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Formation of neutral current sheet and loop coronal transients
Pergamon Journals. Printed in Great Britain 0275-1062/87$10.00+.00
Chin.Astron.Astrophys.11 (1987) 171-178 Chin.J.Sp.Sci. 7 (1987)1-9
FORMATION
HU You-qiu Department Hefei
OF NEUTRAL
CURRENT
SHEET AND LOOP
CORONAL
TRANSIENTS
of Science
& Technology
and JIN Shu-ping of Earth and Space Sciences,
University
Received 1986 April 17
ABSTRACT An eruption of opposite magnetic flux into a bipolar background field is likely to lead to the formation of a natural current sheet between the new emerging field and the background. A numerical study is made on this process, based on the ideal MMD equations, taking into account the interaction between the magnetic field and the coronal plasma. The result shows that a subsonic eruption will give rise to a four region structure; 1) a cool and dense prominence made of the erupting material in the innermost region; 2) a cool and tenuous region further out; 3) a hot and dense loop formed by the concentration of both the erupting material and the coronal material in the neutral current sheet; and 4) a forerunner region outside the loop with density slightly above the background, due to fast magneto-acousticwaves. This structure agrees with the observed features of typical loop coronal transients. Therefore the eruption of opposite magnetic flux into a bipolar background is probably an important mechanism for triggering off such transients.
1.
INTRODUCTION
Coronal transients are large-scale variations in the coronal structure. They are often accompanied by large amounts of matter (+15) - (+16) g, erupting outwards, the energy released in each event is almost equal to that of a flare ((+30) - (+32) erg). The high density regions of the transients show complex structures, the most frequently seen are the loops [2]. Outward from the hot and dense loop, is often a geometrically similar forerunner region, with a density slightly above the unperturbed corona [3]; inward, there is a cool and tenuous region; further in, we have the prominence eruption [41. Various theoretical models have been proposed for the formation of such coronal transients. Some authors believe them to be non-linear wave motion [5-61, some, bulk motion of magnetic flux tubes [8,7], yet others, current sheets expanding outwards, [lO,ll]. It is generally accepted that in the formation and development of coronal transients, magnetic field is the controlling factor and provides the energy. Many past
past models either neglected this effect or so over-simplified its analysis that the results could not fit their observed features. Recently, we have analysed the neutral current sheet formed when opposite magnetic flux is injected into a dipole background field [12] or a double dipolar field [13], and pointed out that the geometry and kinematics of the current sheet are similar to those of the hot dense region of loop coronal transients, and so this could be an important mechanism for their formation. In these analyses, we assumed quasi-static process for convenience and neglected the coupling between the magnetic field and the plasma and restricted ourselves to a discussion of the evolution of the field. Because of these simplifications,our results apply only to the case of strong field; we were also unable to make a quantitative analysis on the thermodynamic structure of the plasma. In this paper, we shall start with the ideal MMD equations and carry out numerical simulation of the neutral current sheet formed when the eruption is into a dipole background. Our numerical results confirm our previous main conclusions based on
HU + JIN
172
analysis [12], and display structural variations in the density of the solar atmosphere in the course of the formation of transients. The variations are basically the same as seen in the coronal transients. Thus, the injection of opposite magnetic flux into a dipolar background field could be an important mechanism in triggering off these events.
2.
BASIC EQUATIONS
Basic Equations For simplicity, we use the two-dimensionalmodel of an ideal magnetic fluid. In rectangular coordinates (x,y), the basic equations are 1.
Here, p is the density, T the temperature, vx, vy the velocity components, R the gas constant. y (=5/3) is the adiabatic index, g the solar surface gravity, A the twodimensional Laplace operator, and $ is the magnetic flux function, related to the magnetic field by
It is easy to verify that the right side of (8) assumes the maximum value $0 at the coordinate origin and that, at the origin, the static and magnetic pressures are equal. Boundary Conditions The region of calculation is taken to be
3.
y<
o
2.
Initial Conditions We assume the initial atmosphere to be in a static, isothermal state, that is
2YOOOkm,
involving four boundaries. The left boundary (x=0) is the boundary of symmetry, at this boundary, we have Y*
=
ilp _.-_
0,
ax
au
&b
r3T
ax
ax
ax
__L”-_“--‘o;
(x- 0) (10)
The values on the right and top boundaries are to be calculated by the method of approximate characteristics [14]. The bottom boundary is the perturbed boundary and the eruption of opposite magnetic flux here is simulated by a particular assignment of $. The assignment we used is
[T(O,",vl= 70,
i Ido,
I,
IdO, XI
-82
Y) Y)
Poe
-
R=o,
U,(O,X,Y)
(11)
(7) =
0.
where The initial magnetic field is assumed to be bipolar, with flux function
+
B
I.’
