The Sun has been unusually “quiet” lately. The reason for the lack of activity is revealed in the graph below.

As can be seen from the graph, there has been a decline in the 11-year cycle of solar activity. Over the past two years, the number of sunspots has been decreasing as solar activity moves from maximum to minimum. A decrease in the number of sunspots means that there are fewer solar flares and coronal mass ejections.

Thus The 24th solar cycle becomes the weakest in the last 100 years.

What is the 11-year activity cycle?

The eleven-year cycle, also called the Schwabe cycle or the Schwabe-Wolf cycle, is a marked cycle of solar activity lasting approximately 11 years. It is characterized by a fairly rapid (about 4 years) increase in the number of sunspots, and then a slower (about 7 years) decrease. The length of the cycle is not strictly equal to 11 years: in the 18th - 20th centuries its length was 7 - 17 years, and in the 20th century - approximately 10.5 years.

What is Wolf number?

The Wolf number is a measure of solar activity proposed by Swiss astronomer Rudolf Wolf. It is not equal to the number of spots currently observed on the Sun, but is calculated using the formula:

W=k (f+10g)
f is the number of observed spots;
g is the number of observed groups of spots;
k is the coefficient derived for each telescope with which observations are made.

How calm is the situation really?

A common misconception is that space weather “freezes” and becomes uninteresting to observe during times of low solar activity. However, even during such periods many interesting phenomena occur. For example, the Earth's upper atmosphere is collapsing, allowing space debris to accumulate around our planet. The heliosphere contracts, causing the Earth to become more open to interstellar space. Galactic cosmic rays penetrate the inner Solar System with relative ease.

Scientists are monitoring the situation as the number of sunspots continues to decline. As of March 29, Wolf's number is 23.

For eleven whole days on the Sun, contrary to the well-known saying, there is not a single spot. This means that our star is entering a period of minimal activity and magnetic storms and X-ray flares will become rare over the next year. We asked Sergei Bogachev, an employee of the Laboratory of X-ray Solar Astronomy of the Lebedev Physical Institute, Doctor of Physical and Mathematical Sciences, to talk about what happens to the Sun when its activity increases again and what explains these declines and rises.

There are no sunspots on the sun today

The average monthly Wolf number on the Sun - an index used by scientists to measure the number of sunspots - dropped below 10 in the first three months of 2018. Before that, in 2017 it remained at the level of 10–40, and a year earlier in some months it reached 60. At the same time Solar flares have almost ceased to occur on the Sun, and along with them the number of magnetic storms on Earth tends to zero. All this indicates that our star is confidently moving towards the next minimum of solar activity - a state in which it finds itself approximately every 11 years.

The very concept of the solar cycle (and by it is meant the periodic change of maxima and minima of solar activity) is fundamental for the physics of the Sun. For more than 260 years, since 1749, scientists have been monitoring the Sun on a daily basis and carefully recording the position of sunspots and, of course, their number. And, accordingly, for more than 260 years, periodic changes have been observed on these curves, somewhat similar to the beating of a pulse.

Each such “beat of the solar heart” is assigned a number, and a total of 24 such beats have been observed since the beginning of observations. Accordingly, this is exactly how many solar cycles are still familiar to humanity. How many of them were there in total, whether they exist all the time as long as the Sun exists, or appear sporadically, whether their amplitude and duration change and what duration, for example, the solar cycle had during the time of the dinosaurs - there is no answer to all these questions, as well as to the question , whether the activity cycle is characteristic of all solar-type stars or exists only on some of them, and if it does, then whether two stars with the same radius and mass will have the same cycle period. We don't know that either.

Thus, the solar cycle is one of the most interesting solar mysteries, and although we know quite a lot about its nature, many of its fundamental principles are still a mystery to us.

Graph of solar activity, measured by the number of sunspots, over the entire history of observations

The solar cycle is closely related to the presence of the so-called toroidal magnetic field. Unlike the earth's magnetic field, which has the form of a magnet with two poles - north and south, the lines of which are directed from top to bottom, the Sun has a special type of field that is absent (or indistinguishable) on Earth - these are two magnetic rings with horizontal lines that encircle Sun. One is located in the northern hemisphere of the Sun, and the second in the southern, approximately symmetrically, that is, at the same distance from the equator.

The main lines of the toroidal field lie under the surface of the Sun, but some lines can float to the surface. It is in these places where the magnetic tubes of the toroidal field penetrate solar surface, and sunspots appear. Thus, the number of sunspots in a sense reflects the power (or more precisely, the flux) of the toroidal magnetic field on the Sun. The stronger this field, the larger the spots, the greater their number.

Accordingly, from the fact that once every 11 years spots on the Sun disappear, we can make the assumption that once every 11 years the toroidal field disappears on the Sun. That is how it is. And actually this - the periodic appearance and disappearance of the solar toroidal field with a period of 11 years - is the cause of the solar cycle. The spots and their number are only indirect signs of this process.

Why is the solar cycle measured by the number of sunspots, and not by the strength of the magnetic field? Well, at least because in 1749, of course, they could not observe the magnetic field on the Sun. The magnetic field of the Sun was discovered only at the beginning of the 20th century by the American astronomer George Hale, the inventor of the spectroheliograph - an instrument capable of measuring with high accuracy the profiles of lines in the solar spectrum, including observing their splitting under the influence of the Zeeman effect. Actually, this was not only the first measurement of the Sun’s field, but in general the first detection of a magnetic field in an extraterrestrial object. So astronomers of the 18th-19th centuries could only observe sunspots, and they had no way to even guess about their connection with the magnetic field.

But why then do spots continue to be counted in our days, when multi-wave astronomy has been developed, including observations from space, which, of course, provide much more accurate information about the solar cycle than simply counting the Wolf number? The reason is very simple. Whatever modern cycle parameter you measure and no matter how accurate it is, this figure cannot be compared with data from the 18th, 19th, and most of the 20th centuries. You simply won't realize how strong or weak your cycle is.

Last cycle of solar activity

SILSO data/image, Royal Observatory of Belgium, Brussels

The only way to make such a comparison is to count the number of spots, using exactly the same method and exactly the same formula as 200 years ago. Although it is possible that in 500 years, when significant series of new data on the number of flares and radio emission fluxes have been accumulated, the series of sunspot numbers will finally lose relevance and will remain only as part of the history of astronomy. So far this is not the case.

Knowledge of the nature of the solar cycle allows us to make some predictions about the number and location of sunspots and even accurately determine the moment when a new solar cycle begins. The last statement may seem dubious, since in a situation where the number of spots has decreased to almost zero, it seems impossible to confidently assert that the spot that was there yesterday belonged to the previous cycle, and the spot today is already part of the new cycle. Nevertheless, there is such a way, and it is connected precisely with knowledge of the nature of the cycle.

Since sunspots appear in those places where the surface of the Sun is pierced by the lines of the toroidal magnetic field, each spot can be assigned a certain magnetic polarity - simply in the direction of the magnetic field. The spot can be “northern” or “southern”. Moreover, since the magnetic field tube must pierce the surface of the Sun in two places, the spots should preferentially form in pairs. In this case, the spot formed in the place where the lines of the toroidal field leave the surface will have northern polarity, and the paired spot formed where the lines go back will have southern polarity.

Since the toroidal field encircles the Sun like a ring and is directed horizontally, pairs of sunspots are oriented predominantly horizontally on the solar disk, that is, they are located at the same latitude, but one is in front of the other. And since the direction of the field lines in all spots will be the same (they are formed by one magnetic ring), then the polarities of all spots will be oriented the same way. For example, the first, leading, spot in all pairs will be northern, and the second, lagging, southern.

