Long-term Modulation Of Cosmic Rays Research Articles

Long-Term Modulation of Cosmic Rays in Solar Cycles 23–24

Long-Term Modulation of Cosmic Rays in Solar Cycles 23–24

Correlation of Long-term Cosmic-Ray Modulation with Solar Activity Parameters

Abstract In this work, we analyze the long-term cosmic-ray modulation observed by the Hermanus neutron monitor, which is the detector with the longest cosmic-ray record, from 1957 July. For our study we use the force-field approximation to the cosmic-ray transport equation, and the newest results on the mean free paths from the scattering theory. We compare the modulation parameter (ϕ) with different rigidity (P) dependences: P, P 2, and P 2/3. We correlate them with solar and interplanetary parameters. We found that (1) these rigidity dependences properly describe the modulation, (2) long-term cosmic-ray variations are better correlated with the magnitude of the heliospheric magnetic field (HMF) than the sunspot number, solar wind speed, and tilt angle of the HMF, and (3) the theoretical dependence of the parallel mean free path on the magnetic field variance is in agreement with the modulation parameter and therefore with the neutron monitor record. We also found that the force-field approximation is not able to take into account the effects of three-dimensional particle transport, showing a poor correlation with the perpendicular mean free path.

Coronal holes in the long-term modulation of cosmic rays

Long term cosmic ray variations in the heliosphere in cycles 21–24 are described using the multiparametric model, including characteristics of solar activity. Long-term observations of the cosmic ray intensity, global solar magnetic field characteristics, and characteristics taking into account sporadic solar activity are the initial data for modeling cosmic ray variations. Data on intensity have been obtained from observations at the global ground network of neutron monitors and stratospheric sounding. The characteristics of the regions with an open magnetic field (coronal holes) have been introduced into the model in order to improve the description of long-term variations. The location (latitude), area, and magnetic flux of coronal holes have been used as parameters of this solar activity type manifestation. The modulation has been modeled for the entire studied period (1976–2012) and independently for periods with identical global solar magnetic field directions with regard to the cosmic ray variation delay relative to variations in the solar activity characteristics. It has been shown that the accuracy of long-term variation description improves when coronal hole characteristics are taken into account.

THE EFFECT OF A DYNAMIC INNER HELIOSHEATH THICKNESS ON COSMIC-RAY MODULATION

The time-dependent modulation of galactic cosmic rays in the heliosphere is studied over different polarity cycles by computing 2.5 GV proton intensities using a two-dimensional, time-dependent modulation model. By incorporating recent theoretical advances in the relevant transport parameters in the model, we showed in previous work that this approach gave realistic computed intensities over a solar cycle. New in this work is that a time dependence of the solar wind termination shock (TS) position is implemented in our model to study the effect of a dynamic inner heliosheath thickness (the region between the TS and heliopause) on the solar modulation of galactic cosmic rays. The study reveals that changes in the inner heliosheath thickness, arising from a time-dependent shock position, does affect cosmic-ray intensities everywhere in the heliosphere over a solar cycle, with the smallest effect in the innermost heliosphere. A time-dependent TS position causes a phase difference between the solar activity periods and the corresponding intensity periods. The maximum intensities in response to a solar minimum activity period are found to be dependent on the time-dependent TS profile. It is found that changing the width of the inner heliosheath with time over a solar cycle can shift the time of when the maximum or minimum cosmic-ray intensities occur at various distances throughout the heliosphere, but more significantly in the outer heliosphere. The time-dependent extent of the inner heliosheath, as affected by solar activity conditions, is thus an additional time-dependent factor to be considered in the long-term modulation of cosmic rays.

