A theoretical study of the formation of a coronal cavity and its relation to a quiescent prominence is presented. It is argued that the formation of a cavity is initiated by the condensation of plasma which is trapped by the coronal magnetic field in a closed streamer and which then flows down to the chromosphere along the field lines due to lack of stable magnetic support against gravity. The existence of a coronal cavity depends on the coronal magnetic field strength; with low strength, the plasma density is not high enough for condensation to occur. Furthermore, we suggest that prominence and cavity material is supplied from the chromospheric level. Whether a coronal cavity and a prominence coexist depends on the magnetic field configuration; a prominence requires stable magnetic support

An, C. H.

Steinolfson, R. S.

Suess, S. T.

Tandberg-Hanssen, E.

English

NASA Technical Reports Server

ON THE FORMATION OF CORONAL CAVITIES
Chang-Hyuk An, Steven T. Suess, and Einar Tandberg-Hanssen
Space Science Laboratory, NASA Marshall Space Flight Center
Huntsville, Alabama 35812
Richard S. Steinolfson
University of California, Irvine, California 92717
ABSTRACT
We present a theoretical study of the formation of a coronal cavity and its relation to a
quiescent prominence. We argue that the formation of a cavity is initiated by the condensation
of plasma which is trapped by the coronal magnetic field in a closed streamer and which then
flows down to the chromosphere along the field lines due to lack of stable magnetic support
against gravity. The existence of a coronal cavity depends on the coronal magnetic field strength;
with low strength, the plasma density is not high enough for condensation to occur. Further-
more, we suggest that prominence and cavity material is supplied from the chromospheric level.
Whether a coronal cavity and a prominence coexist depends on the magnetic field configuration;
a prominence requires stable magnetic support.
I. INTRODUCTION
The coronal cavity is a dark region whose density is lower than in the surrounding
streamer. The close association of coronal cavities with prominences has led to the suggestion
that the coronal cavities are a manifestation of prominence formation by condensation of coronal
plasma (Pneuman, 1983). However, Saito and Tandberg-Hanssen (1973) found that the formation
of a prominence requires much more material than available in the cavity before depletion. They
concluded that prominence material must be supplied from below (e.g., in the form of spicules),
not from the adjacent corona. Here, we investigate further how and when a coronal cavity
forms, and suggest what the relation is between a coronal cavity and a prominence. It is believed
that the global steady corona is a consequence of the interaction between outward flowing solar
wind plasma and the cornal global magnetic field (Pneuman and Kopp, 1971; Steinolfson, Suess,
and Wu, 1982). When interacting with the magnetic field, the plasma adjusts itself for energy as
well as force balance. We believe that the coronal cavity is formed in the process of the dynamic
adjustment. In this paper we study the stability of the streamer model of Steinolfson, Suess, and
Wu (1982) (henceforth referred to as SSW) to the condensation mode. SSW calculated the
dynamic interaction between outward flowing solar wind plasma and a global coronal magnetic
field using a 2-D, time-dependent, ideal MHD computer simulation. In the final steady state, they
found a density enhancement in the closed field region with the enhancement increasing with
increasing strength of the magnetic field. Our stability calculation shows that if density enhance-
ment is higher than a critical value, the plasma is unstable to condensation modes. We describe
how, depending on the magnetic field configuration, the condensation may produce a coronal
cavity and/or initiate the formation of a prominence.
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https://ntrs.nasa.gov/search.jsp?R=19860015167 2020-03-20T15:24:45+00:00Z
I1. CONDENSATION AS A CAUSE OF CORONAL CAVITIES
The initial plasma density from the steady hydrodynamic solar wind equations and the
two final states with t3 = 0.5 and 4 are shown in Figure 1. For/3 = 4 the density is enhanced
about 1.4 times the initial value, while for /3 = 0.5 the maximum enhancement is 4.3 times the
initial value at r = 1.3 Ro. Figure 2(a) shows the magnetic field configuration and plasma velocity
in the nearly steady-state for /3 = 0.5. Note that velocity is zero in the closed region. An
expanded view of the closed field region of the figure is shown in Figure 2(b), with the con-
densation mode growth rate co for /3 = 0.5 and 4 shown on the right side of the vertical axis
(s implies stability).
For evaluation of the stability, we neglect the temperature and density variation along
field lines but consider the variation on each field line of different equatorial height. Heat con-
duction perpendicular to the magnetic field was neglected - only a parallel component was con-
sidered. The ambient heating rate was assumed to be constant in time and is balanced to the
radiation in a steady-state. An (1985) found that the plasma is stable against condensation modes
if the local growth rate 60 = -poq_/3,Po is positive on all the field lines, but unstable if w is
negative on any field line. Here,
• - + (k • Bo )2
Po P Bo 2 tc
and R, To, Po, Bo, and Po are dimensionless radiative energy loss rate, temperature, density,
magnetic field, and pressure, and k is a wave vector. The quantities tr and t c are radiative and heat
conduction timescales defined as t r = 3Po/2R and tc = L2Po/_:oToT/2. Because of the local
nature of the stability we evaluate _o on each field line of the closed field region. Figure 2(b)
shows that the stability of the final states for _ = 0.5 and 4 is significantly different. For/3 = 4,
all the field lines are stable - mainly because the density enhancement over the initial value is
small as seen in Figure 1.. For _ = 0.5 all the field lines of equatorial height less than r = 2.05
R e are unstable. The local growth rate _o is maximum at the field line nearest to r = Ro and
