•A solar modulation model is compared to observations from Voyager 1 and PAMELA.•A heliopause spectrum is subsequently calculated from 1MeV to 50GeV.•A spectral break is found for this spectrum ...between ∼800MeV and ∼2GeV.•Below ∼1GeV it exhibits a power-law E−(1.55±0.05) with E kinetic energy.•Above ∼5GeV a different power law is found, with E−(3.15±0.05).
A heliopause spectrum at 122AU from the Sun is presented for galactic electrons over an energy range from 1MeV to 50GeV that can be considered the lowest possible local interstellar spectrum (LIS). The focus of this work is on the spectral shape of the LIS below ∼1.0GeV. The study is done by using a comprehensive numerical model for solar modulation in comparison with Voyager 1 observations at ∼112AU from the Sun and PAMELA data at Earth. Below ∼1.0GeV, this LIS exhibits a power law with E−(1.55±0.05), where E is the kinetic energy of these electrons. However, reproducing the PAMELA electron spectrum averaged for 2009, requires a LIS with a different power law of the form E−(3.15±0.05) above ∼5GeV. Combining the two power laws with a smooth transition from low to high energies yields a LIS over the full energy range that is relevant and applicable to the modulation of cosmic ray electrons in the heliosphere. The break occurs between ∼800MeV and ∼2GeV as a characteristic feature of this LIS. The power-law form below ∼1GeV produces a challenge to the origin of these low energy galactic electrons. On the other hand, the results of this study can be used as a gauge for astrophysical modeling of the local interstellar spectrum for electrons.
Observations made with the two Voyager spacecraft confirmed that the solar wind decelerates to form the heliospheric termination shock. Voyager 1 crossed this termination shock at ∼94
AU in 2004, ...while Voyager 2 crossed it in 2007 at a different heliolatitude, about 10
AU closer to the Sun. These different positions of the termination shock confirm the dynamic and cyclic nature of the shock’s position. Observations from the two Voyager spacecraft inside the heliosheath indicate significant differences between them, suggesting that apart from the dynamic nature caused by changing solar activity there also may exist a global asymmetry in the north–south (polar) dimensions of the heliosphere, in addition to the expected nose–tail asymmetry. This relates to the direction in which the heliosphere is moving in interstellar space and its orientation with respect to the interstellar magnetic field. In this paper we focus on illustrating the effects of this north–south asymmetry on modulation of galactic cosmic ray Carbon, between polar angles of 55° and 125°, using a numerical model which includes all four major modulation processes, the termination shock and the heliosheath. This asymmetry is incorporated in the model by assuming a significant dependence on heliolatitude of the thickness of the heliosheath. When comparing the computed spectra between the two polar angles, we find that at energies
E
<
∼1.0
GeV the effects of the assumed asymmetry on the modulated spectra are insignificant up to 60
AU from the Sun but become increasingly more significant with larger radial distances to reach a maximum inside the heliosheath. In contrast, with
E
>
∼1.0
GeV, these effects remain insignificant throughout the heliosphere even very close to the heliopause. Furthermore, we find that a higher local interstellar spectrum for Carbon enhances the effects of asymmetric modulation between the two polar angles at lower energies (
E
<
∼300
MeV). In conclusion, it is found that north–south asymmetrical effects on the modulation of cosmic ray Carbon depend strongly on the extent of the geometrical asymmetry of the heliosheath together with the assumed value of the local interstellar spectrum.
After entering our local astrosphere (called the heliosphere), galactic cosmic rays, as charged particles, are affected by the Sun’s turbulent magnetic field. This causes their intensities to ...decrease towards the inner heliosphere, a process referred to as modulation. Over the years, cosmic ray modulation has been studied extensively at Earth, utilizing both ground and space based observations. Moreover, modelling cosmic ray modulation and comparing results with observations, insight can be gained into the transport of these particles, as well as offering explanations for observed features. We review some of the most prominent cosmic ray observations made near Earth, how these observations can be modelled and what main insights are gained from this modelling approach. Furthermore, a discussion on drifts, as one of the main modulation processes, are given as well as how drift effects manifest in near Earth observations. We conclude by discussing the contemporary challenges, fuelled by observations, which are presently being investigated. A main challenge is explaining observations made during the past unusual solar minimum.
