Solar wind disturbances caused by successive flares from the same active region are traced to about 20 AU, using the modeling method developed by Hakamada and Akasofu (1982). It is shown that the flare-generated shock waves coalesce with the co-rotating interaction region of the interplanetary magnetic field, resulting in a large-scale magnetic field structure in the outer heliosphere. Such a structure may have considerable effects on the propagation of galactic cosmic rays

Akasofu, S. I.

Hakamada, K.

English

NASA Technical Reports Server

SOLARWINDDISTURBANCESIN THEOUTERHELIOSPHERE
CAUSEDBY SUCCESSIVESOLARFLARESFROMTHESAMEACTIVEREGION
S.-I. Akasofu
Geophysical Institute
University of Alaska
Fairbanks, Alaska 99701
and
K. Hakamada
Department of Engineering
Chubu Institute of Technology
1200 Matsumoto-cho
Kasugal-shl
Aichl-ken 487
Japan
ABSTRACT
Solar wind disturbances caused by successive flares from the same active
region are traced to about 20 au, using the modeling method developed by Hakamada
and Akasofu (1982). It is shown that the flare-generated shock waves coalesce
with the co-rotating interaction region of the interplanetary magnetic field,
resulting in a large-scale magnetic field structure in the outer heliosphere.
Such a structure may have considerable effects on the propagation of galactic
cosmic rays.
Introduction
During the last decade, a considerable progress has been madein understand-
ing the solar wind flow and the propagation of solar wind disturbances in the
heliosphere (Shea et. al., 1977; Dryer and Steinolfson, 1976; Dryer and Tandberg-
Hanssen, 1980). A somewhatdifferent approach from the standard hydrodynamic and
MHDmethods was considered by Hakamadaand Akasofu (1982) who devised a method
analogous to an aerodynamic technique in simulating someaspects of the disturbed
solar wind with a fair accuracy. They construct first a steady state pattern for
the so-called 'two-sector' or 'two-stream' situation. For this purpose, they
assume that the distribution of the solar wind speed on the source surface (a
spherical surface of radius of 2.5 Ro) has the minimumspeed (V=300 km/sec) along
the heliomagnetic equator which is assumedto be inclined by 20° with respect to
the heliographic equator; the speed is assumed to increase toward higher
latitudes in both the northern and southern hemispheres. The resulting magnetic
field configuration in the equatorial plane is the well-known co-rotating
structure which consists of two 'spiral arms' (the corotating interaction
region), as faster winds interact with slower winds.
Propagating Flare Disturbances
(a) Twosuccessive flares from the sameregion
Effects of solar flares are introduced in this co-rotating structure by
adding a high speed flow from a circular area, centered around a solar flare, on
475
https://ntrs.nasa.gov/search.jsp?R=19840005036 2020-03-22T07:36:49+00:00Z
the source surface. In the circular area, the flow speed is assumedto have a
atGaussian distribution of the 'half-width' o; the flow speed VF __ center of
the circular area is assumedto vary in time as VF = V_ ax _ t • e T) ; thus,
a flare is characterized by six parameters, the latitJ_ (v,, longitude (_) and
the onset time (TF) of a flare, the maximumflOWVF_ax (km/sec) at the center of
the circular area of its size parameterized by a(v)_ and the time variation of
V. by T(hr). For the method of introducing effects of a solar flare, see also
_max
HaEamada and Akasofu (1982). The first flare is located at the magnetic equator
(e = 0°) and the longitude _ = 0°, namely on the crossing point of the positive
x-axis through the source surface. This particular flare is parameterized by the
maximum wind speed VFmax = 800 km/sec, • = 12 hrs and o = 60 ° .
The second flare is introduced 48 hours (2 days) after the first flare. It
is assumed that the same active region is responsible for both flares, which have
rotated by _ = 28.3 ° from the time of the first flare. The second flare is
characterized by a faster flow VFm x = I000 km/sec, the same growth-decay curve
(_ = 12 hrs) and a narrower extent _o = 20 °) than the first one.
Figure la shows the disturbance patterns (< 5 au) in the ecliptic plane at
T=0, 1.5, 3.5 and 7.0 days after the onset of the first flare. In this
particular example, the shock wave associated with the second flare caught up
with the first shock wave on about the 6th day. Note that the spiral structure
continued to rotate, while a part of the inner part of the spiral structure was
destroyed by the first shock. On the 8th day both shocks reached one of the
spiral arms. Behind the shocks, a new spiral arm begins to reform rapidly.
