot cycle 23 descent to an unusual minimum and forecasts for cycle 24 activity,” Advances in Space Research. In press. [5] J. Bartels, Collection of Geomagnetic Planetary Index Kp and Derived Daily Indices Ap and Cp for the Years 1932–1961,North Holland, New York, NY, USA, 1962. [6] H. S. Ahluwalia, “Ap time variations and interplanetary magnetic field intensity,” Journal of Geophysical Research A, vol. 105, no. 12, pp. 27481–27487, 2000. [7] H. S. Ahluwalia, “Meandering path to solar activity forecast for cycle 23,” in Proceedings of the 10th International Solar Wind Conference, M. Velli, R. Bruno, and F. Malra, Eds., vol. CP679, pp. 176–179, The American Institute of Physics, 2003. [8] J. A. Eddy, “The maunder minimum,” Science, vol. 192, no. 4245, pp. 1189–1202, 1976. [9] G. C. Reid, “Influence of solar variability on global sea surface temperatures,” Nature, vol. 329, pp. 142–143, 1987. [10] E. W. Cliver, V. Boriakoff, and J. Feynman, “Solar variability and climate change: geomagnetic aa index and global surface temperature,” Geophysical Research Letters,vol.25,no.7,pp. 1035–1038, 1998. [11] H. S. Ahluwalia, “Three activity cycle periodicity in galactic cosmic rays,” in Proceedings of the 25th International Cosmic Ray Conference, vol. 2, pp. 109–112, Durban, South Africa, 1997. [12] H. S. Ahluwalia, “Cycle 20 solar wind modulation of galactic cosmic rays: understanding the challenge,” Journal of Geophys- ical Research A, vol. 110, no. 10, Article ID A10106, 2005. [13] H. S. Ahluwalia and R. C. Ygbuhay, “The onset of sunspot cycle 24 and galactic cosmic ray modulation,” Advances in Space Research, vol. 48, no. 1, pp. 61–64, 2011. [14] G. Feulner and S. Rahmstorf, “On the effect of a new grand minimum of solar activity on the future climate on Earth,” Geophysical Research Letters, vol. 37, Article ID L05707, 2010. [15] S. Akasofu, “On the recovery from the little ice age,” Natural Science, vol. 2, pp. 1211–1224, 2010. [16] J. Lean, J. Beer, and R. Bradley, “Reconstruction of solar irradiance since 1610: implications for climate change,” Geophysical Research Letters, vol. 22, no. 23, pp. 3195–3198, 1995. [17]C.J.Schrijver,W.C.Livingston,T.N.Woods,andR.A. Mewaldt, “The minimal solar activity in 2008–2009 and its implications for long-term climate modeling,” Geophysical Research Letters, vol. 38, Article ID L06701, 6 pages, 2011. [18] H. S. Ahluwalia, “Timelines of cosmic ray intensity, Ap,IMF, and sunspot numbers since 1937,” Journal of Geophysical Research, vol. 116, Article ID A12106, 9 pages, 2011. [19] E. P. Ney, “Cosmic radiation and weather,” Nature, vol. 183, pp. 451–452, 1959. [20] J. T. A. Ely, J. J. Lord, and F. D. Lind, “Annual modulation of galactic cosmic rays circa 1 GV and relevance to tropospheric processes,” in Proceedings of the 23rd International Cosmic Ray Conference, vol. 3, pp. 586–589, Calgary, Canada, 1993. [21] H. Svensmark and E. Friis-Christensen, “Variation of cosmic ray flux and global cloud coverage—a missing link in solar- climate relationships,” Journal of Atmospheric and Solar- Terrestrial Physics, vol. 59, no. 11, pp. 1225–1232, 1997. [22] H. Svensmark, “Influence of cosmic rays on Earth’s climate,” Physical Review Letters, vol. 81, no. 22, pp. 5027–5030, 1998. [23] D. H. Menzel, Our Sun, Harvard University Press, Cambridge, Mass, USA, 1959. Hindawi Publishing Corporation Advances in Astronomy Volume 2012, Article ID 623709, 5 pages doi:10.1155/2012/623709

Research Article Preliminary Results on Irradiance Measurements from Lyra and Swap

S. T. Kumara,1 R. Kariyappa,2 M. Dominique,3 D. Berghmans,3 L. Dame,´ 4 J. F. Hochedez,4 V. H. Doddamani,5 and Lakshmi Pradeep Chitta2

1 Department of Physics, Auden Technology and Management Academy (ATMA), Bangalore 562112, India 2 Indian Institute of Astrophysics, Bangalore 560 034, India 3 Royal Observatory of Belgium (ROB), Circular Avenue 3, B-1180 Brussels, Belgium 4 LATMOS, 11 Boulevard d’Alembert, 78280 Guyancourt, France 5 Department of Physics, Bangalore University, Bangalore 560056, India

Correspondence should be addressed to S. T. Kumara, kumarapsce@rediﬀmail.com

Received 14 November 2011; Accepted 9 December 2011

Academic Editor: J. Javaraiah

Copyright © 2012 S. T. Kumara et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The first and preliminary results of the photometry of Large Yield Radiometer (LYRA) and Sun Watcher using Active Pixel system detector and Image Processing (SWAP) onboard PROBA2 are presented in this paper. To study the day-to-day variations of LYRA irradiance, we have compared the LYRA irradiance values (observed Sun as a star) measured in Aluminum filter channel (171 A–˚ 500 A)˚ with spatially resolved full-disk integrated intensity values measured with SWAP (174 A)˚ and Ca II K 1 A˚ index values (ground-based observations from NSO/Sac Peak) for the period from 01 April 2010 to 15 Mar 2011. We found that there is a good correlation between these parameters. This indicates that the spatial resolution of SWAP complements the high temporal resolution of LYRA. Hence SWAP can be considered as an additional radiometric channel. Also the K emission index is the integrated intensity (or flux) over a 1 A˚ band centered on the K line and is proportional to the total emission from the chromosphere; this comparison clearly explains that the LYRA irradiance variations are due to the various magnetic features, which are contributing significantly. In addition to this we have made an attempt to segregate coronal features from full-disk SWAP images. This will help to understand and determine the actual contribution of the individual coronal feature to LYRA irradiance variations.

