11-year Modulation Research Articles

Modulation over a 22-year cosmic ray cycle: On the tilt angles of the heliospheric current sheet

The ‘tilt angle’ of the wavy current sheet in the hehosphere has been used very successfully as a proxy for solar activity in cosmic ray (CR) modulation models with particle drifts included. The “Hoeksema tilt angles α” are calculated using two potential field methods: (1) The classic ‘line-of-sight’ computation and (2) the more recent ‘radial’ photospheric field computation. The question of which set of ‘tilt angles’ is the more appropriate to use in modulation models is addressed by utilizing them in a comprehensive time-dependent drift model applied to the 22-year modulation cycle of 1.2 GeV cosmic ray electrons. We found that the ‘classic’ α are better suited than the ‘new’ α as a proxy for solar activity for periods of decreasing α and vice versa for periods of increasing α. By comparing the model with data it was shown that the set of α with the smallest rate of change over a period of decreasing or increasing solar activity provides the best compatibility with CR observations.

The radial distribution of cosmic rays in the heliosphere at solar maximum

To obtain a more detailed profile of the radial distribution of galactic (GCRs) and anomalous (ACRs) cosmic rays, a unique time in the 11-year solar activity cycle has been selected - that of solar maximum. At this time of minimum cosmic ray intensity a simple, straight-forward normalization technique has been found that allows the cosmic ray data from IMP 8, Pioneer 10 (P-10) and Voyagers 1 and 2 (V1, V2) to be combined for the solar maxima of cycles 21, 22 and 23. This combined distribution reveals a functional form of the radial gradient that varies as G 0/r with G 0 being constant and relatively small in the inner heliosphere. After a transition region between ∼10 and 20 AU, G 0 increases to a much larger value that remains constant between ∼25 and 82 AU. This implies that at solar maximum the changes that produce the 11-year modulation cycle are mainly occurring in the outer heliosphere between ∼15 AU and the termination shock. These observations are not inconsistent with the concept that Global Merged Interaction. regions (GMIRs) are the principal agent of modulation between solar minimum and solar maximum. There does not appear to be a significant change in the amount of heliosheath modulation occurring between the 1997 solar minimum and the cycle 23 solar maximum.

Charge-sign dependent modulation in the heliosphere over a 22-year cycle

Abstract. A time-dependent model based on a numerical solution of Parker’s transport equation is used to model the modulation of cosmic ray protons, electrons and helium for full 11-year and 22-year modulation cycles using a compound approach. This approach incorporates the concept of propagating diffusion barriers based on global increases in the heliospheric magnetic field as they propagate from the Sun throughout the heliosphere, combined with gradient, curvature and current sheet drifts and the other basic modulation mechanisms. The model results are compared to the observed 11-year and 22-year cycles for 1.2 GV electrons and 1.2 GV Helium at Earth for the period 1975–1998. The model solutions are also compared to the observed charge-sign dependent modulation along Ulysses’ trajectory for the period 1990–1998. This compound approach to long-term modulation, especially charge-sign dependent modulation, is found to be remarkably successful. It is shown that the model can easily account for the latitude dependence for cosmic ray protons and the lack thereof for cosmic ray electrons by assuming large perpendicular diffusion in the polar direction. This approach contributes to an improved understanding of how diffusion and drifts vary from solar minimum to maximum modulation, and what the time-dependence of the heliospheric diffusion coefficients may be. Key words. Interplanetary physics (energetic particles; cosmic rays; general or miscellaneous)