Figure Ib shows the disturbance pattern within a radial distance < 25 au, T
= 12, 24, 36 and 48 days after the onset of the first flare. On the 24th day,
both shocks reached the second co-rotating structure. Meanwhile, the new spiral
arm is clearly established behind both shocks. As the shocks propagate further,
the inner spiral structure reforms rapidly and expands outward. On the 48th day,
both shocks reach the third co-rotating structure, forming a complex magnetic
field structure in the outer heliosphere.
Note that from the 12th day to the 48th day, the co-rotating structure has
rotated _ I I/3 times. If there is no solar flare disturbance, two spiral arms
pass by regularly at any fixed point in the figure every 27 days, causing two
distinct increases of the solar wind speed and the magnetic field magnitude.
However, the shock waves caused by the solar flares disturb considerably such a
regular pattern. In fact, on the 48th day, two co-rotating structures and the
two shocks pile up at a radial distance of about 17 au and it is no longer
possible to identify individual co-rotatlng structures and the shocks.
(b) Six successive flares from the same active region
In this particular example, we assume an extremely active region which
produces six successive flares in a period of I0 days. The six flares are
parameterized as follows:
Flare I
Flare 2
T = 0, _ = 0° 0 = 0°
VFmax = 800 km/sec, • = 12 hrs, a = 60 °
T = 2.0 days, _ = 28.3 °, 0 = 0 °
VFmax = i000 km/sec, r = 12 hrs, a = 20 °
476
T--0.0 T=I.5
5AU, 5AU
5AU
T=7.0
5AU
5AU 5AU
Figure la. Solar wind disturbances caused by two successive flares in the
ecliptic plane, separated by 48 hours, from the same active region. The
figure shows the propagating structure at T=O (onset), 1.5, 3.5 and 7.0 days
after the onset of the first flare. The outer limit of each circular area is
at 5 au.
477
25AU
Flare 1 TIv=0,_=0",e=0"
Vr I=800, T = 12, o": 60 °
Flare 2 T_'=48,_):28.3",e:O" 25AU
25AU
25AU i 25AU
25AU 25AU
Figure lb. Continuation of Figure la, showing the propagating structure at
T = 12, 24, 36 and 48 days. The outer limit of each circular area is at 25
au.
478
Flare 3 T = 4 days, _ = 56.7 ° , 0 = 0°
VFmax = 800 km/sec, T = 12 hrs, o = 60 °
Figure 2 shows the propagating disturbance pattern at T=7, I0, 17, 15, 19
and 25 days after the onset of the first flare. One can see that all the shock
waves coalesce with the spiral patterns, forming an extensive magnetic field
structure. It is quite likely that such a structure will have considerable
effects on the propagation of galactic cosmic rays in the outer heliosphere.
Acknowledgment. The work reported here was supported in part by a contract
from the U.S.A.F., FI9628-81-K-0024.
References
Dryer, M. and R. S. Stelnolfson, MHD solution of interplanetary disturbances
generated by simulated velocity perturbations, J. Geophys. Res., 81, 5413,
1976.
Dryer, M. and E. Tandberg-Hanssen (ed), Solar and Interplanetary Dynamics, IAO
Symposium No. 91, D. Reldel Pub. Co., 1980.
Hakamada, K. and S.-I. Akasofu, Simulation of three-dimenslonal solar wind
disturbances and resulting geomagnetic storms, Space Sci. Rev. 31, 3, 1982.
Shea, M. A., D. F. Smart and S. T. Wu (ed), Study of Traveling Interplanetary
Phenomena, 1977, D. Reidel Pub. Co., Dordrecht-Holland, 1977.
479
T=7.0
15AU
15AU 15AU
15 AU '_IfIIi
X:20
15AU
X=20"_
15AU t5AU
15AU
_ 15 AU
15AU
Figure 2. Solar wind disturbances caused by six successive flares during a
period of I0 days. The figure shows the propagating structure at T _ 7.0,
I0.0, 17.0, 15.0, 19.0 and 25.0 days after the onset of the first flare. The
outer limit of each circular area is at 15 au.
