Stefan Ferreira

Cosmic ray modulation beyond the heliopause: a hybrid modeling approach

Results from a newly developed hybrid cosmic ray (CR) modulation model are presented. In this approach, the transport of CRs is computed by incorporating the plasma flow from a magnetohydrodynamic model for the heliospheric environment, resulting in representative CR transport. The model is applied to the modulation of CRs beyond the heliopause (HP) and we show that (1) CR modulation persists beyond the HP, so it is unlikely that the Voyager spacecraft will measure the pristine local interstellar spectra of galactic CRs when crossing the HP. (2) CR modulation in the outer heliosheath could maintain solar-cycle-related changes. (3) The modulation of CRs in the outer heliosheath is primarily determined by the ratio of perpendicular to parallel diffusion, so that the value of the individual diffusion coefficients cannot be determined uniquely using this approach. (4) CRs can efficiently diffuse between the nose and tail regions of the heliosphere.

Time evolution of galactic and anomalous cosmic-ray spectra in a dynamic heliosphere

Galactic and anomalous cosmic-ray modulation in a dynamic realistic heliosphere is studied. We present the time evolution of cosmic-ray spectra from solar minima to maxima as computed by a newly developed hybrid model. This model consists of a hydrodynamic part to model the plasma flow of protons in the solar wind and in the LISM, neutral H atoms, and heliospheric H pick-up ions. The heliospheric geometry and plasma flow are then used in a kinetic transport part to calculate cosmic-ray transport. We show that the model results in realistic cosmic-ray modulation as solar activity increases from solar minimum to maximum. In particular it is shown that, depending on energy, fewer cosmic-ray particles are accelerated at the shock for solar maximum. These particles are also more modulated with the modulation amplitude depending on distance, energy, and the polarity of the heliospheric magnetic field. There is also a much smaller dependence of cosmic-ray intensities on solar activity in the heliosheath, compared to other regions. It is interesting that, for the very low energies, e.g., <10 MeV, the computed anomalous spectrum at the shock is not sensitive to solar conditions, but in the inner heliosphere it may well disappear well below the Galactic spectra for solar maximum. Also, we show that depending on energy, there exists a large computed nose-tail asymmetry in the cosmic-ray intensities. Furthermore, the acceleration of these particles at the shock also depends on latitude; e.g., most of the accelerated anomalous cosmic rays are found in the equatorial regions.

Modulation effects of anisotropic perpendicular diffusion on cosmic ray electron intensities in the heliosphere

The modulation of cosmic ray electrons provides a useful tool to study the diffusion tensor applicable to heliospheric modulation. Electron modulation responds directly to the assumed energy dependence of the diffusion coefficients below ∼500 MeV in contrast to protons which experience large adiabatic energy losses below this energy. As a result of this and because drifts become unimportant for electrons at these low energies, conclusions can be made about the appropriate diffusion coefficients. Using a modulation model, we illustrate the role of anisotropic perpendicular diffusion on electron modulation. In general, we find that perpendicular diffusion dominates electron modulation below ∼100 MeV. Enhancing it in the polar direction typically produced an increase in modulation for both the A > O (e.g., ∼1990 to ∼2000) and A < 0 (e.g., ∼1980 to ∼1990) solar magnetic polarity cycles. It also causes the radial dependence of the intensity to become more uniform throughout the heliosphere, and causes a significant reduction in the latitude dependence of the intensities at all radial distances, with the largest effects in the inner heliosphere and at low energies. This agrees with studies of cosmic ray protons, which suggest that perpendicular diffusion enhanced in the polar direction of the heliosphere is required in conventional drift models to explain the small latitudinal gradients observed for protons on board the Ulysses spacecraft. The role of enhanced perpendicular diffusion was further investigated by examining electron modulation as a function of the “tilt angle” α of the wavy current sheet. In general, a reduction occurred between the modulation differences caused by drifts as a function of α for both polarity cycles. This work illustrates that anisotropic perpendicular diffusion has profound effects on the modulation of galactic cosmic ray electrons during both polarity cycles.

Modelling anomalous cosmic ray oxygen in the heliosheath

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.

LATITUDINAL GRADIENTS OF GALACTIC COSMIC RAYS DURING THE 2007 SOLAR MINIMUM

Ulysses, launched in 1990 October in the maximum phase of solar cycle 22, completed its third out-of-ecliptic orbit in 2008 February. This provides a unique opportunity to study the propagation of cosmic rays over a wide range of heliographic latitudes during different levels of solar activity and different polarities in the inner heliosphere. Comparison of the first and second fast latitude scans from 1994 to 1995 and from 2000 to 2001 confirmed the expectation of positive latitudinal gradients at solar minimum versus an isotropic Galactic cosmic ray distribution at solar maximum. During the second scan in mid-2000, the solar magnetic field reversed its global polarity. From 2007 to 2008, Ulysses made its third fast latitude scan during the declining phase of solar cycle 23. Therefore, the solar activity is comparable in 2007-2008 to that from 1994 to 1995, but the magnetic polarity is opposite. Thus, one would expect to compare positive with negative latitudinal gradients during these two periods for protons and electrons, respectively. In contrast, our analysis of data from the Kiel Electron Telescope aboard Ulysses results in no significant latitudinal gradients for protons. However, the electrons show, as expected, a positive latitudinal gradient of ~0.2% per degree. Although our result is surprising, the nearly isotropic distribution of protons in 2007-2008 is consistent with an isotropic distribution of electrons from 1994 to 1995.

