A diffusion model for cosmic ray propagation in the Galaxy

A diffusion model for the propagation of relativistic nuclear cosmic rays in the Galaxy is developed. The model has two nonstandard features: The escape of cosmic-ray particles from the Galaxy is simulated by a term in the diffusion equations, rather than the imposition of boundary conditions on the diffusion solution at the surface of the confinement region. And an age-dependent, locally-averaged effective gas distribution is employed in the diffusion equations. The model simulates free-particle outflow at the Galactic boundary. The model is fit to chemical composition data in the 0.3–5 GeV per nucleon range. It is then consistent with the large-scale Galactic -ray data, radio halo data, energy constraints on the assumed supernova sources, and, when extended to very high energies, cosmic-ray anisotrophy data. From the fit we conclude that the cosmic rays are confined in a large flattened or quasis-pherical halo with a scale height in the range 3–6 kpc and an average Galactic escape time of 10⁸ yr.     

Diffusion of the galactic cosmic rays in the vicinity of the solar system

Cosmic-ray propagation in the vicinity of 1 kpc from the Sun is considered. The data on the 10¹²–10¹⁵ eV particle anisotropy, on 10¹² eV electron spectrum, and on temporal cosmic-ray variations are analyzed. The diffusion coefficientD(10¹²–10¹³ eV)=10²⁹–10³⁰ cm²s^–1 inferred from the analysis coincides with its standard value in the large-halo model withh=15 kpc. The total power of cosmic-ray generation, about 3×10⁴⁹ erg per SN in the proton component and about 10⁴⁸ erg per SN in the electron component, typical of the galactic diffusion model is in agreement with the obtained parameters of local sources.     

An analysis of the longitudinal distribution of gamma rays from SAS-II data

An analysis of the longitudinal distribution of gamma rays from SAS-II data has been carried out using the available information on the gas distribution in the Galaxy. The overall distribution of cosmic rays in the galactic plane can be represented by an exponential function in galactocentric distance with a scale length of 8 kpc upto the solar circle and 10 kpc beyond. There is no evidence for a large gradient of the cosmic ray intensity in the outer parts of the Galaxy. The local emissivities of gamma rays in the energy regionsE >100 MeV and 35 MeV<E <100 MeV are (1.73±0.27)×10^–25 photon/(cm³ s n_H) and (2.40±0.41)×10^–25 photon/(cm³ s n_H) respectively. The contribution of °-decay gamma rays is 80% forE >100 MeV and 20% at lower energies. The electron spectrum required by this analysis has a power law spectral index of about –2.7 below a few hundred MeV. The observed gas distribution towards the galactic centre would predict a gamma-ray flux larger than observed. It is suggested that the molecular gas in the central region may be in the form of dense coudlets, in which low evergy cosmic rays do not penetrate; in this case the centre should be seen as a strong source only at high energies. An analysis of the radio sky survey map of the Galaxy at 408 MHz shows thatB varies with a scale-length of 40 kpc; no significance can be attached to the apparent deviation from the equipartition of energy densities between cosmic rays and magnetic field. The derived local emissivity is (1.46±0.28)×10^–40 W/((m³ Hz), which corresponds toB 5 G. The surface brightness of radio and gamma-ray emissions in the Galaxy decreases from the centre with scale-lengths 6 kpc and 7 kpc respectively. No positive correlation can be noticed with either co-rotation radius or pattern speed, when compared with external spiral galaxies.     

Origin of cosmic rays: Galactic models with halo

Many years ago physical and radio-astronomical arguments and data led to the assumption that cosmic rays in the Galaxy (and probably in other galaxies) fill a more or less extended halo, but are not concentrated in the disk. It was not so long ago, however, that the existence of a radio-halo was discovered, in which the effective dimensions increase with a decrease in frequency. The frequency decrease occurs when relativistic electrons diffuse from the disk, losing energy due to bremsstrahlung and Compton scattering.Meanwhile, some ambiguity on the question of the existence of a radio-halo, and other reasons, have led to a rather wide use of disk models, particularly those in which cosmic rays are present in the Galaxy only for a periodT _cr,d3×10⁶ yr. The authors have repeatedly stated the inadmissibility of such models and, generally, a homogeneous (leaky box) model for the origin of cosmic rays. The new data concerning the amount of radioactive¹⁰Be nuclei in cosmic rays near the Earth in no way contradict the halo models in which the lifetime of cosmic rays isT _cr,h10⁸ yr. In connection with the continuing controversy, the present paper is devoted to a detailed consideration of the difference between the homogeneous and diffusion models. Within the latter models some calculations on the chemical composition of cosmic rays have been carried out, which concern not only stable but also radioactive isotopes.     