Does solar flare activity lag behind sunspot activity

Recently, Wheatland and Litvinenko (2001) have suggested that over the solar cycle both the flaring rate and the magnetic free energy in the corona lag behind the energy supply to the system. To test this model result, we analyzed the evolution of solar flare occurrence with regard to sunspot numbers (as well as sunspot areas), using Hα flare data available for the period 1955–2002, and soft X-ray flare data (GOES 1–8 A) for the period 1976–2002. For solar cycles 19, 21, and 23, we find a characteristic time lag between flare activity and sunspot activity in the range 10≲τ≲15 months, consistent with the model predictions by Wheatland and Litvinenko (2001). The phenomenon turns out to be more prominent for highly energetic flares. The investigation of solar activity separately for the northern and southern hemisphere allows us to exclude any bias due to overlapping effects from the activity of both hemispheres and confirms the dynamic relevance of the delay phenomenon. Yet, no characteristic time lag τ>0 is found for solar cycles 20 and 22. The finding that in odd-numbered cycles flare activity is statistically delayed with respect to sunspot activity, while in even-numbered cycles it is not, suggests a connection to the 22-year magnetic cycle of the Sun. Further insight into the connection to the 22-year magnetic cycle could possibly be gained when a 22-year variation in the energy supply rate is taken into account in the Wheatland and Litvinenko (2001) model. The existence of a 22-year modulation in the energy supply rate is suggested by the empirical Gnevyshev – Ohl rule, and might be caused by a relic solar field.

The 11-year solar cycle, the Sun's rotation, and the middle stratosphere in winter. Part II: Response of planetary waves

The effect of the 11-year solar cycle on the response of planetary wavenumbers 1 and 2 at 10 and 30 hPa in winter to solar activity oscillations on the time scale of the Sun's rotation (27.2 day) is discussed in terms of statistical spectral analysis. The three oscillations studied are the 27.2 d (period of the Sun's rotation), 25.3 d (periodicity caused by modulation of the 27.2 d stratospheric response by annual atmospheric variation), and 54.4 d (doubled period of the solar rotation). A significant effect of the 11-year solar cycle is found for the 54.4 d periodicity in planetary wavenumber 1, and for the 27.2 and 25.3 d periodicities in planetary wavenumber 2. The effect of the 11-year solar cycle is expressed in the evident differences between the amplitudes of responses of planetary waves at maximum and minimum of the solar cycle: the amplitudes are much larger at high than at low solar activity. The 11-year modulation of planetary wave activity is most pronounced at mid-latitudes, mainly at 40–60°N, where the observed variability of planetary waves is large. The results obtained are in good agreement with results of the recent modeling study by Shindell et al. (Science 284 (1999) 305).

Time-dependent cosmic-ray modulation and global merged interaction regions

A brief review is given of past attempts to determine the role of global merged interaction regions in the 11-year cosmic-ray modulation cycle with heliospheric cosmic-ray transport models. Two classes of models are discussed, namely spherically-symmetric diffusion, and axi-symmetric drift dominated models. This is followed by a discussion of current work which, differently from previous work, simulated the spatial evolution of global merged interaction regions, including their interaction with the heliospheric termination shock. It is explained how this advance may affect our understanding of the contribution of global merged interaction regions to the cosmic-ray modulation cycle, and lead to a possible test of estimating the termination shock position from spacecraft observations of cosmic rays.

Hale-cycle effects in cosmic-ray intensity during the last four cycles

Monthly cosmic-ray data from Inuvik (0.16 GV) and Climax (2.96 GV) Neutron Monitor stations has been studied with the aid of solar activity parameters for the time period 1947–1995. Systematic differences in the overall shape of successive 11-year modulation cycles and similarities in the alternate 11-year cycles seem to be related to the polarity reversals of the polar magnetic field of the Sun. This suggests a possible effectiveness of the Hale cycle during even and odd solar activity cycles. Our results can be understood in terms of open and closed models of the heliosphere. Positive north pole of the Sun leads to open heliosphere where particles reach the Earth more easily when their access route is by the heliospheric oolar regions (even cycles) than when they gain access along the current sheet (odd cycles). In this case as the route of access becomes longer due to the waviness of the neutral sheet, the hysteresis effect of cosmic-rays is also longer. This interpretation is explained in terms of different contributions of convection, diffusion and drift mechanisms to the whole modulation process influencing cosmic-ray transport in the heliosphere.

