List of Figures

View Image Figure 1:
The basic features of the global heliospheric geometry according to the hydrodynamic (HD) models of Ferreira and Scherer (2004) in terms of the solar wind density (upper panel) and solar wind speed (lower panel). The heliosphere is moving through the interstellar medium to the right. Typical solar minimum conditions are assumed so that the solar wind speed has a strong latitudinal dependence.
View Image Figure 2:
A schematic view of an asymmetric heliosphere together with the directions of the interstellar magnetic field lines. The measured ENA flux at ∼ 1.1 keV is superposed on the heliopause with the bright ENA ribbon appears to correlate with where the field is most strongly curved around it. (From the Interstellar Boundary Explorer, IBEX spacecraft’s first all-sky maps of the interstellar interaction at the edge of the heliosphere.) See McComas et al. (2009) for details. Image credit: Adler Planetarium/Southwest Research Institute.
View Image Figure 3:
A schematic presentation of how the waviness of the HCS could differ ideally from the nose to the tail regions of the heliosphere. The waviness depicted here corresponds to moderate solar activity. For an elaborate illustration of the dynamics of the HCS obtained with MHD models, see, e.g., Borovikov et al. (2011). Image reproduced by permission from Kóta (2012), copyright by Springer.
View Image Figure 4:
Observed proton, helium, and oxygen spectra for TSP, ACRs and galactic CRs are shown for days in 2005 as indicated when Voyager 1 already had crossed the TS on 16 December 2004. Computed ACR spectra at the TS, assuming diffusion shock acceleration for two values of the TS compression ratio, are shown for comparison. Image reproduced by permission from Stone et al. (2005), copyright by AAAS.
View Image Figure 5:
A display of how the observed TSPs (exhibiting a power-law trent at low energies), ACRs (typically between 10 MeV and 100 MeV) and galactic spectrum (typically above 100 MeV) for helium had evolved and unfolded at Voyager 1 (in red) and Voyager 2 (in blue) from late in 2004 to early in 2008. Voyager 1 and Voyager 2 crossed the TS on 2004.96 and 2007.66 respectively. Image reproduced by permission from Cummings et al. (2008), copyright by AIP.
View Image Figure 6:
An illustration of the 11-year and 22-year cycles in the solar modulation of CRs as observed by the Hermanus NM in South Africa at a cut-off rigidity of 4.6 GV in terms of percentage with March 1987 at 100%.
View Image Figure 7:
The parallel and two perpendicular diffusion orientations, indicated by the corresponding elements of the diffusion tensor, are shown with respect to the HMF spiral direction (left) for illustrative purposes. The arrows with V indicate the radially expanding solar wind (convection). Idealistic global drift patterns of positively charged particles in an A > 0 and A < 0 magnetic polarity cycle are schematically shown in the right panel, together with a wavy HCS as expected during solar minimum conditions. Image reproduced by permission from Heber and Potgieter (2006), copyright by Springer.
View Image Figure 8:
An illustration of the computed intensity distribution caused by drifts for the two HMF polarity cycles, in this case for 1 MeV/nuc ACR oxygen in the meridional plane of the heliosphere. The position of the TS at 90 AU is indicated by the white dashed line. Note how the coloured contours differ in the inner heliosphere for the two cycles and how the intensity decreases towards Earth, and how the distribution is quite different beyond the TS. In this case, the region of preferred acceleration for these ACRs is assumed near the equatorial plane and close to the HP at 140 AU. Image reproduced by permission from Strauss et al. (2011b), copyright by COSPAR.
View Image Figure 9:
Left panels: Computed radial gradients for galactic protons, in % AU–1, as a function of kinetic energy for both polarity cycles and for solar minimum conditions in the equatorial plane at 1, 50, and 91 AU, respectively (top to bottom panels). Right panels: Similar but at a polar angle 𝜃 = 55°. Two sets of solutions are shown in all panels, first without a latitude dependence (black lines) and second with a latitude-dependent compression ratio for the TS (red lines). In this case, the TS is at 90 AU and the HP is at 120 AU. Image reproduced by permission from Ngobeni and Potgieter (2010), copyright by COSPAR.