Structure of magnetic fields in the sunspot region

This pattern will be maintained as long as this field ring exists, that is, all 11 years. In the other hemisphere of the Sun, where the symmetrical second ring of the field is located, the polarities will also remain the same for all 11 years, but will have the opposite direction - the first spots will be, on the contrary, southern, and the second - northern.

What happens when the solar cycle changes? And a rather surprising thing happens, called polarity reversal. North and South magnetic poles The suns change places, and with them the direction of the toroidal magnetic field changes. First, this field passes through zero, this is what is called the solar minimum, and then begins to recover, but in a different direction. If in the previous cycle the front spots in some hemisphere of the Sun had northern polarity, then in the new cycle they will already have southern polarity. This makes it possible to distinguish the spots of neighboring cycles from each other and confidently record the moment when a new cycle begins.

If we return to the events on the Sun right now, we are observing the process of dying of the toroidal field of the 24th solar cycle. Remnants of this field still exist below the surface and even sometimes float to the top (we see isolated faint spots these days), but overall these are the last traces of the dying “sunny summer”, like the last few warm days in November. There is no doubt that in the coming months this field will finally die and the solar cycle will reach another minimum.

IS THE 11-YEAR SOLAR CYCLE COMING?

Mona Lisa Smile Hidden on the lips. What Mona Lisa? Alas and Ah! But what an obsession What came over me? Of course it seemed It flashed and... passed. And again Leonardo In her eyes! So maybe Leonardo Lives for centuries? I don't dare raise my eyes Afraid of scaring him off - Beautiful vision - Leonardo's smile Through the image of Mona Lisa The vision is mine. V. Kozlov, 1996.

Valery Ignatievich Kozlov , Doctor of Physical and Mathematical Sciences, Chief Researcher of the Laboratory of Space Plasma Theory of the Institute of Cosmophysical Research and Aeronomy named after. SOUTH. Shafer SB RAS.

QUESTIONS WITHOUT ANSWERS

Maximum and minimum solar activity, 11-year cycle, sunspots, magnetic storms - these are far from full list recognizable terms appearing in print, on radio and television with enviable consistency approximately every 11 years. The Sun's luminosity (or the total flux of solar radiation in the visible and infrared range, fueled by a thermonuclear source at the center) is practically constant. In this regard, it is often called the solar constant. What is the secret of amazing constancy luminosity of the Sun, what is nature of cyclicality solar activity and, just as important, what is the reason for its long-term failures? There is still no clear answer to these questions. The 11-year cycle is explained from the point of view that it is a property of dynamo processes. Its mechanism is unclear, but it appears that it acts independently of the dynamo, modulating the activity of the latter. Below is the author's hypothesis about the nature of the cyclicity of the Sun, which is able to answer the questions posed above with single positions.

NEW SOLAR ACTIVITY INDEX

It is generally accepted that the 11-year cyclicity of the Sun was established in the middle of the 19th century. by the famous German scientist R. Wolf, based on systematic observations of sunspots discovered by Galileo Galilei after his invention of the telescope. It's been like that since then
called Wolf numbers W (the total number of spots on the visible part of the solar disk) and serve as a characteristic of solar activity, although not the only one (Fig. 1). In modern times, other, more physical characteristics have been proposed. Such, for example, as a flux of radio emission at a fixed wavelength. After the discovery of cosmic rays, a relationship was established between the Wolf numbers in the 11-year cycle and the intensity of galactic cosmic rays (GCRs). Compared to the subjectivity of Wolf number estimates, the flux of solar radio emission and the flux of cosmic rays are more objective, although indirect, characteristics of solar activity. Just as all living things in the process of evolution “learned” to see earthly objects in ordinary light (as if knowing that there could be no movement at a speed greater than the speed of light), we also learned “ see» explosive shock waves from
solar flares in light» cosmic rays, which, by the way, also move at near-light speed. In this, perhaps the only situation, the term " rays"(space) lives up to its name. In reality, cosmic rays are particles. Protons, for example, are what these rays mainly consist of. But unlike photons (light quanta), they have mass and charge. It is obvious that cosmic rays, like all charged particles, are affected by a magnetic field, in this case an interplanetary one. Magnetic field distortions caused by explosions on the Sun have an almost immediate effect on cosmic rays. In this sense, we can say that a kind of “pulse of the Sun” has long been transmitted to us through the modulation of the noise-like background of cosmic radiation. All that was left was to hear it! In the early eighties, the author introduced an index of scintillation (enhanced fluctuations) of GCR intensity. The use of the new index made it possible to obtain new results. In short, they consist in detecting a giant wave of polarity reversal in the general magnetic field of the Sun. More precisely, we are talking about the detection of a non-stationary transient oscillatory process of changing the sign of the general field of the Sun, lasting t = 3 + 1 year. Moreover, the duration of such a transition process back proportional to the amplitude of the 11-year cycle.

WAITING FOR THE DISAPPEARANCE OF THE SUN CYCLE

The inverse dependence of the duration of the transition process on the amplitude of the 11-year cycle that we have identified indicates the presence of the invariant “ duration - amplitude" Something similar was established earlier by other authors. The existence of an inverse relationship between the time of reaching the maximum of the 11-year cycle and its amplitude was previously indicated by Waldmeier. The inverse relationship between the time to reach the maximum of the cycle and the square root of the maximum amplitude of the cycle was also revealed in the recent work of E.V. Kono-novich. All of the above indicates the presence of an invariant or, in other words, constancy of area under the curve of a single 11-year cycle. This means that a decrease in amplitude inevitably entails an increase in cycle duration and vice versa. The time course of the 11-year variation in the GCR scintillation index is shown in the upper part of Fig. 2. For each 11-year cycle (with conventionally accepted numbers 20-23), the moments of change of sign of the general magnetic field of the Sun are noted. In the initial data, the low-frequency trend was previously excluded. During three cycles 20-22, the GCR scintillation index is dominated by a clearly expressed 11-year harmonic. Its location on the scale of variation periods is shown by the horizontal arrow on the left (No. 1). Starting from the 23rd cycle, more precisely, from the end of the previous 22nd cycle (approximately from 1991), the 11-year cyclicity is destroyed. The moment of its failure is shown by a vertical arrow (No. 2). The failure appears in drift maximum of the 11-year harmonic to the region of large periods of variations, that is, in low frequency region. It is marked with a horizontal arrow on the right (No. 3). Only if there is an invariant " amplitude - duration» a decrease in the amplitude of cycle 23 will be accompanied by an increase in its duration, and in the limit - a violation of the 11-year cyclicity. One of the long-term disruptions of solar cyclicity is called the “Maunder minimum” (see Fig. 1). And it was precisely before the Maunder minimum that an increase in the period of the solar cycle was recorded. There are two more arguments in favor of the conclusion that the 11-year cyclicity has begun to break down. Firstly, there is the well-known Gnevyshev-Olya rule, according to which the amplitude of an odd cycle is greater than the amplitude of the previous even one. Unfulfilled predictions about the large amplitude of the current 23rd cycle were based on the use of this particular rule. And it was broken precisely in the 23rd cycle, and according to our data even earlier - at the end of the previous 22 cycle(see Fig. 2). This happens infrequently, and only before long-term disruptions in the 11-year cycle. Violation of the cyclicity of the Sun means a decrease in its activity. The fact that this is possible is independently indicated by the expected minimum of the secular (-100 year) variation of solar activity, the reliability of which (in Wolf numbers) is confirmed modern methods wavelet analysis. Unlike the traditional spectral-temporal representation, wavelet analysis (wavelet, literally - small wave) allows most accurately convey the amplitude-frequency dynamics of the process over time.