Modeling of the Heliospheric Interface, Magnetic Field, and Cosmic-Ray Transport

Magnetized flow and cosmic-ray transport in the local astrosphere are studied. A hybrid numerical model is used to calculate the heliospheric interface, the heliospheric magnetic field, and cosmic-ray modulation. Assuming that the transport parameters scale inversely proportional to the magnetic field, the amplification of the field in the inner heliosheath results in a sudden decrease of these parameters over the shock. This, together with our model calculations showing the compressed and heated solar wind flow is not divergence-free in the postshock region, results in effective adiabatic acceleration of cosmic-ray particles in the heliosheath. In particular, the peak of the computed anomalous particles is not at the shock but some distance into the inner heliosheath, where this region becomes populated with relatively high intensities of heated anomalous particles. However, this effect is largely dependent on the values of the transport parameters in the heliosheath. It is also shown that an improvement in the kinematically transported heliospheric magnetic field leads to a significantly different spatial distribution of cosmic rays compared to a Parker model.

TIME-DEPENDENT MODELING OF PULSAR WIND NEBULAE

A spatially independent model that calculates the time evolution of the electron spectrum in a spherically expanding pulsar wind nebula (PWN) is presented, allowing one to make broadband predictions for the PWN’s non-thermal radiation. The source spectrum of electrons injected at the termination shock of the PWN is chosen to be a broken power law. In contrast to previous PWN models of a similar nature, the source spectrum has a discontinuity in intensity at the transition between the low- and high-energy components. To test the model, it is applied to the young PWN G21.5−0.9, where it is found that a discontinuous source spectrum can model the emission at all wavelengths better than a continuous one. The model is also applied to the unidentified sources HESS J1427−608 and HESS J1507−622. Parameters are derived for these two candidate nebulae that are consistent with the values predicted for other PWNe. For HESS J1427−608, a present day magnetic field of Bage = 0.4 μG is derived. As a result of the small present day magnetic field, this source has a low synchrotron luminosity, while remaining bright at GeV/TeV energies. It is therefore possible to interpret HESS J1427−608 within the ancient PWN scenario. For the second candidate PWN HESS J1507−622, a present day magnetic field of Bage = 1.7 μG is derived. Furthermore, for this candidate PWN a scenario is favored in the present paper in which HESS J1507−622 has been compressed by the reverse shock of the supernova remnant.

Ionization rates in the heliosheath and in astrosheaths - Spatial dependence and dynamical relevance

K.S. and H.F. are grateful to the Deutsche Forschungsgemeinschaft, DFG for funding the projects FI706/15-1 and SCHE334/10-1. M.B. was supported by the Polish Ministry for Science and Higher Education grant N-N203-513-038, managed by the National Science Centre. S.E.S.F. thanks the South African National Research Foundation for financial support.

Supernova remnant evolution in uniform and non-uniform media

Aims. In this work numerical simulations showing the time evolution of supernova remnants (SNRs) in uniform and non-uniform interstellar medium (ISM) are presented. Methods. We use a hydrodynamic model including a kinematic calculation of the interstellar magnetic field. Important parameters influencing SNR evolution include the ejecta mass and energy of the remnant, as well as the ISM density and adiabatic index. Results. By varying these parameters we constructed an analytical expression giving the return time of the SNR reverse shock to the origin, in terms of these parameters. We also found that the reverse shock spends half of its time moving outward and the other half returning to the origin. Also computed is SNR evolution in non-uniform media where the blast wave moves from one medium into either a less or more dense medium. As the SNR moves into a medium of higher density a reflection wave is created at the interface between the two media which is driven back toward the center. This drives mass via a nonspherical flow away from the discontinuity. As this wave moves inward it also drags some of the ISM field lines (if the field is parallel with the interface) with it and heats the inside of the SNR resulting in larger temperatures in this region. When a SNR explodes in a medium with a high density and the blast wave propagates into a medium with a lower density, a cavity is being blown away changing the geometry of the high density region. Also, once the forward shock moves into the medium of less density a second reverse shock will start to evolve in this region.

Modulation of Cosmic-Ray Electrons in a Nonspherical and Irregular Heliosphere

With the Voyager 1 spacecraft approaching the solar wind termination shock, much emphasis is put on numerical models to simulate the physical parameters that can be expected at and beyond the shock. This work emphasizes the modulation of cosmic-ray electrons in a realistic, nonspherical heliosphere; e.g., the effects on electron modulation of a poleward elongation of the heliospheric boundary and shock, as well as an irregular shock geometry, are studied. To achieve this, a new two-dimensional time-dependent transport model is developed including the major modulation mechanisms with a realistic, asymmetric heliosheath and heliopause. Because the mutual interaction of the solar wind plasma and the interstellar medium defines the geometry of the heliosphere, a 3-fluid two-dimensional hydrodynamic model is used to calculate the geometry of the heliosphere (location of the termination shock and heliopause) as input to the transport model. We find that changes in the geometry of the heliosphere caused by solar cycle-related changes in the solar wind speed influence the electron distribution significantly close to the shock and to a lesser extent in the heliosheath and inner heliosphere, but only if there is a significant amount of particle drift present. These effects decrease toward solar maximum when the heliosphere is expected to be diffusion dominated and also for low-energy (<30 MeV) electrons, where drift is not important. The model is also utilized to study the effect of possible nonspherical, irregular incursions in the termination shock geometry on the distribution of cosmic-ray electrons in the shocks vicinity. It is shown that these incursions only affect the electron distribution close to the termination shock and to a lesser extent in the heliopause and are highly dependent on drift. Furthermore, a time dependence and/or incursions in the shock geometry could account for the sudden increase by up to a factor of ~4 in the low-energy electron intensities measured by Voyager 1 with the spacecraft still, e.g., ~2 AU away from the shock.