Energy losses of galactic cosmic rays in the interplanetary medium

Using realistic models of cosmic-ray propagation in interplanetary space we present, for electrons, protons and helium nuclei of a given energy near Earth, calculations of their distribution in energy before entering the solar cavity and their mean energy loss. Interplanetary conditions appropriate for the epochs 1965 and 1969 have been used. Cosmic-ray energies in the range of 20 MeV/nucleon to 1000 MeV/nucleon have been considered.     

Steady-state drift-dominated modulation models for galactic cosmic rays

A number of steady-state drift-dominated modulation models has been developed by the Potchefstroom modulation group. In this review a selection of these models is discussed and briefly compared. A short overview of the relevant drift theory incorporated into the models is also given.     

The modulation of galactic cosmic rays in the interplanetary medium

The anisotropic diffusion of cosmic rays in the interplanetary medium is discussed with the assumption that the fluctuating component of the magnetic field produces a scattering effect which can be described by a simple mean free path treatment. The results of this discussion are applied to a plausible model of the interplanetary medium with the aim of providing a basis for the understanding of the processes causing the more important modulations of the galactic cosmic ray intensity. It is suggested that a gradient of the cosmic ray density exists, and that this plays a significant role in producing the solar cycle and 27-day modulation effects; in addition, the associated cosmic ray pressure gradient might affect the size of the cavity resulting from the interaction between the solar wind and the interstellar medium. Since the gradient could be present even at sunspot minimum it is possible that the energy density of cosmic rays in the galaxy is larger than the maximum value observed at the Earth, and hence this value should be regarded only as a lower limit. The main contribution to the solar diurnal variation of the cosmic ray intensity is suggested to be due to co-rotation of the cosmic rays with the Sun. However above a certain energy, which varies through the solar cycle, the galactic cosmic rays appear to be unaffected by the roughness of the interplanetary magnetic field, thus any streaming which occurs at these higher energies should cause a sidereal diurnal variation of the intensity.     

Understanding galactic cosmic rays

The case is made for most cosmic rays having come from galactic sources. ‘Structure’, i.e. a lack of smoothness in the energy spectrum, is apparent, strengthening the view that most cosmic rays come from discrete sources, supernova remnants being most likely.     

Energy losses of solar cosmic rays in interplanetary space

A simple model of solar cosmic ray propagation which includes diffusion, convection, and energy loss by adiabatic deceleration is studied. A Monte Carlo technique is employed to investigate the variation of mean particle energy in the interplanetary medium after the impulsive release of mono-energetic particles at the Sun. At 1 AU typical energy losses are 43% at 20 h and 64% at 60 h after particle release for a diffusion coefficient (r)= ₀r with =+1/2 and ₀=1.33 × 10²¹ cm² s^–1. When ₀ in this model is reduced by a factor of 4, the energy loss is greater by a factor of 2 at 60 h after particle release. When is increased, the energy losses are greater. Using the model parameters above, an increase in solar wind speed from 300 to 600 km s^–-1 gives rise to energy losses that are greater again by factor of 2 at a time of 60 h. Results are compared with an observation by Murray et al. (1971) of a knee in the energy spectrum of solar protons. It is not considered likely that the change in the energy of the knee with time requires, in addition to adiabatic deceleration, another energy change process which acts to increase the energy of particles.Part of this work was performed while the author was at CSIRO, Division of Radiophysics, Epping, NSW, Australia; also supported in part by the U.S. Atomic Energy Commission.     

