More on a possible modulation barrier in the outer heliosphere

Adv. Space Res. Vol. 9. No. 12. pp. (12)121-(12)124. 1989 Printed in Great Britain. AU rights reserved.

027~l17789$0.00 ÷.50 Copyright © 1989 COSPAR

MORE ON A POSSIBLE MODULATION BARRIER IN THE OUTER HELIOSPHERE M. S. Potgieter and J. A. Le Roux Department of Physics, Potchefstroom University, 2520 Potchefstroom, South Africa

ABSTRACT The new concept of a possible modulation barrier in the outer heliosphere is discussed further. It is argued that since barrier—type modulation is characterized by large radial gradients in the outskirts of the heliosphere, while they remain almost constant in the rest of the heliosphere, it is already contained in drift and in terminal shock acceleration models. Combined with the expected coalescence of transients at large radial distances this may contribute to a very effective modulation barrier at large radial distances. INTRODUCTION The concept of a modulation barrier in the outskirts of the heliosphere is new in the field of cosmic ray modulation. This concept, which have been proposed by Webber and Lockwood /1/, is based on the independence of the observed interplanetary radial gradient of heliocentric distance (out to -30 AU) and time (from 1976—1982), along with properties of the solar wind which suggest that the distance to the pressure balance boundary does not vary by more that ±25%over the 11—year solar cycle /2/. Recently, Potgieter and Le Roux /3,4/ have substantiated this concept further by illustrating that the incorporation of a barrier into a time—dependent, spherically—symmetric (10), numerical model can be responsible, in principle, for a variation of a factor of 3—4 change in the integral proton intensity (E>60 MeV) at Earth, while the radial gradient remains essentially constant in most of the heliosphere. This behaviour is in direct contrast with standard, steady—state model predictions. Based on the relative success of time—dependent models (see also Perko and Fisk /5/) in explaining a constant radial gradient, it seems appropriate to explore the barrier concept further by using more sophisticated models. In this paper we discuss some aspects of barrier modulation and give a preliminary report on the utilization of a two—dimensional (20), time—dependent drift model /see also 6/. BARRIER MODULATION;

RESULTS AND DISCUSSION

The average radial gradient, obtained from the integral proton intensity (E>60 MeV) observed on the network of spacecraft in the heliosphere, and reported by Webber and Lockwood /1/ for 1977 was - 2.7% per AU. It increased slightly to - 3.12% per AU in 1983 and has since steadily declined, to - 1.7% per AU in 1986, with decreasing modulation. If it is assumed that the average radial gradient is almost independent of radial distance and that the boundary radius R (where the local interstellar spectrum is encountered) was, for instance, 60 AU in 1976, then the observed radial gradient for 1983 suggests that R should have been at - 80 AU at that time. Moreover, the present small gradient suggests R 105 AU, implying a factor of 2 difference in R for the two consecutive solar minimum periods, 1976 and 1987. Such a large difference between two solar minima seems unlikely. Webber /2/ presented convincing arguments why R should not vary by more than ±25%over the solar cycle, and that the heliospheric boundary should lie somewhere between 45 and 55 AU. If true, the scenario of large modulation occurring in the vicinity of the heliospheric boundary as pictured by Webber and Lockwood seems a plausible explanation for the observed small gradients between 1 and 40 AU. Figure 1, taken from Potgieter and Le Roux /3/, clearly illustrates the concept of barrier modulation. In this case the barrier develops with increasing activity, and disappears during or after periods of solar minimum, and is caused by the accumulation of regions of enhanced scattering between 40 and 50 AU, without changing any parameter in the rest of the heliosphere. The main features of barrier modulation according to this Figure are: (1) Enhanced modulation (large radial gradients) in the Outer heliosphere over some arbitrary JASR 9:12—!

(12)121

M. S. Potgieter and J. A. Le Roux

(12)122

The radial gradient is, of course, very large in that region but then becomes almost constant over most of the heliosphere. Since a flat neutral sheet drift model is used these solutions are for solar minimum periods. However, the point we want to make is that during a qA>0 epoch drift models predict a barrier effect in the outer heliosphere, and radial gradients essentially independent of radial distance over most of the heliosphere. Its fact, during this period the radial gradient is also to a large extent independent of time for it is well—known that drift models are insensitive to the variation of modulation parameters, e.g., Krr, and the waviness of the neutral sheet, when qA>O /7,81. During a qAO because drifts play a role in cosmic—ray modulation. If this drift barrier combines with the effects of the expected accumulation of transients in the Outer helio— sphere — which happens independently of the IMF polarity — an asymmetric barrier effect w.r.t. the reversal of the IMF polarity may occur. Another possible phenomenon which could contribute to a barrier effect is the termination shock of the solar wind. It seems reasonable to assume that beyond the shock a highly turbulent region may exist and be considered a steady—state, convective part of a large barrier. (See also Lockwood and Quenby /9/). The kind of modulation caused by a 1D termination shock model is illustrated for anomalous oxygen in Figure 3. It is clear that at low energies the modulation, as a function of radial distance, has the features necessary to describe it as boundary modulation. The effect seen- here is primarily caused by the shift in the peak of the energy spectrum towards higher energies with increasing solar activity. In principle, this can also happen t~ other particle species and may cause an additional large energy dependent barrier effect. A most likely origin of barrier—type modulation is the accumulation of transients in the outer heliosphere. There is still an uncertainty about what is happening in the outer heliosphere, but it is well documented that shock episodes periodically appear and that successive shocked regions accumulate into larger almost circular shocks at r > 20 AU /10/. If these regions move outwards they may become a most effective barrier, which could become reinforced with increased solar activity and decline after maximum activity. This is the underlaying mechanism used in the approach Potgieter and Le Roux /3,4/ took to describe a barrier originated 11—year cycle. Using a 2D drift model we found that it was more difficult to obtain a full 11—year cycle caused by the accumulation of Forbush—type decreases in the outer heliosphere. One could argue that it is unrealistic to try and obtain a full 11—year cycle, but in our opinion this would have clearly illustrated the basic principles

