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Particle transport and acceleration at corotating interaction regions
Pergamon www.elsevier.nl/locate/asr
Adv. Space Res. Vol. 23, No. 3, pp. 581-590, 1999 © 1999 COSPAR. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 0273-1177/99 $20.00 + 0.00 PII: S0273-1177(99)00124-6
P A R T I C L E T R A N S P O R T A N D A C C E L E R A T I O N AT COROTATING INTERACTION REGIONS Joe Giacdlone
University of Arizona, Tucson, AZ, 85721
ABSTRACT The transport and acceleration of energetic nuclei associated with corotating interaction regions is discussed with emphasis on its importance relative to global heliospheric phenomena such as anomalous cosmic rays, the distant heliosphere, and propagation to high latitudes. We will discuss aspects of particle acceleration at the forward and reverse shocks bounding CIRs which support the idea that accelerated pickup ions are important contributors to energetic ions in the heliosphere. We will outline our current understanding of the source of CIR-associated energetic nuclei based on multispacecraft observations of the spatial variation of low-energy cosmic rays, as well as that of freshly ionized pickup ions. We will also discuss the propagation of CIR-associated energetic particles to high heliographic latitudes. We will present a model of the interplanetary magnetic field and show results from a numerical simulation which suggest that particles undergo significant latitudinal diffusion. © 1 9 9 9 C O S P A R . P u b l i s h e d by Elsevier Science Ltd.
INTRODUCTION It has been long known that interplanetary disturbances corotating with the sun have associated enhancements in energetic particle intensities (e.g. Barnes and Simpson, 1976; McDonald et al., 1975). These corotating interaction regions (CIRs) are bound by collisionless shocks, one which propagates away from the sun in the solar wind frame (the forward shock) and the other moves towards the sun in the wind frame (the reverse shock). C u r r e n t l y it is thought charged particles are accelerated to several MeV energies at these shock waves. Less clear, however, is the source of these particles. Many observations suggest that the composition of these species are indicative of solar particles (e.g. Gloeckler et al., 1979; Mason et al., 1997). Others, however, show that interstellar pickup ions are the likely source of many of these particles (Gloeckler et al., 1994). Interstellar pickup ions, which are ionized neutrals that enter the solar system due to the sun's motion in the galaxy, represent a suprathermal population which are readily accelerated by shocks in the inner heliosphere. Gloeckler et al. (1994) and Schwadron et al. (1996) have also suggested that the initial acceleration of the pickup ions occurs via the mechanism of transit-time damping of magnetic fluctuations within the CIR. Particles accelerated by CIRs in the inner heliosphere will propagate to the solar wind termination shock, which stands at some 80 AU from the sun, and undergo further acceleration. Some will propagate back into the inner heliosphere. It is fairly well established that anomalous cosmic rays are interstellar pickup ions which are accelerated, at least in part, at the termination shock. An interesting scenario may be that CIRs accelerate pickup ions which are then further accelerated at 581
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the termination shock to anomalous cosmic-ray energies. It is currently not well understood whether this occurs and will be discussed in more detail in this paper. Energy spectra of CIR-associated particles can be complicated. Power-law tails, predicted by the standard diffusive shock acceleration theory, are not typically observed. Fisk and Lee (1980) showed that the inclusion of an adiabatic cooling term in the transport equation (Parker, 1965) gives rise to an exponential-like energy dependence of the shock-accelerated spectra. They found that the intensity at the reverse shock is larger than those associated with the forward shock, in agreement with the majority of observations (Van Hollebeke et al., 1978; Pesses et al., 1984). On the other hand, Giacalone and Jokipii (1997) showed that the acceleration of interstellar pickup ions is strongly favored at the reverse shock over the forward shock and that this naturally leads to larger intensities at the reverse shock, regardless of the acceleration mechanism. This is further discussed below. The propagation of low-energy cosmic rays associated with CIRs to high heliographic latitudes is another topic of current interest owing to the highly successful Ulysses mission. Energetic particles corotating with the sun are seen despite the absence of shocks which remain closer to the ecliptic plane during quiet solar conditions (Simnett et al., 1995). It remains unclear whether these particles reach high latitudes via diffusion across magnetic field lines (Kdta and Jokipii, 1997), or whether there exists a systematic magnetic connection between high and low latitudes and that the particles propagate along the lines of force (Fisk, 1996). This topic is discussed further in this paper. THE PHYSICS OF CHARGED-PARTICLE ACCELERATION BY SHOCKS Charged-particle acceleration by collisionless shock waves is often thought of in terms of two mechanisms, shock-drift acceleration and first-order Fermi acceleration. These are actually contained in the more general diffusive shock theory. Shock-drift acceleration is the term attributed to the mechanism whereby charged particles interact with the shock in the limit of weak scattering (e.g. Armstrong et al., 1985). A charged-particle gradient B drifts along the shock interface in the same direction as the motional electric field. The energy comes from working against the plasma. The m a x i m u m energy gains via this mechanism occurs at shocks where the motional electric field is the largest (those in which the angle between the mean field and shock normal are nearly perpendicular). Diffusive shock acceleration applies when the particle distribution function is nearly isotropic. It contains both drift and Fermi acceleration (Jokipii, 1982; Decker and Vlahos, 1986). The equation which governs diffusive shock acceleration is the transport equation first written down by Parker (1965). This equation is straightforward to solve for simple shock geometries. The Injection Problem The injection problem, which applies primarily to shocks in which the angle, OB,~, between the mean magnetic field and the shock normal direction is > 45 °, stems from the fact that particles do not tend to move normal to the field lines as they convect through the shock and are unable to remain near the shock to be accelerated. The question is whether there is enough scattering to keep the particles near the shock. By requiring the anisotropic diffusive streaming to be small, we find U1 [(rg/Air) 2 sin 2 OBn + (1 -- ~;±/~11)2 sin 2 0s,~ cos 2 0sn] 1/2 <<1 v (m±/~ll) sin2 0Sn + cos 20Bn
(1)
where U1 is the flow speed upstream of the shock, v is the plasma-frame particle speed, x±,ll are the spatial diffusion coefficient normal to and along the mean magnetic field, respectively, All is the mean-
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free path, and rg is the particles Larmor radius. In deriving this condition, we have neglected terms of order nJ_/xa, where NA is the antisymmetric diffusion coefficient. For a very nearly perpendicular shock (0Bn ~ 90°), (1) becomes v >> 3U1)~ll/rg for classical scattering in which x± -~ ~ll(rg/Aii) 2. Clearly pickup ions that convect into a stationary shock cannot meet this criterion since they have speeds such that v = U1 and mean-free paths that are larger than their gyroradii. This criterion is more easily met at propagating shocks as discussed below. Contrary to quasi-perpendicular shocks, those shocks which essentially propagate along the mean magnetic field (quasi-parallel shocks) are known to be efficient injectors of energetic particles. Highenergy tails in the distribution function downstream of quasi-parallel shocks form directly out of the thermal population (Ellison, 1981; Giacalone et al., 1992). Some of the details of the internal structure of collisionless shocks may aid in the injection problem, however, at present this is still not resolved. For instance, Zank et al. (1995) and Lee et al. (1995) have shown that a fraction of freshly-ionized pickup ions can be trapped by the cross-shock potential as they are convected into the shock layer. The trapped particles are accelerated by drifting along the motional electric field as they skim along the shock surface. However, to get significant energization, the shock must have a width on the order of the electron inertial length which is much smaller than typical high-Alfv4n Mach shocks. Propagating shocks more readily inject very low-energy particles than those which stand in the flow of the solar wind (such