480
Comments on "Solar wind disturbances in the outer heliosphere,
caused by successive solar flaresfrom the same active region",
by Akasofu and Hakamada
V. J.Pizzo,
HA0/NCAR
P.O. Box 3000
Boulder, CO 80307
In this paper, a kinemati6 modeling technique (Hakamada and Akasofu, 1982) is used
to simulate the interaction of transient flows with a two-sector corotating flow to large
heliocentric distances. The input transients, which are characterized by several parame-
ters, have peak speeds in the range of 800-1000 km/s. Hence the corotating flows consti-
tute an inhomogenous slower-speed background, into which the transients continually
penetrate. Thus, by 10 AU in the authors' last example (which involves six separate
flares), the interaction of the transients with the corotating flows as well as with each
other produces a very complicated jumble of magnetic fields. It is further asserted that
such contorted magnetic topologies should have important consequences for galactic
cosmic ray transport.
With this last point, I have no particular quibble, other than to mention that the basic
concept has been around for nearly two decades. Parker (1963), for example, broached
the general idea in his book, though he did not offer very specific estimates as to where
substantial magnetic complexes would form or what their dimensions might be. 0nly
recently, in fact, have enough detailed data appeared to permit some assessment of the
validity of the idea (e.g., see McDonald et at., 1982; Burlaga et al., 1982; and Burlaga et al.,
i983).
So the questions to ask are: How faithfully does this modeling technique, with all its
obvious practical advantages, simulate the flow interactions? To what extent is it quanti-
tatively accurate? Are there any regions where it fails even in a qualitative sense?
In considering these questions, it must be recognized from the outset that accuracy
of the sort usually associated with a full MHD model is not required for the authors'
stated purposes. On the other hand, for a model to rank as an effective tool, it must still
successfully predict the gross features of the flow: e.g., the heliocentric distance where
the major structures interact, the spatial scale of the resultant interaction region, the
rate at which CIRs expand, the approximate magnitude of the field enhancements, etc.
It is my contention that the model of Hakamada and Akasofu (1982) meets even these
relaxed criteria only in a limited parameter range and only over a fairly restricted span
of heliocentric distances. Further, I will argue that the particular examples presented by
the authors are in general violation of these limitations and their results are thus
compromised.
*TheNationalCenterforAtmosphericResearchissponsoredby theNationalScienceFoundation.
481
To begin, let us be clear as to the physical content of their model. The Hakamada
and Akasofu (1982) formulation is first and foremost a purely kinematic description, i.e.
the evolution is entirely determined by the input velocity variations; the material in no
way exerts either a gas pressure or magnetic field force. What is especially poignant is
the way the authors handle those regions where fast material overtakes slow. It is inevit-
able that at some point the fluid elements must begin to overlap, corresponding to a
shock in the dynamic case. Here the authors invoke a parameterized curve-fitting
method to keep the usual R-t diagram from becoming double-valued (see Sec. 1.3 and 2.3
inHakamada and Akasofu, 1982). The parameters are chosen such that the resultantV-t
or V-R curves resemble some particular observed streams or dynamic model calculations.
However, the predictive value of any model is measured by its ability to cope with a wide
variety of input flows (such as are encountered in the real solar wind) under a single
parameterization. That is, in practical applications one is forced into picking one param-
eterization that will be in effect throughout the simulation and will have to accurately
describe the evolution of all flow states therein. In general, it will not be possible to
tinker meaningfully with the parameters after the fact, since ifthe model is being used in
the predictive mode, there is obviously nothing to calibrate itagainst.
A single parameterization of the type used by the authors may well allow them to
mimic a few well-chosen streams, as they have demonstrated. And, indeed, were all solar
wind streams more or less alike, such an approach might be viable. However, it hardly
needs any emphasis that solar wind flows differ markedly in speeds, field strengths,
densities--in fact, over the entire gamut of flow parameters. And all the interesting
large-scale interaction phenomena--the rate at which CIR's expand, the rate at which
shocks form and decay, the lateral expansion of a directed blast wave, etc.--all depend
sensitively upon the local properties of the ambient medium and the input shock
strength, i.e. they are inherently dynamic in nature. It is of paramount importance to
recognize that the authors' parameterization of shock propagation, for example, is based
solely upon kinematic considerations. The speed jump is first computed from kinematics
and the ad-hoc parameterization, then density and field are chosen to satisfy flux conser-
vation. Thus, while the Rankine-Hugoniot relations are in some sense satisfied, the ther-
modynamic and magnetic properties of the medium play no role in the determination of
the shock speed. In view of these considerations, then, it is difficult to see how any single
parameterization can suffice for the range of flow states studied by the authors. At least,
they have not demonstrated such a capability.
