Download Magneto-acoustic Effects in Stellar Winds

Magneto-acoustic Effects
in Stellar Winds
Introduction
• The flux of particles from stars is called
stellar wind
• Global parameters are dM/dt and vterminal
• Different stellar models predict different
values for the above parameters
• Radiation pressure of the star is considered
as a main source of stellar wind
• Red giants problem
Alfven model
• The wind is treated as a highly conductive
fluid


 v 


1 B
j   ( E   B)
 E  
c
c t

 
  c 2 
B
c
   (v  B ) 
  (v  B) 
 B
t
4
4
The “frozen” field concept

 
B
   (v  B )
t



d B
B
( )  (  )v
dt 



d 
(x )  (x  )v
dt

d
 (  v ) 
dt
Magnetic field lines
MHD equations


   ( v )  0
t




v
1 
   (v  )v  p 
B  (  B)
t
4

 
B
   (v  B )
t
Linearization
 

 
B( x , t )  B0  B1 ( x , t )


 ( x , t )   0  1 ( x , t )
 
 
 ikx it
u ( x , t )  v1 ( x , t )  v1e
  

2
2
  v1  ( s  v A )( k  v1 )k 
    
     
 (v A  k )[( v A  k )v1  (v A  v1 )k  (k  v1 )v A ]  0
2
p
s 

2
2
B
v A2  0
40
Modes
• If k and vA are perpendicular-longitudinal mode
with ulong2=s2+vA2
• If k and vA are parallel, there are two modes
• Longitudinal with u=s (pure acoustic wave)
• Transverse with u= vA (Alfven wave)
Mass loss rate of red giants
4 7/2
B
dM
17
1
0 R*
 9.1  10
[ M Sun yr units]
3/ 2
13
dt
M * (10  0 )
dM
 8  10 7 [ M Sun yr 1units ]
dt
R*  300 RSun
M *  1M Sun
B0  1Gauss
References
• [1]Henry J.G.L.M. Lamers, Joseph P. Cassinelli
“Introduction to Stellar Winds”,1999
• [2]Peter A. Sturrock “Plasma Physics”,1994
• [3]J.D.Jackson“Classical Electrodynamics”,1975