1. Introduction below 2400 A˚ in the stratosphere and mesosphere is of special interest for life and mankind. However, the photons above The Sun is the primary source of energy responsible for gov- 2000 A˚ get dissociated in the stratosphere and disturb the erning both the weather and climate of Earth. For that reason balance of the ozone (e.g., [4, 5]). This is because the ozone alone one would expect that changes in the amount and type gas is produced naturally in the stratosphere where it strongly of energy Earth received from the Sun could alter weather absorbs incoming UV radiation. But as stratospheric ozone and climate on the Earth. Hence the knowledge of the solar spectral irradiance is of large interest to solar physics, decreases, UV radiation is allowed to pass through, and aeronomy, and to other fields of heliospheric or planetary exposure at the Earths surface increases. Exposure to shorter research. The solar ultraviolet (UV) irradiance below 3000 A˚ wavelengths increases by a larger percentage than exposure is the main source of the energy converted in the Earth’s to longer wavelengths. The UV irradiance variability has sig- ff atmosphere, controlling its thermal structure, dynamics, nificant e ects on human technologies too, currently ad- and chemistry through photodissociation and photoioniza- dressed in the frame of Space Weather studies. tion [1]. Because of these, changes in UV irradiance influence For more than two decades, solar UV irradiance obser- the concentration of the ozone in the Earth’s atmosphere [2, vations have been monitored from several satellites. These 3] and may play a significant role in the process of the global space UV irradiance observations have shown that the warming. The balance of the ozone formed by radiation UV flux changes over the solar cycle, being higher during 2 Advances in Astronomy maximum activity conditions, and short-term changes (from days to months) are superposed on the long-term variation LYRA3SXR LYRA 1 [6, 7]. The long-term UV irradiance variations are attributed LYRA 4 SXR LYRA 2 to the changing emission of bright magnetic elements [8– LYRA 3 10], and the short-term variations are directly associated LYRA 4 with the growth and decay of active regions [11]. The cur- SWAP rent UV irradiance models are based on integrated full-disk X-ray Ultraviolet surrogates; therefore they cannot provide adequate infor- Visible Infrared mation on the physical causes of the observed UV irradiance changes. In the last decade, there are good time se- 1 10 100 1000 quence observations available from several space experi- Wavelength (nm) ments, Solar Heliospheric Observatory/Extreme Ultraviolet Imaging Telescope/Michelson Doppler Imager (SOHO/EIT/ Figure 1: The bandpasses of SWAP and four LYRA channels MDI), to measure the various parameters from spatially over two solar spectra, one from solar maximum and one resolved images of the Sun. And recently we have high- from solar minimum, observed by Thermosphere Ionosphere Mesosphere Energetics and Dynamics Mission/Solar EUV Experi- resolution observations from Solar Dynamic Observatory/ ment (TIMED/SEE) and Solar Radiation and Climate Experiment Atmospheric Imaging Array/Helioseismic-Magnetic Imager (SORCE) (Courtesy: Dr. Sarp Yalim). (SDO/AIA/HMI), Project for Onboard Autonomy 2/Large Yield Radiometer/Sun Watcher using Active Pixel system detector and Image Processing (PROBA2/LYRA/SWAP). All SWAP response of them differ in spectral coverage, time coverage, time 0.0012 3000 cadence, and nature of the instrument (spectrograph, pho- tometer, or imager). In addition, we have ground-based ob- 0.001 Fe X 2500 servations of Ca II K spectroheliograms from NSO/Sac Peak and also from many other observatories in the world. All 0.0008 2000 these observations will provide the best data set so far. The 0.0006 Fe X 1500 strategy is thus to bridge the most reliable observations, with the best possible models (e.g., [12–14]). The spatially 0.0004 1000 resolved full-disk images obtained from space have to be Fe X compared with solar images from ground-based observa- SWAP response (DN/ph) 0.0002 500 Fe X tions. The full-disk precise photometric images and full-disk Active sun response (DN/s/nm) Fe X magnetograms will help to explore the temporal and spatial 0 0 variability of the solar UV irradiance and to determine the 16 16.5 17 17.5 18 18.5 19 19.5 couplings with the magnetic structures. wavelength (nm) PROBA2 is the second satellite in the European Space Calculated bandpass Agency’s series of PROBA low-cost satellites that are being Measured bandpass (DR) used to validate new spacecraft technologies while also car- Active sun response rying scientific instruments. It was launched on November Figure 2: The bandpass of SWAP with its nominal spectral interval 2, 2009, with a Rockot launcher in a sun-synchronous low with peak at 17.4 nm (Courtesy: Dr. Sarp Yalim). Earth orbit at an altitude of 725 km. It provides a technology demonstration platform for testing a number of instruments and techniques relevant to solar physics, space weather, aeronomy, avionics, spacecraft attitude control, power system, unwanted visible, but attenuate seriously the desired UV and propulsion. The orbit of PROBA2 is eclipse-free for nine radiation. LYRA has a very high cadence up to 100 Hz. months per year, thus the orbit is well suited for the solar SWAP [17, 18] telescope is a compact EUV imager on observing instruments onboard, namely, LYRA and SWAP. board the PROBA2 mission that will observe the Sun in LYRA is the solar UV radiometer that will embark in 2006 extreme ultraviolet (EUV) and provides continuous images onboard PROBA2, a technologically oriented ESA micromis- of the Sun (solar corona) in a narrow bandpass with peak at sion [15, 16]. It will be monitoring the solar irradiance in 174 A(˚ Figure 2), corresponding to a formation temperature four carefully selected UV passbands. The channels have of 1 million degree Kelvin. The SWAP instrument was built been chosen for their relevance to solar physics, aeronomy, upon the heritage of the Extreme ultraviolet Imaging Tele- and space weather Figure 1: (1) the 1150–1250 ALyman-˚ α, scope (EIT) which monitors the solar corona since 1996 on (2) the 2000–2200 A˚ Herzberg continuum range, (3) the Alu- board the SOHO mission. SWAP has a field of view of 54 minium filter channel (171–500 A)˚ including He II at 304 A,˚ arcmin. This field of view can easily be extended though and (4) the Zirconium filter channel (10–200 A).˚ LYRA spacecraft offpointings that can be commanded from the benefited from wide bandgap detectors based on diamond. PROBA2 Science Center in a matter of hours. The effective It was the first space assessment of a pioneering UV de- field of view for static coronal structures is therefore 65 tectors program. It makes the sensors radiation hard and arcmin and probably even larger for eruptions. This is “solar-blind”, which makes dispensable filters that block the much larger than the FOV of SOHO/EIT (45 arcmin) or Advances in Astronomy 3 )