View Image Figure 10:
The difference caused by drifts in the computed latitudinal gradients (% degree–1) for protons in the inner heliosphere for the two HMF polarity cycles as a function of rigidity Potgieter et al. (2001). Marked by the black line-point is the latitudinal gradient calculated from a comparison between Ulysses and PAMELA observations for 2007. Image reproduced by permission from De Simone et al. (2011).
View Image Figure 11:
Pseudo-particle traces (trajectories) for galactic protons in the A < 0 HMF cycle projected onto the meridional plane for four values of the HCS tilt angle, shown as red lines. The HP position is indicated by the dashed lines, while the dotted lines show a projection of the waviness of HCS onto the same plane. The simulation is done for 100 MeV protons. Image reproduced by permission from Strauss et al. (2012c), copyright by Springer.
View Image Figure 12:
Binned propagation times for galactic electrons released at Earth at 100 MeV for the A < 0 (left panel), A > 0 (middle panel), and for the no-drift scenarios (right panel). For each computation 10000 particle trajectories were integrated using the SDE approach to modulation modeling. Image reproduced by permission from Strauss et al. (2011a), copyright AAS.
View Image Figure 13:
The propagation times and energy loss of 100 MeV protons propagation from the HP to Earth as a function of the HCS tilt angle (α) for A < 0 polarity cycles of the HMF. Note the change in propagation time at α = 40° and how the energy loss levels off above α = 50°. Image reproduced by permission from Strauss et al. (2012c), copyright by Springer.
View Image Figure 14:
Galactic CR electron observations for two consecutive solar minimum modulation periods in 1965 (open circles) and 1977 (filled circles) compared to the predictions of a first generation drift-modulation model (band between solid lines) containing gradient, curvature, and current sheet drifts. Clearly, a 22-year modulation cycle is portrayed (Potgieter and Moraal, 1985, and references therein).
View Image Figure 15:
Ratios of proton and electron measurements for 1977 (A > 0 polarity cycle) to 1965 – 66 (A < 0 polarity cycle) as a function of kinetic energy compared to the predictions made with a drift-modulation model illustrating how differently protons behave to electrons during two solar minimum periods with opposite solar magnetic field polarity (Webber et al., 1983; Potgieter and Moraal, 1985, and references therein).
View Image Figure 16:
Panel (a): Computed differential intensities of galactic electron at 1, 5, 60 and 90 AU (from bottom to top) in the heliospheric equatorial plane for the A > 0 and A < 0 polarity cycles. Panel (b): Ratio of the computed intensities for the A > 0 and A < 0 cycles as a function of kinetic energy and for the radial distance as in (a). Image reproduced by permission from Ferreira (2005), copyright by COSPAR.
View Image Figure 17:
Observed % changes respectively of helium (1.2 GV), electrons (1.2 GV and 2.5 GV), and protons (2.5 GV), as a function of time (solar activity) for the Ulysses mission from 1990 to 2005. The period from 1990 to 2000 was an A > 0 polarity epoch but changed to an A < 0 epoch around 2000 – 2001. Clearly the electrons exhibited a sharper profile over this A > 0 cycle than protons and helium in accord with predictions of drift-modulation models. Adapted by Heber from Heber et al. (2002, 2003, 2009).
View Image Figure 18:
A comparison of the observed anti-proton to proton ratio (below 10 GeV with first generation drift-model computations for solar minimum conditions with the HCS tilt angle α = 10° and for solar maximum conditions with α = 70°. The – and + signs indicate A < 0 and A > 0 polarity cycles, respectively. The corresponding ratio for the galactic spectra is indicated as IS. Image reproduced by permission from Webber and Potgieter (1989), copyright by AAS.
