27-day variations of the galactic cosmic ray intensity and anisotropy in the minimum of the 23rd solar activity cycle

We study the 27-day variations of the solar wind velocity, galactic cosmic ray (GCR) intensity and anisotropy in the last minimum epoch of solar activity (2007–2009, A < 0). The average amplitude of the 27-day variation of the galactic cosmic ray anisotropy (A27A) in the current minimum epoch of solar activity (2007–2009, A < 0) is lesser than in previous positive polarity period as it is expected from the drift theory. So, polarity dependence rule for the 27-day variation of the GCR anisotropy is fully kept. It is a universal principle for the amplitudes of the 27-day variation of the GCR anisotropy. At the same time, the average amplitude of the 27-day variation of the GCR intensity (A27I) remains at the same level as for previous minimum epoch 1995–1997 (A > 0) showing by the same token an violation of its polarity dependence rule established earlier. We assume that this phenomenon could be generally related with the well established 27-day variation of the solar wind velocity being in anti-correlation with the similar changes of the 27-day variation of the GCR intensity. Generally, a character of the heliolongitudinal asymmetry of spatial large-scale structure of the solar wind velocity (SWV) established in the recent minimum epoch, preferentially pronounces in the behavior of the 27-day variation of the GCR intensity than anisotropy. The formation of the 27-day variation of the GCR anisotropy preferentially takes place in a restricted disk like local vicinity in the helioequatorial region, whilst the 27-day variation of the GCR intensity is formed in the global three dimensional vicinity of the heliosphere.     

Study of the 27-day variations of the galactic cosmic ray intensity and anisotropy

We demonstrate that the general features of the radial and azimuthal components of the anisotropy of galactic cosmic rays can be studied by the harmonic analysis method using data from an individual neutron monitor with cut off rigidity <5 GV. In particular, we study the characteristics of the 27-day (solar rotation period) variations of the galactic cosmic ray intensity and anisotropy, solar wind velocity, interplanetary magnetic field strength and sunspot number. The amplitudes of the 27-day variations of the galactic cosmic ray anisotropy are greater, and the phases more clearly established, in A > 0 polarity periods than in A < 0 polarity periods at times of minimum solar activity. The phases of the 27-day variations of the galactic cosmic rays intensity and anisotropy are opposite with respect to the similar changes of the solar wind velocity in A > 0 polarity periods. No significant dependence of the amplitude of the 27-day variation of the galactic cosmic ray anisotropy on the tilt angle of the heliospheric neutral sheet is found. Daily epicyclegrams obtained by Chree’s method show that the 27-day variations of the galactic cosmic ray anisotropy during A > 0 polarity periods follow elliptical paths with the major axes oriented approximately along the interplanetary magnetic field. The paths are more irregular during A < 0 polarity periods.     

Modeling and experimental study of the 27-day variation of galactic cosmic-ray intensity for a solar wind velocity depending on heliolongitude

We develop a three-dimensional (3-D) model of the 27-day variation of galactic cosmic-ray (GCR) intensity with a spatial variation of the solar wind velocity. A consistent, divergence-free interplanetary magnetic field is derived by solving the corresponding Maxwell equations with a variable solar wind speed, which reproduces in situ observed experimental data for the time interval to be analyzed (24 August 2007–28 February 2008). We perform model calculations for the GCR intensity using the variable solar wind and the corresponding magnetic field. Results are compatible with experimental data; the correlation coefficient between our model predictions and observed 27-day GCR variation is 0.80 ± 0.05.     

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.     

New index of long-term variations of galactic cosmic ray intensity

We find that the soft rigidity spectrum of the Galactic Cosmic Ray (GCR) intensity variations for the maximum epoch and the hard rigidity spectrum for the minimum epoch calculated based on the neutron monitors experimental data (1960–2002) are related with the various dependence of the diffusion coefficient on the GCR particle’s rigidity for different epoch of solar activity. This dependence is stronger in the maximum epoch than in the minimum epoch of solar activity, and is provided by the essential temporal rearrangements of the structure of the Interplanetary Magnetic Field (IMF) turbulence from the maxima to minima epoch of solar activity. We also show that the rigidity spectrum of GCR intensity variations is harder for the effective rigidities ∼(10–15) GV (by neutron monitors data), than for the effective rigidities ∼(25–30) GV (by neutron monitors and muon telescopes data). A general scenario of GCR modulation versus solar activity is settled on the essential temporal rearrangements of the structure of the IMF turbulence. Therefore, the temporal changes of the power law rigidity spectrum exponent can be considered as a vital (new) index to explain the 11-year variations of the GCR intensity. We assume that ∼(70–80)% of the changes of the amplitudes of the 11-year variations of GCR intensity is related with the changes of the IMF turbulence versus solar activity.     