SDO/AIA (41 arcmin). Whereas the AIA imager on SDO 2 −3 ×10 LYRA (01 April 2010–14 March 2011) will provide unprecedented images in spatial and temporal 2.4 2.35 resolution of the solar disk, SWAP is the only EUV imager 2.3 2.25 in space to fill the gap between the solar limb and the far- 2.2 out corona as imaged by the SOHO/LASCO (Large Angle 2.15 2.1 and Spectrometric Coronagraph) coronagraphs. SWAP also Irradiance (W/m 50 100 150 200 250 300 offers the advantage of high image cadence (maximal 3 per Time in days (01.04..2010–14 03.2011) minute, 1 per minute in nominal operations) to monitor (a) transitory phenomena. With this higher cadence, SWAP will SWAP (01 April 2010–14 March 2011) monitor events in the low solar corona that might be relevant 14 for space weather. These events include EIT waves (global 13 waves propagating across the solar disc from the CME erup- 12 tion site), EUV dimming regions (transient coronal holes 11 ff Integrated 10 from where the CME has lifted o ), and filament instabilities intensity (DN/s) 50 100 150 200 250 300 (a specific type of flickering during the rise of a filament). Time in days (01.04..2010–14 03.2011) The H and K lines of ionized calcium have been recognized as useful indicators for identifying regions of chro- (b) mospheric activity on the solar surface. These lines are very Ca ii K emission index (01 April 2010–14 March 2011) sensitive to the variations in temperature and the magnetic 0.093 0.092 field strength. Therefore they are excellent indicators of the 0.091 index 0.09 chromospheric structural changes related to solar magnetic 0.089 1-A emission 0.088 activity. The images observed in Ca II H or K line and in 50 100 150 200 250 300 He II line are identical to each other. The parameter that Time in days (01.04..2010–14 03.2011) best quantifies the chromospheric emission in the K line is the so-called K emission index introduced by [19]. The K (c) ˚ emission index is the integrated intensity (or flux) over a 1 A Figure 3: Time series (day-to-day variations) of LYRA irradiance band centered on the K line and is proportional to the total values of channel 3 (171 A–500˚ A),˚ full-disk integrated intensity emission from the chromosphere [9, 20–25]. The Sun viewed values of SWAP (174 A),˚ and 1 A˚ emission index values of Ca II K as a star through a 1 A˚ passband filter centered on the K (393.4 nm) for the period from 01 April 2010 to 15 Mar 2011. Note line would appear as a variable, showing both the rotational that there is a good correlation in all the three time series. modulation and the 11-year cycle [26].

2. Observations and Data Analysis of LYRA. SWAP is not designed to see flares at full extent. As a consequence of the limited range, flare pixels are soon In this paper, LYRA irradiance observations measured in saturated and so the flares can hardly be seen in SWAVINT channel 3 (Aluminium filter channel: 171 A–500˚ A,˚ including since only a few pixels are affected and saturated immediately. He II at 304 A),SWAP(174˚ A)˚ full-disk integrated intensity (SWAVINT, level-3) values, and Ca II K (393.4 nm) time series values (corresponding to 1 A˚ emission index) for the 3. Results and Discussion period of observations from April 1, 2010 to March 15, 2011 are used. To determine the day-to-day variations of LYRA We have compared the LYRA irradiance values (observed channel-3 (cadence averaged to 1 minute), SWAP (cadence Sun as a star) measured in channel 3 (Aluminium filter averaged to 2 minute) time series, and Ca II K 1 A˚ emission channel: 171 A–500˚ A,˚ which includes He II at 304 A˚ also) index, we have read the fits files of LYRA and SWAP data and with spatially resolved full-disk integrated intensity values carried out the analysis using Solar Software (SSW) library measured in SWAP (174 A)˚ for the period from 01 April 2010 in IDL. SWAVINT is a keyword in the calibrated SWAP fits to 15 Mar 2011. Also we have compared LYRA irradiance files and corresponds to the average intensity of a whole values and SWAP full-disk integrated intensity values with SWAP image (i.e., a fully calibrated image except applying 1 A˚ emission index values of Ca II K (ground based obser- transformation, which is placing the Sun in the center of the vations from NSO/Sac Peak) for the same period. We have image and aligning the solar north to the top of the image) observed from the time series plot (Figure 3) and scatter plot normalized with its exposure time (Figure 4) that the long-term variability of the LYRA channel 3, the Aluminum filter channel has shown a good correlation P with spatially resolved full-disk integrated intensity values of = 1 1 SWAVINT t P DNi,(1)SWAP and the correlation is found to be 60 percent (r = i= 1 0.6). However the correlation between LYRA and Ca II K where t is the exposure time of the image, P is the number of (r = 0.47),aswellasbetweenSWAPandCaIIK(r = pixels which is 1024 × 1024 for the whole image, and DN is 0.5), is comparatively lesser than the correlation between the digital number in pixel i. The unit of SWAVINT is DN/s. LYRA and SWAP. This is because there is a data gap in Ca The dynamic range of SWAP is much smaller than the one II K 1 A˚ emission index values. These results suggest that 4 Advances in Astronomy

LYRA-SWAP (01 April 2010–14 March 2011) Raw image 14 1500 12 10 1000 Integrated 8 intensity (DN/s)

0.003 500 0.0022 0.0024 0.0026 0.0028 0.0032 Irradiance (W/m2) (a) 0 LYRA-Ca ii K (01 April 2010–14 March 2011) 0.102 −500 0.098

index 0.094 − 1-A emission 0.09 1000 0.003 0.0022 0.0024 0.0026 0.0028 0.0032 −1500 Irradiance (W/m2) −1500 −1000 −500 0 500 1000 1500

(b) (a)

SWAP-Ca ii K (01 April 2010–14 March 2011) Segment image 0.102 1500 0.098

index 0.094 1000

1-A emission 0.09 8101214 Integrated intensity (DN/s) 500 (c)

Figure 4: (a) Scatter plot between LYRA irradiance values of 0 channel 3 and full-disk integrated intensity values of SWAP (r = . 0 6). (b) Scatter plot between LYRA irradiance values of channel 3 −500 and 1 A˚ emission Index values of Ca II K (r = 0.47). (c) Scatter plot between full-disk integrated intensity values of SWAP and 1 A˚ emission Index values of Ca II K (r = 0.5). −1000