decreases with height. If we include the gravity in the calculation, the height above which the
plasma is stable is far less than r = 2.05 R o due to the stabilizing effect of the gravity (Wragg
and Priest, 1982; Antiochos and An, 1985).
Next, let us discuss how, depending on the magnetic field configuration, the thermal
instability initiates a coronal cavity or prominence formation. As plasma density increases above
a critical value the plasma becomes unstable to condensation modes. The condensed plasma
accumulates on or falls along the field lines depending on whether or not the field lines provide
stable support against gravity. If the condensed plasma accumulates, the radiative loss rate con-
tinues to increase until the plasma cools to T = 10 s K (An et al., 1983). The plasma keeps
cooling to Tc ("104 K) after the temperature reaches T = 10s K because the radiative energy
loss rate exceeds heat conduction and ambient heating rate. As the temperature approaches Tc,
the ambient heating rate is approximately equal to the radiative energy loss rate and heat con-
duction is negligible in the overall energy balance. The temperature T c (< 10 4 K) and corres-
ponding density Nc are typical of prominence temperature and density.
If the condensed plasma falls down along field lines, runaway condensation is not possible.
During initial condensation, the temperature decreases, density increases, and the radiative energy
loss rate increases. If condensed plasma slips down faster than the radiative energy loss rate
269
(tr = 2 x 104 s for the /3 = 0.5 streamer at r = 0.1 Ro) the radiative energy loss rate decreases
until it reaches an energy balance and the condensation and slippage cease. However, because the
plasma cools during the initial condensation and the temperature change is negligible during the
slippage, energy balance can be reached only after the density is depleted below the initial value
(assuming the ambient heating rate is constant in time). The density depletion causes the plasma
to become stable to the thermal instability. Since SSW considered a simple dipole field which
may not provide stable support, the thermal instability for/3 = 0.5 will lead to a cavity. On the
other hand, for /3 = 4, the streamer is thermally stable and cannot have a cavity. Saito and
Hyder (1968) argue that the difference between prominences with and without clearly defined
coronal cavities could be explained by geometry. Our stability calculation suggests that the
existence of the cavity also depends on the coronal field strength.
Saito and Tandberg-Hanssen (1973) and Saito and Hyder (1968) found that plasma mass
in a cavity is not sufficient to account for the mass of the prominence. The other possibility is
that the material comes from below (Saito and Tandberg-Hanssen, 1973), possibly in the form of
spicules. For a newly formed prominence with height 104 km, it takes about one day for a
spicule material of average flux density F = 1.2 x 101 s cm-2 s-1 (Athay and Holzer, 1982) to fill
the prominence. The time is about equal to the timescale of a quiescent prominence formation
(Zirin, 1978). The spicule plasma which is thermalized in the corona and flowing outward will
be trapped by and accumulated on the closed field. If the accumulation is sufficiently high to
initiate condensation and the magnetic field gives stable support at the base but no such support
above, we will find a prominence at the base below a coronal cavity. In other words, a
prominence below a coronal cavity is formed by the material supplied from below as Saito and
Tandberg-Hanseen (1973) suggested and is a consequence of condensation of the plasmas. The
main difference is that prominences require magnetic support and continuous consideration of
coronal material supplied by spicules for fully developed prominences. We schematically sum-
marize our results in Figure 3, showing four different regions; region 1 is an open field region
and source of solar wind plasma. In region 2 the plasma has reached a steady-state with energy
and force balance. In region 3 condensed plasma flows down along the field lines, leaving a
cavity behind. Region 4 is the local field region in which the condensation initiates prominence
formation. The local sheared magnetic field provides stable support against gravity.
Acknowledgments. We appreciate Dr. R. Moore for valuable discussions during the course
of this work. This research is supported by NAS-NRC, the NASA Office of Solar and Helio-
spheric Physics, and the Office of Space Plasma Physics. RSS was supported by the NASA Solar
Maximum Mission Guest Investigator Program.
270
REFERENCES
An, C.-H., 1985, submitted.
An, C.-H., Canfield, R. C., Fisher, G. H., and McClymont, A. N., 1983, Astrophys. J., 267, 421.
Antiochos, S. K. and An, C.-H., 1985, to be submitted.
Athay, R. G. and Holzer, T. E., 1982, Astrophys. J., 255, 743.
Pneuman, G. W., 1983, Solar Phys., 88, 219.
Pneuman, G. W. and Kopp, R. A., 1971, Solar Phys., 18, 258.
Saito, K. and Hyder, C., 1968, Solar Phys., 5, 61.
Saito, K. and Tandberg-Hanssen, E., 1973, Solar Phys., 31, 105.
Steinolfson, R. S., Suess, S. T., and Wu, S. T., 1982, Astrophys. J., 255, 730.
Wragg, M. A. and Priest, E. R., 1982, Astron. Astrophys., 113, 269.
Zirin, H., 1978, Physics of Solar Prominences, IAU Colloquium No. 44 (E. Jensen, P. Malthy,
and F. Q. Orrall, eds.), Institute of Theoretical Astrophysics, Blidern, Oslo.
9 I I I I I I
INITIAL
_" /3=4FINAL
/3= 0.5 FINAL
8
I I I I I I
1.5 2 2.5 3 3.5 4 (R®)
r
Figure 1. Density profiles in the initial and final states.
271
to
to
5 "J _ (105)(/3=0.5) (/3=4)
- S S
2.0
4
5.2 S
1 1.2
9.1 S
1.0
1 2 3 4 5 7T/2 0 2Tr/3
(a) (b)
Figure 2. (a) The magnetic field configuration and plasma velocity in the nearly steady-state for/3 =
0.5 (from Steinolfson, Suess, and Wu, 1982). The dotted-line is the Alfv_n and the dashed-line is
the sonic curve. (b) The expanded closed field region of (a) with the instability growth rate
cofor/3 = 0.5 and 4 on the right side of the vertical axis (s = stability).
Figure 3. A three-dimensional sketch for a coronal streamer and its fine structures. 
The arrows represent the plasma flows. 


On the formation of coronal cavities

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