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Effects of different solar wind speed profiles in the heliosheath on the modulation of cosmic ray and anomalous protons
Abstract
A previously used model for the heliospheric modulation of cosmic rays including a solar wind termination shock (TS) is extended to include an asymmetrically shaped outer modulation boundary, with respect to the Sun. The model includes particle drifts, adiabatic energy changes, diffusion, convection, and a heliosheath. It is used to study the effects on the modulation of protons and anomalous protons for different scenarios of the solar wind speed (V) in the heliosheath, in accordance with the predictions of a three-dimensional timedependent hydrodynamic model of the heliosphere. This model provides the different scenarios for V in the heliosheath. Significant changes occur for mostly the A < 0 polarity cycle at all radial distances in the equatorial plane when the V-profile is changed from an assumed incompressible fluid in the heliosheath, with V ∞ 1/r2, to V ∞ 1/r8 . The TS is predicted markedly more effective in the heliospheric nose region than in the tail region for the A < 0 polarity cycle. The different scenarios for V in the heliosheath do not have a substantial effect on the intensities in the A > 0 cycle inside the TS. In the heliosheath region, however, the difference can be quite significant, especially at lower energies.
... [24] The results in this paper on O* and companion papers on He* [McDonald et al., 2006] and H* [Webber et al., 2006], which show that the transition between solar magnetic polarities produces complex changes in the intensities and the spectra as well as interesting temporal effects, have not been described in enough detail in the present models for us to make a detailed comparison of this new data with models. More advanced models have been developed for the acceleration of H* nuclei in opposite polarity periods [Florinski et al., 2004; Langner et al., 2006], as well as He* nuclei [Langner and Potgieter, 2004; CaballeroLopez et al., 2005]. These models generally give spectra between 5 –50 MeV, with exponents in the range of À1.2 to À1.5 for the positive polarity periods corresponding to compression ratios $3, and flatter spectra in the negative polarity periods, with correspondingly higher intensities as we observe for O* [e.g., Florinski et al., 2004]. ...
We have studied the temporal and spectral variations of anomalous oxygen nuclei at the Voyager 1 (V1) and 2 (V2) spacecraft in the outer heliosphere from 1990 to the present time in 2006 when V1 is now beyond the heliospheric termination shock. During this time period, the intensities increased from their lowest values in 1990-1991 up to a maximum in 1998-1999 and then decreased rapidly in 2000-2001 in time coincidence with the change in solar magnetic polarity from positive to negative. During the time period after 2001, significant changes in intensities and spectra are observed relative to the earlier period of positive solar magnetic polarity before 2001. It is found that the intensities of O above ~10 MeV/nuc at V1 after ~2002.0 were higher relative to the same galactic cosmic ray He intensity between 150-380 MeV/nuc than in the earlier time period. As a result, by 2006 these intensities were a factor ~3 times those measured at the intensity maximum in 1998-1999 in the previous polarity cycle. The changes observed at V2 followed a similar pattern, but the relative intensity changes of O were a factor ~2 times greater than those observed at V1. Also, above ~10 MeV/nuc, the intensity changes at V1 and V2 were nearly energy independent, and the spectra at all times before and after the solar magnetic polarity change and at all modulation levels remained ~E -3.0+/- 0.2, possibly characteristic of a ``source'' spectrum. When V1 crossed the termination shock, no noticeable spectral or intensity changes were observed.
... In this section we include the effects of momentum diffusion (Fermi II acceleration) into the modulation model in addition to Fermi I acceleration taking place at the TS. Also, adiabatic heating (e.g. Langner et al., 2006), occuring in the heliosheath, is included through our choice of a V sw profile having · V sw < 0. Lastly, we also include a latitude dependent s(θ) and I(θ) as discussed by e.g. Scherer et al. (2006) and Ngobeni and Potgieter (2008). ...