as planetary bow shocks and the termination shock). Qualitatively this is easy to see since interplanetary shocks move only a hundred k m / s or so faster than the solar wind and low-energy particles can remain near the shocks longer and enhance their probability of being accelerated rather than being convected downstream. Quantitatively one replaces U1 in Equation 1 with V8 - U1, where V~ is the shock speed measured relative to the sun. Typically this is less than U1 and (1) is more easily met. Weak shocks which propagate only slightly above the solar wind speed (i.e. V, ~_ U1), are especially good at injecting particles. The resultant shock-accelerated spectrum, on the other hand, will be very soft in this case. ION ACCELERATION AT CIR'S Acceleration at the F / R Shocks One of the earlier analytic attempts to describe observed features of the energy spectra of CIRassociated energetic particles was given by Pisk and Lee (1980). They found that the spectra have an exponential-like energy dependence at 1 AU. The spectral index depends inversely on the flow speed, so that the spectra associated with a reverse shock are harder than those associated with the forward shock, in agreement with the majority of observations. On the other hand, if pickup ions (of either interstellar or local origin) are important contributors to these particles, the asymmetry in the interaction between pickup ions which were first ionized in either the fast or slow solar wind naturally explains many of the observations. For i'nstance, since the pickup ions are moving much faster in the fast wind, acceleration in the fast wind should be more efficient because these particles start with approximately four times as much energy as those in the slow wind. This idea is illustrated in Figure 1 for the case where where the accelerated spectrum is an inverse power law. The power-law tail which connects to the pickup ion distribution has a v -4 dependence which would occur for shock acceleration at a strong shock. A steeper spectrum would produce a larger effect. This general conclusion should hold for a wide variety of acceleration mechanisms. Acceleration in the Absence of Shocks
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There is observational evidence reported by Gloeckler et al. (1994) and Schwadron et al. (1996) that interplanetary shocks may not efficiently accelerate unaccelerated pickup ions. These authors have proposed that rather, a statistical process known as transit-time damping of magnetic fluctuations (the magnetic equivalent to Landau damping), is the initial stage of a two-step process. Low-frequency fluctuations necessary for this process to work are contained within the turbulent regions bounding the shocks associated with corotating interaction regions. Once the particles have been pre-accelerated in this manner, they continue to be accelerated by the shocks which is a more rapid process. 10
0.1
f(v) 0.01
0.001
0.0001
1
10 v/Us~w
Fig. 1: Sketch of the accelerated pickup-ion distribution that were ionized in either the fast or slow wind, as indicated. In this case the acceleration mechanism is independent of the local wind speed so that the spectral index is the same.
It is also possible that acceleration of either pickup ions or solar energetic particles can take place before the forward and reverse shocks form during the development of a CIR. If the particles can diffuse through the velocity gradient, associated with the CIR formation, rapidly enough they will be efficiently accelerated. This gradient can be fairly large since the flow speed changes from about 400 km/s in the slow wind to 800 km/s in the fast wind. Consequently, acceleration of pickup ions can occur before the shocks form and this can lead to a peak in the intensity within the CIR for a time. Once the shocks have formed, the intensity within the CIR will diminish relative to the intensity at the shocks, partly due to adiabatic energy loss, and also because the intensity at the shocks increase due to shock acceleration. After some characteristic time, the peak at the shocks will dominate. This idea may serve as a possible alternative explanation of the observations by Schwadron et al. (1996).
SOURCE OF CIR-ACCELERATED PARTICLES In the previous sections we discussed the injection problem of accelerating very low-energy particles by shocks and suggested that pickup ions are favored for acceleration over thermal solar wind particles. However, it is difficult to accelerate pickup ions when the magnetic field is nearly perpendicular to the direction of a velocity gradient (such as a shock). Thus, it is unclear whether the termination shock can accelerate pickup ions efficiently enough to account for the observed fluxes of anomalous cosmic rays. In the next section we discus~ a two-step preacceleration mechanism whereby the pickup ions are first accelerated by interplanetary shocks in the inner heliosphere and are then convected to the termination shock where they are further energized to cosmic-ray energies. A key assumption in the two-step mechanism described in the next section is that energetic particles observed as recurrent flux enhancements in the distant heliosphere (Decker et al., 1995) are pickup ions and not solar wind. This distinction is important since it is well established that the composition and
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charge state of the anomalous cosmic-ray component does not resemble the solar wind. Spacecraft instruments which measure fluxes in the distant heliosphere have not yet been able to make the distinction between various species. On the other hand, there is a wealth of compositional observations of CIR-associated particles in the inner heliosphere which may clarify the source of these particles. Additionally, there are observations of the radial variation of CIR-associated energetic particles. We now briefly discuss these observations. Van Hollebeke et al. (1978) reported on the radial variation of corotating energetic particle streams and concluded that .-~ 1 MeV protons have a positive radial gradient to a peak at about 4 AU where the intensity declines. Boufaida and Armstrong (1997) averaged over all observations (including solar energetic particle events) of Earth orbiting spacecraft, Ulysses and Voyagers, and determined that low-energy protons (< 1 MeV) have a positive radial gradient out to about 5 AU, whereas highenergy particles (> 1 M e V ) h a v e a negative gradient. Voyager observations reported by Decker et al. (1995) indicate that the peak flux in recurrent enhancements in ,-~ 1 MeV protons fall off as 1/r 2 (r is radial distance). These peaks were observed to be superimposed on a "shoulder" which is above the instrument background. This shoulder falls off less rapidly and is more like a r -°'7 dependence (Decker, private communication). Finally, observations by Hamilton et al. (1997) indicate that ~ 1 MeV protons fall off about as 1/r 2 (perhaps a little less rapidly as indicated in their Figure 2), and 1 MeV Helium falls off much less rapidly (more like l/r). Note that the other energy levels which were studied by Hamilton et al. (ibid) are probably anomalous cosmic-rays. 10 0
~.~ 108
~
10a
E
104
. . . . . . . .
I
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I ' - " : : -'~' ~'' Solar ~Nin'd' '1
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I
i
i
i
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10-~
.0 10-s 105 107 1
10 R (AU)
100
104 1
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100
Fig. 2: Upper left: Pickup hydrogen and solar wind flux versus heliocentric distance. Lower left: the ratio of the pickup-ion to solar wind flux. Right: The normalized outward-directed pickup-ion flux (normalized to the interstellar flux of the various species) for H, He, Ne, and O. These are derived from Vasyliunas and Siscoe (1976) and Gloeckler et al. (1993). The intensities of CIR-related particles in the distant heliosphere are considerably larger than what is expected by simple radial expansion and cooling. For instance, for a power-law spectrum at the position r=r0, the intensity at a given energy will vary as J cx (1"/1"o) -4(1+~¢)/3, where 3' is the spectral index. Thus, for 3' = 1, which occurs for a strong shock, then the intensity at say 40 AU would be more than 5 orders of magnitude smaller than at 1 AU. The effect is even larger for a softer spectrum, or even worse still for an exponential spectrum, which are typically observed at 1 AU. Thus, continued acceleration, or an increased source strength must account for the observations in the distant heliosphere. One may argue that the strength of CIR shocks are at their peak at some 4-5 AU, and this may help explain the observations by Van Hollebeke et al. (1978). However, as shown in Figure 2, pickup protons and oxygen also peak at some 5-10 AU, which may also explain these observations assuming that pickup ions are the source.