α–ω Effect and peculiarities of the 27-day variations of the galactic cosmic rays intensity,solar wind and solar activity parameters

We show that the amplitudes of the 27-day variations of galactic cosmic ray (GCR) intensity, solar wind and solar activity parameters have a periodicity with duration of three to four Carrington rotation periods (3–4 CRP). We assume that the general reason for this phenomenon may be related to similar cyclicity of topological structure of the solar magnetic field lines created owing to the asymmetry of turbulent solar dynamo and solar differential rotation transforming the Sun’s poloidal magnetic field to the toroidal (α–ω effect), and vice versa.     

Modelling of galactic Carbon in an asymmetrical heliosphere: Effects of asymmetrical modulation conditions

Observations of galactic cosmic rays (GCRs) from the two Voyager spacecraft inside the heliosheath indicate significant differences between them, suggesting that in addition to a possible global asymmetry in the north–south dimensions (meridional plane) of the heliosphere, it is also possible that different modulation (turbulence) conditions could exist between the two hemispheres of the heliosphere. We focus on illustrating the effects on GCR Carbon of asymmetrical modulation conditions combined with a heliosheath thickness that has a significant dependence on heliolatitude. To reflect different modulation conditions between the two heliospheric hemispheres in our numerical model, the enhancement of both polar and radial perpendicular diffusion off the ecliptic plane is assumed to differ from heliographic pole to pole. The computed radial GCR intensities at polar angles of 55° (approximating the Voyager 1 direction) and 125° (approximating the Voyager 2 direction) are compared at different energies and for both particle drift cycles. This is done in the context of illustrating how different values of the enhancement of both polar and radial perpendicular diffusion between the two hemispheres contribute to causing differences in radial intensities during solar minimum and moderate maximum conditions. We find that in the A > 0 cycle these differences between 55° and 125° change both quantitatively and qualitatively for the assumed asymmetrical modulation condition as reflected by polar diffusion, while in the A < 0 cycle, minute quantitative differences are obtained. However, when both polar and radial perpendicular diffusion have significant latitude dependences, major differences in radial intensities between the two polar angles are obtained in both polarity cycles. Furthermore, significant differences in radial intensity gradients obtained in the heliosheath at lower energies may suggest that the solar wind turbulence at and beyond the solar wind termination shock must have a larger latitudinal dependence.     

The heliospheric modulation of cosmic rays: Effects of a latitude dependent solar wind termination shock