−1500 −1500 −1000 −500 0 500 1000 1500 the LYRA irradiance variations are due to the variations of solar magnetic features observed in SWAP and Ca II K. The (b) spatial resolution of SWAP complements the high temporal Figure 5: (a) Represents original SWAP image and (b) segregated resolution of LYRA. Hence SWAP can be considered as an (only active regions) SWAP image. additional radiometric channel. Further these comparisons clearly explain the irradiance variations are due to the various magnetic features, which are contributing significantly. In order to understand the actual contribution of the the nature and sources of variations in UV irradiance related individual coronal features to LYRA irradiance variations, we to various bright magnetic features as a function of solar ff are segregating the coronal features from full-disk spatially cycle. The outcome of this research e ort will also be a resolved images obtained from PROBA2/SWAP (174 A).˚ The significant improvement of the current UV irradiance mod- morphological structures (pattern recognition), geometrical els and will have a great importance in both atmospheric and location, intensity levels and gradients, contrasts, and the space physics. This model will be an ideal platform to present sizes will be used as main criteria to recognize and segregate and incorporate the spatially resolved research results into the various coronal features. We have done a very prelimi- it. The results of the segmentation of the coronal features in nary analysis on the SWAP images to segregate different correlation to UV irradiance will be published elsewhere. onal features. A sample of segregated image containing active regions is shown in Figure 5 in comparison with original Acknowledgments image. Further detailed image analysis on large number of full-disk images is in progress. These results are helpful to This research work was carried out under PROBA2 Guest make feature-to-feature correlations and to understand and Investigators Program. A part of this research work was done establish their role and contribution to UV irradiance varia- while R. Kariyappa was visiting Royal Observatory of Belgi- bility. Also these investigations will help better to understand um in 2010 and 2011 as a Guest Investigator. The authors Advances in Astronomy 5 wish to express their sincere thanks to Ingolf Dammasch the AGU Fall Meeting Abstracts, p. B2, San Francisco, Calif, and Sarp Yalim, for their help in using the LYRA irradiance USA, December 2003. and SWAP full-disk integrated intensity data. Thanks to A.A [14] J. L. Lean, H. P. Warren, J. T. Mariska, and J. Bishop, “A new Pevtsov, National Solar Observatory/Synoptic Optical Long- model of solar EUV irradiance variability 2. Comparisons with term Investigations of the Sun-Integrated Sunlight Spec- empirical models and observations and implications for space trometer (NSO/SOLIS-ISS) for providing Ca II K parameter weather,” Journal of Geophysical Research A, vol. 108, no. 2, article no. 1059, 2003. time series data. SOLIS data used here are produced coopera- [15] J. F. Hochedez, W. Schmutz, Y. Stockman et al., “LYRA, a solar tively by National Science Foundation/National Solar Obser- UV radiometer on Proba2,” Advances in Space Research, vol. vatory (NSF/NSO) and National Aeronautics and Space 37, no. 2, pp. 303–312, 2006. Administration/Living with a Star Program (NASA/LWS). [16] A. Benmoussa, I. E. Dammasch, J.-F. Hochedez et al., “Preight They would like to express their sincere thanks to the two calibration of LYRA, the solar VUV radiometer on board referees for their critical comments and suggestions which PROBA2,” Astronomy and Astrophysics, vol. 508, pp. 1085– helped to improve the paper. 1094, 2009. [17] D. Berghmans, J. F. Hochedez, J. M. Defise et al., “SWAP onboard PROBA 2, a new EUV imager for solar monitoring,” References Advances in Space Research, vol. 38, pp. 1807–1811, 2006. [18] J.-P. Halain, D. Berghmans, J.-M. Defise et al., “First light of [1] G. J. Rottman, “Observations of solar UV and EUV variabil- SWAP on-board PROBA2,” in Space Telescopes and Instrumen- ity,” Advances in Space Research, vol. 8, no. 7, pp. 53–66, 1988. tation 2010: Ultraviolet to Gamma Ray, vol. 7732 of Society [2] G. Brasseur, “The response of the middle atmosphere to long- of Photo-Optical Instrumentation Engineers (SPIE) Conference term and short-term solar variability: a two-dimensional Series, July 2010. model,” Journal of Geophysical Research, vol. 982, pp. 23079– [19] O. C. Wilson, “Flux measurements at the centers of stellar h- 23090, 1993. and kLines,” Astrophysical Journal, vol. 153, p. 221, 1968. [3] L. L. Hood, J. L. Jirikowic, and J. P. McCormack, “Quasi- [20] R. Kariyappa and K. R. Sivaraman, “Variability of the solar decadal variability of the stratosphere: in uence of long-term chromospheric network over the solar cycle,” Solar Physics, vol. solar ultraviolet variations,” Journal of Atmospheric Sciences, 152, no. 1, pp. 139–144, 1994. vol. 50, pp. 3941–3958, 1993. [21] R. Kariyappa, J. M. Pap, K. S. Balasubramaniam, and J. R. [4] T. Egorova, E. Rozanov, E. Manzini et al., “Chemical and Kuhn, “Preliminary results of the analysis of CAII K spectro- dynamical response to the 11-year variability of the solar heliograms,” in Helioseismology, vol. 376 of ESA Special Publi- irradiance simulated with a chemistry-climate model,” Geo- cation, p. 429, 1995. physical Research Letters, vol. 31, no. 6, Article ID L06119, [22] R. Kariyappa, “Quiet-sun variability with the solar cycle,” 2004. in High Resolution Solar Physics: Theory, Observations, and [5] E. Rozanov, M. Schraner, M. Wild et al., “Assessment of Techniques,T.R.Rimmele,K.S.Balasubramaniam,andR. the Ozone and Temperature Trends for 1975–2000 with a R. Radick, Eds., vol. 183 of Astronomical Society of the Pacific transient Chemistry-Climate Model,” in Proceedings of the 35th Conference Series, p. 501, 1999. COSPAR Scientific Assembly, J.-P. Paille,´ Ed., vol. 35, p. 2640, [23] R. Kariyappa, “Call K imaging to understand UV irradiance 2004. variability,” Journal of Astrophysics and Astronomy, vol. 21, no. [6] H. Hudson and R. Willson, “The nature of the solar-cycle vari- 3-4, pp. 293–297, 2000. ation of total irradiance,” in Solar Radiative Output Variations, [24] R. Kariyappa and K. R. Sivaraman, “Variability of caII K emis- P. Foukal, Ed., p. 318, 1988. sion flux over the solar cycle,” Bulletin of the Astronomical [7] C. Frohlich, “Irradiance observations of the sun,” in Poster Society of India, vol. 33, pp. 365–365, 2005. Proceedings from IAU Colloquium 143: The Sun as a Variable [25] R. Kariyappa and L. Dame, “Contribution of chromospheric Star: Solar and Stellar Irradiance Variations,J.M.Pap,C.Frohl- features to UV irradiance variability,” in Proceedings of the IAU ich, H. S. Hudson, and S. K. Solanki, Eds., p. 28, 1994. Joint Discussion, vol. 8, August 2006. [8] P.Foukal and J. Lean, “Magnetic modulation of solar luminos- [26] M. K. V. Bappu and K. R. Sivaraman, “K emission-line widths ity by photospheric activity,” Astrophysical Journal, vol. 328, and the solar chromosphere,” Solar Physics,vol.17,no.2,pp. pp. 347–357, 1988. 316–330, 1971. [9] R. Kariyappa and J. M. Pap, “Contribution of chromospheric features to uv irradiance variability from spatially-resolved ca ii k spectroheliograms i. A New Method of Analysis and Preliminary Results,” Solar Physics, vol. 167, no. 1-2, pp. 115– 123, 1996. [10]J.R.Worden,O.R.White,andT.N.Woods,“Evolutionof chromospheric structures derived from Ca II K spectroheliograms: implications for solar ultraviolet irradiance variability,” Astrophysical Journal, vol. 496, no. 2, pp. 998–1014, 1998. [11] J. Lean, “Solar ultraviolet irradiance variations—a review,” Journal of Geophysical Research, vol. 92, pp. 839–868, 1987. [12]H.P.Warren,J.T.Mariska,andJ.Lean,“Anewmodelofsolar EUV irradiance variability 1. Model formulation,” Journal of Geophysical Research A, vol. 106, no. 8, pp. 15745–15757, 2001. [13] T. Woods, F. Eparvier, and D. Woodraska, “Solar ultraviolet variability during the TIMED mission,” in Proceedings of Hindawi Publishing Corporation Advances in Astronomy Volume 2012, Article ID 263818, 6 pages doi:10.1155/2012/263818