2
_ .! *
a-%++,I, The relevant parameters are given the values 1'0 - IO%;, po- 1.67X IO-“g/cm', b - IO'km, +G0 - 5.24X IO'G- km, a,- 0.3,,9- 0.2,y,- 0.26 (9)
arctg
(
+ Yc)’- a’b’ 2dy + Y,) @-,%+tr. .:f_+-
* (12) )I1 (13)
kl, k2 are positive numbers representing the growth rates of a and f3. Since a is ratio of the dipole separations between the newly erupted dipole field and the background dipole field and B is the ratio of the magnetic fluxes, [12], kl and k2 represent
Neutral Sheet
Fig. 1
173
Magnetic configuration at four instants of time
the growth rates in the dipole separation
and magnetic flux of the erupted field. In k2= our calculations,we took kl=O.OOS/s, 0.058 /.a. The equations (11) and (12), simulate the eruption of opposite magnetic field into a dipole background field. At
t= 0, (12) reverts to (8). Eruption of magnetic flux will be accompanied by eruption of matter, the consistent assignment of the velocity at the bottom is found as follows. First, assume matter is moving perpendicular to the field
HU + JIN
174
line @ “‘av
$+ -0
3-0,
y ax
then, assume that ies the frozen-in
(y-0).
the eruption process condition, that is,
u,~+“y~-o,
(Y - 0).
(15)
(14) The values of the three partial derivatives at the bottom can be found from (12), hence we find the values of the velocity components
satisf-
(b)
I =
80s~~.
Neutral Sheet
Fig.
2
(a> 1 = 40%.
175
HU + JIN
(c) f = lxtsec.
Fig. 3
Neutral Sheet
there. The bottom boundary is divided into regions of eruption and non-eruption according as vY is positive or negative. For a region of eruption (vy> 0), the above calculated values of vx and vy hold; for a region of non-eruption, we keep only vx and arbitrarily fixed vY= 0. The parameter values listed above lead to a maximum eruption velocity of 130-140 km/s, and since the sound speed is about 160 km/s, the eruption is subsonic. A considerable portion of prominences belong to this case. According to the near characteristics theory, the number of physical quantities that can be arbitrarily assigned at the bottom layer is at most equal to the number of outgoing near characteristicroots at the point [14]. In the present case, we have at most four arbitrarily assignable quantities. Since velocity (at least one quantity) is found by self-consistent calculation, it cannot be arbitrary, and we can, in principle, arbitrarily assign the temperature and the density. To simulate approximately erupting prominence, we shall specify that the temperature at the bottom of the eruption region varies inversely with the density, so as to mantain a constant pressure,
177
given elsewhere.
3.
RESULTS OF CALCULATION
The eruption of opposite magnetic flux at bottom will alter the field configuration in the corona andthestructure of the plasma. Fig. 1 shows the change of the field configuration in time, t= 0 (Fig. la) corresponds to the initial dipole background. Fig. 1 shows that, following the eruption of the opposite flux, an arch-shapedneutral current sheet is formed between the newly injected field and the background field, and is continuously expanding outwards. When the gas-magneticpressure ratio is far less than 1, we can neglect the reaction of the plasma on the field, or even use an analytic treatment according to the method of [12]. The current sheet is then infinitely thin. Its position is marked by the dashed line in Figs. lb, lc, Id. In the present case, the initial pressure ratio at the origin is s 1, so the suppression of the erupting field by the plasma cannot be neglected, and the current sheet is lowered and is thicker. Figs. 2 and 3 respectively show the perturbed density and temperature fields at various times. As the current sheet forms, TI,=0- To/n, PlYTo=W*. (16) both erupted matter and coronal matter will home on the sheet, forming a hot and dense where n> 1 for eruption region and n= 1 for loop; this is in agreement with a previous non-eruption region. Observations of conclusion [12]. Because the pressure ratio eruption prominences give 21~100. In our is ~1, the density inside the loop will be numerical simulation, we found that the about twice the background value. Below the value of n had a very small effect on the loop, we have a cool and tenuous region, due thermodynamical structure outside the partly to the concentration of the erupted erupting prominence. Too large a value of n matter in the loop, and partly due to the will make it awkward for the numerical rapid expansion of the erupted field. After results to show graphically the thermodynamic a time, fast magneto-acousticwaves will structure in the coronal region. Hence we have got in front of the material flow, and moved further and further ahead, thus forming took n= 3. between the dense loop and the wave front a forerunner region with density slightly 3. Format of Calculation We took Ax= Ay= 1000 km and divided the higher than the background, its relative area to be calculated into a 21x 30 uniformly density amplitude reaching 30%. At the spaced grid. The left boundary (the y-axis) bottom part of the eruption region, the was extended by half a unit, so as to raise erupted matter will directly form a cool and the accuracy of the differences in the dense orominence. As we decrease the gasmagnetic pressure ratio, the above boundary condition (10). To avoid the limitation on the time steplength by magnetic thermodynamic structure remains essentially wave velocity, we used the method of altern- the same, only the loop matter density will be higher and its position closer to the ate directions [15]. To ensure calculating accuracy and stability in the assignment of dashed line of Fig. 1, and the forerunner boundary conditions by the method of near region wider. Obviously, this structure characteristics,we require the time reflects the typical features of coronal steplength to satisfy the following condition: transients.
