close

Вход

Забыли?

вход по аккаунту

?

Black Holes Sources of Ultrarelativistic Cosmic Rays.

код для вставкиСкачать
~liinnleiidcr Physik. 7. Folge, Band 46. Heft 5, 1989.
S. 397-398
VEB J. A. Barth, Leipig
Black Holes Sources of Ultrarelativistic Cosmic Rays
By CORRADO
MASSA
Reggio Emilia, Italy
Schwarzc Locher als Quellen ultrarelativist,ischerkosmisclier Strahlung
If the empirical Schuster’s law [l] applies t o black holes, then a t the distance
from a neutral black hole with spin S there is a magnetic field of strength [ I ]
7
hit for a iiurnerical factor of order unity.
I n (I), c is the speed of light, G is the gravitational constant, n = Sc/GM2, where
Jf = black hole’s mass, and A? = GM/c2.
Near the hole ( r - horizon radius r~ R, hereafter all factors of order unity will be
neglected) the field has the strength
-
B
=~c2/Ii?~G.
(2)
I t is known “4 that a spinning black hole within a magnetic field of strength B surroi~ncled by a ionized interstellar mcdium will build up a net electric charge up t o the value
Q
where Q
=
2BSGJc3,
> 0 (Q < 0) if
(3)
S and B are parallel (antiparallel). Set (2) into (3), and obtain
Q = azRRc2//G.
(4)
A particle of rest mass m and electric charge e , with e/Q > 0, will be repelled by the hole
and its final kinet>icenergy (at infinity) will be
L = eQs+ - L,,,
(5)
s = distance between the hole aid the startpoint of the particle, and L,, = total amount
of electromagnetic energy emitted by the particle during its acceleration [31
L,,,
= A?
90
J (1 -
VZ)-I
+ VA
V [ ( E
- ( E V ) z ]dr ,
(6)
a
where
A
V = particle’s speed/c, E = electric field of strength Qlr2.
Notice: E ( r ) / B ( r )= nr/B (for eqs (l),(4))’ thus, if 01 = 1 (extreme kerr black hole),
R,then E ( r ) B ( r ) ,the inagiietic field is negligible, E and V are parallel,
and if s
and (with V1)
= e2/nL?,
-
+
00
L,,
E2& = ( A & ) ~ s - ~ .
= A2
8
(7)
Ann. Physik Leipzig 46 (1989) 5
398
Now, eq (5) reads (for eqs (4),(7))
L = (c2/lC)( R / s )[ o - ( A c / s )(~R / l @ ] .
(8)
Since e = 4.8 10-l0 esu, A < lO-l3 cm (because m 2 9
g = electron mass),
R 2 lo6 cm (because M 2 5 M ,
1034 9 ) and s $= R, eq (8) can be written in the simple
N
form
L = ( C ” / J C ) ( R / s )e , (s $= 12).
(9)
Set (say) s = lo2 R ; hence L = 1013 erg = 1 Oz5 eV). If S and B are parallel, an extreme
Kerr black hole can accelerate particles up t o energies of loz5eV. Electrons lose their
energy very quickly, whereas protons retain their energy for a very long time. To see
this fact consider a particle which runs away from the black hole and plunges into the
interstellar space, where I3 = 0, and U N 1 0 V gauss = the average magnetic field of
our galaxy and (according to the Schuster law) of a typical spiral galaxy; the electromagnetic energy emitted per unit time by the particle of ultrarelatiristic energy L = L(t)
is [3] cZI,/dt = (-2/3) c ( B A L / ~ Cwhich
~ ) ~ ,integrated gives
L(t)= L( 1
+ @Lt)-l;/9 = (2/3) c(RA/mc2)2,
where L = L(0)is the energy a t time t = 0, given by eq. (9). The particle, with initial
energy L $ mc2, has the energy L ( t ) 1, a t the time t - (@L(t))-l,where 010-14 erg-1 8-1 for an electron, and
L O P erg-1 s-1 for a proton. If initially L =
1025 eV = 1013 erg, theii the energy of an electron is 1020 eV when only t N 106 S N ten
days, and 1018 eV a.he11 t~ 108 .SN ten years.
A proton, on the contrary, retains its initial huge energy for a long time. \\‘hen
t = 1 0 6 years, I, is still of the order of IPSeV, and when t = 1010 years, Ir, is about
I 021 eV.
I n conclusion: if the Schuster law applies to black holes, theii extreme Keri holes
can generate cosmic rays made by protons of energy 5 1 025 eV.
I stress that the origin of the high-speed protons with energy > 1021 eV found in the
cosmic radiation is yet unexplainetl.
<
N
Refcrerices
[l] Mass.%,C.: Ann. Physik (Leipzig) 45 (1988) 518.
r2] W a ~ nROBERT
,
M.: Phys. Rev. D 10 (1974) lfi80.
LANDAU,
L. D.; LIFSHITZ,
E. M.: The Classicid Theory of Fields. Reading, Rfassachusetts:
Addison-Weslcy and London: Pergamon 1971, CIi 9, See. 73, eq. ( 7 ) ; Sec. 74, eq. (10).
Bei der Redaktion eingegangen iun 24. November 1988.
Anschr. d. Verf.: C O R R ~ D OMASSA
Via Fratelli Manfredi 55
1-42100 Reggio Emilict
Itdy
Документ
Категория
Без категории
Просмотров
1
Размер файла
110 Кб
Теги
black, rays, ultrarelativistic, source, cosmic, hole
1/--страниц
Пожаловаться на содержимое документа