Research Article Observations of Correlated Behavior of Two Light Torsion Balances and a Paraconical Pendulum in Separate Locations during the Solar Eclipse of January 26th, 2009

A. F. Pugach1 and D. Olenici2

1 Main Astronomical Observatory of National Academy of Sciences, 03680 Kiev, Ukraine 2 Astronomical Observatory, University of Stefan cel Mare, 720229 Suceava, Romania

Correspondence should be addressed to A. F. Pugach, [email protected]

Received 8 September 2011; Revised 15 November 2011; Accepted 29 November 2011

Academic Editor: J. Javaraiah

Copyright © 2012 A. F. Pugach and D. Olenici. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

On January 26th, 2009, simultaneous observations of the reactions of two very light torsion balances (Kiev, Ukraine) and a paraconical pendulum (Suceava, Romania, 440 km away) were performed during a solar eclipse that was not visible at those locations but only in the Indian Ocean. Signiﬁcant correlation between the behavior of the torsion balances and the pendulum was observed. The conclusion is that a solar eclipse inﬂuences the reactions of torsion balances and pendulums, even in areas of the Earth where it is not optically visible.

1. Introduction answer to the question of how frequent and unique anomalies really are. Despite the numerous positive conclusions, in It has repeatedly been reported that during solar eclipses some cases, ambiguous and even negative results have been ff nonconventional physical e ects are sometimes observed. obtained [8]. The complexity of the issue is exacerbated by During a total solar eclipse on June, 30th 1954, the Nobel the fact that the circumstances of solar and lunar eclipses laureate Maurice Allais observed an abrupt deviation of the never repeat, so that each eclipse evolves under unique con- oscillation plane of a short paraconical pendulum [1], and in ditions different from those of all previous eclipses. Besides, ff 1959, he observed a similar e ect on a weaker level. These no high (certified) standard exists for the measuring appa- reports stimulated the further search for nonconventional ff ratus, and current equipment is mainly manufactured in a e ects associated with solar eclipses. In order to investigate semiartisanal manner. the anomalies arising during a syzygy, a number of experiments have been performed that appeared to show variation Nevertheless, Duif has attempted to analyze the available of the gravitational constant [2, 3], and one experiment ap- pool of provisional findings and has arrived at the overall peared to show change of the atomic frequency standards conclusion that the most likely common factor behind all the during a solar eclipse in December 1992 [4]. successes and failures is a real phenomenon of some influ- However the most easily repeated experiments are rela- ence of solar eclipses on the reaction of physical devices that tively simple ones with torsion balances of different designs cannot be adequately explained in the current framework of and forms including horizontal and vertical, and experi- Newtonian and relativistic physics [9]. ments with a short pendulum supported on a ball (para- In this publication, we present the results of synchronized conical) and with tilt-meters and gyroscopes [5–7]. Several measurements with very light torsion balances and with a dozens of such experiments appear to confirm the reality of paraconical pendulum that we obtained during the solar various different anomalies but have not provided any clear eclipse of January 26th, 2009. 2 Advances in Astronomy

2. Description of the Instruments and π the Measurement Methods b p 2.1. Torsion Balance. In our experiments, we use miniature Ri torsion balances (TBs), the mass of whose mobile element does not exceed 0.5 g. A straw of 110 mm length serves as an asymmetrical beam, at the end of whose short arm (l) a lead counterweight of mass M is attached. This mobile beam is suspended on a thin monoﬁlament of natural silk (d ≈ 20 μ). Ro A visible pointer is attached to the long arm L (mass m). For this device, the following relation holds:

M∗l = m∗L. (1)

