The local interstellar spectra (LISs) for galactic cosmic rays (CRs) cannot be directly observed at the Earth below certain energies, because of solar modulation in the heliosphere. With Voyager 1 ...crossing the heliopause in 2012, in situ experimental LIS data below 100 MeV/nuc can now constrain computed galactic CR spectra. Using galactic propagation models, galactic electron, proton, and light nuclei spectra can now be computed more reliably as LISs. Using the Voyager 1 observations made beyond the heliopause, and the observations made by the PAMELA experiment in Earth orbit for the 2009 solar minimum, as experimental constraints, we simultaneously reproduced the CR electron, proton, helium, and carbon observations by implementing the GALPROP code. Below about 30 GeV/nuc solar modulation has a significant effect and a comprehensive three-dimensional (3D) numerical modulation model is used to compare the computed spectra with the observed PAMELA spectra at these energies. Subsequently the computed LISs can be compared over as wide a range of energies as possible. The simultaneous calculation of CR spectra with a single propagation model allows the LISs for positrons, boron, and oxygen to also be inferred. This implementation of the comprehensive galactic propagation model (GALPROP), alongside a sophisticated solar modulation model to compute CR spectra for comparison with both Voyager 1 and PAMELA observations over a wide energy range, allows us to present new self-consistent LISs (and expressions) for electrons, positrons, protons, helium, carbon, boron, and oxygen for the energy range of 3 MeV/nuc-100 GeV/nuc.
Heliospheric modulation conditions were unusually quiet during the last solar minimum activity between solar cycles 23 and 24. Fortunately, the PAMELA space experiment measured 6 month-averaged ...Galactic positron spectra for the period 2006 July to 2009 December over an energy range of 80 MeV to 30 GeV, which is important for solar modulation. The highest level of Galactic positrons was observed at Earth during the 2009 July-December period. A well-established, comprehensive three-dimensional (3D) numerical model is applied to study the modulation of the observed positron spectra. This model had been used previously to understand the modulation of Galactic protons and electrons also measured by PAMELA for the same period. First, a new, very local interstellar spectrum for positrons is constructed using the well-known GALPROP code, together with the mentioned PAMELA observations. The 3D model is used to distinguish between the dominant mechanisms responsible for the heliospheric modulation of Galactic positrons and understand the effect of particle drift during this unusual minimum in particular, which is considered diffusion-dominant, even though particle drift still had a significant role in modulating positrons. Lastly, the expected intensity of Galactic positrons during an A > 0 polarity minimum, with similar heliospheric conditions than for 2006-2009, is predicted to be higher than what was observed by PAMELA for the 2006-2009 unusual minimum.
With the cosmic ray observations made by the Voyager 1 spacecraft outside the dominant modulating influence of the heliosphere, the comparison of computed galactic spectra with experimental data at ...lower energies is finally possible. Spectra for specifically protons, helium and carbon nuclei, computed by galactic propagation models, can now be compared with observations at low energies from Voyager 1 and at high energies from the PAMELA space detector at Earth. We set out to reproduce the Voyager 1 observations in the energy range of 6 MeV/nuc to 60 MeV/nuc, and the PAMELA spectrum above 50 GeV/nuc, using the GALPROP code, similarly to our previous study for Voyager 1 electrons. By varying the galactic diffusion parameters in the GALPROP plain diffusion model, specifically the rigidity dependence of spatial diffusion, and then including reacceleration, we compute spectra simultaneously for galactic protons, helium and carbon. We present new local interstellar spectra, with expressions for the energy range of 3 MeV/nuc to 100 GeV/nuc, which should be of value for solar modulation modeling.
