Rigidity Spectrum Research Articles

Rigidity spectrum of cosmic ray variations over the periods of large forbush decreases during solar cycles 22 and 23

The paper presents findings of rigidity spectrum of cosmic ray (CR) variations during certain Forbush decreases recorded at the worldwide network of neutron monitors over the period 1991-2005. In the majority of events under consideration, rigidity spectrum of primary CR variations is not described by the power function of rigidity over the energy range to which neutron monitors are most sensitive.

Neutron monitor calibrations: progress report

In order to obtain rigidity spectra from the ~40 stationary neutron monitors around the world, two calibration neutron monitors were built in 2002. Various tests were performed on these neutron monitors, and some calibrations have been done. Due to electronic development during the past ten years, the electronics heads were completely redesigned and rebuilt in 2011. The progress and results of the calibration effort, as well as plans for a network of mini neutron monitors, are reported.

Theoretical and Experimental Studies of the Rigidity Spectrum of the 27-Day Variation of the Galactic Cosmic Ray Intensity in Different Epochs of Solar Activity

We consider the recent, very exceptional, 11-year cycle (2003 – 2009) of solar activity and confirm that the relative amplitude in rigidity spectrum, δD(R)/D(R), which can be approximated by a power law in rigidity R, of the first three harmonics of the 27-day variation of the galactic cosmic ray (GCR) intensity is hard in the maximum and soft in the minimum epochs of solar activity, as was found by neutron monitor data for the period of 1965 – 2002. This property is seen not only in separate minimum and maximum epochs but in individual intervals of a solar Carrington rotation as well: There exist many individual intervals of solar rotation when the expected rigidity spectrum of the 27-day variation of the GCR intensity indeed is hard in the maximum epoch of solar activity and is soft in the minimum epoch. We then construct a three-dimensional model of the 27-day variation of the GCR intensity based on Parker’s transport equation, by implementing in situ measurements of the changes in heliographic longitude of the solar wind velocity and interplanetary magnetic field for different epochs of solar activity.

Effects in cosmic rays in March 1991

Using the spectrographic global survey method, variations in the rigidity spectrum and anisotropy of galactic cosmic rays (March 1991) have been studied using data from ground-based observations of cosmic rays (CR) at the worldwide network of stations. Variations in geomagnetic cutoff rigidity (GCR) have been calculated. The paper also presents latitudinal GCR variations at certain moments of the considered period for different geomagnetic field disturbance levels. Calculation results of GCR variations have been compared with those of effect of the westward current flowing with a strength proportional to the latitude cosine along parallels on the sphere, for different radii of the current ring in the dipole field.

Features of relativistic solar proton spectra derived from ground level enhancement events (GLE) modeling

With the developed by the authors of a ground level enhancements events (GLE) modeling technique, the modeling study of 35 large GLEs for the period 1956 - 2006 has been carried out. The basic characteristics of relativistic solar protons (RSP) are obtained: a rigidity (energetic) spec- trum, anisotropy axis direction, and pitch angle distributions for each event. It is shown that in nearly all events there ex- isted two components (population) of relativistic solar par- ticles: prompt and delayed. The prompt component (PC) prevails in the beginning of the event. It is characterized by an impulsive profile, strong anisotropy and exponential en- ergetic spectrum. The delayed component (DC) dominates during maximum and decline phases of the events. It has a gradual intensity profile, moderate anisotropy and a power law energetic spectrum. The analysis of the large number GLE shows the value of a characteristic energy in the expo- nential spectrum of PC has rather stable meaning 0.5 GeV and well agrees with the spectrum of protons accelerated in an electric field arising during the magnetic reconnection in the solar corona. The value of a spectral exponent of the power law spectrum of DC is distributed from 4 up to 6 with most at 5. This is close to the simulated spectrum arising in the process of stochastic acceleration in turbulent solar plasma. solar protons (RSP) from the data of the worldwide network of neutron monitors. These are: rigidity (energy) spectrum, direction of anisotropy axis, and pitch angle distributions. Dynamics of these parameters in each event were studied. It is shown that in nearly all events there existed two compo- nents (populations) of relativistic solar particles: prompt and delayed ones. The prompt component (PC) prevails in the beginning of the event. It is characterized by an impulsive profile, a strong anisotropy and an exponential energetic spectrum. The de- layed component (DC) dominates during maximum and de- cline phases of the events. It has a gradual intensity profile, a moderate anisotropy and a power law energy spectrum. The averaged parameters of the PC and DC spectra and their pos- sible connection to probable mechanisms of acceleration on the Sun were studied. The acceleration by electric field in the region of magnetic reconnection for the PC and the stochas- tic acceleration in the turbulent plasma for the DC are con- sidered the most probable of these mechanisms.

