Power Law In Rigidity Research Articles

Cosmic-ray spectrum in the local Galaxy

We study the spectral properties of the cosmic-ray spectrum in the interstellar medium within 1 kpc distance from the Sun. We used eight-year exposure data of molecular clouds of the Gould Belt obtained with the Fermi/LAT telescope to precisely measure the cosmic-ray spectrum at different locations in the local Galaxy. We compared this measurement with the direct measurements of the cosmic-ray flux in and around the solar system obtained by Voyager and AMS-02 or PAMELA. We find that the average cosmic-ray spectrum in the local Galaxy in the 1-100 GeV range is well described by a broken power-law in rigidity with a low-energy slope of $2.33^{+0.06}_{-0.08}$ and a break at $18^{+7}_{-4}$ GV, with a slope change by $0.59\pm 0.11$. This result is consistent with an earlier analysis of the gamma-ray signal from the Gould Belt clouds based on a shorter exposure of Fermi/LAT and with a different event selection. The break at 10-20 GV is also consistent with the combined Voyager + AMS-02 measurements in/around the solar system. The slope of the spectrum below the break agrees with the slope of the average cosmic-ray spectrum in the inner part of the disk of the Milky Way that was previously derived from the Fermi/LAT gamma-ray data. We conjecture that it is this slope of 2.33 and not the locally measured softer slope of 2.7-2.8 that is determined by the balance between a steady-state injection of cosmic rays with a power-law slope of 2-2.1 that is due to Fermi acceleration and the energy-dependent propagation of cosmic-ray particles through the turbulent interstellar magnetic field with a Kolmogorov turbulence spectrum. The approximation of a continuous-in-time injection of cosmic rays at a constant rate breaks down, which causes the softening of the spectrum at higher energies.

Cosmic ray propagation and dark matter in light of the latest AMS-02 data

The AMS-02 experiment is measuring the high energy cosmic rays with unprecedented accuracy. We explore the possibility of determining the cosmic-ray propagation models using the AMS-02 data alone. A global Bayesian analysis of the constraints on the cosmic-ray propagation models from the preliminary AMS-02 data on the Boron to Carbon nuclei flux ratio and proton flux is performed, with the assumption that the primary nucleon source is a broken power law in rigidity. The ratio of the diffusion coefficient D0 to the diffusive halo height Zh is determined with high accuracy D0/Zh≃ 2.00±0.07 cm2s−1kpc−1, and the value of the halo width is found to be Zh≃ 3.3 kpc with uncertainty less than 50%. As a consequence, the typical uncertainties in the positron fraction predicted from dark matter (DM) annihilation is reduced to a factor of two, and that in the antiproton flux is about an order of magnitude. Both of them are significantly smaller than that from the analyses prior to AMS-02. Taking into account the uncertainties and correlations in the propagation parameters, we derive conservative upper limits on the cross sections for DM annihilating into various standard model final states from the current PAMELA antiproton data. We also investigate the reconstruction capability of the future high precision AMS-02 antiproton data on the DM properties. The results show that for DM particles lighter than 0∼ 10 GeV and with typical thermal annihilation cross section, the cross section can be well reconstructed with uncertainties about a factor of two for the AMS-02 three-year data taking.

May 2005 Halo CMEs and Galactic Cosmic Ray Flux Changes at Earth’s Orbit

The pressure corrected hourly data from the global network of cosmic ray detectors, measurements of the interplanetary magnetic field (IMF) intensity (B) at Earth’s orbit and its components B x , B y , B z (in the geocentric solar ecliptic coordinates) are used to conduct a comprehensive study of the galactic cosmic ray (GCR) intensity fluctuations caused by the halo coronal mass ejection of 13 May 2005. Distinct differences exist in GCR timelines recorded by neutron monitors (NMs) and multidirectional muon telescopes (MTs), the latter respond to the high rigidity portion of the GCR differential rigidity spectrum. The Forbush decrease (FD) onset in MTs is delayed (∼5 h) with respect to the onset of a geomagnetic storm sudden commencement (SSC) and a large pre-increase is present in MT data before, during, and after the SSC onset, of unknown origin. The rigidity spectrum, for a range of GCR rigidities (≤200 GV), is a power law in rigidity (R) with a negative exponent (γ=−1.05) at GCR minimum intensity, leading us to infer that the quasi-linear theory of modulation is inconsistent with observations at high rigidities (>1 GV); the results support the force field theory of modulation. At present, we do not have a comprehensive model for the FD explaining quantitatively all the observational features but we present a preliminary model listing physical processes that may contribute to a FD timeline. We explored the connections between different phases of the FD and the power spectra of IMF components but did not find a sustained relationship.