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As suggested in Figure 2, there is an inherit difficulty in separating the abundances of pickup ions and solar particles when the observations are made at 1 AU since there are so few pickup H and O while thermal solar wind is difficult to accelerate. Helium, on the other hand, should be dominated by pickup ions. Ne may also be dominated by pickup ions, but this is not as clear. In the distant heliosphere, on the other hand, we believe that there is no reason to discount the possibility that the observed fluxes of CIR-related energetic particles are dominated by interstellar pickup ions. Solar energetic particles, which may dominate in some 1 AU observations, are likely to be much less abundant in the distant heliosphere due to adiabatic losses. PREACCELERATION OF ANOMALOUS COSMIC RAYS We have recently proposed a model (Jokipii and Giacalone, 1996; Giacalone et al., 1997) for anomalous cosmic rays in which the initial acceleration of interstellar pickup ions occurs in the inner heliosphere rather than locally at the termination shock. The ultimate acceleration required to achieve anomalous cosmic-ray energies occurs at the termination shock but only after the pickup ions have been preaccelerated. This is one possible solution to the apparent difficulty in accelerating the previously unaccelerated pickup ions at the stationary, nearly perpendicular termination shock of the solar wind. It is known that interplanetary shocks, or turbulent regions within corotating interaction regions, more readily accelerate pickup ions and this has been observed by Ulysses instruments (Gloeckler et al., 1994; Schwadron et al., 1996). Our results, using Voyager 2 data as a baseline normalization a global transport model, has proven to be promising in that there seems to be enough low-energy particles observed in the outer heliosphere which are presumably accelerated in the inner-heliosphere, to account for the observed intensities of anomalous cosmic rays (see Figure 2 of Giacalone et al., 1997). If these inner-heliosphere-accelerated particles are accelerated pickup ions, as suggested by recent observations (Gloeckler et al., 1994), then this would be a very important stage in the formation of anomalous cosmic rays. Although, the composition of CIR-accelerated ions near 1 AU may not be pickup ions (additional studies of composition are needed), we feel that the CIR-associated particles in the outer heliosphere are dominated by pickup ions. This issue is not well understood at present. LATITUDINAL PROPAGATION OF CIR-ACCELERATED PARTICLES Ulysses observations of corotating energetic particles at high heliographic latitudes by Simnett et al. (1995) reveal that these enhancements persist even in the absence of the CIRs. These particles are accelerated at CIRs and are subsequently transported in latitude. This finding may suggest a magnetic connection between the high latitudes of observation and the lower latitudes where acceleration at CIR's could take place such as that suggested by Fisk (1996). If such a connection exists, the skipping of charged particles across field lines may not be important since the latitudinal excursions of the field lines allows for direct access to various latitudes via parallel transport. One of the main difficulties in this picture is that the particles must propagate a large distance along the field lines and significant adiabatic cooling will take place. Additionally, in order to uniformly populate field lines, there must be some cross-field transport. A quantitative model of cosmic-ray transport in the field suggested by Fisk (1996) has not yet been developed. Alternatively, K6ta and Jokipii (1997) have considered the importance of perpendicular diffusion as an alternative explanation of the observations of Simnett et al. (1995). Their model emphasized the importance of the random walk of field lines (Jokipii and Parker, 1968) and their simulations indicate that low-energy shock-accelerated particles can be expected to appear at high heliographic latitudes. In order to help clarify this issue, we consider the effect of large-scale magnetic turbulence in the solar
Particle Transport at CIRs
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wind on the transport of low-energy cosmic rays. Our model assumes that the observed time and spatial scales occurring at the solar photosphere can be characterized by the random movements of magnetic footpoints (it is currently thought that solar magnetic fields are continually reconnecting and that only a fraction of the field lines open into interplanetary space). The field is carried away from the sun assuming a constant radial flow. Under these assumptions, it follows that the interplanetary magnetic field takes the form.
B~(r) = B~(~o)
(2)
Bo(r, 0, ~, t) = B~(ro)
V~
(3)
B~(r,O,¢,t)= B~(ro)(~)-r°~®sinO + V~(0,6''t')
V~,
(4)
¢'=O-~®t'
(5)
where
t'=t
r-r0
V~
In (3)-(6), r is heliocentric distance and r0 is the solar radius. The field is defined in terms of spherical coordinates. Vw is the solar wind speed and f~® is the solar rotation frequency. Vo and V~ are the speeds at the base of the magnetic footpoints which mimic the flow within the supergranulation network. The nominal Parker-spiral field is retained by setting V0 = 0 and V~ = 0 in equations (4) and (5). We consider a divergence-free flow pattern on the solar surface by requiring
Vo(O, ~ , t ) -
1 ioo_6 ro sin-----~ ~(o, ¢,t)
(6)
10 v,(o,¢,t)- ;oN¢(o,¢,t)
(7)
where ~b(O,¢, t) is an arbitrary function. To model solar supergranulation, we consider ¢ to be a sum of spherical harmonics with random phases, and time dependent amplitudes with random frequencies. 20
20
. . . . . . .
10 ~
0
-10
-10
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~ .
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,,,,
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-1020 "1'0 0 x (AU)
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Fig. 3: Top (upper panels) and side (lower panels) views of field lines generated using the magnetic field determined from the random motions of magnetic footpoints in the solar supergranulation (left panels) and from the standard Parker spiral (right panels).
