Лекции - Конспект лекций по курсу Радиоастрономия
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19
Гл а ва 2. Механизмы радиоизлучения
в астрофизических условиях
-
CGS.
2.1. Распространение радиоволн в плазме.
Генерация радиоизлучения плазменными колебаниями
( ) -
,
z. )].(exp[
0
kztiEE −ω=
. -
:
].[)exp(
0
Hr
c
e
tiEermrm
×+ω=ν+ (2.1)
m –
, ν – (
, ).
:
;
1
rot
t
B
c
E
∂
∂
−=
πρ= 4divD ;
;
14
rot
t
D
c
j
c
H
∂
∂
−
π
=
;0div =B (2.2)
;Ej σ= ;ED ε= .HB µ=
.
-
( )
20
:
()
.
4
2
ikni −=
ω
πσ
−ε=ε
′
(2.3)
(2.3) -
, ,
, n ( -
) k (
).
( 0=H ).
(2.1)
:
()
;
22
2
ν+ω
ν
=σ
m
Ne
()
22
2
4
1
ν+ω
π
−=ε
m
Ne
. (2.4)
ν
:
()
,
37.0
ln
3/122
4
π
=ν
Ne
Tk
N
kT
e
B
v
(2.5)
v
– , N — .
(N ~ 10
8
–3
) ν ~ 1/15
–1
<< ω
, ω
2
+ ν
2
≅ ω
2
.
, z -
ε′ (2.3), -
:
.expexp
00
ω+
ωω
±=
ω+ε
′
ω
±= tikz
c
nz
c
i
Eti
c
i
EE
(2.6)
21
-
.
-
,1
4
1
2
2
2
2
ω
ω
−=
ω
π
−=ε=
p
m
Ne
n
(2.7)
m
Ne
p
2
4π
=ω
(2.8)
( ) -
.
( ) -
.
.)(1098.8
2
)(
33 −−
⋅=
π
=
π
ω
=ν NN
m
e
p
p
(2.9)
, ω ≥ ω
p
0 ≤ n ≤ 1; ω < ω
p
. ,
-
, ~λ.
ω
<
ω
p
.
c
kω
−
(2.6) -
- .
, -
-
22
, ,
:
.
1
2
2
2
2
2
ω
ω
−ω
νω
=
ω
=κ
p
p
c
c
k
(2.10)
. , -
, – -
,
mc
eH
H
=ω (2.11)
:
.)(8.2
2
)( H
H
H
=
π
ω
=ν
(2.12)
22
)( ν>>ω±ω
H
, -
(
),
, .
,
.
, -
,
. , , -
( – 1
– 2) -
.
.
23
: α = 0 α = π/2 (α –
-
). ,
. . [16].
1) α = 0 (
).
. «+» 1
(
), «–» – 2 (
).
()
,1
2
2
2,1
H
p
n
ω±ωω
ω
−=
2
2,1
2
2,1
)(
H
p
mcn ω±ω
νω
=κ
. (2.13)
-
ω ~ ω
H
; -
-
. -
-
,
-
.
2) α = π/2 (
).
-
. HE –
,
. n
1
κ
1
(2.13) 0=H . -
:
()
()
2222
222
2
2
1
Hp
pp
n
ω−ω−ωω
ω−ωω
−=
;
()
[]
()
.
2222
2
22222
2
Hp
Hpp
cn ω−ω−ωω
ωω+ω−ωων
=κ
(2.14)
, - -
22
Hp
ω+ω=ω
-
.
24
. 2.1.
.
2.2. Поляризация излучения
-
. -
,
.
-
-
–
. -
-
,
,
(
. 2.1).
- , z -
-
( , -
,
. 2.1), x y
. E x
y :
),sin()()(),sin()()(
0000 yyyxxx
ttEtEttEtE ψ−ω=ψ−ω= (2.15)
E
0x
/E
0y
ψ
xy
= ψ
x
– ψ
y
χ p.