After the solar wind termination shock crossings of the Voyager spacecraft, the acceleration of anomalous cosmic rays has become a very contentious subject. In this paper we examine several topics pertinent to anomalous cosmic ray oxygen acceleration and transport using a numerical cosmic ray modulation model. These include the effects of drifts on a purely Fermi I accelerated spectra, the effects of introducing higher charge states of oxygen into the modulation model, examining the viability of momentum diffusion as a re-acceleration process in the heliosheath and examining energy spectra, and intensity gradients, in the inner heliosphere during consecutive drift cycles.
... If ( · V) > 0, adiabatic energy losses are described, which become quite large in the inner heliosphere (see the comprehensive review by Fisk, 1979). If ( · V) < 0, energy gains are described, which may be the case for ACRs in the heliosheath (illustrated, e.g., by Langner et al., 2006b; Strauss et al., 2010b). If ( · V) = 0, no adiabatic energy changes occur for CRs, perhaps the case beyond the TS. ...
This is an overview of the solar modulation of cosmic rays in the
heliosphere. It is a broad topic with numerous intriguing aspects so that a
research framework has to be chosen to concentrate on. The review focuses on
the basic paradigms and departure points without presenting advanced
theoretical or observational details for which there exists a large number of
comprehensive reviews. Instead, emphasis is placed on numerical modeling which
has played an increasingly signi?cant role as computational resources have
become more abundant. A main theme is the progress that has been made over the
years. The emphasis is on the global features of CR modulation and on the
causes of the observed 11-year and 22-year cycles and charge-sign dependent
modulation. Illustrative examples of some of the theoretical and observational
milestones are presented, without attempting to review all details or every
contribution made in this ?eld of research. Controversial aspects are discussed
where appro- priate, with accompanying challenges and future prospects. The
year 2012 was the centennial celebration of the discovery of cosmic rays so
that several general reviews were dedicated to historical aspects so that such
developments are brie y presented only in a few cases.
... The HMF thus increases by a factor s at the TS. Beyond the TS, V decreases further as 1/r 2 to the outer boundary which implies that no additional adiabatic energy changes occur beyond the TS for GCRs, which according toLangner et al. (2006)seems to be an oversimplification but only for anomalous cosmic rays. The acceleration mechanism of anomalous cosmic rays beyond the TS has become controversial; see e.g., Fisk and Gloeckler (2009). ...
Observations made with the two Voyager spacecraft confirmed that the solar wind decelerates to form the heliospheric termination shock and that it has begun its merger with the local interstellar medium. The compression ratio of this shock affects galactic cosmic rays when they enter the heliosphere. Hydrodynamic (HD) models show that the compression ratio can have a significant latitude dependence; with the largest value in the nose direction of the heliosphere, becoming significantly less towards the polar regions. The modulation effects of such large latitude dependence are studied, using a well-established numerical drift and shock modulation model. We focus on computing the modulated spectra for galactic protons with emphasis on the radial and polar gradients in the equatorial plane and at a polar angle of θ = 55°, corresponding to the heliolatitude of Voyager 1. Two sets of solutions are computed and compared each time; with and without a latitude dependence for the compression ratio. All computations are done for the two magnetic field polarity cycles assuming solar minimum conditions. Including the termination shock in the model allows the study of the re-acceleration of galactic protons in the outer heliosphere. We find that for the A < 0 polarity cycle the intensity between ∼200 MeV and ∼1 GeV in the vicinity of the shock in the heliospheric equatorial plane may exceed the local interstellar value specified at the heliopause. Unfortunately, at θ = 55°, the effect is reduced. This seems not possible during an A > 0 cycle because significant modulation is then predicted between the heliopause and the termination shock, depending on how strong global gradient and curvature drifts are in the heliosheath. The overall effect of the shock on galactic protons in the equatorial plane is to reduce the total modulation as a function of radial distance with respect to the interstellar spectrum. Making the compression ratio latitude dependent enhances these effects at energies E < 200 MeV in the equatorial plane. At larger heliolatitudes these effects are even more significant. The differences in the modulation between the two drift cycles are compelling when the compression ratio is made latitude dependent but at Earth this effect is insignificant. A general result is that the computed radial gradient changes for galactic protons at and close to the TS and that these changes are polarity dependent. In line with previous work, large polarity dependent effects are predicted for the inner heliosphere and also close to the shock’s position in the equatorial plane. In contrast, at θ = 55°, the largest polarity effect occurs in the middle heliosphere (50 AU), enhanced by the latitude dependence of the compression ratio. At this latitude, the amount of proton modulation between the heliopause and the termination shock is much reduced. If galactic cosmic rays were to experience some diffusive shock acceleration over the 100–1000 MeV range at the shock, the radial gradient should change its sign in the vicinity of the shock, how large, depends on the compression ratio and the amount of drifts taking place in the outer heliosphere. The effective polar gradient shows a strong polarity dependence at Earth but this dissipates at θ = 55°, especially with increasing radial distance. This tendency is enhanced by making the compression ratio latitude dependent.