Observations made with the two Voyager spacecraft confirmed that the solar wind decelerates to form the heliospheric termination shock and that it has begun its merger with the local interstellar medium. The compression ratio of this shock affects galactic cosmic rays when they enter the heliosphere. Hydrodynamic (HD) models show that the compression ratio can have a significant latitude dependence; with the largest value in the nose direction of the heliosphere, becoming significantly less towards the polar regions. The modulation effects of such large latitude dependence are studied, using a well-established numerical drift and shock modulation model. We focus on computing the modulated spectra for galactic protons with emphasis on the radial and polar gradients in the equatorial plane and at a polar angle of θ = 55°, corresponding to the heliolatitude of Voyager 1. Two sets of solutions are computed and compared each time; with and without a latitude dependence for the compression ratio. All computations are done for the two magnetic field polarity cycles assuming solar minimum conditions. Including the termination shock in the model allows the study of the re-acceleration of galactic protons in the outer heliosphere. We find that for the A < 0 polarity cycle the intensity between ∼200 MeV and ∼1 GeV in the vicinity of the shock in the heliospheric equatorial plane may exceed the local interstellar value specified at the heliopause. Unfortunately, at θ = 55°, the effect is reduced. This seems not possible during an A > 0 cycle because significant modulation is then predicted between the heliopause and the termination shock, depending on how strong global gradient and curvature drifts are in the heliosheath. The overall effect of the shock on galactic protons in the equatorial plane is to reduce the total modulation as a function of radial distance with respect to the interstellar spectrum. Making the compression ratio latitude dependent enhances these effects at energies E < 200 MeV in the equatorial plane. At larger heliolatitudes these effects are even more significant. The differences in the modulation between the two drift cycles are compelling when the compression ratio is made latitude dependent but at Earth this effect is insignificant. A general result is that the computed radial gradient changes for galactic protons at and close to the TS and that these changes are polarity dependent. In line with previous work, large polarity dependent effects are predicted for the inner heliosphere and also close to the shock’s position in the equatorial plane. In contrast, at θ = 55°, the largest polarity effect occurs in the middle heliosphere (50 AU), enhanced by the latitude dependence of the compression ratio. At this latitude, the amount of proton modulation between the heliopause and the termination shock is much reduced. If galactic cosmic rays were to experience some diffusive shock acceleration over the 100–1000 MeV range at the shock, the radial gradient should change its sign in the vicinity of the shock, how large, depends on the compression ratio and the amount of drifts taking place in the outer heliosphere. The effective polar gradient shows a strong polarity dependence at Earth but this dissipates at θ = 55°, especially with increasing radial distance. This tendency is enhanced by making the compression ratio latitude dependent.     

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.     

Validation of B0 and B1 in the IRI 2001 model at low solar activity for Ilorin an equatorial station

A new set of data obtained at low solar activity from Ilorin, Nigeria (geog. latitude 8.5°N, geog longitude, 4.6°E, dip 4.1°S) is used to validate the IRI 2001 model at low solar activity. The results show in general a good agreement between model and observed B0 at night but an over estimation during daytime. The overestimation is greatest during the morning period (0600LT–1000LT). The model prediction for B1 is fairly good at night and during the day. A dependence of B0 on solar zenith angle χ is observed during the daytime. A formulation of the form B0 = A[cos(χ)ⁿ] is therefore proposed. Values of the constants n and A were determined for the period of low solar activity for this station.     

Contribution of geometry of interaction between interplanetary and terrestrial magnetic fields into global magnetospheric state and geomagnetic activity

The paper presents results of our study of dependence of geomagnetic activity from geoeffective parameters taking into account mutual orientation of the interplanetary magnetic field, electric field of the solar wind and geomagnetic moment. We attract a reconnection model elaborated by us made allowance for changes of geometry of the solar wind–magnetosphere interaction during annual and diurnal motions of the Earth. We take as our data base the interplanetary magnetic field and solar wind velocity measured at 1 a.u. at ecliptic plane for the period of 1963–2005 and K_p, D_st, a_m indices. Taken as a whole a geoeffective parameter suggested by us explains 95% of observed variations of the indices. Changes of the geometric factor determined by mutual orientation of the solar wind electric field and geomagnetic moment explain larger than 75% of observed statistical variations of D_st and a_m indices. Based on our results we suggest a new explanation of semi-annual and UT variation of geomagnetic activity.     

Variation in the ionospheric propagating factor M(3000)F2 at Ouagadougou,Burkina Faso

We use hourly monthly median values of propagation factor M(3000)F2 data observed at Ouagadougou Ionospheric Observatory (geographic12.4°N, 1.5°W; 5.9^o dip), Burkina Faso (West Africa) during the years Januar1987–December1988 (average F10.7 < 130 × 10⁻²² W/m²/Hz, representative of low solar flux conditions) and for January 1989–December1990 (average F10.7 ? 130 × 10⁻²² W/m²/Hz, representative of high solar epoch) for magnetically quiet conditions to describe local time, seasonal and solar cycle variations of equatorial ionospheric propagation factor M(3000)F2 in the African region. We show that that seasonal trend between solar maximum and solar minimum curves display simple patterns for all seasons and exhibits reasonable disparity with root mean square error (RMSE) of about 0.31, 0.29 and 0.26 for December solstice, June solstice and equinox, respectively. Variability Σ defined by the percentage ratio of the absolute standard deviation to the mean indicates significant dissimilarity for the two solar flux levels. Solar maximum day (10–14 LT) and night (22–02 LT) values show considerable variations than the solar minimum day and night values. We compare our observations with those of the IRI 2007 to validate the prediction capacity of the empirical model. We find that the IRI model tends to underestimate and overestimate the observed values of M(3000)F2, in particular, during June solstice season. There are large discrepancies, mainly during high solar flux equinox and December solstice between dawn and local midnight. On the other hand, IRI provides a slightly better predictions for M(3000)F2 between 0900 and 1500 LT during equinox low and high solar activity and equinox high sunspot number. Our data are of great importance in the area of short-wave telecommunication and ionospheric modeling.     

