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射电天文基础
姜碧沩
北京师范大学天文系
2009/08/24-28日，贵州大学
1
Emission Mechanisms of Continuous
Radiation
• The Nature of Radio Sources
• Radiation from an Accelerated Electron
• The Frequency Distribution of Bremsstrahlung for an
Individual Encounter
• The Radiation of an Ionized Gas Cloud
• Nonthermal Radiation Mechanisms
• Review of the Lorentz Transformation
• The Synchrotron Radiation of a Single Electron
• The Spectrum and Polarization of Synchrotron
Radiation
• The Spectral Distribution of Synchrotron Radiation
• Energy Requirements of Synchrotron Sources
• Low-Energy Cutoffs in Nonthermal Sources
• Inverse Compton Scattering
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2
The Nature of Radio Sources
• Two large families
– Locations: galactic and extragalactic
– SED: The nature of discrete sources was
investigated by measurements at different
frequencies to determine the spectral
characteristics
• Roughly constant flux density with increasing
frequency
• More intense at lower frequency
– Emission mechanisms
• Thermal
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• Nonthermal
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Blackbody Radiation from
Astronomical Objects
• Solar system objects
– Solid bodies, τ=∞
• Dust in molecular clouds


1
 1  e  dust
Tb ( )  T0 
 expT0 / Tdust  1 

 dust  7  10
 21

Z
2
bN H 
Z⊙
• 2.7K cosmic microwave background
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Radiation from an Accelerated Electron
 
ev(t ) sin 
2
E   2
exp  i t 
r

c
 

r 

θ=π/2 points in the direction of v
2
2

1 e v sin 
S
4 c 3
r2
2
2 e 2 v 2 (t )
P(t ) 
3 c3
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
2 e2
W   P (t )dt 
3
3
c

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
2

v
 dt

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The Frequency Distribution of
Bremsstrahlung for an Individual Encounter
An electron
moving past an ion of charge Ze
2
Ze
mv   3 l
l
p
l
cos
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W
 Z 2e6 1
3
2
3
4c m p v
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Spectral Energy Distribution
2
Ze
C (0)  
 m pv
3 2 v
v
g 
 1.851
16 p
p
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The Radiation of an Ionized Gas Cloud
 8 Z 2e6 1
 3 2 2 2
P ( p, v)   3 c m p v
0

4v  m 
f (v ) 


  2kT 
2
3/ 2
3 v
for    g 
32 p
for    g
 mv 2 
exp 

 2kT 
dN (v, p)  2 N i N e vpf (v)dvdp
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Emission and Absorption Coefficients
4 d  P (v, p)dN (v, p)d
2 6
4 Z e Ni Ne
 
3 c3 m2
 
p2
2m
ln
 kT p1

B (T )
4 Z 2e6 Ni Ne
 
3 c
2
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p2
1
ln
3
p1
2 (mkT)
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Emission Measure and Optical Depth
EM

6
pc cm
 Te 
  8.235 10  
K
2
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s / pc

0
1.35
 Ne   s 
 -3  d  
 cm   pc 
  


 GHz 
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2.1
 EM 

 ( , T )
6 
 pc cm 
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SED
0
 Te 
 0.3045 
GHz
K
0.643
  ( , T )EM 

 
6
 pc cm

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0.476
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Nonthermal Radiation Mechanisms
• Relativistic electrons moving in intricately
“tangled” magnetic fields of extended
coronas believed to surround certain kinds of
stars
• Radiation from relativistic cosmic ray
electrons that move in the general interstellar
magnetic field
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Review of the Lorentz Transformation
x   ( x' vt' )
y  y'
z  z'
x'
t   (t '  )
c
v

c
  (1   )
2 1 / 2
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Velocity
dx dx dt '
dt '
'
ux 

  (u x  v)
dt dt ' dt
dt
'

ux 
dt
  1     
dt '
c 

u x'
  1 
c
u || 
u v
'
||
1 
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u
u 
'
||
c
u '
'

u|| 
 1   


c


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a||'   3 a||
a '   2 a 
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Acceleration
a x  u x   3 3 a x'
'


u
y
 2 3 
'
' 
a y  u y     a y   a x


c


a||'   3 a||
a   a
'

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2
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Time
t   t '
 vr 
t  1   t '
c

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The Synchrotron Radiation of a
Single Electron
d
v
( mv )  e(  B)
dt
c
d
2
( mc )  0
dt
dv ||
dv 
e