588
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Illustrated in Figure 3 are magnetic field lines determined from Equations (3)-(6). We use an rms value for the supergranulation characteristic speed of (< V02 + V~ >)1/2 = 0.6 kin/s, and a characteristic scale size of the supergranulation of 104 kin. The wind speed is 400 km/s. To investigate the effect of the above magnetic field configuration on cosmic rays, we have followed the trajectories of 10000 particles. The particles were released with an energy 1 MeV, at r=2 AU, and at a latitude of 30 ° with respect to the solar ecliptic plane. Since turbulence on the scales which resonate with the particles gyroradius are not included in the above description, we mimic their effect by scattering the particles phenomenologically. We assume that the ratio of the particle mean-free path to gyroradius is constant and assume a mean scattering time of 1000 gyroperiods. This corresponds to a mean-free path of 0.2 AU at 1 AU, which is consistent with the standard Palmer "consensus" (Palmer, 1982). We have performed a few additional runs with different mean-free paths and have found that the latitudinal diffusion is increased with increasing mean-free path. This is expected since the particles are essentially propagating along field lines and the decreased diffusion (longer mean-free path) allows for more easy access to high latitudes. Plotted in Figure 4 are histograms of the test particles collected ten days after their release (the release point is shown as the vertical dashed lines). The peak intensity occurs at about 4.5 AU which is consistent with the particles convecting with the solar wind speed as they are scattered isotropically in a frame moving with the wind speed. 100 10
,
,
r
i
I
0.4
018
/
"1
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8 10 .3 104 104 10 -s
I
0
I
4 8 R (AU)
,
0
I
,
30 60 900 latitude (degrees)
1.2
E (MeV)
Fig. 4: Histograms of particles collected ten days after release in the turbulent fields associated with supergranulation. The re/ease point is shown as the verticM dashed lines. Figure 4 indicates that particles readily diffuse in latitude. If the field were the nominal Parker field, then the expected latitudinal diffusion (due to our ad hoe scattering) would be very small. In fact it is straightforward to show that the latitudinal diffusion is more than 2 orders of magnitude smaller than what is seen in Figure 4. We believe that it .is reasonable to expect CIR-associated particles at high latitudes, even in the absence of the CIR itself, simply due to cross-field transport. Note that cross-field diffusion can be regarded as composed of two parts. The first part consists of the actual transfer of particles across the local magnetic field, while the second corresponds to the diffusion along individual field lines which are braided or mixed in the transverse direction. The efficient latitudinal diffusion seen in our model is due primarily to the latter. SUMMARY We have discussed the transport and acceleration of energetic particles associated with corotating interaction regions particularly as it applies to global heliospheric phenomena. For instance, we have previously suggested that a two-step mechanism for the preacceleration of anomalous cosmic rays may occur as interstellar pickup ions are accelerated at CIRs in the inner heliosphere, propagate to the termination shock, and are then further energized to cosmic-ray energies. Although the composition
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of CIR-accelerated ions near 1 AU is not often indicative of interstellar pickup ions, we feel that the CIR-associated particles in the distant heliosphere are dominated by pickup ions. Continued study is needed to resolve this issue. We have also presented a new model for interplanetary magnetic field in which we numerically traced the trajectories of a number of 1-MeV cosmic rays in order to study their latitudinal diffusion. The model field is determined by the motions of magnetic footpoints near the solar photosphere. We have found that the particles readily propagate to high latitudes via cross-field diffusion in the form of field-line random walk. Consequently, we believe that it is reasonable to expect CIR-accelerated energetic particles at high latitudes. ACKNOWLEDGEMENTS I would like to thank J. R. Jokipii and J. Kdta for useful discussions pertaining to many of the ideas discussed here. Additionally, I have greatly benefited from discussions with the participants at the the "Cosmic Rays in the Heliosphere" workshop held at the International Space Science Institute (ISSI) in Bern held Sept. 1996, and March 1997. This work by NASA under grants NAG5-2251 and NAG5-6620. I gratefully acknowledge financial support from ISSI during the above mentioned workshop. REFERENCES Armstrong, T. P., M. E. Pesses, and R. B. Decker, Shock drift acceleration, in Collisionless Shocks in the Heliosphere: Reviews of Current Research, Geophys. Monogr. Ser., vol. 35, edited by B. T. Tsuratani and R. G. Stone. p. 271, AGU, Washington, D. C. (1985). Barnes, C. W., and J. A. Simpson, Evidence for interplanetary acceleration of nucleons in corotating interaction regions, Astrophys. J., 210, L91 (1976). Boufaida, M., and T. P. Armstrong, Spatial variations of 0.2 to 5 MeV protons in the 1-5 AU inecliptic region from Ulysses, Voyager 1 and 2, and IMP-8 gradient studies, J. Geophys. Res., 102, 7103 (1997). Decker, R. B., and L. Vlahos, Numerical studies of particle acceleration at turbulent, oblique shocks with an application to prompt ion acceleration during solar flares, Astrophys. J., 306, 710 (1986). Decker, R. B., Krimigis, S. M., and Kane, M., Spatial gradients, energy spectra, and anisotropies of ions ~ 30 keV at CIR shocks from 1 to 50 AU,Proc. 24th Int. Cosmic Ray Conf. (Rome) 4, 421 (1995). Ellison, D.C., Monte Carlo simulation of charged particles upstream of the Earth's bow shock, Geophys. Res. Lett., 8, 991 (1981). Fisk, L. A., Motion of the foot points of heliospheric magnetic field lines at the Sun: Implications for recurrent energetic particle events at high heliographic latitudes, J. Geophys. Res., 101, 15,547 (1996). Fisk, L. A., and M. A. Lee, Shock acceleration of energetic particles in corotation interaction regions in the solar wind, Astrophys. J., 237, 620 (1980). Giacalone, J., and J. R. Jokipii, Spatial Variation of Accelerated Pickup Ions at Co-Rotating Interaction Regions, Geophys. Res. Left., 24, 1723 (1997). Giacalone, J., D. Burgess, S. J. Schwartz, and D.C. Ellison, Hybrid simulations of protons strongly accelerated by a parallel collisionless shock, Geophys. Res. Lett, 19, 433 (1992). Giacalone, J., J. R. Jokipii, R. B. Decker, S. M. Krimigis, M. Scholer, and H. Kucharek, The preacceleration of anomalous cosmic rays in the inner heliosphere, Astrophys. J, 486, 471 (1997). Gloeckler, G., D. Hovestadt, L. A. Fisk, Observed distribution functions of H, He, C, O, and Fe in corotating energetic particle streams: Implications for interplanetary acceleration and propagation, Astrophys. J., 230, L191 (1979).
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Gloeckler, G., J. Geiss, H. Balsiger, L. A. Fisk, A. B. Galvin, F. M. Ipavich, K. W. Ogilvie, R. yon Steiger, and B. Wilken, Detection of interstellar pick-up hydrogen in the solar system, Science, 261, 70 (1993). Gloeckler, G., J. Geiss, E. C. Roelof, L. A. Fisk, F. M. Ipavich, K. W. Oglivie, L. J. Lanzerotti, R. yon Steiger, and B. Wilken, Acceleration of interstellar pickup ions in the disturbed solar wind observed on Ulysses, J. Geophys. Res., 99, 17,637 (1994). Hamilton, D. C., M. E. Hill, R. B. Decker, and S. M. Krimigis, Temporal and spatial variations in the spectra of low energy ions in the outer heliosphere, Proc. 25th Int. Cosmic Ray Conf. (Durban) 2, 261 (1997). Jokipii, J. R., Particle drift, diffusion, and acceleration at shocks, Astrophys. J., 255, 716 (1982). Jokipii, J.R. and E.N. Parker, Random walk of magnetic lines of force in astrophysics, Phys. Rev. Lett., 21, 44 (1968). Jokipii, J. R., and J. Giacalone, The acceleration of pickup ions, Space Sci Rev., 78, 137 (1996). K6ta, J., J. R. Jokipii, Modeling of 3-D corotating cosmic-ray structures in the heliosphere, Sp. Sci. Rev., 83, 137 (1997). Lee, M. A., V. D. Shapiro, and R. Z. Sagdeev, Pickup ion energization by shock surfing, J. Geophys. Res., 101, 4777 (1996). Mason, G. M., J. E. Mazur, J. R. Dwyer, D. V. Reames, and T. T. von Rosenvinge, New spectral and abundance features of interplanetary heavy ions in corotating interaction regions, Astrophys. J., 486, L149 (1997). McDonald, F. B., B. J. Teegarden, J. H. Trainor, and T. T. yon Rosenvinge, The interplanetary acceleration of energetic nucleons, Astrophys. J., 203, L149 (1975). Palmer, I. D., Transport coefficients of low-energy cosmic rays in interplanetary space, Rev. Geophys., 20, 335 (1982). Parker, E. N., The passage of energetic charged particles through interplanetary space, Planet. Space Sci., la, 9 (1965). Pesses, M. E., J. A. Van Allen, B. T. Tsuratani, and E. J. Smith, High time resolution observations of corotating interaction region proton events by Pioneer 11, J. Geophys. Res., 89, 37 (1984). Schwadron, N. A., L. A. Fisk, and G. Gloeckler, Statistical acceleration of interstellar pickup ions in corotating interaction regions, Geophys. Res. Lett., 21, 2871 (1996). Simnett, G.M., Sayle, K.A., Tappin, S.J., and Roelof, E.C., Co-rotating particle enhancements out of the ecliptic plane, Space Sci. Rev., 72, 307 (1995). Van Hollebeke, M. A. I., F. B. McDonald, H. H. T/rainor, and T. T. yon Rosenvinge, The radial variation of corotating energetic particle streams irt the inner and outer solar system, J. Geophys.Res., 83, 4723 (1978). Vasyliunas, V. M., and G. L. Siscoe, On the flux and the energy spectrum of interstellar ions in the solar system, J. Geophys.Res., 81, 1247 (1976). Zank, G. P., H. L. Pauls, I. H. Cairns, and G. M. Webb, Interstellar pick-up ions and quasiperpendicular shocks: implications for the termination shock and interplanetary shocks, J. Geophys. Res., 101,457 (1996).