We present calculations of the propagation times and energy losses of
cosmic rays as they are transported through the heliosphere. By
calculating these quantities for a spatially 1D scenario, we benchmark
our numerical model, which uses stochastic differential equations to
solve the relevant transport equation, with known analytical solutions.
The comparison is successful and serves as a vindication of the modeling
approach. A spatially 3D version of the modulation model is subsequently
used to calculate the propagation times and energy losses of galactic
electrons and protons in different drift cycles. We find that the
propagation times of electrons are longer than those of the protons at
the same energy. Furthermore, the propagation times are longer in the
drift cycle when the particles reach the Earth by drifting inward along
the heliospheric current sheet. The calculated energy losses follow this
same general trend. The energy losses suffered by the electrons are
comparable to those of the protons, which is in contrast to the
generally held perception that electrons experience little energy losses
during their propagation through the heliosphere.
In recent years the variability of the cosmic ray flux has become one of the main issues not only for the interpretation of the abundances of cosmogenic isotopes in cosmochronic archives like, e.g., ice cores, but also for its potential impact on the terrestrial climate. It has been re-emphasized that the cosmic ray flux is not only varying due to the solar activity-induced changes of the solar wind but also in response to the changing state of the interstellar medium surrounding the heliosphere. We demonstrate the significance of these external boundary condition changes along the galactic orbit of the Sun for the flux as well as spectra of cosmic rays. Such interstellar–terrestrial relations are a major topic of the International Heliophysical Year 2007.
Cosmic ray drift directions depend both on the charge of the particle population under consideration, as well as the heliospheric magnetic field polarity which oscillates within a ˜22 year cycle. The differences in the cosmic ray drift patterns between successive solar cycles manifest themselves in the sign of the latitudinal cosmic ray gradient. For positively charged particles, a positive latitudinal gradient is expected in the qA > 0 polarity cycle, while a negative value is expected in the qA < 0 cycle. For the first time observed radial and latitudinal values for anomalous cosmic ray oxygen are available in both of these cycles. In the present qA 0 cycle, the model predicts a positive latitudinal gradient but for the qA < 0 cycle a latitudinal gradient that is smaller and that can be either positive or negative. It is concluded that drifts and poleward diffusion set up competing latitudinal gradients in the qA < 0 cycle, with the resulting sign of the gradient determined by the most effective of the two processes.
Cosmic ray research began in 1912 when Victor Hess measured the intensity of the then unknown ionizing radiation with an electroscope
in a balloon up to an altitude of about 5,000 m. He discovered that this very penetrating radiation, later called cosmic rays,
was coming from outside the atmosphere (for a historic review, see Simpson, 2001).The systematic experimental study of cosmic
rays began in the 1930s, using ground-based and balloon-borne ionization chambers. In the 1950s it expanded on a much larger
scale with neutron monitors, coordinated world-wide during the International Geophysical Year (IGY) in 1957 (Simpson, 2000).