Sub-iron to iron nuclei in low-energy (50–200 MeV nucl−1) cosmic rays as observed in the Skylab experiment

In this paper we present our most recent results on the sub-iron (Sc to Cr) to Fe nuclei abundance ratios in the low-energy cosmic rays of 50 to 250 MeV nucl.^–1 and their implications as observed in theSkylab experiment. In view of the importance of this ratio in determining the cosmic-ray pathlength in interstellar medium, we have obtained additional data in the same detector module and the results of final analysis are reported. Charge determinations in the Lexan detector were made from an average of about four independent measurements ofZ for each of the cosmic-ray events and the mean charge resolution is obtained asZ/Z0.2. From about 100 events of calcium to nickel in low-energy cosmic rays, sub-iron (Sc to Cr) to Fe–Co ratio is determined as 1.43±0.40 in 50–250 MeV nucl.^–1. This shows a large energy dependence of the ratio as compared to the value of 0.4–0.8 in 200–1000 MeV nucl.^–1 as measured by many investigators. The origin of this large enhancement of the ratios in low-energy cosmic rays is not known at present. Some possible suggestions are briefly mentioned.     

Nuclear gamma-ray lines from Cen A: Evidence for their origin in relativistic plasma

An analysis of the experimental data on nuclear gamma-ray lines from Cen A reveals essential energetic difficulties, associated with the usual interpretation of these lines as a result of interactions of subcosmic rays with interstellar gas; since the necessary instantaneous energy loss rate of the cosmic rays should reach tremendous values of about 10⁴⁸–10⁴⁹ ergs s^–1. These difficulties are eliminated if the gamma rays are produced in the relativistic non-isothermal plasma near a compact source of activity — such as a massive black hole or a magnetoid (spinar).     

Cosmic ray diffusion at energies of 1 MeV to 105 GeV

A supernova remnant accelerates cosmic rays to energies somewhat above 10⁵ GeV by the time that the free expansion phase of its evolution has come to an end. As the remnant's outer shock slows, these highest energy cosmic rays diffuse away from the shock along a magnetic flux tube with a radius comparable to that of the remnant at the end of its free expansion phase and which eventually (over a distance of the order of a kiloparsec) bends into the Galactic halo. A similarity solution exists for the temporal and spatial variations, in such a tube, of both the number density for these ～ 10⁵ GeV cosmic rays and the energy density of the waves on which they resonantly scatter. Wave-wave interactions probably do not dominate the evolution of the energy density of these lowest frequency waves, but we assume that they do establish a Kraichnan wave spectrum at higher wavenumber. Although we cannot rigorously justify this assumption, it does receive some support from the analysis of pulsar signals. There is a large body of observations to which such a model can be applied, yielding constraints that must be met. With the model that we develop here we obtain the following results:

1. The local intensity of ～ 10⁵ GeV cosmic rays implies that the flux tube which currently surrounds the Solar System last contained a remnant in the free expansion phase several times 10⁷ years ago. We comment on the rough agreement between this age and that inferred from Be¹⁰ data.
2. The theoretical value of the cosmic ray diffusion coefficient at ～ 1 GeV in the tube corresponding to that time is in harmony with the value of the diffusion coefficient inferred from cosmic ray composition and synchrotron measurements.

In the light of our inhomogeneous cosmic ray acceleration/propagation model we re-examine our earlier work on the evidence for second order acceleration in a very old remnant. Such evidence is provided by the molecular compositions along several lines of sight to the Perseus OB2 association. We find as a third significant result that the model value of the diffusion coefficient at energies in the range of 1 MeV agrees within about an order of magnitude with that which we infer from the molecular data.     