The origin of galactic cosmic rays

One century ago Viktor Hess carried out several balloon flights that led him to conclude that the penetrating radiation responsible for the discharge of electroscopes was of extraterrestrial origin. One century from the discovery of this phenomenon seems to be a good time to stop and think about what we have understood about Cosmic Rays. The aim of this review is to illustrate the ideas that have been and are being explored in order to account for the observable quantities related to cosmic rays and to summarize the numerous new pieces of observation that are becoming available. In fact, despite the possible impression that development in this field is somewhat slow, the rate of new discoveries in the last decade or so has been impressive, and mainly driven by beautiful pieces of observation. At the same time scientists in this field have been able to propose new, fascinating ways to investigate particle acceleration inside the sources, making use of multifrequency observations that range from the radio, to the optical, to X-rays and gamma rays. These ideas can now be confronted with data.I will mostly focus on supernova remnants as the most plausible sources of Galactic cosmic rays, and I will review the main aspects of the modern theory of diffusive particle acceleration at supernova remnant shocks, with special attention for the dynamical reaction of accelerated particles on the shock and the phenomenon of magnetic field amplification at the shock. Cosmic-ray escape from the sources is discussed as a necessary step to determine the spectrum of cosmic rays at the Earth. The discussion of these theoretical ideas will always proceed parallel to an account of the data being collected especially in X-ray and gamma-ray astronomy.In the end of this review I will also discuss the phenomenon of cosmic-ray acceleration at shocks propagating in partially ionized media and the implications of this phenomenon in terms of width of the Balmer line emission. This field of research has recently experienced a remarkable growth, in that Hα lines have been found to bear information on the cosmic-ray acceleration efficiency of supernova shocks.     

The age distribution of galactic cosmic rays

The general solution for the distribution of ages for primary galactic cosmic rays is given for a class of steady-state, bounded models of cosmic-ray diffusion in the Galaxy. Both one-and threedimensional models are considered, with point sources and distributed sources. In all models, the age distribution, is approximately exponential for ages longer than the average age, although for shorter ages the distribution depends on the details of the model. The leaky-box model, with an exponential age distribution, is thus a good approximation to most diffusive models. It is shown that one-dimensional (disk) models are consistent with both age and anisotropy data for galactic cosmic rays regardless of whether production takes place near the galactic center or throughout the disk.     

The age distribution of galactic cosmic rays

The distribution of ages for secondary and interacting cosmic-ray nuclei is derived for a class of steady-state, bounded models of diffusion in the galaxy. Results are presented in detail for the model in which diffusion is in one dimension, sources are uniformly distributed throughout the scattering region, and particles are observed near the central plane of the galaxy. The leakage-lifetime approximation is shown to be accurate as long as the ratio of the cosmic-ray diffusive lifetime to the mean interaction or decay lifetime is less than about ten.     

Extragalactic cosmic rays and the galactic magnetic field

The origin and behavior of cosmic rays in the Galaxy depends crucially upon whether the galactic magnetic field has a closed topology, as does the field of Earth, or whether a major fraction of the lines of force connect into extragalactic space. If the latter, then cosmic rays could be of extragalactic origin, or they could be of galactic origin, detained in the Galaxy by the scattering offered by hydromagnetic waves, etc. If, on the other hand, the field is largely closed, then cosmic rays cannot be of extragalactic origin (at least below 10¹⁶ eV). They must be of galactic origin and escape because their collective pressure inflates the galactic field and they push their way out.This paper examines the structure of a galactic field that opens initially into intergalactic space and, with the inclusion of turbulent diffusion, finds no possibility for maintaining a significant magnetic connection with an extragalactic field. Unless some mechanism can be found, we are forced to the conclusion that the field is closed, that cosmic rays are of galactic origin, and that cosmic rays escape from the Galaxy only by pushing their way out.     

Pulsed galactic nuclei and the origin of cosmic rays

The possibility that a series of explosions of the galactic nuclei every 5×10⁶ yr can cause a substantial flux of cosmic ray particles at the vicinity of the Earth is investigated. The steady flux of cosmic radiation forces the conclusion that there have been explosions back to 10⁹ yr if this is a dominant source of cosmic rays.     

Ultra-high energy cosmic rays in the galactic corona

On the basis of recent new information on regular and chaotic magnetic fields in coronae of spiral galaxies, we discuss propagation of ultra-high energy cosmic rays of energies exceeding 10¹⁷ eV in the galactic corona. It is shown that the expected regular magnetic field is able to confine to the corona protons of energies up to 3×10¹⁹ eV. Chaotic magnetic fields of the corona play an important role in dynamics of cosmic-ray protons of energy up to 7×10¹⁸ eV.     

