The fermi mechanism and the source spectrum of cosmic ray nuclei

It is shown that the velocity term, occurring in the expression for the rate of energy gain by the Fermi mechanism of acceleration, is to be taken into account in case of acceleration of non-relativistic particles. A spectral form of accelerated particles is derived on this basis and is called the ‘Fermi Spectrum’. At non-relativistic energies this spectral form is significantly different from the currently used forms of power law in total energy per nucleon and in rigidity, and lies about midway between them. It is shown that using this form of source spectrum of cosmic ray nuclei, satisfactory agreement can be obtained between the calculated values and the observed ones of the ratios of H²/He⁴ and He³/He⁴, and the energy spectra of protons and helium nuclei near the Earth.     

The comparative spectra of cosmic-ray protons and helium nuclei

We have re-examined and extended the measurements of the primary cosmic ray proton and helium nuclei intensities in the range from a few MeV nuc^–1 to 100 GeV nuc^–1 using a considerable body of recently published data. The differential spectra obtained from this data are determined as a function of both energy and rigidity. The exponents of the energy spectra of both protons and helium nuclei are found to be different at the same energy/nucleon and to increase with increasing energy between 1 and 100 GeV nuc^–1 reaching a value=–2.70 at higher energies and in addition, theP/He ratio changes from a value 5 at 1 GeV nuc^–1 and below to a value 30 at 100 GeV nuc^–1. On a rigidity representation the spectral exponent for each species is nearly identical and remains virtually constant above several GV at a value of –2.70, and in addition, theP/He ratio is also a constant 7 above 3 GeV. The changingP/He ratio and spectral exponent on an energy representation occur at energies well above those at which interplanetary modulation effects or interstellar ionization energy loss effects can significantly affect the spectra. In effect by comparing energy spectra and rigidity spectra in the intermediate energy range above the point where solar modulation effects and interstellar energy loss effects are important, but in the range where there are significant differences between energy and rigidity spectra, we deduce that the cosmic ray source spectra are effectively rigidity spectra. This fact has important implications regarding the mechanism of acceleration of this radiation and also with regard to the form of the assumed galactic spectrum at low energies. The relationship between the proton and helium spectra derived here and the heavier nuclei spectral differences recently reported in the literature is also examined.If rigidity spectra are adopted for protons and helium nuclei, then the source abundance ratio of these two components is determined to be 7:1. Some cosmological implications of this ratio are discussed.     

Lyman-α production by suprathermal protons

At sufficiently low energies, cosmic ray protons capture electrons from interstellar Hi and become neutral. In the subsequent cascade to the ground state a Doppler-shifted Ly- photon may be emitted. The neutral cosmic ray will be excited collisionally by further encounters with the ambient interstellar gas, emitting additional Doppler-shifted Ly- photons. We give the form of the cosmic ray spectrum down to 10 keV, assuming that there is no cosmic ray injection below 1 MeV. The neutral fraction is evaluated as a function of energy, and the diffuse ultraviolet flux is calculated. Comparison is made with observations in the range 1225–1340 Å. We conclude that far more stringent limits on the flux of subcosmic rays may be obtained by consideration of the heating and ionization of Hi regions.     