11 YEAR CYCLE - TEMPERATURE REGULATION MECHANISM

The constancy of the area contained under the curve of a single 11-year cycle means the constancy of the amount of energy “bleeded off” in a single cycle. This, in turn, indicates the possible nature of the cyclicity of the Sun: the 11-year average cyclicity is a self-oscillating mechanism of temperature regulation that prevents the Sun from “overheating”. Self-oscillatory is a dynamic system that converts the energy of the source into the energy of undamped oscillations, the characteristics of which are determined mainly by the parameters of the system itself. As a possible model of the 11-year cycle, within the framework of which both the appearance and disappearance of the 11-year cyclicity can be explained, the Rayleigh-Benard model of thermogravitational convection is proposed. A similar model, described by the system of Navier-Stokes and thermal conductivity equations, is reduced to the well-known Lorentz system with three independent variables: where the variable X is proportional to the fluid circulation rate; Y characterizes the temperature difference between the ascending and descending flows of liquid; variable Z proportional to the deviation of the vertical temperature profile from the equilibrium value; b- dimensionless parameter that determines the geometry of the system; Prandtl number σ - physical parameter of the liquid, showing the ratio of the coefficients of kinematic viscosity and thermal diffusivity; r-control parameter proportional to the temperature difference, or Rayleigh number normalized to its critical value. The Lorentz system is able
describe the various stages of the evolution of the system: from the emergence of convection - the appearance of self-oscillations in the system when the critical temperature value is exceeded, to its disappearance when the temperature decreases as a result of the release of excess energy by convection. As is known, convection in a conducting medium leads to the generation of a magnetic field through the mechanism of a hydromagnetic dynamo, as a result of which, perhaps, an 11-year cyclicity is observed. On the other hand, indications were received that the phases of the solar cycle correlate with the intensity of the solar neutrino flux. This amazing result, if true, would destroy all existing concepts of the origin of the solar cycle. This would mean that the solar cycle is governed by processes occurring in the deep layers of the Sun, such as Rayleigh-Benard thermogravitational convection. Within the framework of the proposed model, the nature of the origin of the 11-year cyclicity is not related to the mechanism of the hydromagnetic dynamo. The picture described above obviously corresponds to the regime of a regular attractor - a region of stable trajectories of steady-state movements in phase space. In this case, self-oscillations are regular. A further increase in temperature, or an increase in the Rayleigh number, which plays the role of a control parameter, leads to a breakdown of the self-oscillation regime as a result of instability associated with the ambiguity of solutions when the critical value of the Rayleigh number is reached.

AMBIGUITY IN NATURE AND... NOT ONLY

Since time immemorial, we have been fascinated by the vortex movement of the cascading streams of a waterfall, the murmur of a mountain stream, and the elusive flickers of the flame of a night fire. And also, one of the ever-unsolved problems facing natural science for hundreds of years is the description of turbulence. Numerous attempts to prove the correctness of a number of problems described by the Navier-Stokes equations, and, in particular, the existence and uniqueness theorems in the three-dimensional case, have been undertaken by leading mathematicians for decades. They were unsuccessful. This led J. Leray and other researchers to the idea that the reason for the difficulties that arose lies not in the shortcomings of the existing mathematical apparatus, but in the fundamental properties of the Navier-Stokes equations themselves. An alternative hypothesis related to the possible reason for the incorrectness of the hydrodynamic turbulence problem is that a solution to the Navier-Stokes equation exists, but it is not unique. In other words, the same initial data can determine several solutions. Ambiguity is not an unfortunate exception to the rule, but an amazing mechanism for Nature to make qualitative leaps! Naturally, the peculiar “know-how” noticed by natural scientists in Nature - ambiguity -
is also reflected in the works of brilliant artists and musicians, in particular in the paintings of Salvador Dali “Slave Market with a Vanishing Bust of Voltaire” and Leonardo da Vinci’s “La Gioconda”. No less interesting in this regard are the amazing metamorphosis paintings of M. K. Escher (Fig. 3). The operation of the ambiguity mechanism can be illustrated in Fig. 4, where the 2-shaped curve ((r) is a cross-section of the so-called “response surface” of a dynamic system with a continuous change in the control parameter r. Dependence ((r) is an ambiguous function of the variable r. For clarity, the characteristic form of the potential energy of the system is given at different values ​​of the control parameter. The stable state corresponds to the minimum potential energy (it is shown as a thick dot at the bottom of the potential curve). Sudden changes in the state of the system, or “jumps,” occur at points r and r2, where the number of possible responses of the system suddenly changes. 5 quite clearly illustrates such leaps in the field of psychology of perception (including well-known works of art). Among the presented figures, the fourth from the left in the top row is perceived with equal probability as a man's face and as a girl's figure. Thus, we have ambiguity, that is, two possible responses for the same values ​​of control parameters.

MAUNDER MINIMUM IS A STRANGE ATTRACTOR!

The breakdown of the self-oscillatory regime in the Lorentz system is associated with an abrupt exit to a strange attractor. Regular and especially irregular attractors can be most clearly represented using phase portraits. For example, the oscillations of a pendulum on the phase plane (in the coordinates “deflection angle - pendulum speed”) will correspond to a limit cycle - a regular attractor. A sudden breakdown of self-oscillations (regular convection) is possible when the critical value of the Rayleigh number r = 24.74 is exceeded, that is, when the Lorentz system reaches a chaotic or strange attractor (Fig. 6,7). For comparison, in Fig. 7, a shows a three-dimensional picture of the phase trajectory in the case of self-oscillations - limit cycle (r = 17). The destruction of self-oscillations (or limit cycle) at r = 28 corresponds to the mode of chaotic throwing, or yaw of the trajectory in a three-dimensional phase volume in the region of ambiguity (Fig. 7, b). The most important property of a chaotic Lorentz attractor is its roughness, or structural stability, which is preserved when parameters and initial conditions vary, since the attractor is the only one -
The basin of attraction is the entire phase space. Thus, if a dynamic system (the Sun) has already been captured into the region of the chaotic Lorentz attractor, then this will last for a long time - the next Maunder minimum will be realized!? In such a situation, the horizon of predictability is negligibly small. There are at least four possible scenarios for the breakdown of regular convection (or limit cycle). But regardless of the scenario, in all cases of disruption of regular oscillations, a so-called low-frequency “substrate” or low-frequency “pedestal” appears in the chaotic spectrum. Obviously, this is what we are seeing in the current 23rd cycle. This refers to the drift of the solar cyclicity period we discovered into the low-frequency region. It is important to note that from the standpoint of the proposed model, the reason for such failures lies in the characteristics of the system itself, in this case the Sun, and not in any external factors(tidal influence of the “parade of planets”, influence of Jupiter, etc.). In this regard, it should be recalled that the Rayleigh-Benard model of thermogravitational convection, described by the Lorentz system (with its amazing properties), is not a special case of dynamic systems, but is a consequence of the equations of motion derived from conservation laws, which in turn follow from the observed properties space-time, its homogeneity (in time and space) and isotropy.

ANOTHER MYTH ABOUT GLOBAL WARMING?

The failure of the 11-year cyclicity can have far-reaching consequences for earthly civilization. The weakening of solar activity will be accompanied by a decrease in temperature on Earth, caused, for example, by the mechanism proposed by RAS Academician G.F. Crimean. It is known that a decrease in solar activity is inevitably accompanied by an increase in the intensity of the GCP. Cosmic rays ionize the air at cloud heights and promote the formation of water droplets there. This explains the close connection between cloudiness and cosmic rays. Cloudiness, in turn, regulates the flow of solar energy to the Earth. The effect of a decrease in average air temperature during periods of decreased solar activity has been established quite reliably. It is most pronounced during periods of prolonged minimum solar activity. Thus, during the Maunder minimum, the average air temperature on Earth decreased by 1 degree. As mentioned above, an increase in the duration of the solar cycle precedes the failure of the 11-year cyclicity (the Maunder minimum, in particular). In this case, the known effect global warming due to anthropogenic factors may not be as catastrophic as stated in the media mass media. Moreover, another scenario of events is quite likely: instead of global warming, global cooling will occur! And this is a completely different story, both literally and figuratively. If the failure of the 11-year cyclicity predicted by us in the next decade is confirmed, then it will be possible to draw a conclusion in favor of the solar conditionality of not only the weather, but also the climate on Earth, and at intervals of hundreds, thousands and tens of thousands of years. The main provisions of the hypothesis stated above were reported by the author at the All-Russian conference held in the town of Troitsk near Moscow in October 2005 (IZMIRAN).