I = I + I
-
; ρ = I /I -
. ,
25
,
I, Q, U, V:
() ()
()()
()
σρ=
χσρ=
χσρ=
=
,2sin
,2sin2cos
,2cos2cos
,
IV
IU
IQ
II
(2.16)
σ =arctg p. -
x y, -
,
2
,
2
2
0
2
0
I
EI
I
EI
yyxx
+=+= (2.17)
. :
ψ=
ψ=
−=
+=
xyyx
xyyx
yx
yx
EEV
EEU
IIQ
III
sin2
,cos2
,
,
00
00
(2.18)
–
r (
E
-
) l ( ), -
- , -
,
2
,
2
2
0
2
0
I
EI
I
EI
llrr
+=+= (2.19)
2
0r
E
26
2
0l
E , ψ
rl
- -
:
−=
ψ=
ψ=
+=
,
,sin2
,cos2
,
00
00
lr
rllr
rllr
lr
IIV
EEU
EEQ
III
(2.20).
-
, -
,
( . 2.1) -
.
-
. , (§2.5)
.
(§5.5)
100% .
,
. , -
-
,
, -
, ,
.
. -
, -
, -
( - -
n
1
, n
2
, -
, . §2.1).
L ω -
H ( ) -
27
-
:
()
].[)(
]
[18.0
2
2
2
12
λ=
=⋅λ≈−
ω
=θ∆
∫∫
RM
dlHNdlnn
c
LL
(2.21)
H ; l — ; -
λ — . RM [ /
2
] – -
. (
N ~ 10
8
–10
10
–3
, H ~ 1 ), ∆θ ~10
6
. -
( )
.
2.3. Тормозное излучение ионизованного газа
-
– - ( -
«free-free»).
,
.
.
1
)2(33
16
3
2/3
62
νν
ν
π
π
⋅=α g
Tmkhc
Tke
NN
eB
eB
p
(2.22)
N
p
— , g
ν
– (
10 -
):
.ln7.1755.0
2/3
ν
+⋅=
ν
e
T
g
(2.23)
, -
28
T
e
:
.
2
exp
2
4)(
2
2
3
2
v
v
vvv d
Tk
m
Tk
m
NdN
eB
e
B
−
π
π=
(2.24)
(2.22) ,
.
. -
, -
(i k),
, .
, -
:
n
k
A
ki
+ n
k
B
ki
ρ
ik
= n
i
B
ik
ρ
ik
. (2.25)
, , – -
, . n
k
, n
i
– -
k, i, ρ
ik
–- k→i.
.
, ,
:
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−ρ=ρ−ρ
iki
kik
ikikiikkikikiki
Bn
Bn
BnBnBn 1
(2.26)
-
:
,
ik
k
i
ki
B
g
g
B =
(2.27)
g
i
, g
k
– . -
29
:
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
ν
−=
eB
ik
i
k
k
i
Tk
h
n
n
g
g
exp
(2.26) hν << k
B
T
e
( -
– ) :
.1
eB
ikiki
i
k
k
i
ikiki
Tk
h
Bn
n
n
g
g
Bn
ν
ρ≅
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−ρ
(2.28)
, k→i -
,
« » . -
( -
)
.
. ,
-
(2.22)
eB
Tk
hν
. -
, -
:
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
ν
+
ν
⋅≅α
−
ν
2/3
2/3
2
2
*
ln7.17
10
e
e
p
T
T
NN (
–1
). (2.29)
N N
p
–3
, ν — , T
e
— K -
. N = N
p
,
p
NN ⋅ N
2
.
30
-
(2.13) -
κ ( , -
).
.
-
. -
« – »
.
-
∫∫
∝α=τ
νν
XX
dxNdx
00
2*
. (2.30)
(2.30) -
. , τ
ν
-
-
, .
(ME – measure of emission).
–5
;
–6
(
-6
× ).
(1.9),
T
b
= T
c
[1 – exp(–τ
ν
)]. (2.31)
T
c
T
e
(2.24).
*
ν
α
(2.29)
(∝ ν
–2
). ,
*
ν
α , τ
ν
>> 1, T
b
≅ T
c
= const ( ),
–
(1.3)
ν
2
. ,
31
T
b
≅ T
c
τ
ν
. τ
ν
∝ ν
–2
, I
ν
. , -
.
I
ν
∝ ν
–0.1
. ,
, - -
, – (∝ ν
2
)
(
) ( . 2.2).
, τ
ν
~ 1.
:
ME6.0
0
≅ν , (2.32)
ν
0
, ME
–6
.