A periodical analysis of the cosmic-ray diffusion coefficient and the high-speed solar-wind streams

A three-dimensional model for the calculation of cosmic-ray intensity of the Inuvik station during the 20th and 21st solar cycles is given. Especially we have studied the coefficient K of the used parameter of sunspot number in terms of high-speed solar-wind streams and have tried enough successfully to relate this coefficient with the diffusion process of cosmic rays in the interplanetary space.Analyzing these two data sets for the time-period 1964–1985 into a network of trigonometric series we have observed similar period in the two sets. It means that we have the same in general line variations in the high-speed streams as well as to the coefficient K expressed by this way the diffusion coefficient of cosmic-rays.     

Hydrogen flicker and associated high-energy radiation

The accretion of matter onto stars formed by carbon-oxygen cores triggers hydrogen flicker. The development of hydrogen flicker and the shock generation associated therewith are discussed. If the matter thus ejected is halted by a dense gas surrounding a star, a corona of high temperature is formed. This may take place in dense planetary nebulae and is regarded as an origin of starlike X-ray sources. More violent hydrogen flicker takes place at white dwarfs and may be an origin of novae. Nuclear-reaction products ejected are positron sources and they may provide MeV positrons as strong as 10^–3 cm^–2 sec^–1 sr^–1. Nuclides produced by hydrogen flicker and a part of the carbon-oxygen core ejected may contribute to galactic cosmic rays; their chemical composition is like that observed in cosmic rays.     

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.     

Dynamics of dwarf-spheroidals and the dark matter halo of the galaxy

The dynamics of the dwarf-spheroidal (dSph) galaxies in the gravitational field of the Galaxy is investigated with particular reference to their susceptibility to tidal break-up. Based on the observed paucity of the dSphs at small Galactocentric distances, we put forward the hypothesis that subsequent to the formation of the Milky Way and its satellites, those dSphs that had orbits with small perigalacticons were tidally disrupted, leaving behind a population that now has a relatively larger value of its average perigalacticon to apogalacticon ratio and consequently a larger value of its r.m.s. transverse to radial velocities ratio compared to their values at the time of formation of the dSphs. We analyze the implications of this hypothesis for the phase space distribution of the dSphs and that of the dark matter (DM) halo of the Galaxy within the context of a self-consistent model in which the functional form of the phase space distribution of DM particles follows the King model, i.e. the ‘lowered isothermal’ distribution and the potential of the Galaxy is determined self-consistently by including the gravitational cross-coupling between visible matter and DM particles. This analysis, coupled with virial arguments, yields an estimate of ≳270 km s⁻¹ for the circular velocity of any test object at galactocentric distances of ∼100 kpc, the typical distances of the dSphs. The corresponding self-consistent values of the relevant DM halo model parameters, namely, the local (i.e., the solar neighbourhood) values of the DM density and velocity dispersion in the King model and its truncation radius, are estimated to be ∼0.3 GeV cm⁻³, >350 km s⁻¹ and ≳150 kpc, respectively. Similar self-consistent studies with other possible forms of the DM distribution function will be useful in assessing the robustness of our estimates of the Galaxy’s DM halo parameters.     

Heliospheric propagation of galactic cosmic rays depending on the scattering characteristics of the turbulent interplanetary magnetic field

The effect of the solar wind on the spectrum of cosmic rays accelerated in the Galaxy is studied. The coefficient of cosmic-ray diffusion in the interplanetary turbulent magnetic field is assumed to be independent of the particle energy and a power-law function of the distance from the Sun. The particle spectrum at the heliospheric boundary is specified as a power-law function of the total particle energy.     