A comparison of the energy spectra of cosmic ray helium and heavy nuclei

Recent observations of the spectra of cosmic ray helium, M, LH and VH nuclei in the energy range from 200 MeV/nuc to>22 GeV/nuc are reported. The differential spectra of all of these groups of nuclei are found to have a maximum at 300–400 MeV/nuc at sunspot minimum. The average exponents on the integral rigidity spectra in the range 5 to 50 GV are 1.54±0.03 for He nuclei, 1.50±0.04 for M nuclei, 1.47±0.06 for LH nuclei and 1.40±0.08 for VH nuclei. The spectra of these groups of nuclei are compared and it is found that the average He/M, He/LH and He/VH ratios are 16±1, 70±3 and 200±15 respectively. These values are reasonably constant from the highest down to the lowest energies measured although some evidence for a dip is present in the 500–1000 MeV/nuc range for both the He/LH and He/VH ratios. Solar modulation effects on these ratios are discussed and it is concluded that the ratios measured at earth are representative of those existing in interstellar space only if energy loss processes in interplanetary space are unimportant. The influence of interstellar propagation on the spectra and charge ratios at low energies arising from ionization energy loss and nuclear spallation during matter traversal is examined. It is found that propagation models that contain a large number of relatively short path lengths significantly modify the expected effects of ionization energy loss at low energies. Specifically it is suggested that the presently measured charge ratios are consistent with the passage of the average cosmic radiation through enough matter to reproduce the abundances of the so-called fragmentation nuclei, Li, Be, B and He³. Two component models are not required to explain our data. Rather we feel that a better representation of the situation results from considering a continuous spatial distribution of sources which, along with the actual interstellar propagation conditions, leads to a particular distribution of matter path lengths. It is pointed out that large differences exist in the approaches used in the literature to calculate the effects of matter traversal in interstellar space at low energies. These differences play an important role in the interpretation of the experimental results. Significant modifications of the charge ratios at low energies can also be obtained by requiring that some of the matter traversal occur in the cosmic ray sources themselves during the cosmic ray acceleration process. This may be sufficient to produce charge ratios that are essentially flat at low energies even in the presence of interstellar ionization loss.     

The relative abundance of the isotopes of Li,Be and B and the age of cosmic rays

Using a balloon borne double dE/dx x total energy telescope we have determined the isotopic composition of cosmic ray Li, Be and B nuclei in the energy range 100–250 MeV nuc.^–1. The measured mass resolution, for these nuclei is 0.3 AMU. The observed isotopic composition is in agreement with that predicted on the basis of interstellar fragmentation with the exception of a deficiency of Be¹⁰. If the low abundance of Be¹⁰ is attributed to the decay of this radioactive isotope we obtain a mean cosmic ray lifetime of (3.4 _–1.3 ^+3.4 )×10⁶ yr.A recent measurement which we have used in this paper gives this lifetime to be (1.5±0.3)×10⁶ yr (Yiou and Raisbeck, 1972).     

Charge dependence of the solar modulation of multiply charged cosmic ray nuclei

The intensity and energy spectra of multiply charged cosmic ray nuclei, in the energy interval 250–1500 MeV/n, were studied at three different levels of solar activity, viz. in 1963, 1964 and 1967. The same detectors, nuclear emulsion stacks flown from Fort Churchill, Canada, were used to determine simultaneouslty the energy spectra of helium, C, N, O as well as H (Z=10–28) nuclei. An analysis of the measured spectra indicates that these can be interpreted in terms of: (a) the source spectrum as a Fermi spectrum with a spectral index of 2.65; (b) the interstellar propagation as in a Gaussian distribution of path lengths with a mean path length of 4 g cm^–2 and (c) the interplanetary propagation as given by the numerical solution of the Fokker-Planck equation incorporating diffusion, convection and adiabatic deceleration. On comparing the measured ratios of He to H-nuclei (mean Z14) with the theoretically calculated values for the three levels of solar activity, it is found that within experimental uncertainties, the solar modulation is essentially the same for nuclei of same mass to charge ratio and is not dependent on the charge of the nuclei.On leave from Tata Institute of Fundamental Research, Bombay.     

On the modulation and energy spectrum of highly charged cosmic ray nuclei

The intensity and energy spectrum of cosmic ray VH-nuclei (20Z30) has been measured in a stack of nuclear emulsions exposed over Fort Churchill in 1968. The integral intensity above 300 MeV/nucleon was 1.04±0.04 nuclei m^–2 sr^–1 s^–1 and three differential intensities were measured below 750 MeV/nucleon. Because of the current controversy regarding the true intensities of helium nuclei at this phase of the solar cycle we have also measured these nuclei, obtaining results intermediate between those quoted by other workers. Comparison of these results on the VH-and helium nuclei with those obtained in previous observations made at times of low solar modulation leads to the conclusion that there is no significant charge dependence in the modulation process. This conclusion is in conflict with an earlier analysis but depends on results of improved statistical weight and greater reliability for the VH nuclei and on our measurement of the helium nuclei in the same detector.Supported by the Office of Naval Research under Contract No. N00014-67-A-0113-0021.     