Solar Drivers of 11-yr and Long-Term Cosmic Ray Modulation

In the current paradigm for the modulation of galactic cosmic rays (GCRs), diffusion is taken to be the dominant process during solar maxima while drift dominates at minima. Observations during the recent solar minimum challenge the pre-eminence of drift at such times. In 2009, the ∼2 GV GCR intensity measured by the Newark neutron monitor increased by ∼5% relative to its maximum value two cycles earlier even though the average tilt angle in 2009 was slightly larger than that in 1986 (∼20° vs. ∼14°), while solar wind B was significantly lower (∼3.9 nT vs. ∼5.4 nT). A decomposition of the solar wind into high-speed streams, slow solar wind, and coronal mass ejections (CMEs; including post-shock flows) reveals that the Sun transmits its message of changing magnetic field (diffusion coefficient) to the heliosphere primarily through CMEs at solar maximum and high-speed streams at solar minimum. Long-term reconstructions of solar wind B are in general agreement for the ∼1900-present interval and can be used to reliably estimate GCR intensity over this period. For earlier epochs, however, a recent 10Be-based reconstruction covering the past ∼104 years shows nine abrupt and relatively short-lived drops of B to ≲0 nT, with the first of these corresponding to the Spörer minimum. Such dips are at variance with the recent suggestion that B has a minimum or floor value of ∼2.8 nT. A floor in solar wind B implies a ceiling in the GCR intensity (a permanent modulation of the local interstellar spectrum) at a given energy/rigidity. The 30–40% increase in the intensity of 2.5 GV electrons observed by Ulysses during the recent solar minimum raises an interesting paradox that will need to be resolved.

The role of cyclic solar magnetic field variations in the long-term cosmic ray modulation

Updating the semi-empirical model of cosmic rays (CR) modulation proposed in our previous work has been discussed. In order to provide a description of long-term variations, in which the CR modulation would adequately reflect the complex interaction of global and local solar magnetic fields, we have supplemented the model with the following characteristics: the solar magnetic field polarity, the integral index, the partial indices, the tilt of the current sheet, and the index characterizing the X-ray flares. The role of each index in the CR modulation has been determined. In the multi-parameter description of long-term CR variations using the integral index or one of four partial indices, the best fit for the period 1977–1999 has been obtained for the integral index and the sector-odd index characterizing the inclined dipole. The discrepancy between the model and observations increases from the beginning of 2000. Therefore, the problematic features in the behavior and modeling of CR during cycle 23 have been discussed. It is suggested that the cycle-to-cycle decrease of the CR density in the minimum epochs of the past solar activity (SA) cycles could be explained by the decrease of the zone-odd index.

Manifestations of cyclic variations in the solar magnetic field in long-term modulation of cosmic rays

The possibilities of improving the semiempirical model of cosmic ray (CR) modulation, proposed by us previously, are discussed. The following characteristics have been considered as model parameters in order to describe long-period CR variations using a unified model and to more completely reflect solar cycles in CR modulation as a complex interaction between two systems of fields (large-scale and local): the value and sign of the polar solar field, the average strength of the solar magnetic field (the Bss integral index), partial indices (zone-even (ZE) and zone-odd (ZO) and sector-even (SE) and sector-odd (SO) indices), the tilt of the heliospheric current sheet, and the special index (Fx) taking into account X ray flares. The role of each index in CR modulation has been revealed. When we described the long-term CR variations using many parameters and taking into account the integral index or one of four partial indices, the best results of modulation modeling during 1976–1999 were obtained for the Bss total energetic index and SO index. A difference between the model calculations and observations increases beginning from the middle of 2000; the problem features of the CR behavior and the specific features of modeling this behavior in cycle 23 of solar activity (SA) are discussed. It is assumed that a decrease in the CR density at the last SA minimums (from cycle to cycle) can be related to a decrease in the ZO index and to a recently detected similar decrease in the vertical component of the solar dipole magnetic moment.

Heliospheric modulation of high-energy cosmic rays: II. Deformation of the neutral surface

Analysis of neutron monitor data in the periods of negative and positive polarities of the general solar magnetic field has revealed a dependence of the long-term cosmic-ray modulation on both deformation of the neutral surface of the interplanetary magnetic field and solar activity level. The effects of solar activity and neutral surface deformation dominate at positive and negative polarities, respectively. The magnetic drift of cosmic rays with different trajectories in the epochs of positive and negative polarities is responsible for this behavior of the 11-year and annual density modulations.