Intensity variations of >70‐Mev cosmic rays measured by Pioneer 10, Voyager 1 & 2 and IMP in the heliosphere during the recovery period from 1992–1995

Using data from the >70‐MeV channel on the Pioneer 10 and Voyager 1 & 2 spacecraft we have examined the gradients and intensities of cosmic rays in the outer heliosphere between 1992 and 1995. During this time there is a slow increase of intensity towards the next maximum in ∼1997 and the radial gradient is small‐decreasing to ∼0.8%/AU at the end of this period. The latitude gradient has also decreased to only ∼0.1–0.2%/AU but remains negative as it was in the previous 11‐year cycle. These gradients are similar to those for >70‐MeV particles reported recently in the inner heliosphere but quite different from the positive gradients observed at this time throughout the heliosphere by the Ulysses and Voyager spacecraft for anomalous cosmic rays. Overall the cosmic ray intensity is almost uniform in radius, azimuth and latitude at this time in the outer heliosphere‐and far lower than the estimated interstellar intensity. The intensities are, in fact, much lower than would be expected based on data from the previous cycle. This, along with the very slow increase that is observed, suggests that, at the same radial distance, the intensity in 1977 will be much less than in the previous cycle in 1987‐resulting in a large 22‐year modulation wave. The data show some features which suggest that large scale drift patterns, which change when the solar magnetic polarity changes every 11 years, play a important role in the overall intensity distribution in the outer heliosphere‐but specific details, particularly in the present positive polarity cycle beginning in 1990 are not well predicted by current models.

Solar cycle modulation of galactic cosmic rays at high heliographic latitudes: A one‐dimensional simulation

Previous studies have established that large merged interaction regions (MIRs) in the outer heliosphere are the main cause of the 11‐year modulation cycle of galactic cosmic rays in the ecliptic. Those simulations were successful despite their use of a constant convection speed. In this study, we show that a large rise in solar wind speed, seen at higher heliographic latitudes during 1985–1987, combined with MIRs, can generate the difference between the Voyager 1 and Voyager 2 count rates in this period. Also, the difference between the starting times of the new cycle at both spacecraft is directly attributable to the difference between the pattern of MIRs measured at the two spacecraft. In addition, the Voyager 2 simulation exhibits the correct behavior of the 11‐year cycle in the cosmic ray radial gradients between points in the outer heliosphere.

Solar considerations in the development of cutaneous melanoma.

On the basis of these considerations, the possible action spectrum for melanoma can be narrowed considerably, but not confined to any one solar emission band. The physical factors discussed eliminate all but UV, visible, and NIR radiation as possible solar agents. Ionizing radiation fits neither the epidemiologic data nor first-order physical considerations. Wavelengths longer than the NIR wavelengths, although they could conceivably account for the occurrence of melanoma under clothed parts of the body, carry so little energy that they are probably unimportant. Epidemiologic evidence regarding the effects of skin pigment favors UV or visible radiation. A distinction between these two components is not obvious; UV-C and UV-B photons carry greater energy and are more likely to induce biochemical cutaneous effects, but the total flux in the UV-A and visible radiations is far greater. That UV-B radiation may play a role in melanoma is supported; at the same time, one cannot exclude the possibility that the action spectrum for melanoma is, instead, the UV-A, the visible, or even the NIR portion of the sunlight spectrum. The strong differential effect of altitude on the transmission of light of different wavelengths might serve as an important discriminating variable. If solar UV radiation is implicated in the development of melanoma, then altitude should emerge as a significant factor in epidemiologic studies. If visible or IR radiation is the active agent, then differences on the basis of altitude should be small or negligible. Intrinsic solar variations that follow the annual sunspot number appear inadequate in either the UV or the visible band to account directly for the apparent 11-year modulation of melanoma incidence found in some registries. Secondary atmospheric effects brought about by the action of solar UV changes on the ozone layer may be adequate to explain a weak 11-year modulation in melanoma incidence, although continuous measurements of UV-B flux made at sites in the United States through a full solar cycle have shown no such effect. Nor do these early measurements reveal the long-term increase in UV-B intensity expected from the destruction of stratospheric ozone by industrial pollutants over the last 10 years.