( v   B)
0
dt
m
dt
G
 B 
eB
eB
 17.6

B 
G 
 B
MHz
 mc
 Gauss 
mc
tan  
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v
v ||
a    B v
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The Total Power Radiated
2
2e v B  E 
2
2
P



c
u
v
 2
T
B 
3m c  mc 
4 2 2

2 3
Scattered Power P
T 

Incident Power I 0
8

3
2
 e  8 2
 2  
re  6.65  10  25 cm 2
3
 mc 
2
u B  B / 4
2
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The Angular Distribution of Radiation
dP( ,  )
1 e 2 '2
1

a
3 
d
4 c
(1   cos  ) 2
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u
c 1
tan  


u||  v 
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
sin 2  cos 2  
1  2
2
  (1   cos  ) 
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The Frequency Distribution of the Emission
1
1
t  3
  B sin 
tan  
v
v ||

e B sin  
P( )  3
K 5 / 3 ( )d
2

 c  / c
mc
3
3 2
3 3
 c    G sin     B sin 
2
2
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The Spectrum and Polarization of
Synchrotron Radiation
• The instantaneous radiation is in general elliptically
polarized, but since the position angle of the
polarization ellipse is rotating with the electron, the
time averaged polarization is linear. This is true also
for the radiation emitted by an ensemble of
monoenergetic electrons moving in parallel orbits.
3 e 3 B sin 
F ( x)  G ( x)
P 
2
2
mc
3 e 3 B sin 
F ( x)  G( x)
P|| 
2
2
mc
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P  P||
G ( x)
p

P  P|| F ( x)
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The Spectral Distribution of
Synchrotron Radiation from an
Ensemble of Electrons
 ( )   P( , E ) N ( E )dE
E
N ( E )dE  KE  dE 对于 E1  E  E2
 ( )  
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n
n  12 (  1)
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Homogeneous Magnetic Field
3
3 e
 ( )  a(n) K
8 mc 2
I ( )  0.933a(n) KLB
n
 3e 
n 1  n
(
B
sin

)


3 5 
 4 m c 
n 1

 6.26  10

  / GHz
9
n

 Jy rad  2

n 1
p
n  5/3
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Random Magnetic Field
3
e
 ( )  b(n) K
mc 2
n
 3e  n 1  n
B 

3 5 
 4 m c 
I ( )  13.5b(n) KLB
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n 1
 6.26  10

  / GHz
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n

 Jy rad  2

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Energy Requirements of Synchrotron Sources
Wtot  Wpart  Wmag  V (u p  u mag )
u p  K
Emax
E
1
dE
u mag
Emin
Wtot
1 2

B
8
1 2

n 1 / 2
V K G B

B 
8


V n 1  n
S  KH 2 B 
R

7
3 / 7  G
 (6 ) 
S 
4
 H

n
Wtot
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4/7
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R 8 / 7V 3 / 7
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Low-Energy Cut-offs in Nonthermal Sources
• Synchrotron radiation at frequencies below the
low-frequency cutoff ν1 should have a spectral
index of n=1/3
• In synchrotron radiation fields spontaneous
photon emission will be accompanies by
absorption and stimulated emission as in any
other radiation fields. This absorption can
become important in compact, high-intensity
radio sources at low frequencies when the optical
depth becomes large.
• The Razin effect
• Foreground thermal plasma may absorb may
synchrotron emission at lower frequencies
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Inverse Compton Scattering
• Compton Scattering
– An X-ray or gamma-ray photon collides with a
particle, usually an electron. Some of the photon’s
energy is transferred to the particle and the photon
is reradiated at a longer wavelength
• Inverse Compton Scattering
– A low-energy photon collides with a fast-moving
electron. The electron passes on a small
proportion of its energy to the photon, the photon’s
wavelength decreases. The electron has to suffer
a large number of collisions before it loses an
appreciable fraction of its energy
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The Sunyaev-Zeldovich Effect
• Photons from a cold source, the 2.7K
background, interact with a hot foreground
source, a cluster of galaxies. Such clusters have
free electrons with Tk>107K, so the
bremsstrahlung radiation peaks in the X-ray
range. The net effect of an interaction of the
photons and electrons is to shift longer
wavelength photons to shorter wavelength
T 1 3kT
34