,
ν
0
ME
.
. 2.2.
(
).
32
2.4. Циклотронное излучение
.
, . -
-
(E << mc
2
),
, –
. .
H:
.
mc
eH
H
=ω (2.33)
(
)
.
2
2
cceH
mc
r
H
H
H
vvv
π
λ
==
ω
=
(2.34)
v << c
.1
2
<<
λ
π
H
H
r
, ½π,
r
e , -
ω
H
. -
()
,cos1
8
2
3
242
α+
π
ω
=
c
re
I
HH
(2.35)
α – H
k . ω
H
.
33
[15, 18] ,
,
ω = sω
H
,
s = 2, 3,… -
s. , -
-
.
. -
-
. -
, -
()
−
−
π
=
sB
s
sB
ss
Tk
VVm
Tk
m
NVf
2
exp
2
)(
2
2/3
, (2.36)
T
s
, N
s
m – , -
. (2.36) -
S
V . -
HV
S
ν
()
jsj
sBj
j
an
Tkn
c
αβ−ϑ
ν
π
=µ cos1cos
4
22
2
, (2.37)
()
ϑαβ−π
ν
=
µ
=
coscos12
2
22
sj
sBj
j
j
j
nc
Tkna
I
. (2.38)
n
j
β
s
cosα > 1, -
, – .
34
, ,
( ) , -
. .
-
,
. , -
( I ),
(T
b
10
15
K), -
(T
b
10
17
K), ,
(
UV Cet) ( RS CVn).
2.5. Синхротронное излучение
– -
. ,
: .
, -
: , -
( IV V ),
- , ( -
), , , -
, , .
,
,
mc
eH
H
=ω
.
.
, -
c
v
H 90°.
[]
H
c
e
F ×= v
L
-
. -
-
35
.
(
)
2
L
2
2
1
1
γ
≡−≅θ
c
v
, (2.39)
2
2
L
1
1
c
v
−
=γ
– ,
(E = mc
2
γ
L
).
,
H ,
H
ω
πγ
=τ
L
2
, -
H
t
ωγ
=∆
2
L
1
( . 2.3). γ
L
-
.
. 2.3. .
36
, (
) χ (« - ») H ,
H ,
v
:
H
⊥
= Hsinχ. , -
v
||
= vcosχ.
( . . 2.4):
χγ
ω
π
≅
χ
−τ=τ
′
2
L
2
sin
2cos
1
H
c
v
,
(2.40)
v ~ c. -
χγ
ω
=
τ
′
π
=Ω
2
L
sin
2
H
H
. (2.41)
-
χ ( -
) >> 1/γ
L
.
-
- .
, -
( 2.3),
-
H
t
ωγ=
∆
ω
2
Lmax
1
~
. -
.
, ,
,
. [15] -
. 2.4. -
.
37
-
:
,)(
3
)(
/
3/5
2
3
ξξ
ν
ν
=ν
∫
∞
νν
⊥
c
dK
mc
He
P
c
(2.42)
K
5/3
– 5/3, H
⊥
=
= Hsinχ –
,
( χ ),
2
L
2
L
2
L
21.4
4
3
22
3
γ=γ
π
=
π
ω
γ=ν
⊥⊥
HH
mc
e
H
c
. (2.43)
ν
c
P(ν),
c
ν≅
π
ω
=ν 3.0
2
max
max
. P(ν), -
, . 2.5.
, ,
H ~ 10
–5
–10
–6
, γ
L
~ 10
3
–10
5
.
. 2.5.
.
38
. -
-
, -
E
.
.ν >> ν νν2/3( − 1
,ν << ν
=Π
cc
c
)/
½
.
, -
N(E),
P(ν) N(E). P(ν) -
γ
L
, -
ν
c
.
()
∫
ν=ν LdEPENI )()( , (2.44)
L – . -
,
. ,
.
-
:
N(E)dE = KE
–γ
dE. (2.45)
-
(§5.1).
()
2
1
2
1
2
1
532
3
4
3
)(
−γ
−
+γ
−γ
νγ
⎟
⎠
⎞
⎜
⎝
⎛
π
=ν KHa
cm
e
mc
Le
I
. (2.46)
, -