Interplanetary radial cosmic-ray gradients and their implication for a possible large modulation effect at the heliospheric boundary

It is proposed here that a large and time-variable part of the overall 11-year cosmic ray modulation in the heliosphere takes place near the heliosphere boundary itself. This conclusion is reached by examining interplanetary radial gradient measurements which show that out to 30-40 AU this gradient remains nearly independent of heliocentric distance throughout the solar cycle. Properties of the solar wind which suggest that the distance to the pressure balance boundary does not vary by more than + or - 25 percent over the solar cycle are also used in support of the proposal. The importance of the large modulation effect at the boundary could exceed that of interplanetary effects expected from present models.

An empirical model for the 11-year cosmic-ray modulation

An analysis of monthly data from nine world-wide neutron monitoring stations over the period 1965–1975 is carried out for the study of the long-term cosmic-ray modulation. In an attempt to gain insight into the relationships which exist between solar activity, high-speed solar wind streams and various terrestrial phenomena an empirical relation for the cosmic-ray modulation has been found. Accordingly the modulated cosmic-ray intensity is equal to the galactic cosmic-ray intensity corrected by a few appropriate solar, interplanetary and terrestrial activity indices which causes the disturbances in interplanetary space, multiplying with the corresponding time-lag of cosmic-ray intensity from each of these indices. This relation is well explained by a generalization of the Simpson solar wind model which has been proved by the spherically symmetric diffusion-convection theory.

Time-lag of cosmic-ray intensity

The best correlation coefficient between the monthly cosmic-ray intensity of the Inuvik Station and various kinds of solar, interplanetary, and geophysical parameters has been found. It is calculated for different time-lags of cosmic-ray intensity with respect to these parameters. The maximum of these coefficients lead us to a useful empirical model for the 11-year cosmic-ray modulation.

A Summary of the Joint Discussion at Patras on Solar Luminosity Variations

The most interesting result in solar luminosity studies in the past decade has been the detection of significant variations in the total irradiance by precision radiometers on the NIMBUS-7 and SMM spacecraft. A substantial fraction of the observed variation can be attributed to sunspot blocking. Thermal storage models indicate that the blocked flux can be stored in a slight increase of the thermal and potential energy of the convective zone. The thermal storage time is likely to far exceed one solar activity cycle, implying an 11-year modulation of the solar constant at a level of about 0.1%. Direct observations of the 11-year or longer variations are more difficult but there is some evidence for secular trends below about 0.4% amplitude over the 14-year period of modern sampling. Ongoing stellar photometric programs suggest that luminosity changes exceeding 1% may have been detected in young, chromospherically active stars.H. S. Hudson (University of California, San Diego) reviewed observations of short-term solar irradiance variations from spacecraft, commenting principally on the precision measurements of the solar constant (S) made by the Active Cavity Radiometer (ACRIM) on the Solar Maximum Mission (SMM) spacecraft (Willson et al., 1981).

The galactic cosmic-ray radial intensity gradient and large-scale modulation in the heliosphere

Measurements of fluxes from 1 AU on the IMP 8 satellite to 11 AU on the Pioneer 11 and to greater than 24 AU on the Pioneer 10 spacecraft show that the nucleon integral gradient is a function of the level of the approximately 11-year solar modulation cycle. The gradient decreases from approximately 4.5% to 1.5% throughout the solar minimum of 1975-1977, and increases to approximately 2.5-3.0% per AU near maximum modulation. Pioneer 10 at greater than 24 AU is still deep in the modulation region, leading to estimates of 50-70 AU for the radial distance to the heliopause at both solar minimum and solar maximum modulation.

Cosmic-ray intensity related to solar and terrestrial activity indices in solar cycle No. 20

The 11-year modulation of cosmic-ray intensity is studied using the data from nine world-wide neutron monitoring station over the period 1965–1975. From this analysis the following relation among the modulated cosmic-ray intensityI, the relative sunspot numberR, the number of proton eventsN p and the geomagnetic indexA p has been derived which describes the long-term modulation of cosmic rays $$I = C - 10^{ - 3} (KR + 4N_P + 12A_P ),$$ whereC is a constant which depends on the rigidity of each station, andK is a coefficient related to the diffusion coefficient of cosmic rays and its transition in space. The standard deviation between the observed and calculated values of cosmic-ray intensity is about 5–9%. This relation has been explained by a generalization of the Simpson solar wind model which has been proved by the spherically symmetric diffusion-convection theory.