Adv. Space Res. Vol. 23, No. 3, pp. 581-590, 1999 © 1999 COSPAR. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 0273-1177/99 $20.00 + 0.00 PII: S0273-1177(99)00124-6
P A R T I C L E T R A N S P O R T A N D A C C E L E R A T I O N AT COROTATING INTERACTION REGIONS Joe Giacdlone
University of Arizona, Tucson, AZ, 85721
ABSTRACT The transport and acceleration of energetic nuclei associated with corotating interaction regions is discussed with emphasis on its importance relative to global heliospheric phenomena such as anomalous cosmic rays, the distant heliosphere, and propagation to high latitudes. We will discuss aspects of particle acceleration at the forward and reverse shocks bounding CIRs which support the idea that accelerated pickup ions are important contributors to energetic ions in the heliosphere. We will outline our current understanding of the source of CIR-associated energetic nuclei based on multispacecraft observations of the spatial variation of low-energy cosmic rays, as well as that of freshly ionized pickup ions. We will also discuss the propagation of CIR-associated energetic particles to high heliographic latitudes. We will present a model of the interplanetary magnetic field and show results from a numerical simulation which suggest that particles undergo significant latitudinal diffusion. © 1 9 9 9 C O S P A R . P u b l i s h e d by Elsevier Science Ltd.
INTRODUCTION It has been long known that interplanetary disturbances corotating with the sun have associated enhancements in energetic particle intensities (e.g. Barnes and Simpson, 1976; McDonald et al., 1975). These corotating interaction regions (CIRs) are bound by collisionless shocks, one which propagates away from the sun in the solar wind frame (the forward shock) and the other moves towards the sun in the wind frame (the reverse shock). C u r r e n t l y it is thought charged particles are accelerated to several MeV energies at these shock waves. Less clear, however, is the source of these particles. Many observations suggest that the composition of these species are indicative of solar particles (e.g. Gloeckler et al., 1979; Mason et al., 1997). Others, however, show that interstellar pickup ions are the likely source of many of these particles (Gloeckler et al., 1994). Interstellar pickup ions, which are ionized neutrals that enter the solar system due to the sun's motion in the galaxy, represent a suprathermal population which are readily accelerated by shocks in the inner heliosphere. Gloeckler et al. (1994) and Schwadron et al. (1996) have also suggested that the initial acceleration of the pickup ions occurs via the mechanism of transit-time damping of magnetic fluctuations within the CIR. Particles accelerated by CIRs in the inner heliosphere will propagate to the solar wind termination shock, which stands at some 80 AU from the sun, and undergo further acceleration. Some will propagate back into the inner heliosphere. It is fairly well established that anomalous cosmic rays are interstellar pickup ions which are accelerated, at least in part, at the termination shock. An interesting scenario may be that CIRs accelerate pickup ions which are then further accelerated at 581
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the termination shock to anomalous cosmic-ray energies. It is currently not well understood whether this occurs and will be discussed in more detail in this paper. Energy spectra of CIR-associated particles can be complicated. Power-law tails, predicted by the standard diffusive shock acceleration theory, are not typically observed. Fisk and Lee (1980) showed that the inclusion of an adiabatic cooling term in the transport equation (Parker, 1965) gives rise to an exponential-like energy dependence of the shock-accelerated spectra. They found that the intensity at the reverse shock is larger than those associated with the forward shock, in agreement with the majority of observations (Van Hollebeke et al., 1978; Pesses et al., 1984). On the other hand, Giacalone and Jokipii (1997) showed that the acceleration of interstellar pickup ions is strongly favored at the reverse shock over the forward shock and that this naturally leads to larger intensities at the reverse shock, regardless of the acceleration mechanism. This is further discussed below. The propagation of low-energy cosmic rays associated with CIRs to high heliographic latitudes is another topic of current interest owing to the highly successful Ulysses mission. Energetic particles corotating with the sun are seen despite the absence of shocks which remain closer to the ecliptic plane during quiet solar conditions (Simnett et al., 1995). It remains unclear whether these particles reach high latitudes via diffusion across magnetic field lines (Kdta and Jokipii, 1997), or whether there exists a systematic magnetic connection between high and low latitudes and that the particles propagate along the lines of force (Fisk, 1996). This topic is discussed further in this paper. THE PHYSICS OF CHARGED-PARTICLE ACCELERATION BY SHOCKS Charged-particle acceleration by collisionless shock waves is often thought of in terms of two mechanisms, shock-drift acceleration and first-order Fermi acceleration. These are actually contained in the more general diffusive shock theory. Shock-drift acceleration is the term attributed to the mechanism whereby charged particles interact with the shock in the limit of weak scattering (e.g. Armstrong et al., 1985). A charged-particle gradient B drifts along the shock interface in the same direction as the motional electric field. The energy comes from working against the plasma. The m a x i m u m energy gains via this mechanism occurs at shocks where the motional electric field is the largest (those in which the angle between the mean field and shock normal are nearly perpendicular). Diffusive shock acceleration applies when the particle distribution function is nearly isotropic. It contains both drift and Fermi acceleration (Jokipii, 1982; Decker and Vlahos, 1986). The equation which governs diffusive shock acceleration is the transport equation first written down by Parker (1965). This equation is straightforward to solve for simple shock geometries. The Injection Problem The injection problem, which applies primarily to shocks in which the angle, OB,~, between the mean magnetic field and the shock normal direction is > 45 °, stems from the fact that particles do not tend to move normal to the field lines as they convect through the shock and are unable to remain near the shock to be accelerated. The question is whether there is enough scattering to keep the particles near the shock. By requiring the anisotropic diffusive streaming to be small, we find U1 [(rg/Air) 2 sin 2 OBn + (1 -- ~;±/~11)2 sin 2 0s,~ cos 2 0sn] 1/2 <<1 v (m±/~ll) sin2 0Sn + cos 20Bn
(1)
where U1 is the flow speed upstream of the shock, v is the plasma-frame particle speed, x±,ll are the spatial diffusion coefficient normal to and along the mean magnetic field, respectively, All is the mean-
Particle Transport at CIRs
583