Coronal Mass Ejections and Galactic Cosmic‐Ray Modulation

We present a study of the long-term evolution of coronal mass ejections (CMEs) observed by the Large Angle and Spectrometric Coronograph (LASCO) on board SOHO during the ascending, maximum, and part of the descending phases of solar cycle 23 and their relation with the modulation of galactic cosmic-ray (GCR) intensity observed at 1 AU by the Climax neutron monitor and IMP-8 spacecraft. We compare the long-term GCR modulation with the CME occurrence rate at all, low, and high latitudes, as well as the observed CME parameters (width and speed). Twenty-seven day averages of CME occurrence rates and CME properties from 1996 January to 2003 December are presented in the Appendix. The general anticorrelation between GCR intensity and the CME rate is relatively high (~-0.88). However, when we divide the CME rate into low- and high-latitude rates and compare them with the GCR intensity during the ascending phase of solar cycle 23, we find a lower anticorrelation between the low-latitude the CME rate and GCR intensity (~-0.71) and a very high anticorrelation between the high-latitude CME rate and GCR intensity (~-0.94). This suggests that, in general, CMEs could cause the decrease in the GCR flux in the inner heliosphere, as stated by the global merged interaction region (GMIR) theory. In particular, during the ascending phase of cycle 23 (qA > 0), this flux comes mainly from heliospheric polar regions. Thus, high-latitude CMEs may play a central role in the long-term cosmic-ray modulation during this phase of the cycle by blocking the polar entrance of GCRs to the inner heliosphere. This study supports the scenario in which CMEs, among other structures, are the building blocks of GMIRs, although we propose that the spherical shells (GMIRs) are closed separately at polar and equatorial regions by CMEs of different latitudes. Our results suggest that all CME properties show some correlation with the GCR intensity, although there is no specific property (width, speed, or a proxy of energy) that definitely has a higher correlation with GCR intensity.

Long-Term Modulation of Cosmic Rays in the Heliosphere and its Influence at Earth

The temporal variation of the cosmic-ray flux at Earth directly influences the production rate of cosmogenic isotopes in the Earth’s atmosphere. Here we put the emphasis on problems of the modulation of cosmic rays in the heliosphere. The physics of the modulation region, e.g., the heliosphere, is described and also the transport theory of the cosmic rays through the heliosphere is presented. The discussion includes more recent ideas of the modulation in the heliosheath. In the light of these ideas the cosmic-ray fluxes during the Maunder minimum are discussed. It is also discussed, that the 22-year cycle observed in the cosmogenic isotopes is a modulation effect of the cosmic rays, and hence directly connected with the physics of the outer heliosphere.

Modulation of galactic cosmic rays at solar maximum: Observations

The spectra of galactic cosmic rays observed anywhere inside the heliosphere are modulated by the sun because the charged particles must fight their ways inward against the radially expanding solar wind. In the past half a century, galactic cosmic ray fluxes at Earth were continuously monitored by neutron monitors on the ground and instruments on spacecraft in the Earth orbit. It was found that cosmic ray intensities are the lowest at the maximum of the 11-year solar activity cycle when the solar and heliospheric magnetic fields are complex and disturbed by many events on the sun. Our knowledge of comic ray modulation in the global heliosphere was greatly enhanced in the past two decades, thanks to an array of heliospheric missions, Voyagers and Pioneers that covered the outer heliosphere up to ∼75 AU radial distance from the sun and Ulysses that covered the inner heliosphere over almost the entire range of heliographic latitude. It is particularly fortunate that Ulysses was at the highest heliographic latitudes in 2000–2001 making observations of the polar regions of the heliosphere at the solar maximum for the first time. With the observations from the heliospheric network missions, both the spatial variation and the temporal variation of cosmic ray modulation in the three dimensional heliosphere could be investigated. In this paper, observational results of cosmic rays during recent solar maximum periods are reviewed. Comparisons to the cosmic ray observations during the solar minimum are made to show how the modulation changes with the solar activity cycle and solar magnetic fields. Implications of these results to our understanding of the heliospheric magnetic field and solar wind structures and the mechanisms of long-term cosmic ray modulation are discussed.

Reconstructing the long-term cosmic ray intensity: linear relations do not work

Abstract. It was recently suggested (Lockwood, 2001) that the cosmic ray intensity in the neutron monitor energy range is linearly related to the coronal source flux, and can be reconstructed for the last 130 years using the long-term coronal flux estimated earlier. Moreover, Lockwood (2001) reconstructed the coronal flux for the last 500 years using a similar linear relation between the flux and the concentration of cosmogenic 10 Be isotopes in polar ice. Here we show that the applied linear relations are oversimplified and lead to unphysical results on long time scales. In particular, the cosmic ray intensity reconstructed by Lockwood (2001) for the last 130 years has a steep trend which is considerably larger than the trend estimated from observations during the last 65 years. Accordingly, the reconstructed cosmic ray intensity reaches or even exceeds the local interstellar cosmic ray flux around 1900. We argue that these unphysical results obtained when using linear relations are due to the oversimplified approach which does not take into account the complex and essentially nonlinear nature of long-term cosmic ray modulation in the heliosphere. We also compare the long-term cosmic ray intensity based on a linear treatment with the reconstruction based on a recent physical model which predicts a considerably lower cosmic ray intensity around 1900.Key words. Interplanetary physics (cosmic rays; heliopause and solar wind termination) – Geomagnetism and paleomagnetism (time variations, secular and long-term)