Energy dependence of the rigidity spectrum of Forbush decrease of galactic cosmic ray intensity

We show that rigidity spectrum of Forbush decrease (Fd) of galactic cosmic ray (GCR) intensity in September 9–23, 2005 clearly depends on energy. We calculated rigidity spectrum of the Fd based on the neutron monitors and Nagoya muon telescope channels’ data divided in three groups according to their cut off rigidities. We found that temporal changes of rigidity spectrum exponent γ are approximately similar for all cut off rigidity groups, but γ values are the larger the higher are cut off rigidities. We conclude that rigidity spectrum of Fd is hard for lower energy range and is soft for the higher energy range. We believe that an energy dependence of the power law rigidity spectrum of Fd is observed owing to the preferential convection–diffusion mechanism during Fd in September 9–23, 2005. It is a reflection of an influence of the temporal changes of the structure of the interplanetary magnetic field (IMF) turbulence in different range of frequency f during Fd. Particularly, a decisive role in formation of the character of the rigidity spectrum belongs to the changes of the exponent ν of the power spectral density (PSD) of the IMF turbulence (PSD∝f−ν). The exponent ν is greater for high frequency region of the IMF turbulence (responsible for scattering of low rigidity particles of GCR), than for low frequency region of the IMF turbulence (being responsible for scattering of higher rigidity particles). Also, we challenge to estimate an existence of slab/2D structure of solar wind turbulence during the Fd in September 9–23, 2005 based on the distribution of average turbulence energy among the IMF’s components.

Fine structure in the cosmic ray spectrum: Further analysis and the next step

An analysis is made of the fine structure in the cosmic ray energy spectrum: new facets of present observations and their interpretation and the next step. It is argued that less than about 10% of the intensity of the helium ‘peak’ at the knee at ≈5 PeV is due to just a few sources (SNR) other than the single source. The apparent concavity in the rigidity spectra of protons and helium nuclei which have maximum curvature at about 200 GV is confirmed by a joint analysis of the PAMELA, CREAM and ATIC experiments. The spectra of heavier nuclei also show remarkable structure in the form of ‘ankles’ at several hundred GeV/nucleon. Possible mechanisms are discussed. The search for ‘pulsar peaks’ has not yet proved successful.

Analysis of the Forbush effect in May 2005 using the spectrographic global survey method

Based on the data from ground observations of cosmic rays (CRs) obtained by the spectrographic global survey method on the worldwide network of stations, the variations in the rigidity spectrum and anisotropy of galactic cosmic rays were investigated, along with changes in the geomagnetic cutoff rigidity in May 2005. A high degree of anisotropy (∼40–60% for the first spherical harmonics and ∼5–6% for the second spherical harmonics) was observed for particles with a rigidity of 4 GV at the moments of the maximum modulation of cosmic rays.

A model of the long period Galactic Cosmic Ray variations

We develop a two-dimensional (2-D) time dependent model of the long period variation of Galactic Cosmic Ray (GCR) intensity. Besides the well-known fundamental processes responsible for the modulation of GCR intensity, we implement the following in the model: the parameters characterizing temporal changes in the exponent ν of the Power Spectral Density (PSD) of the Interplanetary Magnetic Field (IMF) turbulence, the modulus B of the IMF, the tilt angle δ of the Heliospheric Neutral Sheet (HNS), and changes in the drift effect of the GCR particles upon solar activity. We assume that the drift effect of the GCR particles has the maximal value in the minimum epoch of solar activity, when drift dominates, and that it has the minimal value in the maximum epoch, when diffusion dominates. We show that an acceptable compatibility is maintained for the period between 1976 and 1987 (solar cycle #21), when the expected temporal changes in the GCR particle density are shifted, as regards the temporal changes of the smoothed experimental data on the GCR intensity, for 18 months. We consider a delay time ∼18 months as an effective delay time caused by the combined influence of all parameters implemented in the 2-D model. We also conclude that one of the important indicators of the compatibility of the experimental data (1976–1987) and 2-D time dependent modeling of the long period variations of the GCR intensity is the high correlation between the temporal changes of the rigidity spectrum exponents γ calculated from theoretical model and the experimental data.

