Large scale magnetic field generation by accelerated particles in galactic medium

Transcription

1 Lage scale magnetc feld geneaton by acceleated patcles n galactc medum I.N.Toptygn Sant Petesbug State Polytechncal Unvesty, depatment of Theoetcal Physcs, Sant Petesbug, Russa

2 2.Reason explonatons The man souses of acceleated patcles ae SN emnants, stella wnds of OB stas and especally OB-assocatons; pulsas; pobably, acceton dscs etc. Relatvstc patcles may popagate dstances of ode of galactc sze (ten kpc) and leave the Galaxy. They geneate the lage-scale electc cuent and lage-scale magnetc feld. The estmaton of magnetc feld may gve the nfomaton about the ogn of lage-scale magnetc nhomogenetes n Galaxy. In pevous woks the man attenton was gven to MHD modes wth scales of ode of goadus o tanspot path enegetc patcles (Wentzel 1969; Skllng 1975; Bell 24; Ptuskn and Zakashvl 25 et al.

3 3. Notatons,,e acceleated ons, themal ons, themal electons; n, n, n - Nonequlbum e e ( n, n, n << n ) patcle numbe denstes. j, j, j e - electc cuents; ext e j = j + j + j - total electc cuent Qt ( ) - Total acceleated patcle numbe, emtted n moment t_ (powe of souce). e elementay chage.

4 4. Pncpal appoxmatons 1. Dffuson moton of acceleated end backgound patcles n galactc medum. 2. Homogenety of galactc medum (pmay magnetc feld and statstcal popetes of tubulence). 3. Pont souce of acceleated patcles. 4. Lnea appoxmaton of MHD equatons (seconday magnetc feld s small compae to pmay one).

5 5. Basc equatons fo cuents e Dffuson coeffcents: D, D, D. ab ab ab Electoconductvtes: s, s, s e. ab ab ab s e, ab e, D ab T, D 4p 4pne = Û = - Debye adus D 2 n k k k k j = med + s E, Û k= e,,. a ab ab b xb s << s e, s.

6 jjj 6. Self-consstent equatons fo acceleated and themal patcles k Fou equatons fo thee patcle denstes ( n, k= e,, ) and electc feld E en t en en t t e +Ñ j = eqd( ) d( t-t ), + Ñ j = -eqd ( ) d ( t - t ) e -Ñ j =. Ñ E = 4 p e( n + n -n ). e

7 7. Solutons of tanspot equatons We use Laplace (s) and Foue (k) tansfoms and appoxmatons R e << 1, Û ( k ) << << 1, Û D% >> D% >> D%. 2 2 D 2 D 2 D 2 D L % tanspot path and Hee D = kadabkb, L, R D - Debye adus of acceleated patcles. Dffuson of acceleated patcles s fee. Dffuson of themal patcles s ambpola wth double on dffuson coeffcent: 2 D ab.

8 8. Sceenng effects 1. Isotopc steady dffuson. Absolute electoneutalty: n () + n () - n e () =. of electc cuent : ext j =. Complete sceenng 2. Ansotopc steady dffuson. Not complete, but vey stong electoneutalty: j n n n k n e 2 e k + k - k = ( D) k». Electc cuent s patly sceened: æ ö»- - ¹ ç D% D% è ø D ext abkb D abkb k eq.

9 9. Non-steady solutons Laplace-Foue tansfoms: j ext a éd k 2D k ù - ab b ab b eqe ê, ú ê s+ D% ë s+ 2D% úû st =- - Cuents of acceleated and themal patcles have opposte sgns. Electc cuent s patly sceened. -st e P = ( pv) meanq. 3( s + D % ) The last value s the pessue of acceleated patcles.

10 1. Space-tme soluton fo cuent Dffuson Geen functon: Electc cuent: and pessue 2 2 Q() t é z ù ^ Gt (, ) = exp. 1/2 3/2 ê- - ú D^D (4 pt) êë 4D^t 4Dtúû ext j (,) t =-eqñ [ D G(, t-t) - a b ab -D G (, t-t )]. ab In gven pont at fst ase the cuent of acceleated patcles. Then ncease compensated backgound cuent. But complete compensaton s not pobably owng to dffeent patcle dffuson coeffcents. 1 Pessue: P (,) t = ( pv) meanqg (, t-t). 3

11 11. Magnetc feld calculaton (patcula cases) We use MHD equatons wth extenal cuent, taken nto account the moton of medum. Steady soluton: b ( pv) meanq é 1 D ù = ê - ú. 3 B ( D -D^) ê ^ + z D^( D^ + Dz ^ ) ú ë û Non-statc soluton: t eqn ^ dt ba = ò ég^ ( ^, t-t) G ( zt,, t) ù cv t ë û A t eqn ^ dt - ò ég^ ( ^, t-t) G(,, ztt). ù cv t ë û A

12 12. Estmatons of seconday magnetc feld Man souces of acceleated patcles: 1. OB stella wnds M» - M u» cm s h» ( 1 1 Å, w 3 1 /,.1) Seconday magnetc feld s of ode of pmay feld:»» 3 1 at dstance 1 pc. 6 b B - G 2. SN explosons and the emnants E eg u» cm s h ³ ( 1, /,.1). Pobably, SN emnants poduce magnetc felds not smalle then stella wnds.

13 13. Conclusons Sepaate souces of acceleated patcles may cause the sgnfcant magnetc spots n Galaxy wth szes of tens pasec. Accountng of complete poducton of elatvstc patcles n Galaxy ( Q 1 elatvstc patcles pe second) gve the magnetc feld estmaton of ode seveal mcogauss (see Dolgnov and Toptygn, 24). Thank you vey much! 43