The spectrum of cosmic ray variations during the 19th–22nd solar cycles

The data from the world-wide network of neutron monitors, ionization chambers, stratospheric and satellite observations of cosmic ray intensity are used to investigate the long-term cosmic ray modulation in the period 1937–1991. The rigidity spectrum of the long-term cosmic ray modulation is obtained for the period 1954–1991 in the 1–25 GV rigidity range. The generalized spectral forms are obtained for periods of high and low solar activity. The obtained energy spectrum and the energy spectrum of the primary cosmic rays observed on the ULYSSES near Earth in November 1990 are compared. A satisfactory accordance between these two spectra is found.

The time-dependent transport of cosmic rays in the heliosphere

The modulation of cosmic rays (CRs) in the heliosphere is a dynamic and therefore a highly time-dependent process. Numerical models with only a time-dependent neutral sheet prove to be successful when moderate to low solar activity occurs but fail to describe large and discrete steps in modulated CRs when solar activity is high. To explain this feature of heliospheric modulation, the concept of global merged interaction regions (GMIRs) is required. The combination of gradient, curvature and neutral sheet drifts with these GMIRs has so far been the most successful approach in explaining the 11-year and 22-year cycles in the long-term modulation of CRs.

Cosmic ray modulation in the 3-D heliosphere

The basic physical processes that lead to the long-term modulation of cosmic rays by the solar wind have been known for many years. However our knowledge of the structure of the heliosphere, which determines which processes are most important for the modulation, and of the variation of this structure with time and solar activity level is still incomplete. Study of the modulation provides a tool for probing the scale and structure of the heliosphere. While the Pioneer and Voyager spacecraft are surveying the radial structure and extent of the heliosphere at modest heliographic latitudes, the Ulysses mission is the first to undertake a nearly complete scan of the latitudinal structure of the modulated cosmic ray intensity in the inner heliosphere (R<5.4 AU). Ulysses will reach latitudes of ~80°S in September 1994 and ~80°N in July 1995 during the approach to minimum activity in the 11 year solar cycle. We present a first report of measurements extending to latitudes of ~52°S, which show surprisingly little latitudinal effect in the modulated intensities and suggest that at this time modulation in the inner heliosphere may be much more spherically symmetric than had generally been believed based upon models and previous observations.

Aspects of the long-term cosmic-ray modulation

To investigate the long-term modulation of galactic cosmic rays at the ground-based detector energies, the monthly values of the neutron monitor (Climax, Mt. Washington, Deep River, and Huancayo) and ionization chamber (Cheltenham/Fredericksburg, Huancayo, and Yakutsk) intensities have been correlated with the sunspot numbers (used as a proxy index for transient solar activity) for each phase of sunspot cycles 18 to 22. Systematic differences are found for results concerning odd and even sunspot cycles. During odd cycles (19 and 21) the onset time of cosmic-ray modulation is delayed when compared with the onset time of the sunspot cycle, while they are more similar during even (18, 20, and 22) cycles. Checking the green corona data, on a half-year basis, we found typical heliolatitudinal differences during ascending phases of consecutive sunspot cycles. This finding suggests a significant role of the latitudinal coronal behaviour in the heliospherical dynamics during a Hale cycle. Such effectiveness concerns not only the transient interplanetary perturbations but also the recurrent ones. In fact, when lag between cosmic-ray data and sunspot numbers is considered, the anticorrelation between both parameters is very high (correlation coefficient |r| > 0.9) for all the phases considered, except for the declining ones of cycles 20 and 21, when high-speed solar wind streams coming from coronal holes affect the cosmic-ray propagation, and theRz parameter is no longer the right proxy index for solar-induced effects in the interplanetary medium.

On reproduction of long-term cosmic-ray modulation as seen by neutron monitor stations

The dependence of cosmic-ray intensity on 21st solar cycle phenomena has been studied using monthly cosmic-ray values from nine world wide Neutron Monitoring Stations.