The onset of sunspot cycle 24 and galactic cosmic ray modulation

The annual mean sunspot number (SSN) has a minimum value in 2008, while the monthly mean SSN has a value of zero in August 2009. The galactic cosmic ray modulation for cycle 24 began at earth orbit in January 2010. We study the onset characteristics of the new modulation cycle using data from the global network of neutron monitors. They respond to time variations in different segments of the galactic cosmic ray rigidity spectrum. The corresponding temporal variations in the interplanetary magnetic field intensity ( B) and solar wind velocity ( V) as well as the tilt angle of the heliospheric current sheet are also studied. There is a lag of 3 months between a large, sharp increase of the tilt angle of the heliospheric current sheet and the onset of modulation. Some neutron monitors are undergoing long-term drifts of unknown origin.

A calibration neutron monitor: Statistical accuracy and environmental sensitivity

This paper is a follow-on of that of Krüger et al. [Krüger, H., Moraal, H., Bieber, J.W., Clem, J.M., Evenson, P.A., Pyle, K.R., Duldig, M.L., Humble, J.E. A calibration neutron monitor: energy response and instrumental temperature sensitivity. J. Geophys. Res. 113, A08101, doi:10.1029/2008JA013229, 2008], that describes the characteristics of a pair of calibration neutron monitors that were developed to intercalibrate the count rates of the world’s neutron monitors against each other. Such an intercalibration will allow the calculation of energy (rigidity) spectra, which will enhance the quality of the neutron monitor data. Krüger et al. (2008) investigated the energy and temperature response of the calibrators. This paper studies the statistical accuracy of the calibration procedure, its repeatability, and the sensitivity to its environment. The paper concludes with a calibration procedure that can minimise the uncertainties caused by these five effects, or at least correct for them.

The rigidity spectrum of the harmonics of the 27-day variation of the galactic cosmic ray intensity in different epochs of solar activity: 1965–2002

We study temporal changes of the rigidity ( R) spectrum of the harmonics of the 27-day variation of the galactic cosmic ray (GCR) intensity using neutron monitors (NM) data for the period 1965–2002. We show that the rigidity spectrum of the third harmonic (9 days) of the 27-day variation of the GCR intensity changes in a similar way as the spectra of the first and second harmonics, being hard in the maximum epochs and soft in the minimum epochs of solar activity. We ascribe this finding to the alternation of the sizes of the modulation regions of the 27-day variation of the GCR intensity in different epochs of solar activity. The average size of the vicinity of the corotating interaction regions, causing the 27-day variation of the GCR intensity, is less in the minimum epochs than in the maximum epochs of solar activity. A vicinity of the corotating interaction regions of larger size involves in modulation higher rigidity particles of GCR than the vicinity of smaller size; thus, this statement can be considered as one of the reasons leading to the hardening of the rigidity spectrum of the harmonics of the 27-day variation of the GCR intensity in maximum epochs compared with minimum epochs of solar activity. We also show that the temporal changes of the power rigidity spectrum of the third harmonic of the 27-day variation of the GCR intensity are negatively correlated with the rigidity spectrum of the 11-year variation of the galactic cosmic ray intensity. We found a recurrence in the temporal changes of the amplitudes of the first harmonic of the 27-day variation of the GCR intensity and in some parameters of solar activity and solar wind.