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SERIES OF PROLONGED MINIMUM
SOLAR ACTIVITY

V.G. Lazutkin Krasnoyarsk, professor at MAEN,

International Association of Planetary Scientists (IAP)

USSR Planetology Commission

Solar activity XXI century

The past centuries have contained, on average, 9 11-year cycles of the sun. The 23rd 11-year cycle of its activity has ended. A close connection has been proven between many mass phenomena on Earth, including warming and cooling, with solar activity. Conventionally, we can consider that the 21st century began with a maximum of 23 11-year cycles, 119.6 units of Wolf numbers in 2000, justifying the British forecast of 119 units of Wolf numbers.

What awaits us? Before 1975, it did not assume high cycles, but a decade later and even a prolonged minimum. The estimated data of scientists on solar activity in units of average annual Wolf numbers is 24 cycles lower. Following the scale of the graph of average annual Wolf numbers for 1993-2100. E.N. Chirkova and V.V. Nemov (Fig. 2 p. 67), we get: Table No. 1.

Table No. 1. Cycle maxima XXI century

Cycle number
Maximum year	2003	2012	2021	2029	2038	2048	2060 2067	2078	2088 2094
Wolf numbers

Cycles, except 30, are below average. This means that a prolonged minimum of solar activity, like Maunder or Sperer, is possible

M.G. Ogurtsov restored the decade-average values ​​of Wolf numbers for the time interval from 8005 BC. to 1945 AD using a series of data on radiocarbon concentrations in tree rings. It is shown that the average solar activity in 2005-2045 will most likely be lower than in recent decades.

We borrow from M.G. Ogurtsova. “The main method of experimental paleoastrophysics is the study of the concentration of cosmogenic isotopes in natural archives. Cosmogenic radiocarbon 14 C and radioberyllium 10 Be are generated in the stratosphere and upper troposphere of the Earth under the influence of energetic galactic cosmic rays (GCRs), effectively modulated by solar activity. The resulting molecules with 14 C and 10 Be are quickly oxidized to 14 CO 2 and 10 BeO. After this, beryllium oxide is captured in aerosols, washed out by precipitation and deposited in polar ice and bottom sediments. 14 CO 2 is included in a chain of geophysical and geochemical processes that form a global carbon exchange cycle, at the end of which radiocarbon is fixed in tree rings. Thus, the concentration of 10 Be in ice and radiocarbon in tree rings turns out to depend on solar activity."

Cited by M.G. Ogurtsov’s data is not detailed by year. They focus on a slight decrease in cycle maxima in the long minima of the period 1050-1800. Based on its data, it is possible to determine the maxima (M) of 24 - 26 cycles of the 21st century. The 10-year average Wolf number of the maximum 11-year cycle 1954-1964, giving the minimum of 1964 to the next cycle, will be 96.2 at M = 190.2. At M.G. Ogurtsov’s guideline for the average of 24 cycles is about 55, therefore, M is about 109, and the next 25th cycle is about a third lower, which means M is about 70. The 26th M is about 55. Unfortunately, M.G. Ogurtsov did not detail the forecast. Taking into account the data of M.G. Ogurtsov, according to publications in 2003, about a dozen Russian scientists came to an agreement about the low cycles of the 21st century.

Table 2. Forecasts of maximums

24 - 26 11 year cycles of solar activity

Mausimi Dikpati	155-161 2012 G . *
R . and . Geophysics 09 99	142 2014 G .
M.N. Khramov	127.4 2010.9
IN . G . Lazutkin	122 2013 G .
M . G . Ogurtsov	109
Shova	85 2014
IN . G . Lazutkin**	77.8	103.9	63.3

Interpretation * by the author. ** For reasons of symmetry. The main characteristics of the 11-year sunspot cycles from 648 BC are used. to 2025 AD according to Shova. It can be said that beyond the prolonged minima the maxima of the 11-year cycles of the period 700 BC. to 1700 AD underestimated. 24 cycle maximum forecast range from 78 to over 150 Real 2010 February 18.6 High forecasts have not yet come true

Doctor of Physical and Mathematical Sciences, Chief Researcher of the Laboratory of Space Plasma Theory of the Institute of Cosmophysical Research and Aeronomy named after. Yu. G. Shafer SB RAS V.I. Kozlov admits the possibility of realizing the next Maunder minimum!? During the Maunder Minimum, the average air temperature on Earth decreased by 1 degree. Instead of global warming, we can expect global cooling.

Yu.V. Mizun, Yu.G. Mizun writes that in solar activity there are long periods with a small number of sunspots. It has been proven that during periods of prolonged minima of solar activity, the vegetation of the Earth accumulates carbon with an increased content of the radioactive carbon isotope 14 C. The years concluding such periods are determined up to 3 thousand years BC. The authors report the following: 1645-1715, called the Maunder minimum, 1460-1550, the Sporer minimum. 1450-1700 there was a small glacial period. From what they said: “About 600 years ago, a strong cooling occurred on Earth. From that time on, the green country of Greenland (as its name suggests) gradually became a country covered with ice.”

Before our era, periods of low solar activity were grouped around 400, 750, 1400, 1850 and 3300?? years. For the period 1880-1980. the mentioned authors irrefutably prove the connection between changes in air temperature (increase) for the entire Earth over a hundred years ranging from 0 ° C to 0.5 ° C with changes in Wolf numbers. The period of “climatic optimum” X-XIII centuries. (1100-1250) corresponded to the maximum Wolf numbers.

Valentin Dergachev reports on the collapse of a large number of major civilizations and cultures of the world around 2300±200 BC, the 2400-year “radiocarbon rhythm”, the coordination of solar activity minima such as Maunder, Sperer and Wolf with the coldest eras. He lists five alternating intervals of glacial contraction and expansion, occurring approximately 250, 2800, 5300, 8000, and 10500 years ago. He notes that the intervals of the advance of mountain glaciers are in good agreement with the time intervals of high concentrations of 14 C, and therefore with a colder climate. Approximately 750-850 BC there was a global cooling .

Valentina Prokudina, Mikhail Rozanov. State Astronomical Institute named after. PC. Sternberg. Moscow State University named after M.V. Lomonosov. Moscow. They studied fluctuations in the width of tree rings of pine trees growing in California over the period 800-1960 AD. The range of changes in the growth index is from (I=0-20 units) to (I=180 units). They identified intervals lasting several decades when the average values ​​of wood growth indices decrease. Some of them coincided with long-term minima of Maunder (1645-1715), Sperer (1420-1530), Wolf (1280-1340), and Oort (1010-1050). During which the amplitude of the 11-year solar cycles decreased. When analyzing the time course of annual indices, it was noted: I=150-170 in 1649, 1661, 1682; a sharp decrease in the width of the rings 1430-1460, 1475-1482, 1490-1505, 1515, 1522; 1280-1307 (I=60-70); a sharp decrease in the annual growth index (I<30) 1360-1365, 1378-1379, 1390 гг. Вблизи минимума Оорта замечено понижение среднего уровня годового индекса 1050-1080 гг. Касаясь очень высоких индексов прироста (I >120), said in the Viking era, in 986 the index reached Greenland was very high (I = 130), in 1648 the Russian Pomors passed the Bering Strait, the index value was (I = 170).