4. vmax being the maximum flow velocity on the boundaries of the calculated region. The details of the calculation format will be
CONCLUSION
In this paper, we started from the equations for an ideal magnetic fluid and made a preliminary numerical investigationof the
HU + JIN
178
transient process. A check on the mechanism proposed here requires that, at the same time as we make morphological observations of a transient, we secure detailed data on the evolving magnetic field of the region to distinguish the background field and the newly erupted field and to see whether the fields above and below the high-density are of opposite polarity. The magnetic field on the Sun’s surface, especially in active regions, often displays various complex structures and changes, entirely possessing the conditions necessary for the formation of current sheets; the appearance of a current sheet will markedly alter the coronal structure, while unstable processes occurring inside the sheet will lead to various types of bursts and eruptions. We can definitely say that further advances in the theoryofcurrent sheet will bring about a reformation in the theoretical interpretation of solar physical phenomena.
formation of the neutral current sheet upon the eruption of opposite magnetic flux and the accompanying responses in the coronal atmosphere. The numerical results clearly display the typcial prominence - tenuous region - dense loop - forerunner region structure shown by loop coronal transients, thus confirm our previous prediction [12] that injection of opposite magnetic flux into a dipole background is probably an important mechanism in the formation of loop coronal transients. Usually coronal transients last several hours and extend several solar radii in space. In this paper we used rectangular coordinates, hence we were not able to simulate the above time-scale. Nevertheless,. as a qualitative result, our result is meaningful from the standpoint of exploring physical mechanisms. It reflects, to a certain extent, the physical characteristics of the coronal
REFERENCES R.
Mncqucen,
M.,
Tmnr. R. SW. f,on~on ser., A, vol. 297. p. 605, Solor Phyr.,Vol. 87, p. 191, 1985.
Philor.
Munro, R. II. and D.
G. Sime,
Jackson,
Hindlcr,
B. V.
Fibher,
R.
Wu,
T.,
S.
U.,
Pncuman,
S0I.r
Dryer,
Y.
Phyr.. 4,
Nakahawa
p.
and
Vol. 163,
S.
M.
HU
You-qiu and WU Shi-can Arrroplryr .Jpacr Jw, Vol. YZ, Solur
G.
S.
p.
60,
p.
155,
1976.
1964.
Ap. J, Vol. 218, p. 324, 197s. Scientia .qinica Ser.A (1982) 373, 1983. Han,
Vol. 57, p. 111,1976. Phyr.,Vol. 65, p. 369, 1980. Munro and R. R. Fisher, Ap. .I., Vol.
929.
Phyr.,
W.,
Low, 6. C.. R. Syrova~rkii,
E.
Ad". Sp.ccRex, Vol.
M.
WANGShui. Ilu, W. K.. Anzer,
and
R.,
1960.
H.
Solar
I., Solar
Phyr.,
Vol.
76,
p.
3,
254,p. 335, 1982.
1982.
HU You-aiu. Scientia Sinica Ser.A. (1985) 928. HU You-p’ie’and WANG Yan-quan, Chin.Astron.Astrophys. 11 (1987) 6 (1986) 312-316. = Act.Astron.Sin. I~u. Y. (2. nnd S. T. Wu, J. Compur. I’llyr., Vol. 55, p. 33, 1964. Lindemurh, 1. and .I. Killecn. J. Comput. Phyr..Vol. 13, p. 181, 1973.
