Solar Modulation of Cosmic Rays Potgieter, Marius S.
Living reviews in solar physics,
01/2013, Letnik:
10, Številka:
1
Journal Article
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This is an overview of the solar modulation of cosmic rays in the heliosphere. It is a broad topic with numerous intriguing aspects so that a research framework has to be chosen to concentrate on. ...The review focuses on the basic paradigms and departure points without presenting advanced theoretical or observational details for which there exists a large number of comprehensive reviews. Instead, emphasis is placed on numerical modeling which has played an increasingly significant role as computational resources have become more abundant. A main theme is the progress that has been made over the years. The emphasis is on the global features of CR modulation and on the causes of the observed 11-year and 22-year cycles and charge-sign dependent modulation. Illustrative examples of some of the theoretical and observational milestones are presented, without attempting to review all details or every contribution made in this field of research. Controversial aspects are discussed where appropriate, with accompanying challenges and future prospects. The year 2012 was the centennial celebration of the discovery of cosmic rays so that several general reviews were dedicated to historical aspects so that such developments are briefly presented only in a few cases.
Galactic cosmic rays (GCRs) are affected by solar modulation while they propagate through the heliosphere. The study of the time variation of GCR spectra observed at Earth can shed light on the ...underlying physical processes, specifically diffusion and particle drifts. Recently, the AMS-02 experiment measured with very high accuracy the time variation of the cosmic-ray proton and helium flux between 2011 May and 2017 May in the rigidity range from 1 to 60 GV. In this work, a comprehensive three-dimensional steady-state numerical model is used to solve Parker's transport equation and reproduce the monthly proton fluxes observed by AMS-02. We find that the rigidity slope of the perpendicular mean free path above 4 GV remains constant, while below 4 GV, it increases during solar maximum. Assuming the same mean free paths for helium and protons, the models are able to reproduce the time behavior of the p/He ratio observed by AMS-02. The dependence of the diffusion tensor on the particle mass-to-charge ratio, A/Z, is found to be the main cause of the time dependence of p/He below 3 GV.
Abstract
We continue the numerical modeling of a corotating interaction region (CIR) and the effects it has on solar-rotational recurrent variations of galactic cosmic rays (GCRs). A ...magnetohydrodynamic model is adapted to simulate the background solar wind plasma with a CIR structure in the inner heliosphere, which is incorporated into a comprehensive Parker-type transport model. The focus is on the simulation of the effects of a CIR on GCR protons and the two helium isotopes as a function of heliolongitude. This is to establish whether the difference in composition affects how they are modulated by the CIR in terms of their distribution in longitude. It is demonstrated that particle diffusion and drift influence the effects of the CIR with increasing rigidity from 100 MV up to 15 GV. It is found that protons and helium isotopes are modulated differently with longitude by the CIR and that particle drift influences the modulation effects in longitude. These differences dissipate with increasing rigidity. The final results are focused on the simulated amplitude of these GCR flux variations as a function of rigidity. The amplitude displays a power-law behavior above ∼1 GV with an index similar to the power index of the rigidity dependence of the assumed diffusion coefficients. The simulations further show that below this rigidity, the amplitude at first flattens off, displaying a plateau-like profile, but it then increases systematically with decreasing rigidity below ∼0.3 GV. Again, a power-law behavior is displayed, but it is completely different from that above 1 GV.
Abstract
With continuous measurements from space-borne cosmic-ray detectors such as AMS-02 and PAMELA, precise spectra of galactic cosmic rays over the 11 yr solar cycle have become available. For ...this study, we utilize proton and helium spectra below 10 GV from these missions from 2006 to 2017 to construct a cosmic-ray transport model for a quantitative study of the processes of solar modulation. This numerical model is based on Parker’s transport equation, which includes four major transport processes. The Markov Chain Monte Carlo method is utilized to search the relevant parameter space related to the drift and the diffusion coefficients by reproducing and fitting the mentioned observed spectra. The resulting best-fit normalized
χ
2
is mainly less than 1. It is found that (1) when reproducing these observations the parameters required for the drift and diffusion coefficients exhibit a clear time dependence, with the magnitude of the diffusion coefficients anticorrelated with solar activity; (2) the rigidity dependence of the resulting mean free paths varies with time, and their rigidity dependence at lower rigidity can even have a larger slope than at higher rigidity; (3) using a single set of modulation parameters for each pair of observed proton and helium spectra, most spectra are reproduced within observational uncertainty; and (4) the simulated proton-to-helium flux ratio agrees with the observed values in terms of its long-term time dependence, although some discrepancy exists, and the difference is mostly coming from the underestimation of proton flux.
The intensity of galactic cosmic rays (GCRs) is modulated by solar activity on various timescales. In this study, we performed comprehensive numerical modeling of the solar rotational recurrent ...variation in GCRs caused by a corotation interaction region (CIR). A recently developed magnetohydrodynamic numerical model is adapted to simulate the background solar wind plasma with a CIR structure present in the inner heliosphere. As for the outer heliospheric plasma background, from 27 to 80 au, the Parker interplanetary magnetic field model is utilized. The output of these plasma and magnetic field models is incorporated into a comprehensive Parker-type transport model for GCRs. The local interstellar spectrum for galactic protons is transported to 80 au, specifying the outer boundary condition. The obtained solutions of this hybrid model, for studying the CIR effect, are as follows: (1) the onset of the decrease in the GCR intensity inside the CIR coincides with the increase of the solar wind speed with the intensity depression accompanied by a magnetic field and plasma density enhancement. Additionally, the CIR effect weakens with increasing heliocentric radial distance. (2) This decrease in GCR intensity also appears at different heliolatitudes and varies with changing latitude; the amplitude of the GCR depression exhibits a maximum in the low-latitude region. (3) The CIR affects GCR transport at different energy levels as well. Careful analysis has revealed a specific energy dependence of the amplitude of the recurrent GCR variation in the range of 30-2000 MeV.