On relation of the long period galactic cosmic rays intensity variations with the interplanetary magnetic field turbulence

We study a relationship of the exponent γ of the rigidity R spectrum δD(R)D(R) of the galactic cosmic rays (GCR) intensity variations δD(R)D(R)∝R-γ and the exponent νy of the power spectral density (PSD) of the By component of the interplanetary magnetic field (IMF) (PSD=Pf-νy, where P is power and f is frequency) in the range of the frequency f ≈ 4 × 10−6–10−5 Hz. For this purpose we use data of neutron monitors and the IMF in the period of 1967–2002. We show that the rigidity spectrum of the long-period variations of the GCR intensity is hard in the minimum epochs of solar activity (γ ≈ 0.6) when the exponent νy of the PSD of the IMF is higher (νy ≈ 1.9), and is soft in the maximum epochs (γ ≈ 1.2), when the exponent νy is relatively lower (νy ≈ 1.4). We ascribe these features to the essential rearrangement of the structure of the IMF turbulence during the 11-year cycle of solar activity assuming that the IMF turbulence is homogeneous and isotropy for time scales τ > 1 day. We reveal the relationships among rigidity spectrum exponent γ, exponent νy and the power P of the PSD of the IMF turbulence in different epochs of solar activity. We suppose that the changes of the structure of the IMF turbulence versus solar activity (manifesting in the changes of the exponent γ of the rigidity R spectrum of the GCR intensity variations) is one of the important reasons of the 11-year variation of the GCR intensity for the rigidity of the GCR particles, to which neutron monitors are respond.

Rigidity spectrum of the 27-day variation of the galactic cosmic ray intensity in different epochs of solar activity

We study the temporal evolution of the power rigidity spectrum of the first (27 days) and the second (14 days) harmonics of the 27-day variation of the galactic cosmic ray intensity measured by neutron monitors in the period of 1965–2002. The rigidity spectrum of these variations can be approximated by a power law. We show the rigidity spectra of the first and the second harmonics of the 27-day variation of the galactic cosmic ray intensity have similar time profiles. These spectra are hard ( γ ≈ 0.5 ± 0.1) and soft ( γ ≈ 1.1 ± 0.2) during solar maximum and minimum activity, respectively. We ascribe this to the alternation of the sizes of the modulation regions responsible for the 27-day variation of the galactic cosmic ray intensity in different epochs of solar activity. Especially, the average radial sizes of the modulation regions of the 27-day variation and the heliolatitudinal extension of the heliolongitudinal asymmetry are smaller during solar minimum than during solar maximum. We show also, that the temporal changes of the power rigidity spectra of the first and the second harmonics of the 27-day variation of the galactic cosmic ray intensity are in a negative correlation with the changes of the rigidity spectrum of the corresponding 11-year variation.

Modeling and data analysis of a Forbush decrease

We study the Forbush decrease of the galactic cosmic ray intensity observed in 9–25 September 2005 using the experimental data and a newly developed time-dependent three dimensional modeling. We analyze neutron monitors and muon telescopes, and the interplanetary magnetic field data. We demonstrate a clear relationship between the rigidity ( R) spectrum exponent (γ) of the Forbush decrease and the exponent ( ν) of the power spectral density of the components of the interplanetary magnetic field in the frequency range of ∼ 10 −6–10 −5 Hz. We confirm that an inclusion of the time-dependent changes of the exponent ν makes the newly developed nonstationary three dimensional model of the Forbush decrease compatible with the experimental data. Also, we show that the changes of the rigidity spectrum exponent γ does not depend on the level of convection of the galactic cosmic rays stream by solar wind; depending on the changes of the exponent ν, i.e. on the state of the turbulence of the interplanetary magnetic field.

Solar proton event in December 2006

The variations in the rigidity spectrum and anisotropy of cosmic rays in December 2006 have been studied based on the surface measurements of the cosmic ray intensity at the global network of stations, using the method of global spectrographic survey. It has been indicated that the highest degree of anisotropy (to ∼50%) with the maximal intensity of particles with a rigidity of 4 GV in the direction from the Sun (an asymptotic direction of about −25° and 160°) was observed at 0400 UT on December 13. The parameters of the cosmic ray rigidity spectrum, which reflect the electromagnetic characteristics of the heliospheric fields during the studied period, have been determined when the surface and satellite measurements of protons in the energy range from several megaelectronvolts to several tens of gigaelectronvolts were jointly analyzed. The observed anisotropy and variations in cosmic rays in a wide energy range have been explained based on an analysis of the results.