free path, and rg is the particles Larmor radius. In deriving this condition, we have neglected terms of order nJ_/xa, where NA is the antisymmetric diffusion coefficient. For a very nearly perpendicular shock (0Bn ~ 90°), (1) becomes v >> 3U1)~ll/rg for classical scattering in which x± -~ ~ll(rg/Aii) 2. Clearly pickup ions that convect into a stationary shock cannot meet this criterion since they have speeds such that v = U1 and mean-free paths that are larger than their gyroradii. This criterion is more easily met at propagating shocks as discussed below. Contrary to quasi-perpendicular shocks, those shocks which essentially propagate along the mean magnetic field (quasi-parallel shocks) are known to be efficient injectors of energetic particles. Highenergy tails in the distribution function downstream of quasi-parallel shocks form directly out of the thermal population (Ellison, 1981; Giacalone et al., 1992). Some of the details of the internal structure of collisionless shocks may aid in the injection problem, however, at present this is still not resolved. For instance, Zank et al. (1995) and Lee et al. (1995) have shown that a fraction of freshly-ionized pickup ions can be trapped by the cross-shock potential as they are convected into the shock layer. The trapped particles are accelerated by drifting along the motional electric field as they skim along the shock surface. However, to get significant energization, the shock must have a width on the order of the electron inertial length which is much smaller than typical high-Alfv4n Mach shocks. Propagating shocks more readily inject very low-energy particles than those which stand in the flow of the solar wind (such as planetary bow shocks and the termination shock). Qualitatively this is easy to see since interplanetary shocks move only a hundred k m / s or so faster than the solar wind and low-energy particles can remain near the shocks longer and enhance their probability of being accelerated rather than being convected downstream. Quantitatively one replaces U1 in Equation 1 with V8 - U1, where V~ is the shock speed measured relative to the sun. Typically this is less than U1 and (1) is more easily met. Weak shocks which propagate only slightly above the solar wind speed (i.e. V, ~_ U1), are especially good at injecting particles. The resultant shock-accelerated spectrum, on the other hand, will be very soft in this case. ION ACCELERATION AT CIR'S Acceleration at the F / R Shocks One of the earlier analytic attempts to describe observed features of the energy spectra of CIRassociated energetic particles was given by Pisk and Lee (1980). They found that the spectra have an exponential-like energy dependence at 1 AU. The spectral index depends inversely on the flow speed, so that the spectra associated with a reverse shock are harder than those associated with the forward shock, in agreement with the majority of observations. On the other hand, if pickup ions (of either interstellar or local origin) are important contributors to these particles, the asymmetry in the interaction between pickup ions which were first ionized in either the fast or slow solar wind naturally explains many of the observations. For i'nstance, since the pickup ions are moving much faster in the fast wind, acceleration in the fast wind should be more efficient because these particles start with approximately four times as much energy as those in the slow wind. This idea is illustrated in Figure 1 for the case where where the accelerated spectrum is an inverse power law. The power-law tail which connects to the pickup ion distribution has a v -4 dependence which would occur for shock acceleration at a strong shock. A steeper spectrum would produce a larger effect. This general conclusion should hold for a wide variety of acceleration mechanisms. Acceleration in the Absence of Shocks
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There is observational evidence reported by Gloeckler et al. (1994) and Schwadron et al. (1996) that interplanetary shocks may not efficiently accelerate unaccelerated pickup ions. These authors have proposed that rather, a statistical process known as transit-time damping of magnetic fluctuations (the magnetic equivalent to Landau damping), is the initial stage of a two-step process. Low-frequency fluctuations necessary for this process to work are contained within the turbulent regions bounding the shocks associated with corotating interaction regions. Once the particles have been pre-accelerated in this manner, they continue to be accelerated by the shocks which is a more rapid process. 10
0.1
f(v) 0.01
0.001
0.0001
1
10 v/Us~w
Fig. 1: Sketch of the accelerated pickup-ion distribution that were ionized in either the fast or slow wind, as indicated. In this case the acceleration mechanism is independent of the local wind speed so that the spectral index is the same.
It is also possible that acceleration of either pickup ions or solar energetic particles can take place before the forward and reverse shocks form during the development of a CIR. If the particles can diffuse through the velocity gradient, associated with the CIR formation, rapidly enough they will be efficiently accelerated. This gradient can be fairly large since the flow speed changes from about 400 km/s in the slow wind to 800 km/s in the fast wind. Consequently, acceleration of pickup ions can occur before the shocks form and this can lead to a peak in the intensity within the CIR for a time. Once the shocks have formed, the intensity within the CIR will diminish relative to the intensity at the shocks, partly due to adiabatic energy loss, and also because the intensity at the shocks increase due to shock acceleration. After some characteristic time, the peak at the shocks will dominate. This idea may serve as a possible alternative explanation of the observations by Schwadron et al. (1996).
SOURCE OF CIR-ACCELERATED PARTICLES In the previous sections we discussed the injection problem of accelerating very low-energy particles by shocks and suggested that pickup ions are favored for acceleration over thermal solar wind particles. However, it is difficult to accelerate pickup ions when the magnetic field is nearly perpendicular to the direction of a velocity gradient (such as a shock). Thus, it is unclear whether the termination shock can accelerate pickup ions efficiently enough to account for the observed fluxes of anomalous cosmic rays. In the next section we discus~ a two-step preacceleration mechanism whereby the pickup ions are first accelerated by interplanetary shocks in the inner heliosphere and are then convected to the termination shock where they are further energized to cosmic-ray energies. A key assumption in the two-step mechanism described in the next section is that energetic particles observed as recurrent flux enhancements in the distant heliosphere (Decker et al., 1995) are pickup ions and not solar wind. This distinction is important since it is well established that the composition and
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charge state of the anomalous cosmic-ray component does not resemble the solar wind. Spacecraft instruments which measure fluxes in the distant heliosphere have not yet been able to make the distinction between various species. On the other hand, there is a wealth of compositional observations of CIR-associated particles in the inner heliosphere which may clarify the source of these particles. Additionally, there are observations of the radial variation of CIR-associated energetic particles. We now briefly discuss these observations. Van Hollebeke et al. (1978) reported on the radial variation of corotating energetic particle streams and concluded that .-~ 1 MeV protons have a positive radial gradient to a peak at about 4 AU where the intensity declines. Boufaida and Armstrong (1997) averaged over all observations (including solar energetic particle events) of Earth orbiting spacecraft, Ulysses and Voyagers, and determined that low-energy protons (< 1 MeV) have a positive radial gradient out to about 5 AU, whereas highenergy particles (> 1 M e V ) h a v e a negative gradient. Voyager observations reported by Decker et al. (1995) indicate that the peak flux in recurrent enhancements in ,-~ 1 MeV protons fall off as 1/r 2 (r is radial distance). These peaks were observed to be superimposed on a "shoulder" which is above the instrument background. This shoulder falls off less rapidly and is more like a r -°'7 dependence (Decker, private communication). Finally, observations by Hamilton et al. (1997) indicate that ~ 1 MeV protons fall off about as 1/r 2 (perhaps a little less rapidly as indicated in their Figure 2), and 1 MeV Helium falls off much less rapidly (more like l/r). Note that the other energy levels which were studied by Hamilton et al. (ibid) are probably anomalous cosmic-rays. 10 0
~.~ 108
~
10a
E
104
. . . . . . . .