When the author approximates the average annual Wolf numbers, around 1648 the maximum of the secular cycle of the 17th century is consistently indicated. Below figure No. 1 shows the result of approximation of Wolf numbers for the years 1700-2004 with the close connection of the approximating parameter - Wolf numbers 0.985. The Wolf number curve has sharper peaks. The horizontal axis is years, zero values ​​of Wolf numbers, cycles below the horizontal have the opposite magnetic sign to cycles above the horizontal. vertical axis of the Wolf number unit, time step 1 year.

Figure No. 1

In figures No. 4 - No. 7 it is similar, but the time step is 2 years (simplification of the model) and reading from right to left, bottom to top, cause, planets solar system for observers in the northern hemisphere, they move counterclockwise, making it easier to create a mathematical model.

Approximation of X BC data – XX AD century For the forecast of the 24th cycle, it is desirable to increase the number of approximated data. Data on the last 3 thousand years have been verified, the contradictions in them have been resolved in favor of maintaining the close relationship between the approximating parameter and the average annual Wolf numbers in 1700-2004. Using the method of halves, the years of extrema and the values ​​of the maxima of the Chauve series are normalized to the series of Wolf numbers of the 18th-21st centuries. The areas of non-coincidence between the approximation line and the points of the Chauve series were verified with data that appeared after 1995. In the 1st millennium BC. the errors of the Chauve series, in his opinion, reach 4 years in time (36% of 11 years), the maxima of the cycles are assumed to be W or M, 60 or 85, M or S, 85 or 120 (50% in amplitude).

Epochs of prolonged lows of activity Maunder (1645-1715), Sperer (1420-1530), Wolf (1280-1340), Oort (1010-1050), as well as Medieval (662-702), Greek ( -425 to -375), Homer (-788 to -715), Dalton (1795-1823) coincide with periods of low values ​​of the approximating parameter . The cooling of approximately 750-850 BC, which had a global character according to V. Dergachev, approximately coincided with the Homeric minimum. In the statement of Yu.V. Mizun, Yu.G. Mizun that, before our era, periods of low solar activity were grouped around 400, 750 years, we are talking about the Greek and Homeric minima. See Myth . mif.htm

From the even 14th century to the 21st century inclusive, a trend is visible: even secular cycles are higher than odd ones. Some previous calculations, with a smaller database, predicted the 22nd century cycle to be high, and at the beginning of the 21st century, at the end of the 23rd 11-year cycle, a deep minimum until 2040. Using the data of V. Prokudina and M. Rozanov, we have discrepancies: 1360 activity was high, but the annual wood growth index (I<30), 1515 г. активность не низкая, но резкое уменьшение ширины колец, 1682 г. активность низкая, но (I = 150-170).

Approximating cf. year. Wolf number parameter

is shown in table No. 3, graph in Figure No. 3.

		122
	5
		12
	114.4	77.8	103.9	63.3

The values ​​of cycle maxima are shown in italics based on the “symmetry” of the secular cycle of the 20th century, also in Table No. 2 (author). (Perhaps the English version of forecast 119 was obtained in the same way)

Figure No. 3.

Wolf numbers vertical axis,

years of the 21st century – horizontal axis.

Table No. 3 and Fig. No. 3 were executed by me around 2002-2003 for scientists in St. Petersburg and, probably, they were not satisfied.

The mathematical model successfully describes all long-term minima of solar activity, starting with the collapse of a large number of major civilizations and cultures of the world around 2300±200 BC and the eras of expansion and contraction of glaciers 8500 and 6000 BC. We can also hope that the forecast for the 21st century will be successful; it will be represented by average and slightly higher and lower 11-year cycles. The cycle that forms prolonged lows has already begun to act to lower the 11-year cycles. But if the height of the secular cycle of the 20th century, which is so outstanding above the secular cycles of 3 millennia, is a consequence of the “egocentrism” of observers of the 20th century, then we have already entered a long minimum. Otherwise, this is likely in the 22nd century.

Series of prolonged minima of solar activity

Author's opinion. All objects of the Solar system are located in a single energy-information space containing laws that govern the processes of this space and coordinate these processes with the world surrounding the system. Based on energy information concepts, the author managed to supplement celestial mechanics with a number of equations reflecting the correspondence of the level of activity of the Sun to the configurations of objects in the Solar System, including the Sun, relative to the barycenter of the Solar System. More details in the methodology.

For the first time in science, I have established by calculation the presence of a series of prolonged minima in solar activity. The duration of the series can exceed a thousand years.

Collapse of Cultures and Civilizations

The retroforecast of Wolf numbers from 3950 BC to 950 BC confirms Valentin Dergachev’s message about the collapse of a large number of major civilizations and cultures of the world around 2300±200 BC. e. It is included in a series of prolonged minimums of solar activity between 2600 and 2100. BC. the period of low values ​​of the approximating parameter lasted more than 8 centuries.

According to Yu.V. Mizun, Yu.G. Mizun BC periods of low solar activity clustered around 1400, 1850 and 3300. At the top of the graph is Fig. 4 Egyptian minimum (-1375 to -1305). Both earlier and later, in the half century from 1850 BC, there are long minima of the approximating parameter, between which the cycles are below and slightly above average. 3300 BC low cycles The above is confirmed by a series of solar activity minimums above the century (3950 - 950). BC. drawing No. 4

Figure No. 4 (3950-950 BC) Collapse of civilizations and cultures of the world

near2300±200 BC

expansion of glaciers

In figure No. 4 we also see after the end in 3800 BC. e. a high two-secular cycle (the lower part of the curve, the right corner of figure No. 4 and the same upper right corner of figure No. 5) is the beginning of a series of super-secular, long-term minima of solar activity. Cooling began and glaciers expanded. I believe that it is for this process that Valentin Dergachev indicates the approximate center of the interval of glacier expansion 5300 years ago, i.e. 3300 BC Graph No. 4 does not contradict this.

Figure No. 5 (6950-3350 BC) beginning and end

compression of glaciers transition to cooling

Figure No. 6 (9950-6950 BC) Expansion of glaciers.

Glacier expansion

Report by V. Dergachev on the compression of glaciers and expansion of glaciers 6000 and 8500 BC. correspond to the graphs of figures No. 5 and No. 6

Thus, V. Dergachev confirmed with his data the greatest discovery I made by calculation - the existence in solar activity of a series of prolonged minima of its activity. Another mysticism - a large number of scientists shamelessly did not notice this, or were not competent, or pretended not to receive the materials.

The horizontal lines of drawings No. 4 - No. 7 are 600 year old, they mark the zero level of solar activity, in the negative area the absolute value is taken, but with the opposite magnetism relative to the positive area. Let us take into account the similarity of the curves in Figures 4, 6, 7 (a series of prolonged minimums of solar activity) and the difference from them in Figure 5. Despite the insufficient detail of the figures, there is obvious confirmation of the close connection of high solar activity with warm epochs, and low activity with cold ones.

Let's compare the upcoming fig. No. 7 with past rice No. 6 and No. 4, conclusion, the Kyoto Protocol is not justified, cold weather is approaching. Earthlings, increasing their total mass, survived thousands of similar eras. You should prepare for cold weather. Move industrial and especially agricultural production and the maintenance of part of the population to lower latitudes, insulating civil and industrial buildings, using energy-saving technologies, leaving only cost-effective production to the north.

Figure No. 7 (2050-5050 AD) another collapse

On the graph of the figure out of 30 centuries, we can say 20 with low solar activity. In the current millennium, from 2750, a series of prolonged minima of solar activity begins.

I am very grateful to the scientists who gave me the opportunity to check the quality of the mathematical model with indirect data on the activity of the sun BC and who clarified it in AD. and those who gave me feedback, incl. hard. One should not think that those who made unfulfilled forecasts worked in vain.

