A PLASMA MODEL OF CRAB NEBULA AND PULSAR Np0532 RADIATION IN ROENTGEN AND GAMMA RANGES

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Submitted on 1 Jan 1979

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A PLASMA MODEL OF CRAB NEBULA AND PULSAR Np0532 RADIATION IN ROENTGEN AND

GAMMA RANGES

G. Machabeli, V. Usov

To cite this version:

G. Machabeli, V. Usov. A PLASMA MODEL OF CRAB NEBULA AND PULSAR Np0532 RADI- ATION IN ROENTGEN AND GAMMA RANGES. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-715-C7-716. �10.1051/jphyscol:19797346�. �jpa-00219340�

JOURNAL DE PHYSI&UE CoZZoque C7, s u p p l d m e n t a u n07, Tome 40, J u i Z Z e t 1979, page C7- 715

A PLASMA MODEL OF CRAB N E B U A AND PULSAR NpO532 RADIATION IN ROENTGEN AND GAMMA RANGES

G.Z. Machabeli, V.V. Usov.

Abastumani A s t r o p h y s i c a Z O b s e r v a t o r y , Academy o f S c i e n c e s , GSSR, %i Zisi, U. S. S. R., S p a c e R e s e a r c h I n s t i t u t e , Academy o f S c i e n c e s , U. S . S . R., Moscow, U.S. S. R.

L a t e l y , a s i g n i f i c a n t p r o g r e s s i n t h e e l o n g a t e d t a i l without humps /I/. Such an study of p r o c e s s e s , t a k i n g p l a c e i n pul- asymmetric one-dimensional d i s t r i b u t i o n s a r magnetospheres h a s been achieved; It a p p e a r s t o be u n s t a b l e w i t h r e s p e c t t o a l l o w s t o develope c o n s i s t e n t p u l s a r r a - p e r t u r b a t i o n s , e x c i t e d a t t h e c y c l o t r o n d i a t i o n models. Namely, it was shown t h a t resonance w i t h beam p a r t i c l e s .

n e a r t h e p u l s a r s u r f a c e a r a p i d b i r t h of The i n s t a b i l i t y e v o l u t i o n r e q u i r e s e l e c t r o n - p o s i t r o n p n i r s must t a k e p l a c e . a number of r e s t r i c t i o n s . I n p a r t i c u l a r ,

A s a r e s u l t , two-component e l e c t r o n - t h e c o n d i t i o n of t h e l a c k of hose i n s t a - p o s i t r o n plasma, moving from a neutron b i l i t y , smalness of damping on plasma par- s t a r along magnetic f o r c e l i n e s w i t h velo- t i c l e s and resonance

c i t i e s corresponding t o L o r e n t z - f a c t o r s Considering a l s o

lo2-lo3

^{and lo5-10} 7 i s g e n e r ~ t e d i n pul- ₍

B3 ,

^\b

-

magnetic f i e l d s t r e n g t h and

s a r magnetosphere. plasma d e n s i t y n e a r a neutron s t a r s u r -

I n Np0532 c a s e t h e e l e c t r o n - p o s i t r o n f a c e , 2, s t a r r a d i u s ) . I n an o b s e r v e r ' s plasma c o n c e n t r a t i o n n e a r p u l s a r s u r f a c e

a t t a i n s 10~'cm-~. Plasma p a r t i c l e s i n a s t r o n g magnetic f i e l d

8

^%

lo1*

q u i c k l y l o s e t r a n s v e r s e momentum and t h e momentum d i s t r i b u t i o n of p a r t i c l e s r e l a x e s t o a one-dimensional. T h i s one-dimensional d i s - t r i b u t i o n appears t o be u n s t a b l e w i t h r e s - p e c t t o o s c i l l a t i o n s , e x c i t e d i n e l e c t r o n - p o s i t r o n r e l a t i r i s t i c plasma. Among them t h e l o n g i t u d i n a l Langmuire o s c i l l a t i o n s a r e c h a r a c t e r i z e d by t h e l a r g e s t growth r a t e . T h e i r r a p i d e v o l u t i o n l e a d s t o a p l a t o u formation on t h e d i s t r i b u t i o n func- t i o n due t o q u a s i - l i n e a r i n t e r a c t i o n of resonance p a r t i c l e s w i t h Langmuire o s c i l - l a t i o n s , A s a r e s u l t , p a r t i c l e d i s t r i b u - t i o n r e l a x e s t o a one-dimensional one w i t h

system we s h a l l g e t i n e q u i l i t g

Magnetic f i e l d is s l i g h t l y inhomoge- neous and i n t h e presence of v e l o c i t y t r a n s v e r s e components it can s i g n i f i c a n t l y i n f l u e n c e t h e p a r t i c l e d i s t r i b u t i o n charac- t e r . I n t h e weakly inhomogeneous f i e l d a f o r c e , d i r e c t e d t r a n s v e r s e t h e magnetic f i e l d would a f f e c t a p a r t i c l e . T h i s f o r c e a t t h e r e l a t i v i s t i c c h a r a c t e r of t h e mo-

1

t i o n s h o u l d have a form

GA1 - ^hi

_k

_3&+

Pitch-angles appearance, on account of owing q u a s i - l i n e a r d i f f u s i o n 5 e s u l t s i n magnetic bremsstrahlung and braking-byra- d i a t i o n f o r c e o r i g i n . T h i ~ l a t t e r one h a s b o t h t r a n s v e r s e and l o n g i t u d i n a l compo

-

^'

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797346

Dents.

- d V j Ft=-d.Wx(

> ci.8

h2

²

b/e

Then from k i n e t i c e q u a t i o n we o b t a i n

hn'LC3

.

Here

p= xi, 3%

H

-

a c e r t a i n f i n i t e

number.^;(&\, eLL ^d?-

During t h e c y c l o t r o n waves r e l a x a - t i o n time t

.

^{The beam i s} taken o u t

.

.

from t h e r e g i o n of i n t e r a c t i o n w i t h s p e c t - rum depending only on c y c l o t r o n n o i s e s s e t - f l e d .

From t h e energy balance e q u a t i o n a t t h e proper boundary c o n d i t i o n s we s h a l l g e t

-

is beam Lorentz-factor b e f o r e t h e beginning of c y c l o t r o n i n s t a b i l i t y evolu-

3s.

, t i o n .

Using (2) and (3) and e x p r e s s i o n s f o r e f f e c t i v e pitch-angle we o b t a i n

Using (3) we s h a l l f i n d synchrotron ir- r a d i a t i o n spectrum, which f a l l s i n roent- gen and

r-

ranges region

I J

^{s \)}

^-

^d

where

-

spectrum index appears t o be

1 ,

^{t h a t i s} i n a good accordance w i t h observed curves. The g r e a t e r p a r t of beam ,energy, due t o a d i a b a t i c inva- r i a n t e x i s t a n c e , is c a r r i e d o u t beyond t h e l i g h t c y l i n d e r i n t o Crab nebula and is i r r a d i a t e d t h e r e . Only a s m a l l p a r t of t h e energy (about 1%) is i r r a d i a t e d d i r e c t l y from t h e p u l s a r w i t h a c l o s e spectrum i n d i c e .

REFERENCES

1. Lominadze J.G.

,

hlikhailovsky A.B.

,