Cosmic-ray production of deuterium,He3, lithium,beryllium, and boron in the Galaxy

The production of deuterium, He³, lithium, beryllium, and boron by galactic cosmic rays in the interstellar medium, over the life of the Galaxy, is calculated. It is found that high-energy - reactions contribute in an essential way to the observed lithium. When allowance is made for the interchange of material between stars and the interstellar gas and for the change of cosmic-ray intensity with time, the Li⁶, Be⁹, and boron produced turn out to be ample to explain the observed abundances, and with remarkable internal consistency. Deuterium and He³ arenot produced in significant amounts, nor Li⁷ in sufficient amount, however. To explain the Li⁷/Li⁶ ratio measured terrestrially and in chondritic meteorites, we invoke cosmological production of Li⁷. This implies the production of deuterium, He³, and He⁴ as well, in amounts consistent with observation. The theory in its present form cannot explain a solar-system Li⁷/Li⁶ ratio of 12and stellar ratios as low as 3, but additional processes can be adduced to reconcile them. The consistency of the numbers when cosmological production is included lends additional support to the big-bang hypothesis. An incidental result is that the mean luminosity of the Galaxy over its lifetime has been about 3 times its present luminosity.     

Origin of low energy cosmic ray positrons at energies ≳2 MeV

It is shown that an appreciable flux of positrons below a few MeV in the cosmic radiation could arise from the decay of cobalt nuclei in the decay chain⁵⁶Ni⁵⁶Co⁵⁶Fe, which occurs in the silicon burning shells of supernovae just after their ejection at relativistic velocities. The equilibrium spectrum of positrons in the interstellar space has been calculated on the assumption that the observed abundance of iron nuclei in the cosmic radiation is the result of the above process. It is found that the observation below about 10 MeV can be well explained with a moderate acceleration of the positrons in the expanding envelope of supernovae prior to their propagation in the interstellar space. The total⁵⁶Ni content in the shells of supernova necessary to account for the observed positrons is in agreement with that required to explain the peak luminosity during the supernova outburst. Since this model deals with positrons created at the time of injection of cosmic rays into the interstellar space, it becomes possible to study the shape of the injection spectrum of cosmic rays.On leave from Tata Institute of Fundamental Research, Bombay, India.     

Signatures of the Interplanetary Helium Cone Reflected by Pick-up Ions

As known for a long time, interstellar wind neutral helium atoms deeply penetrate into the inner heliosphere and, when passing through the solar gravity field, form a strongly pronounced helium density cone in the downwind direction. Helium atoms are photoionized and picked-up by the solar wind magnetic field, but as pick-up ions they are not simply convected outwards with the solar wind in radial directions as assumed in earlier publications. Rather they undergo a complicated diffusion-convection process described here by an appropriate kinetic transport equation taking into account adiabatic cooling and focusing, pitch angle scattering and energy diffusion. In this paper, we solve this equation for He⁺pick-up ions which are injected into the solar wind mainly in the region of the helium cone. We show the resulting He⁺pick-up ion density profile along the orbit of the Earth in many respects differs from the density profile of the neutral helium cone: depending on solar-wind-entrained Alfvénic turbulence levels, the density maximum when looking from the Earth to the Sun is shifted towards the right side of the cone, the ratio of peak-densities to wing-densities varies and a left-to-right asymmetry of the He⁺-density profile is pronounced. Derivation of interstellar helium parameters from these He⁺-structures, such as the local interstellar medium (LISM) wind direction, LISM velocity and LISM temperature, are very much impeded. In addition, the pitch-angle spectrum of He⁺pick-up ions systematically becomes more anisotropic when passing from the left to the right wing of the cone structure. All effects mentioned are more strongly pronounced in high velocity solar wind compared to the low velocity solar wind.     