1. The approximation covers the interval of 764 BC. to 2004 AD Until 1700, only the values ​​of extrema points are given for 11 year cycles. For this interval, the epochs of the minimums (maximums) of the values ​​of the Wolf numbers coincide with those of the approximating parameter, incl. all prolonged minima of activity with those of the approximating parameter.

2. The correlation coefficient 1700-2004 is very high. 3. In retrospect, to 9950 BC. epochs of low values ​​of the approximating parameter coincided with epochs of glacier expansion and unfavorable conditions for people, and epochs of high values ​​coincided with epochs of glacier compression. Conclusion: warming is a myth. Realistically there is a cooling with a center of 3550±800 years, similar to a cooling with a center of about 2300±200 years BC

It is not uncommon to talk about the uncertainty of scientific results and the risks of decision-making that arise from this. Given the uncertainty in forecasts for the maximum 24-11 year cycle of solar activity in the current century, high cycles have already begun to fail.

The uncertainty of the forecast for the next series of prolonged minima of solar activity may be as follows: The discovery of this phenomenon by calculation was sudden for the author, there are witnesses to my requests for indirect data to verify my results before 2000, which has now been confirmed in principle by Valentin Dergachev, M.G. Ogurtsov, etc.

However, the determination of the centers and durations of the series, as well as the depths of the long-term minima of solar activity that constitute the series cannot be considered established indisputably. This requires a collective, comprehensive, thorough, lengthy review. A serious revision of the correspondence between direct and indirect data on solar activity and the range of its variability is necessary. Please see : Global warming is a myth.

BIBLIOGRAPHY

1. Dergachev V. Isotopes on cyclical and abrupt climate changes // Astronomy of ancient societies. M.: Nauka, 2002. p. 317-322.

2. Kozlov V.I. Is a failure of the 11-year solar cycle coming // Science and technology in Yakutia. 2006. No. 1 (10).

3. Lazutkin V.G., Tikhonov A.A. Approximation, retroforecast and forecast of average annual Wolf numbers from 1000 BC to 2300 // Bioenergoinformatics. Volume 1, Barnaul, 1998. p. 204-206.

4. Lazutkin V.G., Tikhonov A.A. Approximation of Wolf numbers //Bioenergoinformatics and bioenergy information technologies. Volume 3, part 2, Barnaul, 2001. Methodology.

5. Lazutkin V.G. On forecasts of the maximum of the 23rd cycle of solar activity // Bioenergoinformatics and bioenergy information technologies. Volume 2, Barnaul, 2000.

6. Mizun Yu.V., Mizun Yu.G. The unknown pulse of the Earth. M.: Veche, 2005.

7. Ogurtsov M.G. Modern achievements of solar paleo-astrophysics and problems of long-term forecast of solar activity // Astronomical Journal, 2005. volume 82, no. 6, p. 555-560.

8. Prokudina V., Rozanov M. Study of climatic anomalies in the XI-XX centuries. according to dendrochronological data //Astronomy of ancient societies. M: Nauka, 2002. p. 323-333. 11. M.: 1999. p. 10.

11. The sun will show itself yet // World of News No. 27 (654), p. 22.

12. Chirkova E.N. and Nemov V.V. Spectrum of long-term rhythms of Wolf numbers since 1749 and forecast of the dynamics of solar activity in the 21st century // Consciousness and physical reality, Volume 2, No. 4, 1997. p. 64-69.

In the middle of the last century, amateur astronomer G. Schwabe and R. Wolf first established the fact that the number of sunspots changes over time, and the average period of this change is 11 years. You can read about this in almost all popular books about the Sun. But few even among specialists have heard that back in 1775 P. Gorrebov from Copenhagen dared to assert that there is a periodicity of sunspots. Unfortunately, the number of his observations was too small to establish the duration of this period. The high scientific authority of opponents of Gorrebov's point of view and the artillery shelling of Copenhagen, which destroyed all his materials, did everything to ensure that this statement was forgotten and not remembered even when it was proven by others.

Of course, all this does not in any way detract from the scientific merits of Wolf, who introduced the index of relative numbers of sunspots and was able to restore it from 1749 based on various observational materials of amateur and professional astronomers. Moreover, Wolf determined the years of maximum and minimum sunspot numbers from the time of observations G. Galileo, i.e. from 1610. This allowed him to strengthen the very imperfect work of Schwabe, who had observations for only 17 years, and for the first time determine the duration of the average period of change in the number of sunspots. This is how the famous Schwabe-Wolf law appeared, according to which changes in solar activity occur periodically, with the length of the average period being 11.1 years (Fig. 12). Of course, at that time only the relative number of sunspots was discussed. But over time, this conclusion was confirmed for all known solar activity indices. Numerous other periods of active solar phenomena, especially shorter ones, that have been discovered by solar researchers over the past 100-plus years have been consistently refuted, and only the 11-year period has always remained unshakable.

Curve of average annual Zurich relative sunspot numbers...

Although changes in solar activity occur periodically, this periodicity is special. The fact is that the time intervals between years of maximum (or minimum) Wolf numbers vary quite a lot. It is known that from 1749 to the present day their duration fluctuated from 7 to 17 years between the years of maximums and from 9 to 14 years between years of minimums in the relative number of sunspots. Therefore, it would be more correct to speak not about an 11-year period, but about an 11-year cycle (i.e., a period with disturbances, or a “hidden” period) of solar activity. This cycle is extremely important both for gaining insight into the essence of solar activity and for studying solar-terrestrial connections.

But the 11-year cycle manifests itself not only in changes in the frequency of solar new formations, in particular sunspots. It can also be detected by changes in the latitude of sunspot groups over time (Fig. 13). This circumstance attracted the attention of the famous English solar researcher R. Carrington back in 1859. He discovered that at the beginning of the 11-year cycle, spots usually appear at high latitudes, on average at a distance of ±25-30° from the equator of the Sun, while at the end cycle prefer areas closer to the equator, on average at latitudes ±5-10°. Later, the German scientist G. Sperer showed this much more convincingly. At first this feature was not given much importance. But then the situation changed dramatically. It turned out that the average duration of the 11-year cycle can be determined much more accurately from changes in the latitude of sunspot groups than from variations in Wolf numbers. Therefore, now Sperer's law, which indicates a change in the latitude of sunspot groups with the course of the 11-year cycle, along with the Schwabe-Wolf law, acts as the basic law of solar cyclicity. All further work in this direction only clarified the details and explained this variation in different ways. But they, nevertheless, left the formulation of Sperer's law unchanged.

Butterfly diagram of sunspot groups...

We now turn to the 11-year cycle of solar activity, which has been the focus of solar research for more than a hundred years since its discovery. Behind its apparent astonishing simplicity, there actually lies such a complex and multifaceted process that we always face the danger of losing everything, or at least much of what it has already revealed to us. One of the most famous experts in solar activity forecasts, German astronomer V. Glaisberg, was right when in one of his popular articles he said the following: “How many times did solar activity researchers think that they had finally managed to finally establish all the basic patterns of the 11-year cycle . But then a new cycle began, and its very first steps completely threw away all their confidence and forced them to reconsider what they considered to be definitively established.” Perhaps these words are a little condensed, but their essence is certainly true, especially when it comes to forecasting solar activity.

As we have already said, in certain years Wolf numbers have a maximum or minimum value. These years, or even more precisely defined moments in time, such as quarters or months, are called, respectively, the epochs of maximum and minimum of the 11-year cycle, or, more generally, epochs of extremes. Average monthly and average quarterly values ​​of the relative numbers of sunspots, in addition to generally regular, smooth changes, are characterized by very irregular, relatively short-term fluctuations (see Section 5 of this chapter). Therefore, epochs of extremes are usually identified by the so-called smoothed monthly Wolf numbers, which represent the values ​​of this index obtained from observations averaged in a special way over 13 months, or by the upper and lower envelopes of the change curves in the quarterly average values ​​of the relative numbers of sunspots. But sometimes the use of such methods can lead to false results, especially in low cycles, i.e. cycles with a small maximum Wolf number. The time interval from the epoch of minimum to the epoch of maximum of the 11-year cycle was called the growth branch, and from the epoch of maximum to the epoch of the next minimum - the branch of its decline (Fig. 14).

