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.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. 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. 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. 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.
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. 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. 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. 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.
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. 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 2 2 2 2 ( 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. Estmatons of seconday magnetc feld Man souces of acceleated patcles: 1. OB stella wnds M» - M u» cm s h» -6-7 8 ( 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 51 9 8 ( 1, 1 3 1 /,.1). Pobably, SN emnants poduce magnetc felds not smalle then stella wnds.
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