The Long-Term Heliospheric Modulation of Galactic Cosmic Rays according to a Time-dependent Drift Model with Merged Interaction Regions

So far, little work has been done to study the effect of merged interaction regions (MIRs) on the long-term modulation of cosmic rays in more comprehensive simulations of the heliosphere We therefore present calculations for protons with a two-dimensional time-dependent drift model with an emulated wavy heliospheric neutral sheet (HNS) which include MIRs as large, idealized outward propagating regions with regions of enhanced interplanetary magnetic fields (IMF). The discussion features three classes of MIRs: namely global merged interaction regions (GMIRs), corotating merged interaction regions (CMIRs) and local merged interaction regions (LMIRs) according to the classification of Burlaga, McDonald, &amp; Ness (1993). It was found that the recovery rate (t<SUB>r</SUB>) from a single GMIR-induced step decrease in the proton intensity is clearly polarity-dependent, being slower during an A &lt;0 polarity cycle (northern hemispheric IMF directed toward the Sun) than during an A &gt; 0 cycle (northern hemispheric IMF directed away from the Sun). It plays a crucial role in determining the contribution of GMIRs toward long-term cosmic-ray modulation. The recovery rate is charge dependent, that is, faster for electrons than for protons during A &lt;0 periods and vice versa during A &gt; 0 periods. A simulation of the declining intensity phase of the modulation cycle with a changing wavy HNS and two successive GMIRs revealed that this approach gives a very natural and convincing explanation for the observed step decreases in long-term modulation. A study of the radial and energy dependence of the calculated declining intensity phase of the modulation cycle showed that two successive GMIRs produced a significant part of the total long-term modulation. In fact, the simulated GMIRs dominated long-term modulation for energies above ∼5 GeV and radial distances (r) larger than ∼40 AU. Similar calculations, but for the intensity recovery part of the modulation cycle indicated that: (i) Consecutive GMIRs are more successful in delaying the long-term proton intensity recovery during A &lt;0 cycles compared to A &gt; 0 cycles and (ii) are less successful in the delay of the recovery of electrons in relation to protons during A &lt;0 cycles than during A &gt; 0 cycles. It was realized that LMIRs and CMIRs contribute little toward long-term modulation. The CMIRs, in conjunction with rarefaction regions (RRs), only cause minor short-term periodic variations in the cosmic-ray intensity. In conclusion, time-dependent long-term modulation from the viewpoint of a two-dimensional MIR rift model is basically a process caused by the interplay between a changing wavy HNS and successive outward propagating GMIRs with the HNS dominating the process during periods of low solar activity and the GMIRs in dominance during times of large solar activity.

The simulation of merged interaction regions in the outer heliosphere

So far, little work has been done to study the effect of merged interaction regions (MIRs) on the long-term modulation of cosmic rays in more complex two-dimensional (2D) simulations of the heliosphere. In order to address this shortcoming we present calculations for protons with a 2D time-dependent drift model with an emulated wavy heliospheric neutral sheet (HNS) which include MIRs as large idealized outward propagating regions of enhanced interplanetary magnetic field (IMF) magnitude. We find the recovery rate (tr) from the MIR induced cosmic-ray intensity decrease to be polarity dependent, being slower during an A < 0 IMF polarity cycle than during an A > 0 cycle. This slower (tr) causes successive MIRs to contribute quantitatively more toward long-term modulation during such cycles, stressing the decisive role (tr) plays in the modulation process. We also expect MIRs to dominate the long-term modulation of cosmic rays relative to the wavy HNS at neutron monitor energies, large radial distances (r), and with effective crossfield diffusion (K⊥).

A time-dependent drift model for the long-term modulation of cosmic rays with special reference to asymmetries with respect to the solar minimum of 1987

Un modele de derive dependant du temps est developpe avec un feuillet neutre ondule dans lequel les variations dans l'ondulation du feuillet se propagent radialement vers l'exterieur a la vitesse du vent solaire. En utilisant un taux asymetrique de la variation dans l'angle d'inclinaison α du feuillet neutre ondule dans le modele, on peut expliquer la reponse moindre observee de l'intensite du rayonnement cosmique vis-a-vis des variations temporelles dans α apres le minimum solaire de 1987 ainsi que le comportement asymetrique du profil intensite-temps par rapport a 1987. Les angles d'inclinaison reels du feuillet neutre sont ensuite incorpores dans le modele, et les intensites calculees sont comparees avec les intensites mesurees par le satellite IMP 8 de 1976 a 1989.