4. Role of Gravitation
|
Figure 3
|
[17] The calculations in which real plasma parameters in the solar corona
were specified and the gravitational forces of the Sun were taken into
account have shown that, because of a high
P at the start of calculations, the effect of gravitation is nearly
unnoticeable, and the distributions of plasma parameters at
t<25 turn out
to be similar to those in the absence of gravitation (Figure 3). As the
corona expands, the velocity maximum moves away from the Sun. The
highest velocity is
5.5
107 cm s
-1.
The maximum velocity of plasma flow
is reached at the portion of the
X axis where density and temperature
gradients are not zero. However, as the corona expands and the gradients
of the plasma density and temperature decrease, the force
P and
gravitational force near the left boundary become comparable, and the
flow velocity becomes lower than in the calculations assuming zero
gravitation. A local decrease in velocity leads to a local plasma
accumulation, i.e., to an increase in the density. As this takes place, the
gradient near the left boundary
(nkT)/nMi again increases, and the
plasma velocity directed away from the Sun restores its value. This again
causes smoothing of the gradient, i.e., the flow is no longer stable. This
leads to the conclusion that an additional acceleration is needed for the
stable generation of the solar wind in the presence of gravitation. Such an
additional acceleration mechanism could be MHD waves generated on
the photosphere and absorbed in the corona
[Chashey, 1997].
[18] The nonstationarity of the flow in the vicinity of the Sun obtained in
calculations allowing for gravitation can also be a result of an incorrect
choice of the dimensionless parameter
b0 = 8 pn0kT0/B02.
It follows from
the approximate Parker's formula that the solution is very sensitive to the
integration constant, and the solar wind can be formed only under clearly
defined conditions in the corona. By assuming that in the corona
kT = 200 eV and
n =2
107 cm
-3,
we take into consideration only a pressure
gradient of the electron gas. However, it can hardly be expected that the
electron temperature of the corona considerably exceeds the ion
temperature because the time during which the electron and proton
temperatures become equal, estimated as
t(c)
2
107 Te3/2/n, is not
longer than an hour. Direct measurements of the electron temperature
obtained from an ionization equilibrium and the ion temperature through
Doppler broadening of spectral lines also point to
Te
200 eV and
Te
Ti [Doschek and Feldman, 2000;
Seely et al., 1997].
Here,
Te is the
electron temperature in eV, and
n is the number of electrons in cm
-3.
If
the electron temperature
Te in the corona plasma is comparable to the ion
temperature
Ti, the dimensionless parameter of pressure force should be
written as
8 pn0k(Te + Ti)/B02. At
Te = Ti the dimensionless coefficient of
pressure force in (3) should be taken to be
2 b0 rather than
b0.
|
Figure 4
|
[19] To understand whether, in principle, the stationary outflow of solar wind
can exist due to additional acceleration, we performed the calculations in
which the pressure force was increased by a factor of 2, i.e., the
dimensionless coefficient of pressure force in equation (3) was taken to
be
2 b0. The results of calculations are depicted in Figure 4. Figure 4a
shows distributions of plasma parameters along the
X axis for
t=11.29.
The increases in plasma density and temperature occur here within the
computational domain, and the velocity maximum has not yet reached
the right boundary. The maximum velocity exceeds
5
107 cm s-1.
It is
reached at the portion of the
X axis where the pressure gradient is not
zero. The magnetic field lines are extended at this portion by the flow of
expanding plasma (Figure 4b). However, in the region nearer to the right
boundary, where the plasma flow has not yet arrived, the field lines differ
only slightly from the dipole ones. The velocity maximum shifts beyond
the computational domain to the moment of time
t
40. Distributions of
the plasma parameters and the field lines for
t=127.29, when the
stationary flow is about to be established, are shown in Figures 4c and
4d. No local minima in velocity obtained in calculations ignoring ion
temperature gradient (Figure 3) are observed near the left boundary. In
this case acceleration by the pressure gradient is more effective, and
influence of gravitation is not considerable. The cross marks the point of
transition of the plasma flow to the supersonic regime. The transition
occurs smoothly at a distance of
2.8 R from the center of the Sun,
while at neglecting ion pressure the distance of transition is
4.5 R. In
both cases the magnetic field lines are extended in the entire
computational domain, formation of the heliospheric current sheet in the
computational domain takes place.
|
Figure 5
|
[20] Formation of the current sheet leads to
turn
of the magnetic field
vectors. An increase of the radial component of the magnetic field near
the sheet and a decrease of the transverse component in the sheet occur
(Figures 5a and 5b). Distributions of the radial component of the
magnetic field, plasma flow velocity, plasma density and current density
across the sheet at a distance of 8 solar radii are shown in Figures 5c and
5d. These dependences have the regularities similar to those clearly
observed at crossings of the current sheet by spacecrafts at large
heliocentric distances. The current sheet is located inside a thicker layer
with an increased plasma concentration, the minimum of the solar wind
velocity is inside the sheet
[Borrini et al., 1981;
Smith, 2001].
|
Figure 6
|
[21] Comparison of the results of calculations involving the coefficients of
pressure force of
b0 and
2 b0 shows that taking into account the ion
temperature gradient provides the stationary thermal expansion of the
solar corona plasma in the presence of gravitation and formation of the
heliospheric current sheet. If this is so, introduction of the coefficient less
than unity before the term in the equation of motion will lead to a change
in the direction of velocity in the calculations including typical
parameters of the corona and accretion of material. Figure 6 shows
results of calculations for the coefficient equal to
(5/8) b0.
Here, a local
minimum of velocity arises near the left boundary already at
t
20,
but
the velocity is still directed away from the Sun, and the magnetic field
lines are extended in this region. Later, the minimum becomes even
deeper, and the velocity reverses the direction. The plasma flow from the
corona changes the direction, and the plasma accumulates near the left
boundary, where the boundary conditions are taken to be a constant
corona density and plasma velocity corresponding to the loss of the solar
mass. Thus, for the stable solar wind generation to take place, ions in the
corona must be heated to the temperature close to the electron
temperature.
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