Theoretical and Experimental Studies of the Rigidity Spectrum of the 27-Day Variation of the Galactic Cosmic Ray Intensity in Different Epochs of Solar Activity

We consider the recent, very exceptional, 11-year cycle (2003 – 2009) of solar activity and confirm that the relative amplitude in rigidity spectrum, δD(R)/D(R), which can be approximated by a power law in rigidity R, of the first three harmonics of the 27-day variation of the galactic cosmic ray (GCR) intensity is hard in the maximum and soft in the minimum epochs of solar activity, as was found by neutron monitor data for the period of 1965 – 2002. This property is seen not only in separate minimum and maximum epochs but in individual intervals of a solar Carrington rotation as well: There exist many individual intervals of solar rotation when the expected rigidity spectrum of the 27-day variation of the GCR intensity indeed is hard in the maximum epoch of solar activity and is soft in the minimum epoch. We then construct a three-dimensional model of the 27-day variation of the GCR intensity based on Parker’s transport equation, by implementing in situ measurements of the changes in heliographic longitude of the solar wind velocity and interplanetary magnetic field for different epochs of solar activity.

Galactic cosmic ray modulation for sunspot cycle 23

We present a study of the galactic cosmic ray modulation for sunspot cycle 23. We use the monthly and the annual mean hourly, pressure corrected, data from neutron monitors of the global network (monthly rate is calculated as the average of the hourly pressure corrected values). We draw attention to an asymmetry in the galactic cosmic ray (GCR) recovery during odd and even cycles for the monthly mean hourly rate data. For over half a century of observations, we find that the recovery for the odd cycles is to a higher level than for the even cycles. Qualitatively the effect is ascribed to charged particle drifts in inhomogeneous interplanetary magnetic field. Even so it has not been possible to arrive at a quantitative, self-consistent, explanation in terms of drifts at higher and lower GCR rigidities. We also study the rigidity dependence of the amplitude of 11-year modulation over a wide range (1–200 GV) of GCR spectrum; it is a power law in rigidity with an exponent −1.22. We discuss the implication of these findings on quasi-linear diffusion theories of modulation. We reflect on GCR recovery pattern for 2006–2009.

The ground level event 70 on December 13th, 2006 and related effective doses at aviation altitudes

The 70th ground level event in the records of the Neutron Monitor network occurred on 13 December 2006 reaching a maximum count rate increase at the Oulu station of more than 90 % during the 5 min interval 3.05-3.10 UTC. Thereafter, count rates gradually decreased registering increases of a few per cent above the galactic cosmic ray background after a few hours. The primary proton spectrum during the first 6 h after the onset of the event is characterised in this work by fitting the energy and angular distribution by a power law in rigidity and a linear dependence in the pitch angle using a minimisation technique. The results were obtained by analysing the data from 28 Neutron Monitor stations. At very high northern and southern latitudes, the effective dose rates were estimated to reach values of 25-30 microSv h(-1) at atmospheric depth of 200 g cm(-2) during the maximum of the event. The increase in effective dose during north atlantic and polar flights was estimated to be in the order of 20 %.

