R E P L Y TO THE C O M M E N T S F R O M V I N O D K R I S H A N ON OUR

P A P E R

S U R E S H C H A N D R A and L A L A N P R A S A D

Department of Physics, University of Gorakhpur, Gorakhpur, India

(Received 19 September, 1991)

Abstract. Krishan (1991) has commented on our paper (Chandra and Prasad, 1991). The aim of this short communication is to reply to her comments.

Recently Chandra and Prasad (1991; hereafter referred to as CP) discussed two- dimensional steady-state pressure structure in a coronal loop. They utilized the cylindri- cal coordinates and represented the loop structure by a cylinder of radius R and length L. In the investigation, the magnetic field and fluid velocity were expressed in terms of the superposition of two Chandrasekhar-Kendall functions and found a two- dimensional (radial and axial) pressure structure as

P = Po + �89 2 {1 - Jo2(yo r) - J2(7or)} +

+ 2Co C1 t/o th 22 { 72 - [2171Jl (7or)J1 (71 r) +

q- 7?Jo(~)or)Jo(71r)] cos (klZ)} -}- (C 1/11 ~?)2 x

X {1 - [Jo2(71 r) + J12(ylr)] c o s ( 2 k l Z ) } ] ,

where

(1)

k 1 = 2 n / L , 22 = 712 + k~,

C o = 8 . 4 8 2 • lO-6cm 1/2,

~/o = 5.522 x 1022 erg 1/2 cm,

R = 109 cm,

2o= So, --~71~3.8, 7o

C1 = 3.670 • 10-6 cm - 1/2,

01 = 1.104 x 10 22 erg 1/2 cm,

L = 5 • 109cm,

Astrophysics and Space Science 193: 329-331, 1992. �9 1992 Kluwer Academic Publishers. Printed in Belgium.

and Po is the pressure at r = 0, z = 0. The symbols have their usual meanings as discussed by CP. Equation (1) differs from the corresponding expression of Krishan (1985)

p =po + �89 2 {1 - J 2 ( 7 o r ) - J?(7o0} +

+ 2Co c , ~o~1~2 {~? - [2171sl(~,'or)Jl(z, l r ) +

+ 712Jo(yor)Jo(ylr)] cos (klz)} ] . (2)

Equations (1) and (2) show explicitly that the terms multiplied by cos (2klz) were not available in the paper of Krishan (1985). It has been accepted by Krishan (1991).

330 SURESH CHANDRA AND LALAN PRASAD

Besides that, the density term p was not available in her paper (Krishan, 1985) probably she took it equal to unity.

We calculated (p - Po)/P from Equation (1) for various values of yor and z. The values of (p - Po)/P as a function of 7or and three values of z = O, L/4, L /2 are plotted in Figure l(a) whereas the values of (p - Po)/P as a function ofz for different values of yor are shown in Figure 2(a). In order to exhibit the difference between our investigation (CP) and that of Krishan (1985), explicitly the values of p - P o obtained from Equation (2) are plotted in Figures l(b) and 2(b). A comparison of Figure l(a) with l(b) and that of Figure 2(a) with 2(b) shows that the terms multiplied by cos (2klz) play an important role and, therefore, cannot be neglected by saying that they are higher-order terms as Krishan (1991) argued. Consequently, the conclusions of our paper CP) are not the same as that of Krishan (1985), but show modifications at large scale.

0.6

0.4

t !

0.2

O ~ I I i i i i 0 0

0 0.2 0.4 0.6 0.8 1.0 0

~o r

(bl

Z ~ L / 2

L / 4

0 ,2 0-4 0 ,6 0-8 1.0

Fig. 1. Radial variation of pressure in a steady-state loop for ?oR = 1 and z = 0, L/4, L/2. (a) shows the present values of (p - Po)/P as a function of ?or (Equation (1)). (b) exhibits the values of (p - Po) as a

function of ?or (Equation (2)).

We do not agree with the statement of Krishan (1991): 'the slight curvature present in their Figure 2(b) may be due to more accurate graphical representation'. In our paper (CP), we explicitly reported 'Equation (2) for convenience may be expressed as

P - Po = A(r) + B(r) cos ( k l z ) , (3)

where A(r) and B(r) are the functions of r only. This equation obviously shows that for a given value of r, (p - Po) cannot vary linearly with z'. Therefore, the curvature present in our Figure 2(b) is not due to a more accurate graphical representation but due to the cosine factor. At this juncture, we may take liberty to state that the results of Krishan (1985) are not free from mistakes.

REPLY TO THE COMMENTS FROM VINOD KRISHAN ON OUR PAPER 331

o . 2

Oil I l I I I J I i "

0 L / 8 L / 4 3 L / 8 L /2 0 L / 8 L / 4 3 L / 8 L I 2

Z

Fig. 2. Axial variation of pressure in a steady-state loop for 7o R = 1, and 7o r = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0. (a) shows the present values of(p - Po)/P as a function ofz (Equation (1)). (b) exhibits the values of(p - Po)

as a function of z (Equation (2)).

Krishan (1985) did not mention her intention about neglecting tile terms multiplied

by cos (2klZ) and later on we (CP) found them missing. Therefore, our report about the

terms multiplied by cos (2klz) should not be a point of strong protest. Moreover, the

contribution of our paper (CP) for the extention of the work of Krishan (1985) cannot

be treated as trivial.

Acknowledgement

Financial support from the Council of Science and Technology, Lucknow is gratefully

acknowledged.

References

Chandra, S. and Prasad, L.: 1991, Solar Phys. 134, 99. Krishan, V.: 1985, Solar Phys. 97, 183. Krishan, V.: 1991, Solar Phys. 134, 109.