Radial gradients and anisotropies due to galactic cosmic rays

Numerical calculations have been made of the radial gradients and the anisotropyvector atr=1 AU due to galactic cosmic-ray protons and helium nuclei. The model used assumes transport by convection and anisotropic diffusion, and includes the energy losses due to adiabatic deceleration. The present calculations are for the 1964–65 solar minimum. An important constraint applied ineach case was that the model reproduces the electron modulation known from deductions of the galactic spectrum and observations of the near-Earth spectrum; and also reproduces the near-Earth proton and helium nuclei spectra. The diffusion coefficients have been based upon those deduced from magnetic-field power spectra.The principal aim has been to provide estimates of radial gradients and anisotropies, particularly at kinetic energiesT100 MeV/nucleon, by the complete solution of realistic models. Typical values for protons, obtained with a galactic differential number density (total energy)^–2.5, atT50 MeV are: radial gradient, 25%/AU; radial anisotropy, –0.2%; azimuthal anisotropy, 0.2%. These values change markedly when the galactic spectrum is cut-off or greatly enhanced atT<150 MeV, but the intensity spectrum near Earth remains substantially unchanged.It has been shown that it is possible to obtain negative radial gradients and positive radial anisotropies atT50 MeV for galactic particles and thus to mimic solar sources. The radial gradient for 1964–65 reported by Anderson (1968) and by Krimigis and Venkatesan (1969) are shown to be consistent with the diffusion coefficient deduced from the magnetic-field power spectrum; those reported by O'Gallagher are higher than expected and that for 20T30 MeV protons appears to be inconsistent. More precise data on conditions throughout the solar cavity are required if more definitive gradients and anisotropies are to be determined.     

Propagation of galactic cosmic rays in the outer heliosphere

The propagation of galactic cosmic rays in heliospheric magnetic fields is studied. An approximate solution to the cosmic ray transport equation has been derived on the basis of a method that takes into account the small value of anisotropy of particle angular distribution. The spatial and energy distributions of the cosmic ray intensity and anisotropy have been investigated, and estimates of cosmic ray energy flux have been carried out.     

Cosmic neutrinos from the sources of galactic and extragalactic cosmic rays

Although kilometer-scale neutrino detectors such as IceCube are discovery instruments, their conceptual design is very much anchored to the observational fact that Nature produces protons and photons with energies in excess of 10²⁰ eV and 10¹³ eV, respectively. The puzzle of where and how Nature accelerates the highest energy cosmic particles is unresolved almost a century after their discovery. From energetics considerations we anticipate on the order of 10–100 neutrino events per kilometer squared per year pointing back at the source(s) of both galactic and extragalactic cosmic rays. In this context, we discuss the results of the AMANDA and IceCube neutrino telescopes which will deliver a kilometer-square-year of data over the next 3 years.     

Intensity of galactic cosmic rays in the early sun epoch

The process of heliospheric modulation of intensity of galactic cosmic rays is investigated by solving the transport equation. The spatial-energetic distribution of cosmic rays in the present epoch and in the past is analyzed. It is demonstrated that the particle density and the energy density of cosmic rays in the Solar System in the distant past were much lower than the corresponding current values. The cosmic ray intensity modulation in the early heliosphere was especially strong in the case of low-energy particles.     

Active galactic nuclei flow velocities and the highest energy cosmic rays

The dependence of the maximum energy cosmic rays can reach via diffusive shock acceleration in AGN jets on flow speeds is discussed. It is shown that in highly inclined termination shocks where the speed of the de Hoffman-Teller frame is crucial, a good independent knowledge of the jet speed is required to properly assess the extent of the cosmic ray spectrum.     

The dynamical coupling of cosmic rays and magnetic field in galactic disks

In this paper we demonstrate the importance of cosmic rays for the dynamics of the interstellar medium. We present the first 3D-MHD numerical simulations of the Parker instability triggered by cosmic rays accelerated in supernova remnants. We show that in the presence of galactic rotation a net radial magnetic field is produced as a result of the cosmic ray injection. This process provides a very efficient magnetic field amplification within the general frame of so called fast galactic dynamo proposed by Parker (1992). This revised version was published online in September 2006 with corrections to the Cover Date.     

On the magnitude and direction of the anisotropy of galactic cosmic rays

The results of measuring the diurnal cosmic-ray intensity variations in the energy range 1–100 TeV are discussed. Whereas the phase of the first harmonic of the sidereal daily wave directly determines the phase (right ascension) of the cosmic-ray anisotropy vector, the amplitude and declination of the true anisotropy cannot be reconstructed directly from the amplitude of the first harmonic. However, they can be determined by invoking data on the zero harmonic. The results of some recent experiments purporting to measure the cosmic-ray anisotropy with a particularly high accuracy are shown to be interpreted erroneously.