That being said, we must now ask how all this specifically impacts the authors'
results. The answer will be split into three parts : the model's treatment of the corotat-
ing structure alone; its treatment of isolated impulsive flows into an ambient medium;
and, its treatment of the interaction between transient and corotating flows.
First, with regard to purely corotating flows, recent observational and theoretical
efforts (Burlaga, 1983; Pizzo, this conference) seem to concur that by about I0 AU all the
fast material in high-speed streams has been pretty well consumed in the interaction and
that the subsequent evolution is governed by large-scale pressure-wave dynamics. In this
regime, a kinematic approach is totally irrelevant. The authors are able to maintain an
identifiable stream structure to large heliocentric distances only through careful mani-
pulation of input conditions at the inner boundary: their input structure is longitudinally
very broad, with the gentlest of velocity gradients. Thus their CIRs do not even form until
about 7 AU and are still reasonably compact at 20 AU (see Fig. 1.5 in Hakamada and
Akasofu, 1982). In consequence of all the observational experience gained through
Pioneer and Voyager, the authors' background flow therefore appears highly unrealistic,
to say the least.
482
Next, in the case of an isolated, impulsive transient penetrating into a uniform
ambient flow, there are two major shortcomings in this model. First, since all features of
the shock propagation in the model are solely contingent upon the input velocity struc-
ture, there is no distinction, really, between strongly driven shocks and simple blast
waves, which are known to have quite different evolutionary properties (e.g. Hundhausen
and Gentry, 1969) . Again, the parameterization in the model could be adjusted for one
class, but then it would be inappropriate for the other. Second, an important feature of
multi-dimensional shock propagation is that the forward shock expands near the sun to
cover a much broader angular span than does the input disturbance, while the reverse
shock remains fairly localized within the driver gas (e.g. D'Uston et al., 1981). The lateral
expansion of the forward shock front is a purely dynamic phenomenon and has great sig-
nificance for the field structure. In the kinematic model, of course, the shock is confined
to the input angular cone and there is simply no way to reproduce the important spread-
ing effects.
Finally, when transients and corotating streams are allowed to interact, it has long
been known that the density (and presumably magnetic) structure of the ambient coro-
taring flow plays at least as large a role in the interaction as does the velocity structure
(Heinemann and Siscoe, 1974; Hirschberg eta/., 1974). Shock speeds and transit times
are thus going to be very poorly modeled in the authors' formulation, particularly when
the disturbances are traced over many AU and across many intervening structures.
In light of all these considerations, it is hard to see how the authors' model can pos-
sibly provide a quantitatively adequate representation of the flow systems presented in
this paper. Their corotating background flow is quantitatively unrealistic inside about 10
AU and is not even qualitatively appropriate beyond that point. And, owing to the serious
deficiencies in their treatment of the very complex transient-corotating interaction as
outlined above, it is evident that their quantitative estimates for the important physical
properties of the flow (the location, dimensions, and amplitude of the resultant magnetic
structures) at large heliocentric distances must be regarded with critical suspicion. It is
to be stressed that what is at issue here is not a dry technical debate over some trifling
10-20% discrepancies among alternative methods of calculation. Rather, I conte:_d that
the kinematic model, as in the grossly over-extended application witnessed m the
authors' treatise, is susceptible to such large quantitative error that the accompanying
Figures are best viewed as little more than computer-generated schematics.
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Burlaga, L. F., Corotating pressure waves without streams in the solar wind, submitted to
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Burlaga, L. F., F. B McDonald, R. Schwenn, and A. Lazarus, Interplanetary flow systems
associated with cosmic ray modulation in 1977_1980, (abstract) APS Bulletin, 27, 571,
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D'Uston, C., M. Dryer, S. M. Han, and S. T. Wu, Spatial structure of flare-associated pertur-
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Solar wind disturbances in th outer heliosphere caused by successive solar flares from the same active region

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