Лекции - Конспект лекций по курсу Радиоастрономия
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98
. « »
l = 270°–360° → 0°–90°, « -
» – l = 90°–270°. l = const, z = 0 ( . . b = 0).
l
dR
d
R
R
lRR
d
r
dV
r
sinsin
0
2
0
2
ω
−=
. (5.22)
–
,
.
(5.20)–(5.22)
(
, -
)
-
. -
V
r
-
r
. , -
, -
-
. ,
-
, -
-
-
.
(5.20)–(5.22)
-
-
-
. -
-
, -
. 5.4. .
. 5.5. 21 -
l = 110°.
99
b: -
.
:
ω(R), . -
. -
l ,
V
r
.
V
rmax
, ó V
r
l -
. V
rmax
21
. V
rmax
(l),
ω(R). -
.
(V
rmax
) - -
( 10 / ), - -
.
∆l = ±15°
(l = 0°)
(l = 180°)
-
-
, -
-
V
r
= 0.
-
. ,
,
.
-
, 21
n
H
(r), , -
n
H
(r) . ,
( )
( -
– ).
. 5.6. .
100
. 5.6 [ -
V(R), V(R) = ω(R)R], -
21 . ( -
)
R
RGM
RV
)(
)( =
, M(R) – -
, R. -
, -
.
CO, V(R)
. 5.7. [McGee R.X. et al., Austral.
J. Phys., 1967, 20, 407].
–
( ).
– , -
21 . – -
OH 18 (§6.1). -
– OH (§5.5).
101
R ~ 18 , -
.
R
0
21 8.2 . R
0
6 10 . -
OH H
2
O ( . §6.1)
R
0
, -
R
0
= 7.1 ± 1.5 ( . .
).
. 5.8.
21 .
102
~1.4⋅10
9
M ,
~2% .
~400 .
0.5
2 .
-
– , .
,
-
( ). –
, -
21
V
rmax
.
, -
21 . -
T
s
~ 125 K. -
HI 1960– 1970- . T
s
-
. -
21 : -
, « », -
. T
b
– -
, T
b
′ – -
,
T
0
– -
.
∆T = T
b
– T
0
= (T
s
– T
0
){1 – exp[–τ(ν)]}. (5.23)
, -
, :
T
b
′ = T
s
{1 – exp[–τ(ν)]}, (5.24)
103
. .
. .
,
. -
T
s
. -
:
1)
, -
, τ >> 1; ,
T
s
= T
b
→ T
s
< 125 K ( 30 K);
2)
(τ ~ 0.03), -
; τ << 1
125>>
τ
=
ν
b
s
T
T
K; -
T
s
≥ 1000 K.
, -
(n
H
~ 1–4
–3
) (T
~ 80–150 K)
. T
~ 5000–6000 K
n
H
~ 0.1
–3
, -
. -
.
– -
. – ,
–
.
21
CO. - ,
:
.
HI. -
V
r
( –200 / ),
. , .
: , -
, , -
.
104
.
21 , -
. , -
2
H – (D)
3
H – (T). -
-
4 (I – , F
l
F
u
– -
).
1420.4
, -
.
5.3. Зоны HII
, . 2.2.
, HII ,
– , ,
HII , ( . 2). -
ν
0
, τ =1, HII -
4
-
I F
l
F
u
,
A,
–1
1
H
2
S
1/2
½ 0 1 1420.4058
2.88⋅10
–15
2
H (D)
2
S
1/2
1 ½ 3/2 327.3843
4.70⋅10
–17
3
H (T)
2
S
1/2
½ 0 1 1516.7015
3.51⋅10
–15
3
He
+
2
S
1/2
½ 0 1 8665.6499
1.95⋅10
–12
14
N
4
S
3/2
1 ½
3/2
3/2
5/2
15.6764
26.1273
1.29⋅10
–20
4.28⋅10
–20
23
Na
2
S
1/2
3/2 1 2 1771.6262
8.35⋅10
–15
27
Al
2
P
1/2
5/2 2 3 1506.1010
6.33⋅10
–16
105
:
,6.0
0
ME=ν (5.25)
ν
0
,
∫
= dlnME
e
2
–6
.