1000:

>‘~

~1O

Anomalous Oxygen

—01

UI

C

a,

~ icr°2

UeVfnuc 100

—

do —03 1 a, :

30 20

L -

‘4-

~_10 —~4.

0

I

I

I

I

I

I

I

I

I

5

10

15

20

25

30

35

40

45

Radial

Distance

50

(Au)

Fig. 3. The concept of barrier—type modulation in the outer heliosphere illustrated for anomalous oxygen with a 1D terminal shock acceleration model. This barrier effect has a strong energy dependence.

(12)123

Modulation Barrier in the Outer Heliosphere

10

00

I GeV Protons

:

-

(A

.~

—,

~•

—.~

— —-———....

——.—

~ ....

———--—

—

-D

...,

—-——

-----:....-

.•>~

a ~

————

..—.—--

.—~

~

———

.—.

—— . —

0

I

I

1

I

I

I

I

I

I

5

10

15

20

25

30

35

40

45

50

Radial Distance (AU) Fig. 1. 50 AU).

Barrier modulation in the outer heliosphere (between 40 and A one—dimenional (10) time—dependent model was used.

1.00~

I GeV Protons

0.80

~0.60

(a)

(b)

.

0

a,

N

~0A0

E

0

z

Cc)

0.20

o• oc 0

5

Cd)

10

I

15

I

20

I

25

I

30

I

35

I

40

I

45

I

50

Radial Distance (AU) Fig 2. Normalized 1 GeV proton intensity as a function of radial distance obtained with steady—state models: (a) A 2D drift model with qA < 0, (b) qA > 0. (c) A 2D, non—drift model, and (d) a 10 model. Note the barrier effect of (b). distance. (2) Radial gradients almost independent of radial distance and time in the rest of of the heliosphere. (3) A heliospheric boundary radius which does not move appreciably during an 11—year—cycle. Using these features as a starting point, inspection of the results of a steady—state drift model /7,8/ shows that a barrier effect is a characteristic of this model during periods when particles are being transported from the polar to the equatorial regions of the heliosphere and out along the neutral sheet (qA>O). This effect seems to disappear when the polarity of the interplanetary magnetic field (IMF) reverses (qAO.

.

M. S. Potgieter and J. A. Le Roux

(12)124

of barrier modulation in an advanced model. The reason why it is more difficult is because it becomes difficult to control the recovery time of a Forbush—type decrease. This is caused by the various additional 2D effects in an axially—symmetric heliosphere, e.g., perpendicular diffusion, which contribute to smaller recovery times. On average the recovery was found to be much quicker than in a ID model. With this 1D model it is possible to produce large step—like decreases in the long term modulation of cosmic—rays by simply letting individual disturbances propagate outward from the Sun without accumulation at large radial distances /5,11/. The reason is because the recovery in intensity, when a disturbance passes the Earth, for instance, can be made very slow so that when the next disturbance passes the intensity has not yet recovered from the previous one. This slow recovery is virtually impossible to obtain in a full drift model. Furthermore, in this model Forbush decreases seem to disappear quickly with increasing radial distances /6/, so that even with a heliosphere full of closely spaced consecutive disturbances a factor of - 4 decrease in the intensity at Earth could not be obtained. These results indicate that the coalescence (spatial evolution) of disturbances over several AU’s in the outer heliosphere is necessary to get large long term modulation. Another fact to consider is that full drift effects are too large, especially when a flat neutral sheet is used /12/. We found that the recovery rate of a Forbush decrease could be slowed down significantly if drifts were reduced by a factor of - 2. However, several alternatives still have to be considered and studied before any conclusive arguments about the role of transients, as barriers, in long term modulation with a time—dependent drift model can be made. We intend to study these effects more intensively. CONCLUSIONS Barrier modulation is basically characterized by three features: (1) large modulation over some arbitrary distance in the outer heliosphere, (2) radial gradients essentially independent of radial distance and time in the rest of the heliosphere, and (3) a heliospheric outer boundary that varies by no more than ±25%over the 11—year cycle. Using these features as criteria to define barrier—type modulation, it is shown that this type of modulation manifests itself in drift models when particles drift out of the heliosphere along the neutral sheet (qA