83-86
Chin.Astron.Astrophys.11 (1987) 171-178 Chin.J.Sp.Sci. 7 (1987)1-9
FORMATION
HU You-qiu Department Hefei
OF NEUTRAL
CURRENT
SHEET AND LOOP
CORONAL
TRANSIENTS
of Science
& Technology
and JIN Shu-ping of Earth and Space Sciences,
University
Received 1986 April 17
ABSTRACT An eruption of opposite magnetic flux into a bipolar background field is likely to lead to the formation of a natural current sheet between the new emerging field and the background. A numerical study is made on this process, based on the ideal MMD equations, taking into account the interaction between the magnetic field and the coronal plasma. The result shows that a subsonic eruption will give rise to a four region structure; 1) a cool and dense prominence made of the erupting material in the innermost region; 2) a cool and tenuous region further out; 3) a hot and dense loop formed by the concentration of both the erupting material and the coronal material in the neutral current sheet; and 4) a forerunner region outside the loop with density slightly above the background, due to fast magneto-acousticwaves. This structure agrees with the observed features of typical loop coronal transients. Therefore the eruption of opposite magnetic flux into a bipolar background is probably an important mechanism for triggering off such transients.
1.
INTRODUCTION
Coronal transients are large-scale variations in the coronal structure. They are often accompanied by large amounts of matter (+15) - (+16) g, erupting outwards, the energy released in each event is almost equal to that of a flare ((+30) - (+32) erg). The high density regions of the transients show complex structures, the most frequently seen are the loops [2]. Outward from the hot and dense loop, is often a geometrically similar forerunner region, with a density slightly above the unperturbed corona [3]; inward, there is a cool and tenuous region; further in, we have the prominence eruption [41. Various theoretical models have been proposed for the formation of such coronal transients. Some authors believe them to be non-linear wave motion [5-61, some, bulk motion of magnetic flux tubes [8,7], yet others, current sheets expanding outwards, [lO,ll]. It is generally accepted that in the formation and development of coronal transients, magnetic field is the controlling factor and provides the energy. Many past
past models either neglected this effect or so over-simplified its analysis that the results could not fit their observed features. Recently, we have analysed the neutral current sheet formed when opposite magnetic flux is injected into a dipole background field [12] or a double dipolar field [13], and pointed out that the geometry and kinematics of the current sheet are similar to those of the hot dense region of loop coronal transients, and so this could be an important mechanism for their formation. In these analyses, we assumed quasi-static process for convenience and neglected the coupling between the magnetic field and the plasma and restricted ourselves to a discussion of the evolution of the field. Because of these simplifications,our results apply only to the case of strong field; we were also unable to make a quantitative analysis on the thermodynamic structure of the plasma. In this paper, we shall start with the ideal MMD equations and carry out numerical simulation of the neutral current sheet formed when the eruption is into a dipole background. Our numerical results confirm our previous main conclusions based on
HU + JIN
172
analysis [12], and display structural variations in the density of the solar atmosphere in the course of the formation of transients. The variations are basically the same as seen in the coronal transients. Thus, the injection of opposite magnetic flux into a dipolar background field could be an important mechanism in triggering off these events.
2.
BASIC EQUATIONS
Basic Equations For simplicity, we use the two-dimensionalmodel of an ideal magnetic fluid. In rectangular coordinates (x,y), the basic equations are 1.
Here, p is the density, T the temperature, vx, vy the velocity components, R the gas constant. y (=5/3) is the adiabatic index, g the solar surface gravity, A the twodimensional Laplace operator, and $ is the magnetic flux function, related to the magnetic field by
It is easy to verify that the right side of (8) assumes the maximum value $0 at the coordinate origin and that, at the origin, the static and magnetic pressures are equal. Boundary Conditions The region of calculation is taken to be
3.
y<
o
2.
Initial Conditions We assume the initial atmosphere to be in a static, isothermal state, that is
2YOOOkm,
involving four boundaries. The left boundary (x=0) is the boundary of symmetry, at this boundary, we have Y*
=
ilp _.-_
0,
ax
au
&b
r3T
ax
ax
ax
__L”-_“--‘o;
(x- 0) (10)
The values on the right and top boundaries are to be calculated by the method of approximate characteristics [14]. The bottom boundary is the perturbed boundary and the eruption of opposite magnetic flux here is simulated by a particular assignment of $. The assignment we used is
[T(O,",vl= 70,
i Ido,
I,
IdO, XI
-82
Y) Y)
Poe
-
R=o,
U,(O,X,Y)
(11)
(7) =
0.
where The initial magnetic field is assumed to be bipolar, with flux function
+
B
I.’