Measurements of cosmic-ray Li,Be and B nuclei in the energy range 100 MeV/nuc to >22 BeV/nuc

We report on new measurements of the spectra of Li, Be and B nuclei in the primary cosmic radiation in the energy range 100 MeV/nuc to >22 BeV/nuc. The differential spectrum of these light nuclei is found to have a maximum at 400 MeV/nuc in 1966. The L/M ratio is found to be equal to 0.25±0.01, constant over the entire energy range of the measurement. Atmospheric and solar modulation effects on the L nuclei and the L/M ratio are discussed. It is concluded that this ratio is representative of conditions in interstellar space. Using the most recently available fragmentation parameters gives a material path length of 3.6 g/cm² of hydrogen for the particles producing the L nuclei. The absence of any variation of the L/M ratio with energy places severe constraints on models for the propagation of cosmic rays. Models in which the material path length is a strong function of energy — or that exhibit an exponential path-length distribution for a fixed energy are incompatible with these results. An examination of the abundance ratios of the individual L nuclei separately reveals major discrepancies with the predictions of interstellar diffusion theory based on presently accepted fragmentation parameters. The constancy of the measured Li/M and B/M ratios with energy is not in accord with the large energy dependence of these ratios expected from the energy dependence of the fragmentation cross-sections. The low Li/M ratio and high B/M ratio to be expected if these nuclei are created at a much lower energy than we observe are also not found. This presents difficulties for theories which suggest that the passage through matter has occurred at low energies subsequently followed by considerable acceleration.The Be/M ratio in cosmic rays is anomalous in that it is 40% larger than expected on the basis of the fragmentation cross-sections. Evidence presented here on the isotopic composition of Be nuclei suggests that this discrepancy is due to an enhanced abundance of Be⁹ or Be¹⁰ in cosmic rays. This discrepancy complicates the determination of a cosmic-ray age using the decay of Be¹⁰ into B.Nevertheless the Be/B ratio is observed to remain constant at 0.42±0.03 over the energy range from 100 MeV/nuc to over 10 BeV/nuc. Unless the fragmentation parameters into the various isotopes of Be and B are such that e.g. (Be/B)<0.05 as a result of this decay, then the age of cosmic rays is either >3×10⁸ years or <10⁶ years. The further observation that the mass to charge ratio of all Be nuclei of energy 1 BeV/nuc is =2.05±0.1 suggests that Be¹⁰ is present at these energies. This supports the idea of a short lifetime.     

The retention of spallation products in interstellar grains

Stimulated by recent studies indicating the possible survival of presolar grains in certain meteorites, the importance of recoil loss for the retention of spallation products in submicrometer-sized interstellar dust during irradiation by high-energy cosmic ray protons has been calculated. The model presented incorporates range straggling effects, a realistic distribution of interstellar grain sizes, and utilizes an accurate theoretical formalism for the fragmentation recoil momenta. Apart from an only vague understanding of possible grain composition, the greatest uncertainty concerns the intrinsic material density of interstellar dust which determines the recoil range for any given momentum. It is found that even allowing for a fivefold variation of density values, the retention against recoil is substantial: for example, some 20 to 50% of all ³⁸Ar nuclei resulting from high-energy interaction remain trapped, depending on the target element considered. Retentivities for the various spallation reactions contributing to ³⁸Ar have been calculated and are used to deduce an interstellar spallogenic production rate. The results are then considered in the light of recent discoveries of ⁴⁰Ar³⁹Ar apparent ages in excess of 4.53×10⁹ years for some inclusions from the meteorite Allende. Limitations of both the theoretical and experimental efforts presently preclude conclusive statements regarding the question of interstellar grain survival. However, a procedure is outlined whereby this issue might be clarified in future investigations.     

Energy losses and modulation of galactic cosmic rays

Numerical solutions of the cosmic-ray transport equation for the interplanetary region and including the effects of diffusion, convection, and energy loss, have been obtained for a galactic differential number-density spectrum of gaussian form, central kinetic energyT ₀, and a width at half height maximum of 0.1T ₀. These solutions have been used to show the redistribution in energy, and the reduction in number density, within the solar cavity. The mean energy loss is shown to be usefully approximated by the force-field potential when /T ₀1/2. The principal finding is that galactic cosmic-ray protons and helium nuclei, with kinetic energies less than about 80 MeV/nucleon, virtually, are completely excluded from near Earth by convective effects. As a result of this exclusion, it is found that it is not possible to demodulate the proton and helium-nuclei spectra, observed in 1964–65, to obtain information about low-energy galactic cosmic rays.     