A more-detailed description of the instrument and its characteristics can be found in [10]. B The mobile part of the torsion balance (beam, pointer, and counterweight) is suspended inside a sealed glass housing. An external webcam registers movement of the beam. + Images sent by the webcam to a computer are analyzed by 0◦ A a special program which, once every minute, records the − azimuth of the beam and the time (UT). This registration system has good noise immunity and provides high accuracy Figure 1: A schematic representation of the PP experiment. readings with the average error of one measurement being around ±0.175◦, that is, about 10 arc minutes [11]. In addition, direct observations or statistical analysis of conjunction of the Sun and the Moon in right ascension took the observations revealed that TB does not respond to chan- place at 8 h 06 m UT. Since the eclipse was neither visible in ges in Ukraine nor in Romania, no times of local maximum phase (i) gravitation potential; were defined. (ii) temperature of the device itself; 2.2. Paraconical Pendulum. As well as using conventional (iii) meteorological parameters (wind, pressure, humid- Foucault pendulums, recently, several observers of syzygy ity); effects have begun to use shorter pendulums equipped with (iv) static electric field; a special suspension proposed by Maurice Allais, in which (v) moderate magnetic field; the pendulum is supported upon a small highly accurate steel ball. Such a pendulum not only can oscillate in two perpen- (vi) degree of ionization of the ionosphere; dicular planes but also can rotate around the vertical axis. (vii) operation of electromechanical units; Our paraconical pendulum consists of a 13.3 kg bob B (viii) change in the load on the TB thread; made from brass in a lenticular form 24 cm in diameter and 6 cm in thickness, a suspension rod Ro also of brass (ix) possible microvibration of the floor; (68 cm length, 3.3 cm diameter and 5 kg mass), and an upper (x) sound waves of moderate intensity; suspension ring Ri of aluminium (inner diameter 15 cm, (xi) radio waves and cell phones; outer diameter 24 cm, 5 cm thick, and 3.7 kg mass). A pivot π is fixed at the inner side of the upper part of the ring Ri. (xii) convective air movement inside the TB housing to a This pivot rests upon a highly accurate steel ball b (diameter minimum; and it may not be the cause of significant 6 mm) which rolls upon a highly planar support plate p.The vibration readings. total mass of the pendulum is 22 kg. The distance between Five days before the eclipse, two nearly identical apparatuses the point of oscillation and the centre of the bob is 85 cm. The motion is monitored by an alidade A that reads to an WEB-1 and WEB-2 were installed in an insulated, heated, and dry room with tightly closed windows and doors. Access accuracy of 12 of arc. One of these pendulums (Figure 1) to the room was only available to the leader of the experiment has been permanently installed in the Planetarium of Stefan (the first author). cel Mare University, Suceava, Romania. Measurements began on 23 January at 17 h UT and lasted Also, an automated identical paraconical pendulum was about 6 days without interruption, up to 23 h 59 m UT on installed in another place in the Planetarium. January 28. Thus, the reaction of the TBs to the surrounding The results obtained with these two pendulums, one circumstances was tracked for about 3 days before the eclipse monitored manually and the other automatically, were iden- and 2.5 days after. The eclipse on Earth began on 26 January tical. This fact demonstrates that the human factor does at4h 56m UTandendedat11h00m UT.Thegeocentric not influence the behavior of the pendulum. An example is Advances in Astronomy 3

Solar eclipse of January 26th 2009 26.01.2009 solar eclipse (WEB-1) Results of WEB1-camera observations for 23–28 of January 10 Background-free resulting observations 92 T T T T 8 1 3 4 6 90 6 88 Error bar 4 86 2 84

Angle 0

82 Angle (degrees) −2 80 −4 78 −6 76 048121620 0 4 8 12 16 20 24 UT (h) T (hours) T1: Start of partial eclipse (04 h 56 m) Mean for 25–27, ommiting for 26 T Mean for 23–28, ommiting for 26 3: Start of central eclipse (06 h 08 m) 26 of January T4: End of central eclipse (09 h 48 m) Figure 2: WEB-1 observations: the averaged daily variation (in T6: End of partial eclipse (11 h 00 m) black and grey) and the variation on January 26th, 2009, the day Figure 3: Record of the solar eclipse freed from the inﬂuence of of the solar eclipse (in blue). T is local (Kiev) time. normal daily variations.

Solar eclipse on January 26th 2009 the graphs obtained with these two pendulums during the Comparison WEB-1 versus WEB-2 measurements solar eclipse of August 1st, 2008 [12]. 60 50 T1 T3 T4 T6 Error bar 3. Measurements 40 WEB-2 Error bar 3.1. Torsion Balances (TBs). The results obtained on 23, 24, 30 WEB-1 25, 27, and 28 January are considered as being background or baseline measurements. They allow us to determine the 20 response of the devices during exterior circumstances free 10 of any eclipse effect. The analysis showed that in these days Angle (normalized values) nothing particularly significant was registered, except for the 0 usual minor daily variations. Figure 2 shows the average background WEB-1 observa- −10 0 4 8 12 16 20 tions for January 25, and 27 (narrow window background, black) and the average background for January 23, 24, 25, UT 27, and 28 (wide window background, grey). A comparison WEB-1 of these wide- and narrow-window background curves shows WEB-2 that they are almost completely similar, so it is arguable that Figure 4: Comparison of the “pure” results obtained with WEB-1 the background varied in the same manner on January 26— and WEB-2 devices on 26.01.2009. the eclipse day—and that the mean background value of these five days can be applied to the day of the eclipse. The continuous blue line in this figure shows the measurements obviously have a high correlation coefficient within time in- on the eclipse day, that is, January 26. terval T1–T6. The reduced “clean” result after subtracting the mean background is shown in Figure 3. The vertical lines on the 3.2. Paraconical Pendulum (PP). Figure 5 shows the changes graph indicate the main stages of the eclipse. of the PP oscillation plane in the period from 22 h 00 m A similar result was obtained by observations with the UT (25.01) to 14 h 24 m UT on 26 January. The azimuth is instrument WEB-2 over the period 23–28 January. The measured from south, but this is not particularly important, procedure described above for measuring and subtracting because these measurements as well as the TB measurements the background fluctuations provided a clean result when are essentially qualitative in nature, and therefore the angular applied to the WEB-2 observations, thus eliminating the reference system can be chosen arbitrarily. influence of daily variations. Comparison of the “pure” re- In Figure 5, the numbers from 1 to 85 are the serial sults obtained with the instruments WEB-1 and WEB-2 is numbers of consecutive measurements of the change of the shown in Figure 4. These results are qualitatively similar and oscillation plane azimuth of the pendulum over 55 minutes. 4 Advances in Astronomy

Pendulum observations of the solar eclipse on Comparison WEB-1 on WEB-2 January 26th 2009 only for period 04 h 56 m to 11 h 00 m UT T T 3 1 6 Solar eclipse on January 26th 2009 2 40 1 0 −1 147101316 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 30 −2 −3 20 −4 Azimuth (degrees) Azimuth −5

0 2468101214 WEB-1 10 UT (h) 0 Figure 5: Changes in the pendulum oscillation plane on the date Correlation coeﬃcient = 0.892 of the solar eclipse. Numbers on the linear scale in the center of the −10 ﬁgure indicate the sequential number of measurements that were taken every 11 minutes. 0 1020304050 WEB-2