An asymmetric solar wind termination shock (TS) model is used to study the effects on the modulation of cosmic-ray protons for different scenarios of the solar wind speed (V) in the heliosheath. This ...two-dimensional model is applied using predictions for V the heliosheath that were calculated with a time-dependent three-dimensional hydrodynamic model. Decreases stronger than the generally assumed V 8 1/r super(2) in the heliosheath are studied, as well as an extreme case, V 8 r super(2), where r is the radial distance. The effect of the TS is enhanced under certain circumstances, and "barrier"-type modulation in the heliosheath also depends on the chosen V-profiles. Significant changes occur mostly for the A < 0 solar magnetic polarity cycle, at all distances in the equatorial plane, when the V is changed from an incompressible fluid (V 8 1/r super(2), v. = 0) in the heliosheath, to V 8 1/r super(8), in a symmetrical model. For the asymmetrical case the TS is predicted to be more effective in the heliospheric nose than in the tail, especially for the A < 0 cycle during solar minimum conditions. The different profiles for V do not have a significant effect on the intensities inside the TS, but in the heliosheath the difference can be quite significant. It is found that V 8 1/r super(2) in the heliosheath is an oversimplification. The consequent effects of having v. 0 in the heliosheath prove to be relevant for cosmic-ray modulation and acceleration, especially now that the Voyager 1 spacecraft encountered the TS and entered the heliosheath.
Observations of galactic cosmic rays (GCRs) from the two Voyager spacecraft inside the heliosheath indicate significant differences between them, suggesting that in addition to a possible global ...asymmetry in the north–south dimensions (meridional plane) of the heliosphere, it is also possible that different modulation (turbulence) conditions could exist between the two hemispheres of the heliosphere. We focus on illustrating the effects on GCR Carbon of asymmetrical modulation conditions combined with a heliosheath thickness that has a significant dependence on heliolatitude. To reflect different modulation conditions between the two heliospheric hemispheres in our numerical model, the enhancement of both polar and radial perpendicular diffusion off the ecliptic plane is assumed to differ from heliographic pole to pole. The computed radial GCR intensities at polar angles of 55° (approximating the Voyager 1 direction) and 125° (approximating the Voyager 2 direction) are compared at different energies and for both particle drift cycles. This is done in the context of illustrating how different values of the enhancement of both polar and radial perpendicular diffusion between the two hemispheres contribute to causing differences in radial intensities during solar minimum and moderate maximum conditions. We find that in the A>0 cycle these differences between 55° and 125° change both quantitatively and qualitatively for the assumed asymmetrical modulation condition as reflected by polar diffusion, while in the A<0 cycle, minute quantitative differences are obtained. However, when both polar and radial perpendicular diffusion have significant latitude dependences, major differences in radial intensities between the two polar angles are obtained in both polarity cycles. Furthermore, significant differences in radial intensity gradients obtained in the heliosheath at lower energies may suggest that the solar wind turbulence at and beyond the solar wind termination shock must have a larger latitudinal dependence.
Time-dependent cosmic ray modulation Manuel, R.; Ferreira, S.E.S.; Potgieter, M.S. ...
Advances in space research,
05/2011, Letnik:
47, Številka:
9
Journal Article
Recenzirano
Time-dependent cosmic ray modulation is calculated over multiple solar cycles using our well established two-dimensional time-dependent modulation model. Results are compared to Voyager 1, Ulysses ...and IMP cosmic ray observations to establish compatibility. A time-dependence in the diffusion and drift coefficients, implicitly contained in recent expressions derived by Teufel and Schlickeiser (2002), Shalchi et al. (2004), Minnie et al. (2007), Engelbrecht (2008), is incorporated into the cosmic ray modulation model. This results in calculations which are compatible with spacecraft observations on a global scale over consecutive solar cycles. This approach compares well to the successful compound approach of Ferreira and Potgieter (2004). For both these approaches the magnetic field magnitude, variance of the field and current sheet tilt angle values observed at Earth are transported time-dependently into the outer heliosphere. However, when results are compared to observations for extreme solar maximum, the computed step-like modulation is not as pronounced as observed. This indicates that some additional merging of these structures into more pronounced modulation barriers along the way is needed.