2
_ .! *
a-%++,I, The relevant parameters are given the values 1'0 - IO%;, po- 1.67X IO-“g/cm', b - IO'km, +G0 - 5.24X IO'G- km, a,- 0.3,,9- 0.2,y,- 0.26 (9)
arctg
(
+ Yc)’- a’b’ 2dy + Y,) @-,%+tr. .:f_+-
* (12) )I1 (13)
kl, k2 are positive numbers representing the growth rates of a and f3. Since a is ratio of the dipole separations between the newly erupted dipole field and the background dipole field and B is the ratio of the magnetic fluxes, [12], kl and k2 represent
Neutral Sheet
Fig. 1
173
Magnetic configuration at four instants of time
the growth rates in the dipole separation
and magnetic flux of the erupted field. In k2= our calculations,we took kl=O.OOS/s, 0.058 /.a. The equations (11) and (12), simulate the eruption of opposite magnetic field into a dipole background field. At
t= 0, (12) reverts to (8). Eruption of magnetic flux will be accompanied by eruption of matter, the consistent assignment of the velocity at the bottom is found as follows. First, assume matter is moving perpendicular to the field
HU + JIN
174
line @ “‘av
$+ -0
3-0,
y ax
then, assume that ies the frozen-in
(y-0).
the eruption process condition, that is,
u,~+“y~-o,
(Y - 0).
(15)
(14) The values of the three partial derivatives at the bottom can be found from (12), hence we find the values of the velocity components
satisf-
(b)
I =
80s~~.
Neutral Sheet
Fig.
2
(a> 1 = 40%.
175
HU + JIN
(c) f = lxtsec.
Fig. 3
Neutral Sheet
there. The bottom boundary is divided into regions of eruption and non-eruption according as vY is positive or negative. For a region of eruption (vy> 0), the above calculated values of vx and vy hold; for a region of non-eruption, we keep only vx and arbitrarily fixed vY= 0. The parameter values listed above lead to a maximum eruption velocity of 130-140 km/s, and since the sound speed is about 160 km/s, the eruption is subsonic. A considerable portion of prominences belong to this case. According to the near characteristics theory, the number of physical quantities that can be arbitrarily assigned at the bottom layer is at most equal to the number of outgoing near characteristicroots at the point [14]. In the present case, we have at most four arbitrarily assignable quantities. Since velocity (at least one quantity) is found by self-consistent calculation, it cannot be arbitrary, and we can, in principle, arbitrarily assign the temperature and the density. To simulate approximately erupting prominence, we shall specify that the temperature at the bottom of the eruption region varies inversely with the density, so as to mantain a constant pressure,
177
given elsewhere.
3.
RESULTS OF CALCULATION
The eruption of opposite magnetic flux at bottom will alter the field configuration in the corona andthestructure of the plasma. Fig. 1 shows the change of the field configuration in time, t= 0 (Fig. la) corresponds to the initial dipole background. Fig. 1 shows that, following the eruption of the opposite flux, an arch-shapedneutral current sheet is formed between the newly injected field and the background field, and is continuously expanding outwards. When the gas-magneticpressure ratio is far less than 1, we can neglect the reaction of the plasma on the field, or even use an analytic treatment according to the method of [12]. The current sheet is then infinitely thin. Its position is marked by the dashed line in Figs. lb, lc, Id. In the present case, the initial pressure ratio at the origin is s 1, so the suppression of the erupting field by the plasma cannot be neglected, and the current sheet is lowered and is thicker. Figs. 2 and 3 respectively show the perturbed density and temperature fields at various times. As the current sheet forms, TI,=0- To/n, PlYTo=W*. (16) both erupted matter and coronal matter will home on the sheet, forming a hot and dense where n> 1 for eruption region and n= 1 for loop; this is in agreement with a previous non-eruption region. Observations of conclusion [12]. Because the pressure ratio eruption prominences give 21~100. In our is ~1, the density inside the loop will be numerical simulation, we found that the about twice the background value. Below the value of n had a very small effect on the loop, we have a cool and tenuous region, due thermodynamical structure outside the partly to the concentration of the erupted erupting prominence. Too large a value of n matter in the loop, and partly due to the will make it awkward for the numerical rapid expansion of the erupted field. After results to show graphically the thermodynamic a time, fast magneto-acousticwaves will structure in the coronal region. Hence we have got in front of the material flow, and moved further and further ahead, thus forming took n= 3. between the dense loop and the wave front a forerunner region with density slightly 3. Format of Calculation We took Ax= Ay= 1000 km and divided the higher than the background, its relative area to be calculated into a 21x 30 uniformly density amplitude reaching 30%. At the spaced grid. The left boundary (the y-axis) bottom part of the eruption region, the was extended by half a unit, so as to raise erupted matter will directly form a cool and the accuracy of the differences in the dense orominence. As we decrease the gasmagnetic pressure ratio, the above boundary condition (10). To avoid the limitation on the time steplength by magnetic thermodynamic structure remains essentially wave velocity, we used the method of altern- the same, only the loop matter density will be higher and its position closer to the ate directions [15]. To ensure calculating accuracy and stability in the assignment of dashed line of Fig. 1, and the forerunner boundary conditions by the method of near region wider. Obviously, this structure characteristics,we require the time reflects the typical features of coronal steplength to satisfy the following condition: transients.