Twenty-two year modulation of cosmic rays associated with polarity reversal of polar magnetic field of the sun

The existence of the 22-year modulation of cosmic ray intensity is pointed out, using data of the ion chamber at Huancayo and the neutron monitors at Ottawa and Deep River for about four solar cycles. The modulation consists of two discrete states (high and low intensities), corresponding respectively to those of the polarity of the polar magnetic field of the Sun. This can be interpreted on the basis of the following hypothesis; when the polar magnetic field of the Sun is nearly parallel to the galactic magnetic field, they could easily connect with each other, so that galactic cosmic rays could intrude more easily into the heliomagnetosphere along the magnetic line of force, as compared with those in the anti-parallel state of the magnetic fields. The observed intensity difference between two states is about 4.3 ± 0.2% for neutron monitor ( P c = 1.5GV). The abnormal increase in proton (0.28–0.42 GV) and electron (0.41-3.24 GV) fluxes in the 20th solar cycle and the sudden appearance of anomalous components (He +, etc.) since 1972 can be also explained on the basis of the present hypothesis. The transition between the two states has a time lag behind the polarity reversal, depending on the cosmic ray rigidity, such as about 1 year for the neutron monitor ( P c = 1.5 GV) and about 3.5 years for low rigidity components (P < 1 GV). These time lags could be explained on the basis of the generalized Simpson's coasting solar wind model and the general diffusion-convection theory on some assumptions.

Observations of the eleven-year cosmic-ray modulation cycle

This paper reviews the available observations and the present state of knowledge of the long-term modulation of the intensity of galactic cosmic rays. This modulation occurs in response to the 11-year cycle of solar activity. The propagation of solar cosmic rays, as well as short-term modulation changes, are not explicitly discussed. The main theme of the paper is to interpret the observations in terms of the existing modulation theories. The theoretical model describes the propagation of cosmic rays in the interplanetary medium in terms of diffusion, convection, and energy changes. The topic is introduced with a brief description of how the cosmic-ray diffusion tensor is calculated from the fluctuations in the interplanetary magnetic field (Section 2). The cosmic-ray transport equations are discussed in Section 3. Observations of cosmic-ray intensity spectra, density gradients and anisotropies, and the evolution of the 11-year modulation cycle, are described in Sections 4, 5, and 6 respectively. It is shown that the principles of the modulation are understood in terms of the theoretical models. However, measurements of low-energy cosmic rays (kinetic energies ≲ 50 MeV nucleon−1) during the last few years, indicate that the models may be incomplete. On the other hand, it is also pointed out that the available observations are not always sufficient to evaluate the full consequences of the theoretical models. In particular, we need observations out of the ecliptic plane, as well as an increased effort to measure the density gradients and anisotropies at a single position (e.g. Earth) and as function of time.

The force field approach to the 11-year cosmic ray modulation cycle as observed by stationary neutron monitors

Observations from five stationary neutron monitors are used to demonstrate certain interesting effects in the 11-year modulation cycle of galactic cosmic rays. These effects are large-scale rigidity-dependent hysteresis structures, steplike modulation changes, and double minima in cosmic ray intensities over the modulation cycle. A technique is developed to interpret these effects in terms of the force field solution of the cosmic ray equation of streaming. It is found that all these effects can be explained in a spherical symmetric modulation model in which the cosmic ray diffusion coefficient is separable in rigidity-dependent and heliocentric-dependent parts. The results are then compared with those of other experiments, and general agreement is found between these experiments. This agreement indicates that the specific force field approach used here is valid. In the final section it is shown, however, that spherical symmetric modulation models, and consequently the force field approximation, may be oversimplifications of the true modulation mechanism.

Change in the eleven-year modulation at the time of the June 8, 1969, Forbush decrease

The functional form of the modulation for the 11-year variation changed abruptly after the Forbush decrease of June 8, 1969. This change in the 11-year modulation suggests that this Forbush decrease was an integral part of the 11-year variation. Some details of the change as observed by neutron monitors and by spacecraft at low energies are discussed.