Cosmic-ray observations made by the Voyager 1 spacecraft outside the dominant modulating influence of the heliosphere finally allow the comparison of computed galactic spectra with experimental data ...at lower energies. These computed spectra, based on galactic propagation models, can now be compared with observations at low energies by Voyager 1 and at high energies by the PAMELA space detector at Earth. This improves understanding of basic propagation effects and also provides solar modulation studies with reliable input spectra from 1 MeV to 100 GeV. We set out to reproduce the Voyager 1 electron observations in the energy range of 6-60MeV, as well as the PAMELA electron spectrum above 10 GeV, using the GALPROP code. By varying the source spectrum and galactic diffusion parameters, specifically the rigidity dependence of spatial diffusion, we find local interstellar spectra that agree with both power-law spectra observed by Voyager 1 beyond the heliopause. The local interstellar spectrum between ~1 MeV and 100 GeV indicates that it is the combination of two power laws, with E super(-(1.45+ or -0.15)) below ~100 MeV and E super(-(3.15+ or -0.05)) above ~100MeV. A gradual turn in the spectral shape matching the power laws is found, between 2.0 + or - 0.5) GeV and (100 + or - 10) MeV. According to our simplified modeling, this transition is caused primarily by galactic propagation effects. We find that the intensity beyond the heliopause at 10MeV is (350 + or - 50) electrons m super(-2) s super(-1) sr super(-1) MeV super(-1), decreasing to (50 + or - 5) electrons m super(-2) s super(-1) sr super(-1) MeV super(-1) at 100 MeV.
Abstract
Simultaneous and continuous observations of galactic cosmic-ray electrons (
e
−
) and positrons (
e
+
) from the PAMELA and AMS02 space experiments are most suitable for numerical modeling ...studies of the heliospheric modulation of these particles below 50 GeV. A well-established comprehensive three-dimensional modulation model is applied to compute full spectra for
e
−
and
e
+
with the purpose of reproducing the observed ratio
e
+
/
e
−
for a period that covers the previous long and unusual deep solar minimum activity and the recent maximum activity phase, including the polarity reversal of the solar magnetic field. For this purpose, the very local interstellar spectra for these particles were established first. Our study is focused on how the main modulation processes, including particle drifts, and other parameters, such as the three major diffusion coefficients, evolved and how the corresponding charge-sign dependent modulation subsequently occurred. The end result of our effort is the detailed reproduction of
e
+
/
e
−
from 2006 to 2015, displaying both qualitative and quantitative agreement with the main observed features. Particularly, we determine how much particle drift is needed to explain the time dependence exhibited by the observed
e
+
/
e
−
during each solar activity phase, especially during the polarity reversal phase, when no well-defined magnetic polarity was found.
The global features of the modulation of galactic cosmic ray protons and helium nuclei in a very quiet heliosphere are studied with a comprehensive, three-dimensional, drift model and compared to ...proton and helium observations measured by PAMELA from 2006 to 2009. Combined with accurate very local interstellar spectra (VLIS) for protons and helium nuclei, this provides the opportunity to study in detail how differently cosmic ray species with dissimilar mass-to-charge ratio (
A
/
Z
) are modulated down to a few GV. The effects at Earth of the difference in their VLIS’s and those caused by the main modulation mechanisms are illustrated. We find that both the PAMELA proton and helium spectra are reproduced well with the numerical model, assuming the same set of modulation parameters and diffusion coefficients. A comparative study of
3
He
2
(He-3) and
4
He
2
(He-4) modulated spectra reveals that they do not undergo identical spectral changes below 3 GV mainly due to differences in their VLIS’s. This result is important to uncover and investigate the effects on the proton to total helium ratio (
p
/He) caused by the difference in their VLIS’s and those by
A
/
Z
. The computed
p
/He displays three modulation regimes, reflecting the complex interplay of modulation processes in the heliosphere. At rigidities above ∼3 GV, the
p
/He ratio at the Earth is found to deviate modestly from a value of ∼5.5, largely independent of the assumed modulation conditions. This result indicates that the PAMELA measurement of
p
/He reveals at these rigidities the shapes of their VLIS’s. Below ∼0.6 GV,
p
/He increases with decreasing rigidity from 2006 to 2009 and significant variations are predicted depending on the assumed solar modulation conditions. This result indicates that as modulation levels decreased from 2006 to 2009, the contribution of adiabatic energy changes dissipated faster for protons than for helium nuclei at the same rigidity mainly due to different slopes of their VLIS’s. The differences between modulation effects for protons and helium are found to be the consequence of how the combined interplaying modulation mechanisms in the heliosphere affect the modulated spectra based on their
A
/
Z
and particularly on their VLIS’s.