N
L

2
.
24

10
Te N e L
T
e
2
T
2 me c
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Energy Loss from High-Brightness Sources
1 dE
8
 2.4  10  u ph
E dt
EL Compton
EL synchrotron
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 10
6
u ph
uB
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Exercise
• The Orion hot core is a molecular source with an average
temperature of 160K, angular size 10", located 500pc from
the Sun. The average local density of H2 is 107cm-3.
– Calculate the line-of-sight depth of this region in pc, if this is taken
to be the diameter
– Calculate the column density N(H2) which is the integral of density
along the line-of-sight. Assume that the region is uniform
– Obtain the flux density at 1.3mm using Tdust=160K, the parameter
b=1.9 and solar metallicity in equation (9.7)
– Use the Rayleigh-Jeans relation to obtain the dust continuum main
beam brightness temperature from this flux density in a 10" beam.
Show that this is much smaller than Tdust.
– At long millimeter wavelengths, a number of observations have
shown that the optical depth of such radiation is small. Then the
observed temperature is T=Tdustτdust, where the quantities on the
right hand side of this equation are the dust temperature and dust
optical depth. From this relation determine τdust.
– At what wavelength is τdust=1 if τdust~λ-4?
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Exercise
• From Fig. 9.1, determine the ‘turnover’ frequency of the
Orion A HII region, that is the frequency at which the flux
density stops rising and starts to decrease. This can be
obtained by noting the frequency at which the linear
extrapolation of the high and low frequency parts of the plot
of flux density versus frequency meet. At this point, the
optical depth τff of free-free emission through the center of
Orion A is unity, that is τff =1, call this frequency ν0.
• From equation (9.36) in ‘Tools’, the relation of turnover
frequency, electron temperature Te and emission measure
EM=Ne2 is ν0=0.3045(Te )-0.643(EM)0.476. This relation applies
to a uniform density, uniform temperature region, actual HII
regions have gradients in both quantities, so this relation is
at best only a first approximation. Determine EM for an
electron temperature Te=8300K
• The FWHP size of Orion A is 2.5’, and Orion A is 500pc from
the Sun. What is the linear diameter for the FWHP size?
Combine the FWHP size and emission measure to obtain
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the RMS electron density.
Exercise
• The source Cas A is a cloud of ionized gas
associated with the remnant of a star which
exploded about 330 years ago. The radio
emission has the relation of flux density as a
function of frequency shown in Fig. 9.1 in
‘Tools’. For the sake of simplicity, assume that
the source has a constant temperature and
density, in the shape of a ring, which
thickness 1’ and outer radius of angular size
5.5’. What is the actual brightness
temperature at 100MHz, 1GHz, 10GHz,
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100GHz?
热和非热射电源的一些例子
•
•
•
•
•
•
•
宁静太阳
HII区的射电辐射
超新星和超新星遗迹
超新星遗迹的流体动力学演化
较老的超新星遗迹的射电演化
脉冲星
河外源
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宁静太阳
• 太阳射电辐射的检测
– 射电天文史前
•
•
•
•
19世纪末：探测器的低灵敏度
20世纪初：观测的停滞
Jansky：太阳活动极小年
1942年：宁静太阳和活动太阳的射电辐射
• 辐射源
– 日冕
– 热辐射
• 等离子体对低频端的影响
– 非直线的传播
• 逆转的温度结构
– 中频段的临边增亮现象
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HII区的射电辐射
• HII区Orion A的热辐射
– 轫致辐射
– 距离：450pc
– 两个波段的比较
•
•
•
•
分辨率
核的亮温度
辐射量度的计算
大小
– 简单模型的改进
• 电离星风的射电辐射
– 热辐射
– 非热辐射
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超新星和超新星遗迹
• 超新星
– 分类
• 大质量红巨星的爆发：II型
• 白矮星和的双星系统：I型
– 银河系中发生的频率
• 预计：50年一个
• 已知最近的观测：1606年，Kepler超新星；1667，Cas A
• 遗迹的证认
– 形状：展源
• 距离：银河系内天体
• 能谱：与HII区的区别
– 膨胀的壳层
– 与脉冲星成协
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较老的超新星遗迹的射电演化
• 同步辐射的强度
• 参数的变化
– 磁场强度
– 电子能量
– 谱指数
• 辐射流量的变化
• Cas A的情况
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超新星遗迹的流体动力学演化
• 自由膨胀阶段
– 被膨胀壳层扫过的气体质量小于初始质量
– Rt
– 几十年
• 绝热阶段
– 遗迹以被扫荡的物质为主
– 辐射损耗比超新星产生的总能量小得多
– Rt2/5
• 辐射阶段
– 辐射损耗
– Rt1/4
• 耗散阶段
射电天文暑期学校
– 激波速度降低到声速以下，与星际介质混合
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脉冲星
•
•
•
•
•
•
•
探测和源的本质
距离估算和在银河系的分布
强度谱和脉冲形状
脉冲星定时
旋转变慢和磁矩
双星脉冲星和毫秒脉冲星
射电辐射机制
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河外源
• 类型
– AGN：类星体，Seyfert星系，射电星系
• 辐射机制：同步辐射
– 射电星系
• 苏尼阿耶夫－泽尔多维奇效应
• 相对论效应和时变
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