Temporal and spatial evolution of the solar energetic particle event on 20 January 2005 and resulting radiation doses in aviation

The solar energetic particle event on 20 January 2005 was one of the largest ground level events ever observed. Neutron monitor stations in the Antarctic recorded count rate increases of several thousand percent caused by secondary energetic particles, and it took more than 36 h to return to background level. Such huge increases in high energetic solar cosmic radiation on the ground are obviously accompanied by considerable changes in the radiation environment at aviation altitudes. Measurements of 28 neutron monitor stations were used in this work to numerically approximate the primary solar proton spectra during the first 12 h of the event by minimizing the differences between measurements and the results of Monte‐Carlo calculated count rate increases. The primary spectrum of solar energetic protons was approximated by a power law in rigidity and a linear angular distribution. The incoming direction of the solar energetic particles was determined and compared to the interplanetary magnetic field direction during the event. The effects on the radiation exposure at altitudes of about 12 km during that time were estimated to range from none at low latitudes up to almost 2 mSv/h for a very short time in the Antarctic region and about 0.1 mSv/h at high latitudes on the Northern Hemisphere. After 12 h, dose rates were still increased by 50% at latitudes above 60° whereas no increases at all occurred at latitudes below 40° during the whole event.

Two intense Forbush decreases of solar activity cycle 22

We study two intense Forbush decreases that occurred during two adjacent SOLTIP (Solar connection of Transient Interplanetary Processes) intervals; namely SOLTIP 1 (22–27 March 1991) and SOLTIP 2 (1–17 June 1991); galactic cosmic ray intensity at the depth of the second Forbush decrease was the lowest ever recorded since continuous monitoring by Climax neutron monitor began in 1951 (58% below the solar minimum value of 1954), indicating extreme conditions in the heliosphere that prevented galactic cosmic rays from reaching the Earth. These decreases were seen propagating in outer heliosphere by the deep space missions Voyagers 1, 2 and Pioneer 10, 11, with suitable time delays. We analyze hourly, pressure corrected, neutron monitor data from the global sites in both hemispheres, and muon telescopes located underground; they respond to 10–300 GV range of the galactic cosmic ray spectrum. This circumstance provides us an ideal opportunity to study the rigidity dependence of the amplitudes of the two Forbush decreases. In both cases the amplitude is found to be a power law in rigidity, with negative exponents.

Heavy ion abundances and spectra from the large solar energetic particle events of October–November 2003

Observations from the Solar Isotope Spectrometer and the Ultra Low Energy Isotope Spectrometer on the ACE spacecraft during the extremely large events of October and November 2003 are combined to create heavy ion spectra over more than 3 decades in energy. The resulting spectra differed substantially in shape from event to event, as well as from element to element within a given event, resulting in energy‐dependent abundance ratios. Although the effects of strong local shock acceleration are apparent in the intensities of the 28 and 29 October events, these do not explain the order of magnitude differences between the event‐integrated abundances obtained at 0.64–0.91 MeV/nucleon and those at 12–60 MeV/nucleon. The higher‐energy abundances relative to the lower‐energy ones show trends with nuclear charge or charge‐to‐mass ratio that are similar for all the events and suggest that heavier ions are less efficiently accelerated to high energies. The position of the breaks in the energy spectra of O, Ne, Mg, Si, S, Ca, and Fe can be understood in terms of leakage from the shock region, if the mean free path is assumed to be a power law in rigidity. The resulting rigidity dependence is consistent with a source of wave turbulence in the vicinity of the shock when the ions are accelerated.

New results on source and diffusion spectral features of Galactic cosmic rays: I $\vec{B/C}$ ratio

In a previous study (Maurin et al., 2001), we explored the set of parameters describing diffusive propagation of cosmic rays (galactic convection, reacceleration, halo thickness, spectral index and normalization of the diffusion coefficient), and we identified those giving a good fit to the measured B/C ratio. This study is now extended to take into account a sixth free parameter, namely the spectral index of sources. We use an updated version of our code where the reacceleration term comes from standard minimal reacceleration models. The goal of this paper is to present a general view of the evolution of the goodness of fit to B/C data with the propagation parameters. In particular, we find that, unlike the well accepted picture, and in accordance with our previous study, a Kolmogorov-like power spectrum for diffusion is strongly disfavored. Rather, the $\chi^2$ analysis points towards $\delta\gtrsim 0.7$ along with source spectra index $\lesssim 2.0$. Two distinct energy dependences are used for the source spectra: the usual power-law in rigidity and a law modified at low energy, the second choice being only slightly preferred. We also show that the results are not much affected by a different choice for the diffusion scheme. Finally, we compare our findings to recent works, using other propagation models. This study will be further refined in a companion paper, focusing on the fluxes of cosmic ray nuclei.