Precise time-dependent measurements of the Z = 2 component in the cosmic radiation provide crucial information about the propagation of charged particles through the heliosphere. The PAMELA ...experiment, with its long flight duration (2006 June 15-2016 January 23) and the low energy threshold (80 MeV/n) is an ideal detector for cosmic-ray solar modulation studies. In this paper, the helium nuclei spectra measured by the PAMELA instrument from 2006 July to 2009 December over a Carrington rotation time basis are presented. A state-of-the-art three-dimensional model for cosmic-ray propagation inside the heliosphere was used to interpret the time-dependent measured fluxes. Proton-to-helium flux ratio time profiles at various rigidities are also presented in order to study any features that could result from the different masses and local interstellar spectra shapes.
Abstract
Time-dependent energy spectra of galactic cosmic rays (GCRs) carry fundamental information regarding their origin and propagation. When observed at the Earth, these spectra are significantly ...affected by the solar wind and the embedded solar magnetic field that permeates the heliosphere, changing significantly over an 11 yr solar cycle. Energy spectra of GCRs measured during different epochs of solar activity provide crucial information for a thorough understanding of solar and heliospheric phenomena. The PAMELA experiment collected data for almost 10 years (2006 June 15–2016 January 23), including the minimum phase of solar cycle 23 and the maximum phase of solar cycle 24. In this paper, we present new spectra for helium nuclei measured by the PAMELA instrument from 2010 January to 2014 September over a three-Carrington-rotation time basis. These data are compared to the PAMELA spectra measured during the previous solar minimum, providing a picture of the time dependence of the helium-nuclei fluxes over a nearly full solar cycle. Time and rigidity dependencies are observed in the proton-to-helium flux ratios. The force-field approximation of the solar modulation was used to relate these dependencies to the shapes of the local interstellar proton and helium-nuclei spectra.
Very local interstellar spectra (vLIS’s) for protons and total Helium (He) were observed in situ by Voyager 1 below about 340 MeV/
since it had moved across the heliopause (HP). Together with high ...precision PAMELA and AMS observations at the Earth, we previously reported on new vLIS calculated from 1 MeV to 100 GeV for protons, electrons, total He, Oxygen, Carbon, and Boron. We now follow this up to report on the vLIS’s for positrons and for the isotopes He-3, He-4, and Deuteron (H-2) by combining computations with the galactic propagation code, GALPROP, and our 3D modulation model for GCRs in the heliosphere as done previously. Similarly, we also have computed updates of the vLIS’s for antiprotons and antideuteron. We assume that the modulation processes between the HP and the Earth for protons and other GCR nuclei are essentially similar, which is also the case for electrons and positrons, except for particle drifts of oppositely charged particles. The procedures followed to obtain these updates are summarized and a compilation of the mentioned vLIS’s is presented.
Precision measurements of the Z = 2 component in cosmic radiation provide crucial information about the origin and propagation of the second most abundant cosmic ray species in the Galaxy (9% of the ...total). These measurements, acquired with the PAMELA space experiment orbiting Earth, allow to study solar modulation in details. Helium modulation is compared to the modulation of protons to study possible dependencies on charge and mass. The time dependence of helium fluxes on a monthly basis measured by PAMELA has been studied for the period between July 2006 to January 2016 in the energy range from 800
MeV/n
to ~ 20
GeV/n
.
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