A machine learning method to separate cosmic ray electrons from protons from 10 to 100 GeV using DAMPE data

DArk Matter Particle Explorer(DAMPE) is a general purpose high energy cosmic ray and gamma ray observatory, aiming to detect high energy electrons and gammas in the energy range 5 Ge V to 10 Te V and hundreds of Te V for nuclei. This paper provides a method using machine learning to identify electrons and separate them from gammas, protons, helium and heavy nuclei with the DAMPE data acquired from 2016 January 1 to 2017 June 30, in the energy range from 10 to 100 Ge V.     

ISOCAM Long Wave Detector Glitches: Data and Ray-Tracing Simulations

The affected pixel number distribution of the ISOCAM Long-Wave (LW) detector in cosmic ray-induced glitchesis calculated. The methods employed are Monte Carlo ray-tracing techniques and the taxi metric, which allows direct calculation of the affected pixels based on the knowledge of entry and exit points of the ray. The simulation results are compared with long-term experimental data. Based on the simulations combined with the CREME96 cosmic ray model for solar quiet period, it is estimated that the detector is on average traversed by 0.3 cosmic ray protons per second. For the experimental data, a corresponding minimum bound of 0.14 cosmic ray protons per second is obtained. Deviations in the simulated and measured pixel number distributions are discussed.     

Ionization states and the origin of low energy cosmic ray nuclei

The origin of the new component of cosmic ray nuclei in 1–30 MeV amu^–1 recently detected through space vehicles in interplanetary space is investigated in detail. It is assumed that these particles may originate from nearby sources, e.g., from novae type explosions, which have peculiar C, N and O compositions. These particles are further assumed to be accelerated and modulated within the heliosphere. The charged states of these ions in the interstellar space have been calculated in detail and it is shown that the same charged states are preserved in the heliosphere when they are accelerated to energies of the order of 10⁷eV amu^–1 from energies of 10⁵ ev amu^–1. Modulation of these ions are calculated and it is found that because of low charged states of the ions these have high rigidities and are modulated in such a way as to enhance the O-ion abundances as compared to C-ions. A comparison is made of the demodulated composition of C to Si-ions with available abundance data of some novae.     

Contributions to the theory of spiral structure. II. The density wave theory and the very hot interstellar gas component

Starting from the argument that the density wave theory of spiral structure is incompatible with the existence of a stationary very hot extended component of the interstellar gas, we develop a cyclic model, in which an interstellar gas of a temperature around 10⁴ K is heated to roughly 10⁶ K by type II supernovae resulting from the enhanced star formation triggered by the density wave, and cools down again to 10⁴ K after the supernova activity subsides to be ready for shock compression in the next sweep of the density wave pattern. The time scales for heating by supernovae and subsequent cooling turn out to be consistent with current density wave theory. The scenario proposed is corroborated by recent results on cosmic ray composition and -ray observations.     

The relative energy spectra of carbon and oxygen nuclei in the primary cosmic radiation

Measurements of the energy spectra of carbon and oxygen nuclei in the primary cosmic radiation over the energy range from 140 MeV/nuc to 30 BeV/nuc are reported. An average C/O ratio of 1.11±0.02 is obtained at the top of the atmosphere. This ratio is found to be constant to within 5% over the entire energy range. The energy spectra of these two nuclei are presented and compared with earlier measurements and with satellite observations at low energies. After correction for propagational effects in 4 g/cm² of interstellar hydrogen the source C/O ratio is found to be 0.9. The astrophysical implications of this C/O ratio are discussed.     

A classification of the available astrophysica data of particularHii regions

We have calculated the energy spectra of cosmic ray secondary antiprotons and positrons using the latest available data on inclusive reactions. Using the measured positron spectrum, we have found that the amount of matter traversed by the cosmic rays in the few GeV region to bem≈4.7±1.5 g cm^?2 of interstellar hydrogen. The computed antiproton to proton ratio is about 4×10^?4 for energies 5–10 GeV. This is sufficient to make observations of antiprotons feasible from balloon flights. We have also pointed out the type of information that can be obtained if accurate information of the spectra of these two components becomes available.