HII, -
( 1):
T
b
= T
0
e
–τ
+ T
e
(1 – e
–τ
), (5.26)
T
0
– , T
e
– -
HII (~10
4
K). (τ > 1,
ν < ν
0
) T
b
= T
0
e
–τ
+ T
e
.
T
0
<< T
e
, τ < 1, T
b
= T
e
τ, . .
HII -
. HII
),1(
2
HIIHII
2
2
τ−
ΩΩ
−
′
=Ω
ν
=Ω=
∫∫
eSdT
c
k
IdS
b
B
(5.27)
Ω
HII
HII, S′ –
,
T = T
e
( . . -
HII).
, τ = 1, S = = S′(1 – e
–1
) = 0.63S′.
( -
-
) n
e
T
e
.
, HII, -
,
OB, –
, -
. HII, ,
106
.
– HII -
Ori A ( ), Sgr B2,
M8
, -
ν = 1415 : W3,
W33, W49, W75.
-
(§5.5). ,
HII, -
-
O B. HII ~ 0.1 , -
10
6
–10
7
–3
. HII
-
, -
.
5.4. Рекомбинационные радиолинии
, HII -
,
n.
n n + ∆n :
()
∆+
−=ν
22
2
11
nn
n
RcZ
. (5.28)
Z – , R – ,
M:
−=
∞
M
m
RR
e
1 , (5.29)
R
∞
– -
107
. -
, n >> ∆n,
3
2
2
n
n
RcZ
∆
≈ν . (5.30)
-
: Hn(∆n), – , -
( ), n –
, -
∆n
α ∆n = 1, β ∆n = 2, γ ∆n = 3 . .
Lα – H1α, Hα – H2α, Hγ – H2γ, Brackettγ
– H4γ.
n~ 20–60 ∆n =
= 1
, n ~ 60–130 –
n > 130 – -
. -
: H42α – 3.3 , H109α – 6 , H157α – 18 , H300α – 1.25 .
-
,
n.
, ,
( ).
, , –
HII
.
. -
dI ∝ dN(v).
, -
. :
0
½
2
2
2ln4 ν
=ν∆
mc
Tk
B
. (5.31)
, -
108
3⋅10
4
K.
.
( -
):
()
nnnnnn
BNBNf
h
′′′
−ν
π
ν
=νκ )(
4
)(
, (5.32)
f(ν) –
, N
n′
, N
n
– n′
(
), n ( ), B
nn′
, B
n′n
–
. ,
,
, -
( ). -
:
n
n
Tk
h
n
n
n
n
b
b
e
g
g
N
N
B
′
ν
−
′′
⋅= (5.33)
b
n
– n ,
-
( , §1.2). b
n
n
. 5.9. -
γ
′
′
ν
−
′
′
ν
∆−κ=−ν
π
ν
=νκ
h
Tk
n
dn
bd
be
b
b
BNf
h
Bn
n
Tk
h
n
n
nnn
B
ln
11)(
4
)(
,
(5.34)
:
()
()
nnn
eB
BNf
Tk
h
′
ν
π
ν
=κ
2
4
, (5.35)
n
N – n .
109
(γ) . -
γτ=τ
′
nLL
b . (5.36)
()
enLL
TBb
ν
′
κ=α . (5.37)
()
[]
{}
Lc
Lc
Lc
cL
III τ+τ−−
κ+κ
α+α
=+= exp1
. (5.38)
()
[]
{}
Lc
Lc
Lc
cL
III τ+τ−−
κ+κ
α+α
=+= exp1
, (5.39)
() ( )
()
[]
)(exp1exp
LeLceL
TBTBI τ≅τ−−τ−=
νν
τ
c
<< 1.
()
cec
TBI τ≅
ν
. (5.40)
, HII
, HII -
- ,
.