Context. Since the Pioneer 10 flyby of Jupiter it has become well known that electrons of Jovian origin dominate the lower MeV range of charged energetic particles in the inner heliosphere. Aims. ...Because the Jovian source can be treated as point-like in numerical models, many attempts to investigate charged particle transport in the inner heliosphere have utilized Jovian electrons as test particles. The reliability of the derived parameters for convective and diffusive transport processes are therefore highly dependent on an accurate estimation of the Jovian source spectrum. In this study we aim to provide such an estimation. Methods. In this study we have proposed a new electron source spectrum, specified at the boundary of the Jovian magnetosphere, fitted to flyby measurements by Pioneer 10 and Ulysses, with a spectral shape also in agreement with measurements at Earth’s orbit by Ulysses, Voyager 1, ISEE and SOHO. Results. The proposed spectrum is consistent with all previous theoretical suggestions, but deviates considerably in the lower MeV range which was inaccessible to those studies.
A study is performed of phases of solar cycle minima in sunspots, the heliosphere, and the intensity of Galactic cosmic rays (GCRs). Times of maximum GCR intensity in the minima of the last five ...cycles (including the current one), corresponding main heliospheric factors, and relationships between them are determined. The dependence of the near-Earth GCR proton spectrum on heliospheric factors of their linear trend in the minima of solar cycles 21/22, 22/23, and 23/24 (1987, 1997, 2009) is calculated and analyzed with emphasis on the behavior of crossover energy for successive minima.
The time-dependent modulation of galactic cosmic rays in the heliosphere is studied over different polarity cycles by computing 2.5 GV proton intensities using a two-dimensional, time-dependent ...modulation model. By incorporating recent theoretical advances in the relevant transport parameters in the model, we showed in previous work that this approach gave realistic computed intensities over a solar cycle. New in this work is that a time dependence of the solar wind termination shock (TS) position is implemented in our model to study the effect of a dynamic inner heliosheath thickness (the region between the TS and heliopause) on the solar modulation of galactic cosmic rays. The study reveals that changes in the inner heliosheath thickness, arising from a time-dependent shock position, does affect cosmic-ray intensities everywhere in the heliosphere over a solar cycle, with the smallest effect in the innermost heliosphere. A time-dependent TS position causes a phase difference between the solar activity periods and the corresponding intensity periods. The maximum intensities in response to a solar minimum activity period are found to be dependent on the time-dependent TS profile. It is found that changing the width of the inner heliosheath with time over a solar cycle can shift the time of when the maximum or minimum cosmic-ray intensities occur at various distances throughout the heliosphere, but more significantly in the outer heliosphere. The time-dependent extent of the inner heliosheath, as affected by solar activity conditions, is thus an additional time-dependent factor to be considered in the long-term modulation of cosmic rays.
This paper discusses a numerical modulation model to describe anomalous cosmic ray acceleration and transport in the heliosheath, the portion of the heliosphere between the termination shock and the ...heliopause. The model is based on the well known Parker transport equation and includes, in addition to diffusive shock acceleration at the solar wind termination shock, momentum diffusion (Fermi II, stochastic acceleration) and adiabatic heating occurring in the heliosheath together with both a latitude dependent compression ratio and injection efficiency as inferred from hydrodynamic heliospheric models. The model is applied to the study of anomalous cosmic ray oxygen, with the resulting intensities compared to recent Voyager 1 spacecraft observations in the heliosheath. Comparison shows that the model is able to very satisfactorily reproduce these observations, which includes a modulated spectral form at the termination shock and subsequent unfolding into the heliosheath. It is concluded that a combination of momentum diffusion and adiabatic heating, under certain realistic assumption of the solar wind speed in the heliosheath, form a viable re-acceleration mechanism, or continuous acceleration process, to explain the very contentious anomalous cosmic ray observations in the heliosheath.
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