The Absolute Flux of Protons and Helium at the Top of the Atmosphere Using IMAX

The cosmic-ray proton and helium spectra from 0.2 GeV nucleon^(-1) to about 200 GeV nucleon^(-1) have been measured with the balloon-borne experiment Isotope Matter-Antimatter Experiment (IMAX) launched from Lynn Lake, Manitoba, Canada, in 1992. IMAX was designed to search for antiprotons and light isotopes using a superconducting magnet spectrometer together with scintillators, a time-of-flight system, and Cherenkov detectors. Using redundant detectors, an extensive examination of the instrument efficiency was carried out. We present here the absolute spectra of protons and helium corrected to the top of the atmosphere and to interstellar space. If demodulated with a solar modulation parameter of Φ = 750 MV, the measured interstellar spectra between 20 and 200 GV can be represented by a power law in rigidity, with (1.42 ± 0.21) × 10^4R^(-2.71±0.04) (m^2 GV s sr)^(-1) for protons and (3.15 ± 1.03) × 10^3R^(-2.79±0.08) (m^2 GV s sr)^(-1) for helium.

Propagation of galactic cosmic rays under diffusive reacceleration

view Abstract Citations (62) References (43) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Propagation of Galactic Cosmic Rays under Diffusive Reacceleration Heinbach, U. ; Simon, M. Abstract The propagation of cosmic rays in the galaxy is understood as a diffusive process where the magnetic field irregularities serve as scattering center. In this paper we pursue the idea that particles which interact with turbulent magnetic fields should naturally also gain energy due to a stochastic second-order Fermi type of acceleration. This link between diffusion and reacceleration is based on general physical principles, and we can show that the cosmic-ray data can be explained in this 'Diffusive Reacceleration Model.' As a consequence, the escape length lambdaesc(E), which defines the particles path in the galaxy, becomes a power-law in rigidity with an exponent of -1/3, which would indicate a Kolmogorov-type spectrum of magnetic turbulences. The increase of lambdaesc(E) combined with the increase of the amount of reacceleration to low energies in then interpreted as a decrease of the diffusion coefficient or an increase of the frequencies of scattering center. Publication: The Astrophysical Journal Pub Date: March 1995 DOI: 10.1086/175350 Bibcode: 1995ApJ...441..209H Keywords: Astronomical Models; Cosmic Rays; Diffusion; Particle Acceleration; Turbulence; Kolmogorov Theory; Magnetohydrodynamics; Mathematical Models; Radiative Transfer; Stochastic Processes; Transport Theory; Astrophysics; ACCELERATION OF PARTICLES; DIFFUSION; ISM: COSMIC RAYS; MAGNETOHYDRODYNAMICS: MHD; TURBULENCE full text sources ADS |

Measurement of the cosmic ray proton and helium fluxes from 200 MeV nucl−1 to 100 GeV nucl−1 during the 1987 solar minimum

Abstract The galactic cosmic ray proton and helium spectra have been measured with a balloon-borne superconducting magnetic spectrometer over the energy range from 200 MeV nucl−1 to 100 GeV nucl−1 during the 1987 solar minimum between the 21st and 22nd solar cycle. The absolute fluxes were approximately equal to the highest fluxes observed at the previous solar minimum in 1977. Above 10 GV the observed spectra are represented by a power law in rigidity with spectral indices of 2.74± 0.02 for protons and 2.68 ± 0.03 for helium. The data are consistent with rigidity power law interstellar spectra modulated with the solar modulation parameter φ = 500 MV.