Cosmic Ray Production Rates in Supernova Remnants

Supernova Remnants (SNRs) are the most likely sources of the galactic cosmic rays up to energies of about 10¹⁵ eV/nuc. The large scale shock waves of SNRs are almost ideal sites to accelerate particles up to these highly non-thermal energies by a first order Fermi mechanism which operates through scattering of the particles at magnetic irregularities. In order to get an estimate on the total amount of the explosion energy E _SNconverted into high energy particles the evolution of a SNR has to be followed up to the final merging with the interstellar medium. This can only be done by numerical simulations since the non-linear modifications of the shock wave due to particle acceleration as well as radiative cooling processes at later SNR stages have to be considered in such investigations. Based on a large sample of numerical evolution calculations performed for different ambient densities n _ext, SN explosion energies, magnetic fields etc. we discuss the final ‘yields’ of cosmic rays at the final SNR stage where the Mach number of the shock waves drops below 2. At these times the cosmic rays start to diffuse out of the remnant. In the range of external densities of10^-2 ≤ n _ext/[cm^-3] ≤ 30 we find a the total acceleration efficiency of about 0.15 E _SN with an increase up to 0.24 E _SN at maximum for an external density of n _ext = 10 cm^-3. Since for the larger ambient densities radiative cooling can reduce significantly the total thermal energy content of the remnant dissipation of Alfvén waves can provide an important heating mechanism for the gas at these later stages. From the collisions of the cosmic rays with the thermal plasma neutral pions are generated which decay subsequently into observable γ-rays above 100 MeV. Hence, we calculate these γ-ray luminosities of SNRs and compare them with current upper limits of ground based γ-raytelescopes. The development of dense shells due to cooling of the thermal plasma increases the γ-ray luminosities and e.g. an external density of n _ext = 10 cm^-3 with E _SN = 10⁵¹ erg can lead to a γ-ray flux above 10^-6 ph cm^-2 s^-1 for a remnant located at a distance of 1 kpc. This revised version was published online in July 2006 with corrections to the Cover Date.     

Enhanced diffusion in strongly magnetized astrophysical plasmas

We demonstrate that the diffusion coefficient for low energy particles, tied to a magnetic field which random walks, may be considerably larger than previously estimated in a strongly magnetized system — like the solar wind or the Galaxy. This is of interest with respect to propagation and lifetime considerations of low energy cosmic rays in the solar wind and the Galaxy.     

Propagation of the cosmic-ray iron group at intermediate energies

Elemental abundances of the VH group of cosmic radiation have been measured in the energy interval 250–550 MeV nucl^–1 in a balloon exposure at Sioux Falls (South Dakota) of a plastic detector LeXAN stack. The so obtained abundances have been extrapolated to the sources in the frame of the homogeneous model correcting for energy loss. After taking into account solar modulation, the best fit to model values has led to a escape mean free path _e = 5E ^–0.4 g cm^–2, whereE is the energy in GeV nucl^–1, forE>1 GeV nucl^–1, and a constant _e = 5 g cm^–2 forE1 GeV nucl^–1. When turning to the diffusion model, also including an energy loss term, a diffusion coefficientD=3×10²⁸ cm² s^–1 has been estimated.     

The ionization state of oxygen ions in anomalous cosmic rays: Results from the ANURADHA experiment in Spacelab-3

We report the first results on the determination of the ionization states of oxygen ions in the anomalous cosmic rays (ACR) from the measurements of their flux in the cosmic-ray experiment in Spacelab-3 (SL-3) mission of NASA flown at 350 km altitude during 29 April–6 May, 1985. The detectors used were specially prepared CR-39 plastics of very high sensitivity for recording tracks of ions withZ>2. The measured orbit averaged flux of ACR oxygen is (2.9±1.3)×10^–4 particles m^–2sr^–1s^–1 (MeV N^–1) at an energy of 23 MeV N^–1. We made an independent estimate of the expected ACR oxygen flux at SL-3 orbit from interplanetary data and compared this with the measured flux to infer the ionization states of ACR oxygen ions. The flux and energy spectra of ACR oxygen at 1 AU outside the magnetosphere is obtained from the data of Voyager-2, during the same epoch as the SL-3 flight, and using the measured radial intensity gradient of 15%/AU for ACR oxygen between 1–17 AU. We calculate the geomagnetic transmission factors for ACR oxygen ions of charge states O⁺¹, O⁺², etc., from the known cut-off rigidities in the world grid and using the SL-3 trajectories for 116 orbits in the 6-day mission to obtain the expected flux at SL-3 for different charge states. When these flux values are compared with our measured flux, the averge ionization state of ACR oxygen ions in the energy interval of 20–26 MeV N^–1 is obtained as O⁺¹.     