View Image Figure 19:
Left: Computed electron to positron ratios at Earth for two polarity cycles (A > 0, e.g., 1997, 2020 and A < 0, e.g., 1985, 2009) of the HMF compared to the ratio of the LIS at the heliopause (120 AU). Differences above about 80 MeV are caused by gradient, curvature, and current sheet drifts in the heliosphere during solar minimum activity. Right: Similar to left panel, but for computed ratios of galactic protons to anti-protons (Langner and Potgieter, 2004a).
View Image Figure 20:
Normalized proton (light-red lines) and electron (light-blue lines) differential intensities at (0.75 ± 0.2) GV as a function of time, from July 2006 to December 2009. The red and blue symbols represent the average intensities of protons and electrons, respectively. These intensity-time profiles are normalized to the intensity measured in July 2006. Image reproduced by permission from Vos (2011). See also Di Felice (2010) and De Simone (2011).
View Image Figure 21:
Computed 1.2 GV e− ∕He ratio at Earth for 1976 – 2000 in comparison with the observed e− ∕He obtained from electron measurements of ISEE3/ICE, He measurements from IMP and electron measurements from KET (Heber et al., 2003). The shaded areas correspond to the period with no well-defined HMF polarity. Two periods indicated by labels A and B with relatively large differences between the computed ratios and the observations require further investigation. Image reproduced by permission from Ferreira et al. (2003a), copyright by COSPAR.
View Image Figure 22:
Computed 2.5 GV electron to proton ratio (e− ∕p) as a function of time along the Ulysses trajectory (solid line) and at Earth (dotted line) in comparison with the 2.5 GV ratio observed with KET (Heber et al., 2002). Top panels show the position of Ulysses. In order to simulate this observed ratio as a function of time, the latitude dependence of both electrons and protons must be correctly modeled (Ferreira et al., 2003a; Ferreira, 2005). Image reproduced by permission from Ferreira et al. (2003b), copyright by EGU.
View Image Figure 23:
Percentage of drifts (continuous line) in the compound model that gives realistic modulation for various stages of the solar cycle for both the 2.5 GV electron and protons. As a proxy for solar activity the tilt angles, as used in the model are shown for illustrative purposes. Image reproduced by permission from Ndiitwani et al. (2005), copyright by EGU.
View Image Figure 24:
Computed percentage of galactic CR modulation in the heliosheath with respect to the total modulation (between 120 AU and 1 AU) for the two magnetic polarity cycles (A > 0 and A < 0), for solar minimum (α = 10°) and for moderate maximum (α = 75°) conditions, in the equatorial plane in the nose direction of the heliosphere. Negative percentages mean that the galactic CRs are reaccelerated at the TS under these assumed conditions (Langner et al., 2003).
View Image Figure 25:
Proton spectra, averaged over one Carrington rotation, as observed by the PAMELA space instrument from July 2006 to the beginning of 2010 (see the colour coding on the left). The spectrum at the end of December 2009 was the highest recorded. See Adriani et al. (2013) and also Potgieter et al. (2013).
View Image Figure 26:
Computed ratios of differential intensities for selected periods in 2007, 2008, 2009 with respect to Nov. 2006 as a function of kinetic energy in comparison with PAMELA proton observations (Potgieter et al., 2013).
View Image Figure 27:
The 5-day running average of the 6 – 14 MeV electrons and E > 200 MeV protons intensities measured at Voyager 1 from 2008.5 to 2012. Note the first sudden intensity increase of electrons at 2009.70 (111.2 AU) and the change in radial gradients of both electrons and protons before and after this increase. Similar behaviour followed n the second sudden intensity increases of both electrons and protons at 2011.2 (116 AU). The continuing increase of electron and proton intensities after 2011.3 is a notable feature. Image reproduced by permission from Webber et al. (2012), copyright by AGU.
View Image Figure 28:
Extraordinary changes were found in the 5 day running average intensities of 0.5 MeV protons (mainly ACR), 6 – 14 MeV galactic electrons and E > 100 MeV protons from 2009.0 to the end of the data set as observed by Voyager 1. Note how the 0.5 MeV proton intensity drops while the E > 100 MeV protons count rate went up. Image reproduced from the preprint of Webber and McDonald (2013).