4. vmax being the maximum flow velocity on the boundaries of the calculated region. The details of the calculation format will be
CONCLUSION
In this paper, we started from the equations for an ideal magnetic fluid and made a preliminary numerical investigationof the
HU + JIN
178
transient process. A check on the mechanism proposed here requires that, at the same time as we make morphological observations of a transient, we secure detailed data on the evolving magnetic field of the region to distinguish the background field and the newly erupted field and to see whether the fields above and below the high-density are of opposite polarity. The magnetic field on the Sun’s surface, especially in active regions, often displays various complex structures and changes, entirely possessing the conditions necessary for the formation of current sheets; the appearance of a current sheet will markedly alter the coronal structure, while unstable processes occurring inside the sheet will lead to various types of bursts and eruptions. We can definitely say that further advances in the theoryofcurrent sheet will bring about a reformation in the theoretical interpretation of solar physical phenomena.
formation of the neutral current sheet upon the eruption of opposite magnetic flux and the accompanying responses in the coronal atmosphere. The numerical results clearly display the typcial prominence - tenuous region - dense loop - forerunner region structure shown by loop coronal transients, thus confirm our previous prediction [12] that injection of opposite magnetic flux into a dipole background is probably an important mechanism in the formation of loop coronal transients. Usually coronal transients last several hours and extend several solar radii in space. In this paper we used rectangular coordinates, hence we were not able to simulate the above time-scale. Nevertheless,. as a qualitative result, our result is meaningful from the standpoint of exploring physical mechanisms. It reflects, to a certain extent, the physical characteristics of the coronal
REFERENCES R.
Mncqucen,
M.,
Tmnr. R. SW. f,on~on ser., A, vol. 297. p. 605, Solor Phyr.,Vol. 87, p. 191, 1985.
Philor.
Munro, R. II. and D.
G. Sime,
Jackson,
Hindlcr,
B. V.
Fibher,
R.
Wu,
T.,
S.
U.,
Pncuman,
S0I.r
Dryer,
Y.
Phyr.. 4,
Nakahawa
p.
and
Vol. 163,
S.
M.
HU
You-qiu and WU Shi-can Arrroplryr .Jpacr Jw, Vol. YZ, Solur
G.
S.
p.
60,
p.
155,
1976.
1964.
Ap. J, Vol. 218, p. 324, 197s. Scientia .qinica Ser.A (1982) 373, 1983. Han,
Vol. 57, p. 111,1976. Phyr.,Vol. 65, p. 369, 1980. Munro and R. R. Fisher, Ap. .I., Vol.
929.
Phyr.,
W.,
Low, 6. C.. R. Syrova~rkii,
E.
Ad". Sp.ccRex, Vol.
M.
WANGShui. Ilu, W. K.. Anzer,
and
R.,
1960.
H.
Solar
I., Solar
Phyr.,
Vol.
76,
p.
3,
254,p. 335, 1982.
1982.
HU You-aiu. Scientia Sinica Ser.A. (1985) 928. HU You-p’ie’and WANG Yan-quan, Chin.Astron.Astrophys. 11 (1987) 6 (1986) 312-316. = Act.Astron.Sin. I~u. Y. (2. nnd S. T. Wu, J. Compur. I’llyr., Vol. 55, p. 33, 1964. Lindemurh, 1. and .I. Killecn. J. Comput. Phyr..Vol. 13, p. 181, 1973.
83-86