I
. . . . . .
I ' - " : : -'~' ~'' Solar ~Nin'd' '1
N~............ . .
10"
102 10°
'I
,T I,I
. . . . . . .
I
i
i
i
i~1,~
10-~
.0 10-s 105 107 1
10 R (AU)
100
104 1
10
R (AU)
100
Fig. 2: Upper left: Pickup hydrogen and solar wind flux versus heliocentric distance. Lower left: the ratio of the pickup-ion to solar wind flux. Right: The normalized outward-directed pickup-ion flux (normalized to the interstellar flux of the various species) for H, He, Ne, and O. These are derived from Vasyliunas and Siscoe (1976) and Gloeckler et al. (1993). The intensities of CIR-related particles in the distant heliosphere are considerably larger than what is expected by simple radial expansion and cooling. For instance, for a power-law spectrum at the position r=r0, the intensity at a given energy will vary as J cx (1"/1"o) -4(1+~¢)/3, where 3' is the spectral index. Thus, for 3' = 1, which occurs for a strong shock, then the intensity at say 40 AU would be more than 5 orders of magnitude smaller than at 1 AU. The effect is even larger for a softer spectrum, or even worse still for an exponential spectrum, which are typically observed at 1 AU. Thus, continued acceleration, or an increased source strength must account for the observations in the distant heliosphere. One may argue that the strength of CIR shocks are at their peak at some 4-5 AU, and this may help explain the observations by Van Hollebeke et al. (1978). However, as shown in Figure 2, pickup protons and oxygen also peak at some 5-10 AU, which may also explain these observations assuming that pickup ions are the source.
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As suggested in Figure 2, there is an inherit difficulty in separating the abundances of pickup ions and solar particles when the observations are made at 1 AU since there are so few pickup H and O while thermal solar wind is difficult to accelerate. Helium, on the other hand, should be dominated by pickup ions. Ne may also be dominated by pickup ions, but this is not as clear. In the distant heliosphere, on the other hand, we believe that there is no reason to discount the possibility that the observed fluxes of CIR-related energetic particles are dominated by interstellar pickup ions. Solar energetic particles, which may dominate in some 1 AU observations, are likely to be much less abundant in the distant heliosphere due to adiabatic losses. PREACCELERATION OF ANOMALOUS COSMIC RAYS We have recently proposed a model (Jokipii and Giacalone, 1996; Giacalone et al., 1997) for anomalous cosmic rays in which the initial acceleration of interstellar pickup ions occurs in the inner heliosphere rather than locally at the termination shock. The ultimate acceleration required to achieve anomalous cosmic-ray energies occurs at the termination shock but only after the pickup ions have been preaccelerated. This is one possible solution to the apparent difficulty in accelerating the previously unaccelerated pickup ions at the stationary, nearly perpendicular termination shock of the solar wind. It is known that interplanetary shocks, or turbulent regions within corotating interaction regions, more readily accelerate pickup ions and this has been observed by Ulysses instruments (Gloeckler et al., 1994; Schwadron et al., 1996). Our results, using Voyager 2 data as a baseline normalization a global transport model, has proven to be promising in that there seems to be enough low-energy particles observed in the outer heliosphere which are presumably accelerated in the inner-heliosphere, to account for the observed intensities of anomalous cosmic rays (see Figure 2 of Giacalone et al., 1997). If these inner-heliosphere-accelerated particles are accelerated pickup ions, as suggested by recent observations (Gloeckler et al., 1994), then this would be a very important stage in the formation of anomalous cosmic rays. Although, the composition of CIR-accelerated ions near 1 AU may not be pickup ions (additional studies of composition are needed), we feel that the CIR-associated particles in the outer heliosphere are dominated by pickup ions. This issue is not well understood at present. LATITUDINAL PROPAGATION OF CIR-ACCELERATED PARTICLES Ulysses observations of corotating energetic particles at high heliographic latitudes by Simnett et al. (1995) reveal that these enhancements persist even in the absence of the CIRs. These particles are accelerated at CIRs and are subsequently transported in latitude. This finding may suggest a magnetic connection between the high latitudes of observation and the lower latitudes where acceleration at CIR's could take place such as that suggested by Fisk (1996). If such a connection exists, the skipping of charged particles across field lines may not be important since the latitudinal excursions of the field lines allows for direct access to various latitudes via parallel transport. One of the main difficulties in this picture is that the particles must propagate a large distance along the field lines and significant adiabatic cooling will take place. Additionally, in order to uniformly populate field lines, there must be some cross-field transport. A quantitative model of cosmic-ray transport in the field suggested by Fisk (1996) has not yet been developed. Alternatively, K6ta and Jokipii (1997) have considered the importance of perpendicular diffusion as an alternative explanation of the observations of Simnett et al. (1995). Their model emphasized the importance of the random walk of field lines (Jokipii and Parker, 1968) and their simulations indicate that low-energy shock-accelerated particles can be expected to appear at high heliographic latitudes. In order to help clarify this issue, we consider the effect of large-scale magnetic turbulence in the solar
Particle Transport at CIRs
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wind on the transport of low-energy cosmic rays. Our model assumes that the observed time and spatial scales occurring at the solar photosphere can be characterized by the random movements of magnetic footpoints (it is currently thought that solar magnetic fields are continually reconnecting and that only a fraction of the field lines open into interplanetary space). The field is carried away from the sun assuming a constant radial flow. Under these assumptions, it follows that the interplanetary magnetic field takes the form.
B~(r) = B~(~o)
(2)
Bo(r, 0, ~, t) = B~(ro)
V~
(3)
B~(r,O,¢,t)= B~(ro)(~)-r°~®sinO + V~(0,6''t')
V~,
(4)
¢'=O-~®t'
(5)
where
t'=t
r-r0
V~
In (3)-(6), r is heliocentric distance and r0 is the solar radius. The field is defined in terms of spherical coordinates. Vw is the solar wind speed and f~® is the solar rotation frequency. Vo and V~ are the speeds at the base of the magnetic footpoints which mimic the flow within the supergranulation network. The nominal Parker-spiral field is retained by setting V0 = 0 and V~ = 0 in equations (4) and (5). We consider a divergence-free flow pattern on the solar surface by requiring
Vo(O, ~ , t ) -
1 ioo_6 ro sin-----~ ~(o, ¢,t)
(6)
10 v,(o,¢,t)- ;oN¢(o,¢,t)
(7)
where ~b(O,¢, t) is an arbitrary function. To model solar supergranulation, we consider ¢ to be a sum of spherical harmonics with random phases, and time dependent amplitudes with random frequencies. 20
20
. . . . . . .
10 ~
0
-10
-10
20 "--20 -10 0 ,
~ .
I
.
,
.
.
~
.
~'
20
,,
@
10
y (AU) 0
30
. . . . . . .