Estimation of Galactic Cosmic Ray exposure inside and outside the Earth’s magnetosphere during the recent solar minimum between solar cycles 23 and 24

The evidently low solar activity observed between solar cycles 23 and 24 during the years 2008–2010 led to a substantial increase in the Galactic Cosmic Ray (GCR) intensity in comparison with preceding solar minima. As the GCRs consist of highly-ionizing charged particles having the potential to cause biological damage, they are a subject of concern for manned missions to space. With the enhanced particle fluxes observed between 2008 and 2010, it is reasonable to assume that the radiation exposure from GCR must have also increased to unusually high levels. In this paper, the GCR exposure outside and inside the Earth’s magnetosphere is numerically calculated for time periods starting from 1970 to the end of 2011 in order to investigate the increase in dose levels during the years 2008–2010 in comparison with the last three solar minima. The dose rates were calculated in a water sphere, used as a surrogate for the human body, either unshielded or surrounded by aluminium shielding of 0.3, 10 or 40 g/cm².     

F3 layer feature under low and medium solar activity observed at a Chinese low latitude station Fuke

Ionogram observations from the ionosonde at Fuke (9.5°N geomagnetic latitude), a Chinese low latitude station, in 2010–2012 are analyzed to present the features of F3 layer under low and moderate solar activity conditions. Structure of the ionogram, displaying the F3 layer, was more distinct and clear during MSA than LSA periods especially during spring to summer. Start time of occurrence of the F3 layer is about at 0830–0900 LT and is approximately the same for LSA and MSA conditions. The average duration time of the F3 layer occurrence was 181 min per day under F_10.7 = 75 condition, 263 min in F_10.7 = 99 and 358 min in F_10.7 = 125, respectively. The differences of h′F2 and h′F3 exhibited obvious semiannual variation observed at Fuke from March 2010 to June 2012 and increased with increasing solar activity. The difference of foF2 and foF3 in the months February, March, September, October and November is less evident in the middle solar activity period 2011–2012 than the low solar activity 2010 and in the other period it shows a slight increase (0.5 MHz) or keeps constant. The results show that the solar activity dependence of the F3 layer occurrence at low latitude away from the magnetic equator is different from that at near the magnetic equator.     

Empirical model of cosmic ray spectrum in energy interval 1 MeV–100 GeV during 11-year solar cycle

The galactic cosmic rays (GCR) are the main ionization source at altitude of ∼3–35 km in the atmosphere. For high latitude anomalous cosmic ray (ACR) component has also a significant influence on the atmospheric ionization. We propose an empirical model for differential spectra D(E) of galactic and anomalous cosmic rays in energy interval 1 MeV–100 GeV during solar cycle. In the model data are used which cover three solar cycles: 20, 22 and 23. The LEAP87, IMAX92, CAPRICE94, AMS98 and BESS experimental spectra for protons and alpha particles are fitted to the proposed empirical model. The modulated GCR differential spectra are compared with force-field approximation to the one-dimensional transport equation and with solutions of two-dimensional cosmic ray transport equation. For experimental spectra, the calculation of the model parameters is performed by Levenberg–Marquardt algorithm, applied to the special case of least squares. Algorithm that combines the rapid local convergence of Newton–Raphson method with globally convergent method for non-linear systems of equations is applied for theoretically obtained differential spectra. The described programmes are realized in algorithmic language C++. The proposed model gives practical possibility for investigation of experimental data from measurements of galactic cosmic rays and their anomalous component.     