The determinations began on 25.01 at 21 h UT and ended on Figure 6: Correlation of readings of WEB-1 versus WEB-2 during the time interval T1–T6. 26.01 at 15 h 55 m UT. It is well known that over time, due to the force of friction, the amplitude of oscillation is damped, and also the Cross-correlation function for pendulum oscillations become very elliptical. 1 and torsion balance measurements In order to eliminate these problems, the pendulum was 0.8 started once every hour, during which the damping of the amplitude of the oscillations was small and the oscillations 0.6 cient

remained almost linear. In every hour, five readings were ffi . taken at intervals of 11 minutes, and the last five minutes was 0 4 used for preparing to restart the pendulum. 0.2 The most negative values were observed in the period between measurement number 35 (04 h 48 m UT) and meas- 0 Correlation coe Correlation R =− . urement number 45 (06 h 48 m UT). The extreme value of −0.2 Radius of hightest correlation c 1 59 h −4.2◦ was seen at 06 h 00 m UT, that is, more than 100 minutes before the geocentric Sun/Moon conjunction. −0.4 The pendulum was operated in a chamber at Suceava −4 −3 −2 −1 0 1 Planetarium, where the temperature was substantially con- Correlation radius (hours) stant at 20◦. Also outside (as can be checked via the Wolfram Alpha service), the temperature on January 26th, 2009 varied Figure 7: Cross-correlation function for the series of pendulum and very little (as is normal during winter at our location). The torsion observation. air pressure was not constant on that day but increased a few millibars quite steadily with no relation to the eclipse (which was not visible in Suceava). random. This conclusion is confirmed by the fact that such correlation is absent outside of the time interval T1–T6. It 4. Analysis of Results may appear that in the time interval 6.9 h–7.8 h UT, there was no correlation between WEB-1 and WEB-2, but, in fact, this Since all the measurements were essentially qualitative in is not the case. The reactions of the devices remained strictly nature and no theoretical or quantitative model of the phe- correlated, but the sign of the correlation was reversed. nomenon yet exists, the only possible procedure for analysis Comparison of the PP and the TB observations is of paris comparative. A positive outcome of the analysis would be ticular interest. to demonstrate that the rotations of the TB arms and the From preliminary visual comparison of the results, it ap- deflection of the plane of oscillation of the pendulum during peared that the TB graph in the interval T1–T6 almost this solar eclipse were not aleatory, but resulted from some exactly repeated the PP graph, the latter being somewhat external cause, the nature and structure of which remain to earlier. In order to clarify the value of this temporal advance, be elucidated. an crosscorrelation analysis of the two series of measure- Figure 4 shows that in the interval T1–T6, the readings ments (TB and PP) was carried out. The results of the cal- of WEB-1 and WEB-2 varied in a similar manner. Figure 6 culations are shown in Figure 7. shows how these readings of WEB-1 and WEB-2 correlate. The crosscorrelation function reaches a maximum at a Calculations show that, in this time interval, the correlation correlation spacing close to one and a half hours. An accurate coefficient CC = 0.892. Such a high value of CC indicates numerical analysis shows that the correlation spacing is 1.59 that the reactions of the WEB-1 and WEB-2 devices were not hours, the correlation coefficient being equal to 0.921. This Advances in Astronomy 5

Correlation between torsion Torsion balances and paraconical pendulum 92 balance and paraconical penulum readings observations of January 26th 2009 solar eclipse = . (at time shift 1 59 h) 50 T1 T3 T4 T6 90 40 88 1 30 Paraconical 0 86 pendulum 20 −1 84 WEB-2 10 −2 Torsion balance Torsion 82 −3 0 80 Correlation coeﬃcient −