When Parker (1958) described the solar wind, the theoretical research of cosmic rays began, stimulated by the beginning of
in situ space observations that have led over four decades to important space missions, including the Ulysses mission to high heliolatitudes.
The observation of the directional distribution of energetic and cosmic ray particles has been done with the Voyager spacecraft over a long period. Since 2002, when the first flux enhancements of charged particles associated with the approach of Voyager 1 to the solar wind termination shock were observed, these anisotropy measurements have become of special interest. They play an important role to understand the magnetic field and shock structure and the basics of the modulation of cosmic ray and anomalous particles at and beyond the termination shock. They also serve as motivation to study the spatial behavior of galactic and anomalous cosmic ray anisotropies with numerical modulation models in order to illustrate how the radial anisotropy, at different energies, change from upstream to downstream of the termination shock. Observations made by Voyager 1 indicate that the termination shock is a complicated region than previously thought, hence the effects of the latitude dependence of the termination shock’s compression ratio and injection efficiency on the radial anisotropies of galactic and anomalous protons will be illustrated. We find that the magnitude and direction of the radial anisotropy strongly depends on the position in the heliosphere and the energy of particles. The effect of the TS on the radial anisotropy is to abruptly increase its value in the heliosheath especially in the A > 0 cycle for galactic protons and in both polarity cycles for anomalous protons. Furthermore, the global effect of the latitude dependence of the shock’s compression ratio is to increase the radial anisotropy for galactic protons throughout the heliosphere, while when combined with the latitude dependence of the injection efficiency this increase depends on modulation factors for anomalous protons and can even alter the direction of the radial anisotropy.
A numerical model, based on Parker’s transport equation, describing the modulation of anomalous cosmic rays and containing diffusive shock acceleration is applied. The role of radial perpendicular diffusion at the solar wind termination shock, and as the dominant diffusion coefficient in the outer heliosphere, is studied, in particular the role it plays in the effectiveness of the acceleration of anomalous protons and helium when its latitude dependence is changed. It is found that the latitudinal enhancement of radial perpendicular diffusion towards the heliospheric poles and along the termination shock has a prominent effect on the acceleration of these particles. It results in a ‘break’ in the energy spectrum for anomalous protons at ∼6.0 MeV, causing the spectral index to change from E−1.38 to E−2.23, but for anomalous helium at ∼3.0 MeV, changing the spectral index from E−1.38 to E−2.30. When approaching the simulated TS, the changes in the modulated spectra as they unfold to a ‘steady’ power law shape at energies below 50 MeV are much less prominent as a function of radial distances when radial perpendicular diffusion is increased with heliolatitude.
The interaction of the solar wind with the local interstellar medium (LISM) is attracting renewed interest, thanks to the
possibility that the Voyager spacecraft may, in the not too distant future, cross the heliospheric termination shock. This
has spurred the development of increasingly sophisticated models which attempt to describe various aspects of the physics
underlying the interaction of the solar wind and the LISM. A comprehensive review of the subject is presented here.
The interest in the role of the solar wind termination shock and heliosheath in cosmic ray modulation studies has increased significantly as the Voyager 1 and 2 spacecraft approach the estimated position of the solar wind termination shock. The effect of the solar wind termination shock on charge-sign dependent modulation, as is experienced by galactic cosmic ray Helium (He++) and anomalous Helium (He+), is the main topic of this work, and is complementary to the previous work on protons, anti-protons, electrons, and positrons. The modulation of galactic and anomalous Helium is studied with a numerical model including a more fundamental and comprehensive set of diffusion coefficients, a solar wind termination shock with diffusive shock acceleration, a heliosheath and particle drifts. The model allows a comparison of modulation with and without a solar wind termination shock and is applicable to a number of cosmic ray species during both magnetic polarity cycles of the Sun. The modulation of Helium, including an anomalous component, is also done to establish charge-sign dependence at low energies. We found that the heliosheath is important for cosmic ray modulation and that its effect on modulation is very similar for protons and Helium. The local Helium interstellar spectrum may not be known at energies <~1GeV until a spacecraft actually approaches the heliopause because of the strong modulation that occurs in the heliosheath, the effect of the solar wind termination shock and the presence of anomalous Helium.