T
e
HII. -
T
e
~ ~6⋅10
3
K, . . ,
HII (~10
4
K). ,
:
110
. 5.9. b
n
-
-
-
d(lnb
n
)/dn -
n T
e
= 10
4
K
n
e
.
,
.
HII ,
HII.
He, C .
.
, -
, .
, . .
, -
(5.28). -
-
(5.29) -
-
. -
( . 5.10). ,
λ ~ 6
~2.7
-
.
-
.
. -
H He -
-
-
He
+
/H
+
≤ 0.02–
0.06,
-
-
-
111
. -
. ,
(24 ) ,
(13.6 ).
( ).
,
.
, ,
(11.1 ) , . -
, , -
. B- (
, B2), - ,
HII . , -
,
. 5.10. 92α
Ori A.
112
. « CII», -
.
(
C732α, ν = 16 )
(Cas A .)
, ,
, -
.
n,
, -
n ~ 1000. -
-
.
τ .
,
, ∆ν ~ 1/ τ . ∆ν
, . ,
. -
n ~0.1 , . .
.
5.5. Спектральные радиолинии молекул
(CH, CH
+
, CN)
1930- . -
- .
.
: ,
Λ- .
. -
E :
E = E
el
+ E
vib
+ E
rot
, (5.41)
113
E
el
– , E
vib
–
, , E
rot
–
. -
, , ,
. -
-
, . . ( -
) -
- . -
- (
) , -
E
rot
, E
el
E
vib
. -
- ,
– - , -
– - , -
.
, -
: Λ- (OH, CH) -
(NH
3
). .
. -
()
)1(1
8
2
2
rot
+=+
π
= JhBJJJ
I
h
E , (5.42)
I –
, B –
(
), J –
(J = 0, 1, 2, 3,…).
m
1
m
2
r
12
21
21
2
12
mm
mmr
I
+
=
. (5.43)
114
1±=∆J . -
, , -
)1(2
1
1
+=
−
=ν
+
→+
JhB
h
EE
JJ
JJ
, (5.44)
J –
, -
ν
J+1→J
= 2B, 4B, 6B . . -
B . -
( – OH, CH) B
, -
. , CH J = 1–0 λ = 559 .
CO λ(J = 1–0) = 2.6 .
J = 1–0
: HC
11
N ( )
H–C≡C–C≡C–C≡C–C≡C–C≡C–C≡N
B = 160
.
,
.
-
, . -
I
||
I
⊥1
I
⊥2
.
( CH
4
)
: I
||
= I
⊥1
= I
⊥2
.
-
.
I
⊥1
= I
⊥2
= I
⊥
≠ I
||
;
2
rot
)()1( KBAhJhBJE −++= , (5.45)
⊥||
π
=
π
=
I
h
B
I
h
A
22
8
,
8
, (5.46)
115
J, K –
, -
:
J = 0, 1, 2,…; K = 0, ±1, ±2,…, ±J.
: J
K
.
: ∆K = 0, ∆J = 0, ±1. -
(I
||
< I
⊥
) E
rot
K, -
(I
||
> I
⊥
) – . ,
K, . . E
rot
K, ,
.
.
( ,
H
2
O H
2
CO). -
:
cba
I
h
C
I
h
B
I
h
A
222
8
,
8
,
8 π
=
π
=
π
=
. (5.47)
, I
a
< I
b
< I
c
. -
C
A
CAB
−
−−
=κ
2
. (5.48)
κ = 1, κ = –1,
–1 < κ < 1. -
,
κ. . 5.11
-
κ. -
:
+−
−KK
J ( )
+−
KK
J , K
–
K
+
– K
.
116
Λ
- . -
. -
. ,
-
( , , , ).
, -
, , ,
.
. 5.11.
κ.
117
a -
.
:
, . -
LS- ( - -
). , , -
L, -
– . Λ.
, Λ = 0, 1, 2, 3,…
. 5.12. Λ– -
OH.