,;
,
10 20 ,
,' t
",,
•
-20
,
I
,
f~
,
,
,
-20 -10 ~
30
~
•
20
,
,,30 O
I
,
10 20 ....
,,,,
,t
z,,o,,o 0
0
-1020 "1'0 0 x (AU)
10 20-10-20 . -10 . . 0 . 10 20 x (AU)
Fig. 3: Top (upper panels) and side (lower panels) views of field lines generated using the magnetic field determined from the random motions of magnetic footpoints in the solar supergranulation (left panels) and from the standard Parker spiral (right panels).
588
J. Giacalone
Illustrated in Figure 3 are magnetic field lines determined from Equations (3)-(6). We use an rms value for the supergranulation characteristic speed of (< V02 + V~ >)1/2 = 0.6 kin/s, and a characteristic scale size of the supergranulation of 104 kin. The wind speed is 400 km/s. To investigate the effect of the above magnetic field configuration on cosmic rays, we have followed the trajectories of 10000 particles. The particles were released with an energy 1 MeV, at r=2 AU, and at a latitude of 30 ° with respect to the solar ecliptic plane. Since turbulence on the scales which resonate with the particles gyroradius are not included in the above description, we mimic their effect by scattering the particles phenomenologically. We assume that the ratio of the particle mean-free path to gyroradius is constant and assume a mean scattering time of 1000 gyroperiods. This corresponds to a mean-free path of 0.2 AU at 1 AU, which is consistent with the standard Palmer "consensus" (Palmer, 1982). We have performed a few additional runs with different mean-free paths and have found that the latitudinal diffusion is increased with increasing mean-free path. This is expected since the particles are essentially propagating along field lines and the decreased diffusion (longer mean-free path) allows for more easy access to high latitudes. Plotted in Figure 4 are histograms of the test particles collected ten days after their release (the release point is shown as the vertical dashed lines). The peak intensity occurs at about 4.5 AU which is consistent with the particles convecting with the solar wind speed as they are scattered isotropically in a frame moving with the wind speed. 100 10
,
,
r
i
I
0.4
018
/
"1
10 .2
8 10 .3 104 104 10 -s
I
0
I
4 8 R (AU)
,
0
I
,
30 60 900 latitude (degrees)
1.2
E (MeV)
Fig. 4: Histograms of particles collected ten days after release in the turbulent fields associated with supergranulation. The re/ease point is shown as the verticM dashed lines. Figure 4 indicates that particles readily diffuse in latitude. If the field were the nominal Parker field, then the expected latitudinal diffusion (due to our ad hoe scattering) would be very small. In fact it is straightforward to show that the latitudinal diffusion is more than 2 orders of magnitude smaller than what is seen in Figure 4. We believe that it .is reasonable to expect CIR-associated particles at high latitudes, even in the absence of the CIR itself, simply due to cross-field transport. Note that cross-field diffusion can be regarded as composed of two parts. The first part consists of the actual transfer of particles across the local magnetic field, while the second corresponds to the diffusion along individual field lines which are braided or mixed in the transverse direction. The efficient latitudinal diffusion seen in our model is due primarily to the latter. SUMMARY We have discussed the transport and acceleration of energetic particles associated with corotating interaction regions particularly as it applies to global heliospheric phenomena. For instance, we have previously suggested that a two-step mechanism for the preacceleration of anomalous cosmic rays may occur as interstellar pickup ions are accelerated at CIRs in the inner heliosphere, propagate to the termination shock, and are then further energized to cosmic-ray energies. Although the composition
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of CIR-accelerated ions near 1 AU is not often indicative of interstellar pickup ions, we feel that the CIR-associated particles in the distant heliosphere are dominated by pickup ions. Continued study is needed to resolve this issue. We have also presented a new model for interplanetary magnetic field in which we numerically traced the trajectories of a number of 1-MeV cosmic rays in order to study their latitudinal diffusion. The model field is determined by the motions of magnetic footpoints near the solar photosphere. We have found that the particles readily propagate to high latitudes via cross-field diffusion in the form of field-line random walk. Consequently, we believe that it is reasonable to expect CIR-accelerated energetic particles at high latitudes. ACKNOWLEDGEMENTS I would like to thank J. R. Jokipii and J. Kdta for useful discussions pertaining to many of the ideas discussed here. Additionally, I have greatly benefited from discussions with the participants at the the "Cosmic Rays in the Heliosphere" workshop held at the International Space Science Institute (ISSI) in Bern held Sept. 1996, and March 1997. This work by NASA under grants NAG5-2251 and NAG5-6620. I gratefully acknowledge financial support from ISSI during the above mentioned workshop. REFERENCES Armstrong, T. P., M. E. Pesses, and R. B. Decker, Shock drift acceleration, in Collisionless Shocks in the Heliosphere: Reviews of Current Research, Geophys. Monogr. Ser., vol. 35, edited by B. T. Tsuratani and R. G. Stone. p. 271, AGU, Washington, D. C. (1985). Barnes, C. W., and J. A. Simpson, Evidence for interplanetary acceleration of nucleons in corotating interaction regions, Astrophys. J., 210, L91 (1976). Boufaida, M., and T. P. Armstrong, Spatial variations of 0.2 to 5 MeV protons in the 1-5 AU inecliptic region from Ulysses, Voyager 1 and 2, and IMP-8 gradient studies, J. Geophys. Res., 102, 7103 (1997). Decker, R. B., and L. Vlahos, Numerical studies of particle acceleration at turbulent, oblique shocks with an application to prompt ion acceleration during solar flares, Astrophys. J., 306, 710 (1986). Decker, R. B., Krimigis, S. M., and Kane, M., Spatial gradients, energy spectra, and anisotropies of ions ~ 30 keV at CIR shocks from 1 to 50 AU,Proc. 24th Int. Cosmic Ray Conf. (Rome) 4, 421 (1995). Ellison, D.C., Monte Carlo simulation of charged particles upstream of the Earth's bow shock, Geophys. Res. Lett., 8, 991 (1981). Fisk, L. A., Motion of the foot points of heliospheric magnetic field lines at the Sun: Implications for recurrent energetic particle events at high heliographic latitudes, J. Geophys. Res., 101, 15,547 (1996). Fisk, L. A., and M. A. Lee, Shock acceleration of energetic particles in corotation interaction regions in the solar wind, Astrophys. J., 237, 620 (1980). Giacalone, J., and J. R. Jokipii, Spatial Variation of Accelerated Pickup Ions at Co-Rotating Interaction Regions, Geophys. Res. Left., 24, 1723 (1997). Giacalone, J., D. Burgess, S. J. Schwartz, and D.C. Ellison, Hybrid simulations of protons strongly accelerated by a parallel collisionless shock, Geophys. Res. Lett, 19, 433 (1992). Giacalone, J., J. R. Jokipii, R. B. Decker, S. M. Krimigis, M. Scholer, and H. Kucharek, The preacceleration of anomalous cosmic rays in the inner heliosphere, Astrophys. J, 486, 471 (1997). Gloeckler, G., D. Hovestadt, L. A. Fisk, Observed distribution functions of H, He, C, O, and Fe in corotating energetic particle streams: Implications for interplanetary acceleration and propagation, Astrophys. J., 230, L191 (1979).
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