We present evidence for the emergence of a measurable anomalous cosmic-ray hydrogen component in 1987
which may account for 20%-40% of the total hydrogen flux at 60 MeV. Comparing this flux with that of
anomalous cosmic-ray helium, we estimate that the H I/He I ratio in the very local interstellar medium is ~4,
consistent with determinations from solar ultraviolet backscatter measurements.
As Voyager 1 and 2 approach the solar wind termination shock, the hydrogen energy spectrum exhibits a
rapidly increasing flux of anomalous cosmic-ray hydrogen, consistent with that observed for other anomalous
cosmic-ray species. These results are consistent with the evidence for anomalous cosmic-ray hydrogen reported
from Voyager observations during the period of minimum solar modulation in 1987.
It is expected that the position of the modulation boundary in the equatorial and polar regions of the heliosphere depends on solar activity and possibly also on the polarity of the heliospheric magnetic field. In general, it can be assumed that the changing outward solar wind pressure causes a dynamic boundary position. Since the solar wind plasma quantities are not isotropic, as was confirmed by recent Ulysses spacecraft observations, the geometry of the modulation boundary may significantly deviate from the assumed sphere used in modulation models. We have studied the effect of non-spherical boundaries on the modulation of cosmic rays in the heliosphere using a drift model. In particular a pole-ward elongated heliosphere and the consequences of this approach on the generally too large cosmic-ray latitudinal gradients predicted by drift models are investigated for solar minimum conditions.
Marshall Rosenbluth's contributions to the magnetic mirror research program are briefly reviewed. (MOW)
A modulation model that includes shock acceleration of cosmic rays at
the solar wind termination shock is used to study the characteristics of
anomalous cosmic ray hydrogen, guided by the 1987 solar minimum spectra
as observed by IMP 8, Voyager 2, and Pioneer 10. This first attempt at a
comprehensive data fit excludes the effects of drifts and must therefore
be considered as preliminary. It is found that an anomalous component
dominates hydrogen spectra in the outer heliosphere but, due to large
radial gradients, the anomalous contribution in the inner heliosphere is
negligible. Similar model fits are shown for anomalous cosmic ray He and
O to demonstrate the degree of internal consistency of the model.
In this paper, it is shown that a steady state model for the combined
acceleration and modulation of cosmic rays in the heliosphere is
possible. In this first of a series of papers, a spherically symmetric
heliosphere with a termination shock at 50 AU is adopted. It is shown
that the accelerated spectrum develops naturally from the shock boundary
condition and that the low-energy source of particles to be accelerated
need not be specified explicitly. The demonstration solutions on the
shock are the expected power laws, and it is shown where shock curvature
and acceleration time scale effects set in. Some of the basic features
of the anomalous cosmic-ray component are explained by the solutions,
but, as expected, a detailed comparison with observations must await
more extensive and realistic models.
In this review much of the current knowledge about the physics of anomalous cosmic rays is surveyed. These energetic particles are, most probably, accelerated at the so-called heliospheric shock which terminates the supersonic solar wind expansion. After a presentation of the general scenario embracing a description of the heliosphere, the basic paradigm explaining the existence of anomalous cosmic rays and the relevant observations, the main problems connected to the physics of this particular cosmic-ray component are identified and discussed in detail. To this end, the characteristics of the progenitor as well as descendant particle populations, i.e. interstellar neutral atoms, pick-up ions, and energetic neutral atoms, and those of galactic cosmic rays are described from an observational as well as a theoretical perspective, as far as they are related to heliospheric research. The relevance of heliospheric physics is pointed out as a vital link between basic (plasma) physics and (extra-heliospheric) astrophysics as well as a test bed for astrophysical concepts.