The duration of the 11-year cycle is determined much better by minimum epochs than by maximum epochs. But even in this case, a difficulty arises, which lies in the fact that the next cycle, as a rule, begins earlier than the previous one ends. Now we have learned to distinguish groups of spots of the new and old cycles by the polarity of their magnetic field. But such an opportunity arose a little over 60 years ago. Therefore, in order to maintain the homogeneity of the methodology, one still has to be content not with the true length of the 11-year cycle, but with a certain “ersatz” of it, determined by the epochs of the minimum Wolf numbers. It is quite natural that these numbers usually combine groups of spots of the new and old 11-year cycles. The 11-year sunspot cycles differ not only in their different lengths, but also in their different intensities, i.e., different values ​​of the maximum Wolf numbers. We have already said that regular data on the average monthly relative numbers of sunspots of the Zurich series have been available since 1749. Therefore, the first Zurich 11-year cycle is considered to be the cycle that began in 1775. The cycle preceding it, containing incomplete data, apparently for this reason received a zero number. If over the 22 cycles that have passed since the beginning of the regular determination of Wolf numbers (including the zero cycle and the current one that has not yet ended, but has already passed its maximum), the maximum average annual Wolf number averaged 106, then in various 11-year cycles it fluctuated from 46 to 190 The 19th cycle, which ended in 1964, was especially high. At its maximum, which occurred at the end of 1957, the average quarterly Wolf number was 235. The second place after it is occupied by the current, 21st cycle, the maximum of which occurred at the end of 1979 with an average quarterly relative number of sunspots of 182. The lowest cycles sunspots date back to the beginning of the last century. One of them, 5th according to Zurich numbering, is the longest of the observed 11-year cycles. Some researchers of solar activity even doubt the reality of its duration and believe that it is entirely due to the “activity” in the field of science of Napoleon I. The fact is that the French emperor, completely absorbed in waging victorious wars, mobilized almost all the astronomers of the observatories of France and the countries he conquered into the army . Therefore, in those years, observations of the Sun were carried out so rarely (no more than a few days per month) that one can hardly trust the Wolf numbers obtained then. It is difficult to say how well-founded such doubts are. By the way, indirect data on solar activity during this time do not contradict the conclusion about the low level of relative numbers of sunspots at the beginning of the 19th century. However, these doubts cannot be simply dismissed, since they make it possible to get rid of some exceptions, especially for individual 11-year cycles. It is curious that the second lowest cycle, the maximum of which dates back to 1816, was only 12 years long, unlike its predecessor.

Since we have data for more than two hundred years only on Wolf numbers, all the main properties of 11-year cycles of solar activity are derived specifically for this index. With the light hand of the venerable discoverer of the 11-year cycle, for more than fifty years, solar activity researchers have been mainly busy searching for the full set of cycles lasting from several months to hundreds of years. R. Wolf, convinced that solar cyclicity is the result of the influence of the planets of the solar system on the Sun, himself initiated this search. However, all these works contributed much more to the development of mathematics than to the study of solar activity. Finally, already in the 40s of this century, one of Wolf’s “successors” in Zurich, M. Waldmeier, dared to doubt the correctness of his “scientific great-grandfather” and transferred the cause of the 11-year cyclicity inside the Sun itself. It was from this time that the real study of the main internal properties of the 11-year sunspot cycle actually began.

The intensity of the 11-year cycle is quite closely related to its duration. The more powerful this cycle, i.e., the greater its maximum relative number of spots, the shorter its duration. Unfortunately, this feature is rather of a purely qualitative nature. It does not allow one to reliably determine the value of one of these characteristics if the second one is known. The results of studying the connection between the maximum Wolf number (more precisely, its decimal logarithm) and the length of the growth branch of the 11-year cycle, i.e., that part of the curve that characterizes the increase in Wolf numbers from the beginning of the cycle to its maximum, look much more confident. The greater the maximum number of sunspots in this cycle, the shorter the growth branch. Thus, the shape of the cyclic curve of the 11-year cycle is largely determined by its height. In high cycles it is characterized by a large asymmetry, and the length of the growth branch is always shorter than the length of the decline branch and is equal to 2-3 years. For relatively weak cycles this curve is almost symmetrical. And only the weakest 11-year cycles again show asymmetry, only of the opposite type: their growth branch is longer than the decline branch.

In contrast to the length of the growth branch, the length of the decline branch of the 11-year cycle is greater, the higher its maximum Wolf number. But if the previous connection is very close, then this one is much weaker. This is probably why the maximum relative number of sunspots only qualitatively determines the duration of the 11-year cycle. In general, the growth branch and the decline branch of the main cycle of solar activity behave differently in many respects. To begin with, if on the growth branch the sum of the average annual Wolf numbers almost does not depend on the height of the cycle, then on the decline branch it is determined precisely by this characteristic. It is not surprising that attempts to represent the curve of the 11-year cycle as a mathematical expression not with two, but with one parameter were so unsuccessful. On the growth branch, many connections turn out to be much clearer than on the decline branch. It seems that it is precisely the features of the increase in solar activity at the very beginning of the 11-year cycle that dictate its character, while its behavior after the maximum is generally approximately the same in all 11-year cycles and differs only due to the different lengths of the decline branch. However, we will soon see that this first impression needs one important addition.

Evidence in favor of the determining significance of the growth branch of the 11-year cycle was provided by studies of cyclic changes in the total area of ​​sunspots. It turned out that the maximum value of the total area of ​​spots can be fairly reliably determined from the length of the growth branch. It was already mentioned earlier that this index implicitly includes the number of sunspot groups. It is therefore quite natural that for it we obtain essentially the same conclusions as for the Wolf numbers. The patterns of the 11-year cycle for the frequency of other solar activity phenomena, in particular solar flares, are much less well known. Purely qualitatively, we can assume that for them they will be the same as for the relative numbers and total area of ​​sunspots.

Until now we have dealt with solar activity phenomena of any power. But, as we already know, phenomena on the Sun vary greatly in intensity. Even in everyday life, hardly anyone would put a light cirrus cloud and a large black cloud on the same level. Until then, that's exactly what we did. And here's what's interesting. Once we divide active solar formations by their power, we arrive at rather contradictory results. Phenomena of weak or moderate intensity generally give the same 11-year cycle curve as the Wolf numbers. This applies not only to the number of sunspots, but also to the number of flare sites and to the number of solar flares. As for the most powerful active formations on the Sun, they most often occur not at the very epoch of the maximum of the 11-year cycle, but 1-2 years after it, and sometimes before this epoch. Thus, for these phenomena the cyclic curve either becomes two-peaked or shifts its maximum to years later in relation to the Wolf numbers. This is exactly how the largest groups of sunspots, the largest and brightest calcium flocculi, proton flares, and bursts of type IV radio emission behave. The curves of the 11-year cycle for the intensity of the green coronal line, the flux of radio emission at meter waves, the average strength of magnetic fields and the average lifespan of groups of sunspots, i.e., indices of the power of the phenomena, have a similar shape.