Since 2011 May, the Alpha Magnetic Spectrometer (AMS-02) on board the International Space Station has provided monthly cosmic proton fluxes for various low-rigidity levels (P < 50 GV). These precise ...measurements, in terms of high time and rigidity resolution, have provided a good opportunity to study cosmic ray modulation over a wide range of rigidities, together with transient events. Subsequently, a comprehensive numerical transport model has been constructed, based on Parker's transport equation that includes all known physical mechanisms: diffusion, convection, drift, and adiabatic cooling. Propagating diffusion barriers to simulate Forbush decreases (Fds) and global merged interaction regions (GMIRs) have also been incorporated: (1) utilizing a time-varying tilt angle of the heliospheric current sheet and interplanetary magnetic field, the general trend of the time variation of cosmic proton fluxes has been reproduced; (2) the Fd events in 2011 October and 2012 March have been simulated, and the first GMIR event in solar cycle 24 has also been simulated and studied; and (3) the rigidity dependence of the proton fluxes, as revealed by the AMS-02 data, has been reproduced with the appropriate chosen rigidity dependent diffusion coefficients. In order to reproduce the proton observations, we find that apart from the transient events, the derived mean free paths in interplanetary space also need to be changed with time.
Based on the reduced diffusion mechanism for producing Forbush decreases (Fds) in the heliosphere, we constructed a three-dimensional (3D) diffusion barrier, and by incorporating it into a stochastic ...differential equation (SDE) based time-dependent, cosmic-ray transport model, a 3D numerical model for simulating Fds is built and applied to a period of relatively quiet solar activity. This SDE model generally corroborates previous Fd simulations concerning the effects of the solar magnetic polarity, the tilt angle of the heliospheric current sheet (HCS), and cosmic-ray particle energy. Because the modulation processes in this 3D model are multi-directional, the barrier's geometrical features affect the intensity profiles of Fds differently. We find that both the latitudinal and longitudinal extent of the barrier have relatively fewer effects on these profiles than its radial extent and the level of decreased diffusion inside the disturbance. We find, with the 3D approach, that the HCS rotational motion causes the relative location from the observation point to the HCS to vary, so that a periodic pattern appears in the cosmic-ray intensity at the observing location. Correspondingly, the magnitude and recovery time of an Fd change, and the recovering intensity profile contains oscillation as well. Investigating the Fd magnitude variation with heliocentric radial distance, we find that the magnitude decreases overall and, additionally, that the Fd magnitude exhibits an oscillating pattern as the radial distance increases, which coincides well with the wavy profile of the HCS under quiet solar modulation conditions.
Because of the precise measurements of the cosmic ray electron flux by the PAMELA and AMS02, Electron Forbush decreases (Fds) have recently been observed for the first time. This serves as motivation ...to perform a numerical study of electron Forbush decreases with an advanced time-dependent, three-dimensional (3D) stochastic differential equation model, developed earlier to study proton Fds. The model includes a realistic interstellar electron spectrum reconstructed from Voyager observations, and diffusion and drift coefficients to reproduce the modulated spectrum observed by PAMELA in 2009. On the basis of this numerical model, electron Fd profiles for a range of rigidities are simulated. In addition, a systematic comparison between electron and proton Fds during different solar polarity epochs is performed. This approach gives insight into the rigidity dependence of the heliospheric diffusion coefficients and of drift effects over two magnetic field polarity cycles. We find that during an A > 0 epoch, the recovery time of a 1 GV proton Fd is remarkably shorter than the 1 GV electrons, whereas the electron Fd display a faster recovery during an A < 0 epoch. This model clear predicts a charge-sign dependent effect in the recovery time of Fds but less so for their magnitude.
We review recent observations and modeling developments on the subject of galactic cosmic rays through the heliosphere and in the Very Local Interstellar Medium, emphasizing knowledge that has ...accumulated over the past decade. We begin by highlighting key measurements of cosmic-ray spectra by Voyager, PAMELA, and AMS and discuss advances in global models of solar modulation. Next, we survey recent works related to large-scale, long-term spatial and temporal variations of cosmic rays in different regimes of the solar wind. Then we highlight new discoveries from beyond the heliopause and link these to the short-term evolution of transients caused by solar activity. Lastly, we visit new results that yield interesting insights from a broader astrophysical perspective.
Abstract
The transport of energetic particles in the heliosphere is reviewed regarding the treatment of their drifts over an entire solar cycle including the periods around solar maximum, when the ...tilt angles of the heliospheric current sheet increase to large values and the sign of the magnetic polarity changes. While gradient and curvature drifts are well-established elements of the propagation of cosmic rays in the heliospheric magnetic field, their perturbation by the solar-activity-induced large-scale distortions of dipole-like field configurations and by magnetic turbulence is an open problem. Various empirical or phenomenological approaches have been suggested, but either lack a theory-based motivation or have been shown to be incompatible with measurements. We propose a new approach of more closely investigating solar magnetograms obtained from GONG maps, leading to a new definition of (i) tilt angles that may exceed those provided by the Wilcox Solar Observatory during high activity and of (ii) a “noninteger sign” that can be used to reduce the drifts during these periods as well as to provide a refinement of the magnetic field polarity. The change of sign from
A
< 0 to
A
> 0 of solar cycle 24 can be in this way localized to occur between Carrington Rotations 2139 and 2140 in mid 2013. This treatment is fully consistent in the sense that the transport modeling uses the same input data to formulate the boundary conditions at the heliobase as do the magnetohydrodynamic models of the solar wind and the embedded heliospheric magnetic field that exploit solar magnetograms as inner boundary conditions.
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