Changes in sea-level pressure over South Korea associated with high-speed solar wind events

We explore a possibility that the daily sea-level pressure (SLP) over South Korea responds to the high-speed solar wind event. This is of interest in two aspects: first, if there is a statistical association this can be another piece of evidence showing that various meteorological observables indeed respond to variations in the interplanetary environment. Second, this can be a very crucial observational constraint since most models proposed so far are expected to preferentially work in higher latitude regions than the low latitude region studied here. We have examined daily solar wind speed V, daily SLP difference ΔSLP, and daily log(BV²) using the superposed epoch analysis in which the key date is set such that the daily solar wind speed exceeds 800 km s⁻¹. We find that the daily ΔSLP averaged out of 12 events reaches its peak at day +1 and gradually decreases back to its normal level. The amount of positive deviation of ΔSLP is +2.5 hPa. The duration of deviation is a few days. We also find that ΔSLP is well correlated with both the speed of solar wind and log(BV²). The obtained linear correlation coefficients and chance probabilities with one-day lag for two cases are r ? 0.81 with P > 99.9%, and r ? 0.84 with P > 99.9%, respectively. We conclude by briefly discussing future direction to pursue.     

Sunspot activity and cosmic ray modulation at 1 a.u. for 1900–2013

The descent of sunspot cycle 23 to an unprecedented minimum of long duration in 2006–2009 led to a prolonged galactic cosmic ray (GCR) recovery to the highest level observed in the instrumental era for a variety of energetic charged particle species on Earth, over a wide range of rigidities. The remarkable GCR increase measured by several ground-based, balloon-borne, and detectors on a satellite is described and discussed. It is accompanied by a decrease in solar wind velocity and interplanetary magnetic field at 1 a.u., reaching the lowest values since measurements of the solar wind began in October 1963; the solar polar field strength (μT) measured at the Wilcox Solar Observatory (WSO) is also significantly reduced compared to prior cycles since the start of the program in 1976, the polar field in the northern hemisphere reversed in June 2012 and again in February 2014, that in the southern hemisphere reversed in July 2013. If updates of WSO data confirm the second reversal in northern solar hemisphere, it would pose a serious challenge to the Dynamo Theory. The long-term change in solar behavior may have begun in 1992, perhaps earlier. The physical underpinnings of these solar changes need to be understood and their effect on GCR modulation processes clarified. The study discusses the recent phenomena in the context of GCR modulation since 1900. These happenings affected our empirical predictions for the key parameters for the next two sunspot cycles (they may be progressively less active than sunspot cycle 24) but it enhanced support for our prediction that solar activity is descending into a Dalton-like grand minimum in the middle of the twentyfirst century, reducing the frequency of the coronal mass ejections; they determine the space weather affecting the quality of life on Earth, radiation dose for hardware and human activities in space as well as the frequency of large Forbush decreases at 1 a.u.     

Sunspot numbers,interplanetary magnetic field,and cosmic ray intensity at earth: Nexus for the twentieth century

The pivotal role played by the interplanetary magnetic field (B) in modulating galactic cosmic ray (GCR) intensity in the heliosphere is described. We show that the inverse correlation observed by Forbush (1958) between GCRs and sunspot numbers (SSNs) is reflected in high correlation between SSNs and B (cc = 0.94). The SSN data are available since 1700 and the derived B data since 1835. The paleo-cosmic ray data are available for several millennia in the form of ¹⁰Be radionuclide sequestered in polar ice. The data of the ion chambers (ICs) at the Cheltenham–Fredericksburg–Yakutsk (CFY) sites are combined to create a data string for 1937–1988. In turn, these data are used to extend the measurements of the low energy GCR ions (>0.1 GeV) at balloon altitudes at high latitudes in Russia to 1937. These data are then correlated to B and the fit parameters are used to extend the low energy ion data to 1900, creating the instrumental era GCR time series for the twentieth century. The derived GCR time series is compared to ¹⁰Be measured at two sites in Greenland, namely Dye 3 and NGRIP for 1900–2000 to check the internal consistency of datasets for the long-term trend. We find that the annual mean rate (%) for 1965 at NGRIP is an outlier. We replace it with the mean of 1964 and 1965 rates and construct a new re-normalized time series at NGIP, improving the agreement with the derived instrumental era GCR time series for the twentieth century as well. This should encourage its use by heliophysics community for varied applications.