Cosmic ray interactions with lunar materials: Nature and composition of species formed

The solar and galactic cosmic rays interact directly with lunar surface materials, and the dominant nature of interactions is essentially the complete absorption of corpuscles. These corpuscles damage the lattice structure, and induce a complex set of reactions in the materials producing various species. The cosmic ray damage of the lattice would not produce an amorphous layer, similar to that produced by the solar wind, because the solar wind erosion rate is faster than the cosmic ray-induced amorphous layer formation rate. The species formation rate considered in this paper are those produced by protons, the dominant component of cosmic rays. Protons produce H, H₂, OH, H₂O, and hydrogenated species of carbon, nitrogen, sulfur, etc. These species, while migrating in the material, encounter oncoming cosmic ray corpuscles, and undergo a complex set of reactions. Although a variety of species are produced by protons, the dominant contributor to the atmosphere is H₂. The H₂ flux (molecules cm^–2 sec^–1) is about 1.5 × 10⁵ as compared to the H flux of 8.4 × 10¹ and the H₂O flux of 4.6 × 10^–2. These fluxes are about 10^–3 smaller than the fluxes of the same species produced by the solar wind protons. Thus the contributions of the cosmic ray-induced species to the atmosphere is very small compared to the solar wind-induced species. Although simulated experiments showed high concentractions of OH and H₂O in the terrestrial materials of lunar type, these species concentrations in the lunar materials under the lunar environment is much smaller than those observed in the simulated experiments.     

Decaying nuclei and the age of cosmic rays in the galaxy

The propagation of radioactive nuclei of cosmic rays in a flat diffusion galactic model (sources and the main gaseous mass are concentrated in the galactic disc) is considered. The corresponding results are not reducible to the results of a simple homogeneous model. It is shown that the recent data on the Be¹⁰ nuclei abundance in cosmic rays do not contradict the occurrence of a large cosmic ray halo.     

An estimate of the energy spectrum of gamma rays from the central region of the Galaxy and some implications

High resolution surveys of the galactic centre suggest the existence of an extended nonthermal source (Bulge) with an intensity much larger than the total background radiation in that direction. In this paper, we have first evaluated the physical conditions existing in this restricted region of space from an analysis of the radio spectrum and shown that if the distribution of matter, magnetic fieldB(r) and cosmic ray densityk(r) in the plane of the Galaxy is of gaussian type then at the centreB (0)=25–30 G andk(0)=25–35 times that in the near interstellar space. It is also found that most of the absorption in the Sagittarius A spectrum at low frequencies takes place in the Bulge and one requires a small additional absorption to take place in the line of sight corresponding to n _e ²10 cm^–6 pc at a temperature typically of clouds 100 K. The gamma ray spectra from the Bulge arising from interactions of cosmic rays with matter and radiation are then calculated in detail. A comparison made with the estimated background gamma ray spectra from the disk reveals that a detector with angular resolution 6° having a threshold of a few times 10^–6 photons cm^–2 s^–1 can detect this source; this bulge is not found to be a good X-ray source for detection. From a comparison of these calculations with the observed flux above 100 MeV, the following inferences have been deduced: (i) the lower limit to the magnetic field strength at the centre is 12 G, (ii) the observed gamma ray flux towards the Anti-centre can be well explained as due to interactions of cosmic rays with matter alone and a similar explanation towards the center reveals that cloud complexes could be more in the inner parts of the Galaxy than in the outer parts, and (iii) the observed flux values are found to be inconsistent with the existence of submillimeter radiation in the galactic scale.     

Outer pseudoring in the galaxy

The kinematics of the Sagittarius (R = 5.7 kpc),Carina (R = 6.5 kpc), Cygnus (R = 6.8 kpc), and Perseus (R = 8.2 kpc) arms suggests the existence of two spiral patterns in the Galaxy that rotate with different speeds. The inner spiral pattern that is represented by the Sagittarius arm rotates with the speed of the bar, Ω_b = 60 ± 5 km s⁻¹ kpc⁻¹, while the outer spiral pattern that includes the Carina, Cygnus, and Perseus arms rotates with a lower speed, Ω_s = 12–22 km s⁻¹ kpc⁻¹.The existence of an outer slow tightly wound spiral pattern and an inner fast spiral pattern can be explained by numerically simulating the dynamics of outer pseudorings. The outer Lindblad resonance of the bar must be located between the Sagittarius and Carina arms. The Cygnus arm appears as a connecting link between the fast and slow spiral patterns.