Measurement of cosmic-ray proton and helium spectra during the 1987 solar minimum

The differential cosmic-ray proton and helium spectra have been measured during the 1987 solar minimum using a balloon-borne superconducting magnetic spectrometer launched from Prince Albert, Canada. The changing geomagnetic cutoff along the balloon trajectory was observed in the low-energy proton data to be about 25 percent below the nominal calculated values. The absolute particle fluxes were approximately equal to the highest fluxes observed at the previous solar minimum in 1977. Above 10 GV the observed spectra are represented by a power law in rigidity with spectral indices of 2.74 + or - 0.02 for protons and 2.68 + or - 0.03 for helium. The measurements above 200 MeV per nucleon are consistent with rigidity power-law interstellar spectra modulated with the solar modulation parameter phi = 500 MV. The energy dependence of the proton-to-helium ratio is consistent with rigidity power-law injection spectra and rigidity-dependent propagation without reacceleration.

Characteristics of energetic solar flare electron spectra

A 55 event survey of energy spectra of 0.1-100 MeV interplanetary electrons originating from solar flares as measured by two spectrometers onboard the ISEE 3 (ICE) spacecraft for the years 1978-1982 has been completed. Spectra generated using the maximum flux of a given event in each energy channel were restricted to events with a well-defined flux rise time. Two broad groups of electron spectra are considered. In one group, the spectra are well represented by a single power law in rigidity with spectral index in the range 3-4.5. The spectra in the other group deviate from a power law in rigidity systematically in that they harden with increasing rigidity. Events with near power-law spectra are found to be correlated with long-duration soft X-ray events, whereas those with hardening spectra are correlated with short-duration events. The possible variation of acceleration and propagation processes with the properties of the flare site is discussed, using the duration of the soft X-ray flare emission as an indicator of the physical parameters of the flare site (flare volume, density, coronal height, and magnetic field geometry).

Electron Acceleration in Solar Flares

AbstractFor the period September 1978 to December 1982 we have identified 55 solar flare particle events for which our instruments on board the ISEE-3 (ICE) spacecraft detected electrons above 10 MeV. Combining our data with those from the ULEWAT spectrometer (MPI Garching and University of Maryland) electron spectra in the range from 0.1 to 100 MeV were obtained. The observed spectral shapes can be divided into two classes. The spectra of the one class can be fit by a single power law in rigidity over the entire observed range. The spectra of the other class deviate from a power law, instead exhibiting a steepening at low rigidities and a flattening at high rigidities. Events with power-law spectra are associated with impulsive (< 1 hr duration) soft X-ray emission, whereas events with hardening spectra are associated with long-duration (> 1 hr) soft X-ray emission. The characteristics of long-duration events are consistent with diffusive shock acceleration taking place high in the corona. Electron spectra of short-duration flares are well reproduced by the distribution functions derived from a model assuming simultaneous second-order Fermi acceleration and Coulomb losses operating in closed flare loops.

The isotopic composition of helium in the cosmic radiation above 11 gigavolts

The He-3/He-4 abundance ratio above 11 GV has been measured with a balloon-borne experiment that employs the geomagnetic method of isotope separation near earth's equator. Above a kinetic energy of approximately 6 GeV per nucleon, the He-3/He-4 ratio is measured to be 0.24 + or - 0.05 under the assumption that the helium spectrum at earth is a power law in rigidity of the form R to the -2.65th. The implied interstellar mean escape pathlength of about 15 g per sq cm, with this assumption, is considerably greater than values determined from observations of heavier elements. Propagation models more complex than the standard simple leaky box would be required to simultaneously understand the propagation of both the lighter and heavier components of cosmic rays.

A cosmic ray density gradient perpendicular to the ecliptic plane

The B × ▽n streaming due to a cosmic ray density gradient perpendicular to the ecliptic plane introduces a component into the diurnal variation that depends on the sense and direction of the interplanetary magnetic field (ipmf). We have made a detailed study of this effect in the diurnal variation data for 1967 and 1968 from a variety of cosmic ray monitors. The results are consistent with a north-south gradient anisotropy expressed by a power law in rigidity, δI I = 2.8 × 10 −4 R 0.4 to an upper limiting rigidity of ≈ 100 GV. These results imply an effective north-south gradient of ≈ 1.3 per cent/A.U. for a high latitude neutron monitor. A cursory analysis of the effect in 1965–1966 indicates an even smaller north-south gradient for these years. These results are compared with estimates of the gradient from annual wave measurements.