Azimuth (torsion balances) (torsion Azimuth 4 CC = 0.921 −10 WEB-1

78 pendulum) (paraconical Azimuth 567891011 −5 −4 −3 −2 −10 1 2 Universal time (hours) Paraconical pendulum T1: Start of partial eclipse (04 h 56 m) ffi Figure 8: Correlation and the correlation coe cient between these T3: Start of central eclipse (06 h 08 m) series of observations at a correlation spacing of 1.59 hours. T4: End of central eclipse (09 h 48 m) T6: End of partial eclipse (11 h 00 m) Figure 9: Comparison of the results of observations in Kiev (blue means that the observations with the TB repeated the ob- and purple) with observations in Suceava (red line). In order to servations with the PP with a very high degree of similarity, align the curves, the graph for the PP is shifted forward by 1.59 h. but lagging behind in time by 1 hour 35.4 minutes. In order to confirm the high degree of similarity of the results of the PP and TB observations in the range T1–T6, the correlation coefficient CC between these two curves was These nonconventional solar eclipse observations have ff calculated. It was found to be CC = 0.921 (see Figure 8), shown that this phenomenon is accompanied by e ects that suggesting that these two curves are strongly mutually cannot yet be explained within the current physical picture dependent. of the world. The above data gives grounds to assert that the changes in Comparing these observations with other available data the azimuth of the paraconical pendulum oscillation plane collected from previous years reveals several features that and the changes in the angles of the TB beams on January characterize, to some extent, all the observations. 26th, 2009 were not accidental. The behavior of the two TBs (1) Within a few hours before the solar eclipse, the indicates that, in the period from −2 h to 11 h UT, the beam readings of devices are minimized and remain stable angle variations were similar in nature. Moreover, in the time within a narrow fluctuation band. This trend is interval T1–T6, the TB pointer variations coincided with the clearlyseeninobservationsofsomepastsolareclipses variations of the PP oscillation plane. Such coincidence of the [13]. results of different instruments clearly indicates the presence of some dominating signal and excludes any assumption of (2) The most significant fluctuations of the arm pointer accident. do not coincide, as a rule, with the optical phenome- To illustrate the high degree of correlation of the re- non maximum. ff sults between these essentially di erent types of apparatus (3)Inmostcases,anactivereactionoftheTBtoan (the TBs and the pendulum), we present Figure 9,which eclipse seems first to be manifested as a pointer rota- compares the results of measurements with instruments tion clockwise as seen from above, with subsequent WEB-1 and WEB-2 (blue and purple) with the results of the relaxation in the opposite direction afterwards. pendulum measurements in the interval T1–T6 (red line) shifted by 1.59 hours. This artificial time shift at 1.59 an hour (4) In most cases, when several instruments were used, is introduced to demonstrate how similar the graphs are, their reactions were similar to each other, but always ff taking into account that the observations were carried out there were significant di erences of unknown nature. with different instruments in different places. Apart from the We consider that, most likely, this is associated with ff overall character of the graphs, some smaller details are also di erences of the devices from one other. identical as, for example, peaks at approximately 7.8 h UT. However, the most important point is that the very high 5. Conclusion correlation between WEB-1, WEB-2, and the paraconical pendulum was only noted in the interval T1–T6, that is, from Another independent confirmation has been obtained of the the beginning of the solar eclipse on the Earth up to its ter- previously established fact that at the time of solar eclipses, mination. Outside this interval, the correlation disappeared. a specific reaction of the torsion balance can be observed. From this fact, it can unequivocally be concluded that the During a solar eclipse, the readings of two neighboring TBs solar eclipse was a determining factor for the readings. seem to be correlated. This fact demonstrates the nonaleatory 6 Advances in Astronomy character of the reactions of TBs. Consequently, the reaction Professor Stefan Pintilie and students Alina Puha and Ionel of these devices is deterministic, not random. A solar eclipse Popescu for help with the observations. is such a determinant, since upon termination of a solar eclipse, the correlation becomes insignificant. This conclusion References is supported by the PP observations. The PP graph and the TB graphs showed obvious similarity, with the coefficient of [1] M. F. C. Allais, “Mouvement du pendule paraconique et correlation of these two independent curves being close to 1. eclipse totale de Soleli du 30 juin 1954 ,” ComptesRendusde This is the second collective observation, which has regis- l’Académie des Sciences, vol. 245, pp. 2001–2003, 1957. tered both TB reaction and PP reaction during an astronom- [2] Q. S. Wang, X. S. Yang, C. Z. Wu, H. G. Guo, H. C. Liu, and ical phenomenon. The first observation referred to the solar C. C. Hua, “Precise measurement of gravity variations during eclipse on August 1st, 2008 when simultaneous reactions of a total solar eclipse,” Physical Review D,vol.62,no.4,Article several TBs, two PPs, and one Foucault pendulum was de- ID 041101, pp. 1–3, 2000. tected [12]. [3] X. S. Yang and Q. S. Wang, “Gravity anomaly during the Mohe total solar eclipse and new constraint on gravitational It is noteworthy that a significant correlation between the shielding parameter,” Astrophysics and Space Science, vol. 282, reactions of the pendulum and the TBs was valid only in no. 1, pp. 245–253, 2002. the time interval when the lunar shadow was passing over [4] S. W. Zhou and B. J. Huang, “Abnormalities of the time com- the Earth. Outside this time interval T1–T4, the correlation parisons of atomic clocks during the solar eclipses,” Il Nuovo was absent. This fact is another strong argument in favor Cimento C, vol. 15, no. 2, pp. 133–137, 1992. of the conclusion that the solar eclipse was the cause of the [5] T. Kuusela, “Effect of the solar eclipse on the period of a correlated variations. torsion pendulum,” Physical Review D, vol. 43, no. 6, pp. 2041– 2043, 1991. The reason for the time shift between the TB and PP [6] T. Kuusela, “New measurements with a torsion pendulum dur- readings remains unclear, although it can be assumed that ing the solar eclipse,” General Relativity and Gravitation, vol. ff the shift is due to the di erence in geographic coordinates of 24, no. 5, pp. 543–550, 1992. the observations. It is possible that some unknown effect in [7] E. J. Saxl and M. Allen, “1970 Solar eclipse as “seen” by a the form of a wave was moving in space at a relatively low torsion pendulum,” Physical Review D, vol. 3, no. 4, pp. 823– speed (on the astronomical scale). 825, 1971. The effects described above are specific in themselves. [8] L. Jun, L. Jianguo, Z. Xuerong, V. Liakhovets, M. Lomonosov, Nevertheless, they cannot be contradictory to the univer- and A. Ragyn, “Observation of 1990 solar eclipse by a torsion sal laws that are actually manifested in the external universe. pendulum,” Physical Review D, vol. 44, no. 8, pp. 2611–2613, 1991. They organically complement a whole set of nonconvention- [9] C. Duif, “A review of conventional explanations of anomalous al phenomena including other phenomena observed during observations during solar eclipses,” in Proceedings of the Con- solar eclipses. Most of these are not yet understandable. In ference on the Pioneer Anomaly, Bremen, Germany, May 2004, particular, we wonder how any physical momentum can be Preprint gr qc/0408023. transferred to our instrument during a solar eclipse. Gravity [10] A. F. Pugach, M. M. Medvedskii, and N. N. Peretyatko, “The can hardly suffice as an explanation even for understanding first experience of solar eclipse observations with a miniature the results of the PP measurements. The gravitational po- torsion balance ,” Kinematics and Physics of Celestial Bodies, tential grows slowly and smoothly over a number of days vol. 24, no. 5, pp. 253–258, 2008. before eclipse and then declines smoothly afterwards without [11] A. F. Pugach and D. P. Vorobyev, “A device for recording posi- any sudden variations, but we see relatively short-term tions of a beam of an extralight torsion balance,” Kinematics events. Moreover, gravity is certainly not applicable to the and Physics of Celestial Bodies, vol. 26, no. 6, pp. 326–330, 2010. explanation of the results of the TB observations, since the [12] T. J. Goodey, A. F. Pugach, and D. Olenici, “Correlated anomalous effects observed during the August 1st 2008 solar TB is not sensitive to changes in gravitational potential. eclipse ,” Journal of Advanced Research in Physics, vol. 1, no. 2, The cause of the time lag between the response of the Article ID 021007, 2010. device in Suceava and the reactions of the devices in Kiev [13] A. F. Pugach, “Observations of the astronomical phenomena also remains unknown. What can be this force which acts so by torsion balance,” Physics of Consciousness and Life, Cosmol- selectively in space and time? ogy and Astrophysics, vol. 9, no. 2, pp. 30–51, 2009. The anomalies found, that defy understanding in terms [14] H. Munera, Ed., Should the Laws of Gravitation be reconsidered? of modern physics, are in line with other anomalies, de- Apeiron, Monreal, Spain, 2011. scribed in a recently published compendium “Should the Laws of Gravitation be reconsidered?” [14]. Together, these phenomena presented suggest that the classical theory of gravity is in need of significant additions and amendments.

Acknowledgments Both authors thank Thomas Goodey for help with the preparation of this article. A. F. Pugach thanks D. P. Vorobiov for maintenance of the apparatus, and D. Olenici thanks