The 11-year cycle in Sperer's law for various processes of solar activity is most uniquely manifested. As we already know, for groups of sunspots it is expressed in a change in the average latitude of their appearance from the beginning to the end of the cycle. Moreover, as the cycle develops, the speed of this “sliding” of the sunspot zone towards the equator gradually decreases and 1-2 years after the epoch of maximum Wolf numbers it stops altogether when the zone reaches the “barrier” in the latitude range 7°.5-12°, 5. Further, only oscillations of the zone around this average latitude occur. It seems that the 11-year cycle “works” only up to this time, and then gradually “dissolves,” as it were. It is known that the spots cover fairly wide areas on both sides of the Sun's equator. The width of these zones also changes over the course of the 11-year cycle. They are narrowest at the beginning of the cycle and widest at its maximum. This explains the fact that in the most powerful cycles, such as the 18th, 19th and 21st Zurich numbering, the highest latitude groups of sunspots were observed not at the beginning of the cycle, but in the years of maximum. Groups of small and medium-sized sunspots are located almost across the entire width of the “royal zones”, but prefer to concentrate towards their center, the position of which is increasingly approaching the equator of the Sun as the cycle develops. The largest groups of spots “choose” the edges of these zones and only occasionally “condescend” to their inner parts. Judging only by the location of these groups, one might think that Sperer's law is just a statistical fiction. Solar flares of different powers behave in a similar way.

On the decline branch of the 11-year cycle, the average latitude of sunspot groups, starting from ±12°, does not depend on the height of the cycle. At the same time, in the year of maximum it is determined by the maximum Wolf number in this cycle. Moreover, the more powerful the 11-year cycle, the higher the latitudes where its first groups of sunspots appear. At the same time, the widths of the groups at the end of the cycle, as we have already seen, are essentially the same on average, regardless of what its power is.

The northern and southern hemispheres of the Sun behave very differently with regard to the development of 11-year cycles in them. Unfortunately, Wolf numbers were determined only for the entire solar disk. Therefore, we have on this issue rather modest material from the Greenwich Observatory on the number and areas of sunspot groups for about a hundred years. But still, the Greenwich data made it possible to find out that the role of the northern and southern hemispheres changes noticeably from one 11-year cycle to another. This is expressed not only in the fact that in many cycles one of the hemispheres definitely acts as a “conductor”, but also in the difference in the shape of the cyclic curve of these hemispheres in the same 11-year cycle. The same properties were discovered in the number of groups of sunspots and in their total areas. Moreover, the cycle maximum epochs in the northern and southern hemispheres of the Sun often differ by 1-2 years. We will talk more about these differences when considering long cycles. For now, as an example, let us only remember that in the highest 19th cycle, solar activity definitely prevailed in the northern hemisphere of the Sun. Moreover, the epoch of maximum in the southern hemisphere came more than two years earlier than in the northern hemisphere.

Until now, we have considered the features of the development of the 11-year cycle of solar activity only for phenomena occurring in the “royal zones” of the Sun. At higher latitudes, this cycle appears to begin earlier. In particular, it has long been known that an increase in the number and area of ​​prominences in the latitude range ±30-60° occurs approximately a year before the start of the 11-year cycle of sunspots and low-latitude prominences. It is curious that if in the “royal zones” the average latitude of the appearance of prominences gradually decreases as the cycle progresses, similar to what happens with groups of sunspots, then higher latitude prominences have on average a smaller latitude at the beginning of the cycle than at its end. Something similar is observed in coronal condensations. Some researchers believe that for the green coronal line the 11-year cycle begins about 4 years earlier than for sunspot groups. But now it is still difficult to say how reliable this conclusion is. It is possible that, in fact, a high-latitude zone of coronal activity is constantly preserved on the Sun, which, taking into account the data obtained for lower latitudes, leads to this apparent result.

Weak magnetic fields near its poles behave even more unusually. They reach a minimum intensity value approximately in the years of maximum of the 11-year cycle and at the same time the polarity of the field changes to the opposite. As for the minimum epoch, during this period the field strength is quite significant and their polarity remains unchanged. It is curious that the change in field polarity near the north and south poles does not occur simultaneously, but with a gap of 1-2 years, i.e. all this time the polar regions of the Sun have the same polarity of the magnetic field.

The number of polar faculae changes in parallel with the magnitude of the field strength near the poles of the Sun in each of its hemispheres (by the way, anticipating almost the same change in Wolf numbers after about 4 years). Therefore, although we have data on weak polar magnetic fields for less than three 11-year cycles, the results of observations of polar flare sites allow us to draw a very definite conclusion regarding their cyclic changes. Thus, magnetic fields and faculae in the polar regions of the Sun are distinguished by the fact that their 11-year cycle begins at the maximum of the 11-year sunspot cycle and reaches a maximum near the epoch of sunspot minimum. The future will show how reliable this result is. But it seems to us that if we do not delve into the details, it is unlikely that subsequent observations will lead to a significant change in it. It is curious that polar coronal holes have exactly the same 11-year variation pattern.

Although the solar constant, as already mentioned, does not experience noticeable fluctuations over the course of the 11-year cycle, this does not mean that individual regions of the solar radiation spectrum behave in a similar way. The reader could already be convinced of this when the fluxes of radio emission from the Sun were considered. The changes in the intensity of the violet lines of ionized calcium H and K are somewhat weaker. But these lines at the maximum epoch are approximately 40% brighter than at the minimum epoch of the 11-year cycle. There is evidence, although not entirely indisputable, about changes in the depth of lines in the visible region of the solar spectrum as the cycle progresses. However, the most impressive variations in solar radiation belong to the X-ray and far ultraviolet wavelength ranges, which have been studied by artificial Earth satellites and spacecraft. It turned out that the intensity of X-ray radiation in the wavelength intervals 0-8 A, 8-20 A and 44-60 A from the minimum to the maximum of the 11-year cycle increases by 500, 200 and 25 times. No less noticeable changes occur in the spectral regions of 203-335 A and near 1216 A (by 5.1 and 2 times).

As has been discovered using modern mathematical methods, there is a so-called fine structure of the 11-year cycle of solar activity. It boils down to a stable “core” around a maximum epoch spanning about 6 years, two or three secondary maxima, and a splitting of the cycle into two components with average periods of about 10 and 12 years. Such fine structure is revealed both in the form of a cyclic curve of Wolf numbers and in a “butterfly diagram”. In particular, in the highest 11-year cycles, in addition to the main sunspot zone, there is also a high-latitude zone, which persists only until the maximum epoch and shifts with the course of the cycle not to the equator, but to the pole. In addition, the “butterfly diagram” for groups of spots is not a single whole, but is, as it were, composed of so-called impulse chains. The essence of this process is that, appearing at a relatively high latitude, a group of sunspots (or several groups) shifts towards the equator of the Sun over 14-16 months. Such impulse chains are especially noticeable on the growth and decline branches of the 11-year cycle. Perhaps they are associated with fluctuations in solar activity.

Soviet solar researcher A.I. Ol established another fundamental property of the 11-year cycle of solar activity. Studying the relationship between the index of recurrent geomagnetic activity for the last four years of the cycle and the maximum Wolf number, he found that it was very close if the Wolf number belonged to the next 11-year cycle, and very weak if it belonged to the same cycle as geomagnetic activity index. It follows that the 11-year cycle of solar activity originates “in the depths” of the old one. Recurrent geomagnetic activity is caused by coronal holes, which, as we know, arise, as a rule, above unipolar regions of the photospheric magnetic field. Consequently, the true 11-year cycle begins in the middle of the decline branch with the appearance and intensification of not bipolar, but unipolar magnetic regions. This first stage of development ends at the beginning of the 11-year cycle with which we are accustomed to dealing. At this time, its second stage begins, when bipolar magnetic regions and all those phenomena of solar activity that we have already talked about develop. It lasts until the middle of the decline branch of the usual 11-year cycle, when a new cycle begins. It is curious that such an important feature of the 11-year cycle was not noticed directly on the Sun, but it was established when studying the influence of solar activity on the Earth’s atmosphere.