Primary and secondary effects in cosmic-ray variations at solar proton events

The variations of the cosmic-ray rigidity spectrum in the energy range from 0.8 MeV to several dozen GeV at solar proton events in January 2005 and December 2006 have been analyzed. A comparison of the observed and model spectra revealed the power range of direct detection of solar cosmic rays and moments of their observations.

Forbush decrease of the galactic cosmic ray intensity: experimental study and theoretical modeling

We study the temporal changes of the power law rigidity spectrum of the Forbush decrease (Fd) of the galac- tic cosmic ray (GCR) intensity. We show that the power law rigidity spectrum of Fd for the period of 6-20 Novem- ber 2004 found by neutron monitors and ground muon tele- scopes experimental data, gradually is hardening during the decreasing phase of the intensities and then steadily is soft- ening during the recovery phase. A relation of the rigidity spectrum exponent of the Fd of the GCR intensity with the exponent of the power spectral density (PSD) of the compo- nents of the interplanetary magnetic field (IMF) turbulence is established. We develop three dimensional (3-D) non sta- tionary model of the Fd and show that the results of the theo- retical modeling are in good agreement with the experimen- tal data. We suppose that temporal changes of the rigidity spectrum exponent of the Fd of GCR intensity can be used to calculate the exponent of the PSD of the IMF turbulence for the arbitrary period, which is not achievable by the in situ measurements of the IMF.

Investigation of the multiple‐component structure of the 20 January 2005 cosmic ray ground level enhancement

Worldwide observations of the cosmic ray ground level enhancement (GLE) of 20 January 2005 are used to investigate a commonly observed but poorly understood feature of this class of event. It is argued that the GLE comprised two distinctly different cosmic ray populations. The first resulted in an impulsive, highly anisotropic, field‐aligned pulse with a relatively hard rigidity spectrum and significant velocity dispersion. The characteristics of the anisotropy were almost identical to those for similar impulsive increases observed during GLEs in 1960, 1978, and 1989. The π0γ ray observations from the RHESSI and CORONAS‐F spacecraft and Type III radio emissions yield a path length of 1.76 ± 0.1 AU to Earth for the first pulse. After the highest energies in the initial anisotropic pulse had passed Earth, another field‐aligned but mildly anisotropic cosmic ray pulse developed slowly worldwide, exhibiting the characteristics of the conventional GLE. The risetime and anisotropy of this second population indicate substantial scattering, apparently at variance to the essentially scatter‐free nature of the initial pulse. We show that the coexisting scatter‐free initial impulsive increase and the diffusive character of the second pulse are consistent with the standard quasi‐linear theory of pitch angle diffusion. Throughout the GLE, the anisotropy remained field‐aligned, and a third maximum, seen by some stations, is shown to be due to changes in the direction of the heliospheric magnetic field (HMF). Examination of 22 large (>20%) GLEs in the historical record shows that the impulsive pulse never occurs after the commencement of the P2 pulse, indicating that the impulsive‐gradual combination is not due to a chance sampling of differing scattering regions of the HMF. It is further shown that impulsive pulses, or their equivalents, have been observed in 13 out of the 15 GLEs associated with solar activity in the solar longitude range 24°–98°W, leading us to propose that the event of 20 January 2005 should be regarded as the defining example of the GLE. The observations lead us to propose two separate acceleration episodes in the typical GLE: (1) acceleration directly associated with the flare itself and located in the lower corona and (2) acceleration by a supercritical shock driven by the associated coronal mass ejection, located at ∼3–5 solar radii and farther in the upper corona. A one‐to‐one association with so‐called impulsive and gradual solar energetic particle events at lower energies is proposed. On the basis of these observations, a generic model for the GLE is proposed.

The method for predicting solar proton events

Dynamic processes in the interplanetary space have been investigated using time variations in time parameters of the cosmic-ray rigidity spectrum. Change of heliosphere electromagnetic characteristics has been found out to precede sporadic phenomena on the Sun. In particular, it is shown that sporadic phenomena are followed by generation of local polarization electric fields, decrease of the magnetic-field strength in small-scale heliospheric structures, and increase of the potential difference between the pole and the plane of the ecliptic. These features allow prediction of solar proton events in advance (from several hours to several tens of hours) with a high degree of confirmation.