Lecture 3
(1)黑洞的基本物理
(2)解释AGN的连续谱辐射的产生机制
• UV－optical
• IR
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黑洞的形成
Rees图
Rees（1984）
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黑洞的定义
牛顿力学：
广义相对论：
（1）球对称（Schwarzschild）,无角动量
c=G=1
进入视界的粒子在有限的时间内不可避免地落到中心。因此，视界包围的部分不
是恒星那样的实体，而更像一个“洞”。视界包围的部分称为黑洞，更准确地说，
史瓦西黑洞。
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黑洞的定义
（2）轴对称（Kerr-Newman），有电荷，有角动量。 Q＝0  Kerr解
c=G=1
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Fuelling Rate
As in stars, the rate at which energy is emitted by the nucleus gives us the rate
at which energy must be supplied to the nuclear source by accretion:
能量平衡

dE
L
  M c2
dt
To power a typical AGN requires an accretion rate
L
3  L44 
1
M  2  1.8  10 
M
yr
e
  
c

Accretion: conversion of gravitational potential energy to radiation.

dU GM dm GM m
L


dt
r dt
r
η的计算， Soltan假设
Most important !
有效势能取极小的位置即最内稳定
圆轨道（Last stable circular
orbit）
If we ignore relativistic effects, set r=5Rs (which is about where most
of the optical/UV continuum radiation is expected to originate):
GMm
GMm
2
U


0.1mc
5Rs
10GM / c 2
0.1, which is an order of magnitude more efficient than fusion of
hydrogen to helium (=0.007).
取0.1， LQSO1046erg s-1

M
L
3  L44 
1

1.8

10
M
yr
e
  
c 2
 2M e yr 1
If we ignore relativistic effects, set r=5Rs (which is about where most
of the optical/UV continuum radiation is expected to originate):
GMm
GMm
2
U


0.1mc
5Rs
10GM / c 2
ASCA
(Tanakathan
et al.
1995) of
0.1, which is an order of magnitude more
efficient
fusion
hydrogen to helium (=0.007).
取0.1， LQSO1046erg s-1

M
L
3  L44 
1

1.8

10
M
yr
e
  
c 2
 2M e yr 1
Problem of Angular Momentum
The mass accretion rate necessary to sustain the Eddington

luminosity.
LE
1
M Edd 
c
2
 2.2M 8 M e yr
In the simple spherical accretion model, Eddington accretion
rate is a maximum possible accretion rate for mass M. This
critical rate can easily be exceeded with the models that are
not spherically symmetric, such as mass accretion occurs in a
disk. （accrete ionized hydrogen gas）
The major problem with fuelling a quasar by gravitational
accretion is not the energy requirement, but angular
momentum, since the accretion disk is so small.
Infalling gas must lose most of its AM before reaching the
AD, where further AM transfer can occur through viscosity.
Problem of Angular Momentum
The AM per unit mass is L/m=(GMr)1/2, where M is the mass
interior to r, i.e., M=1011Msun and r=10kpc.If this unit mass is
moved to within 0.01 pc of a 107 Msun central BH, where the
viscosity might become important, its AM per unit mass
must decrease to (107 x 0.01pc/1011x104pc)~10-5 of its initial
value.
Gravitational interactions with other galaxies are sometimes
suspected of playing a major role in fuelling AGNs.
Tidally-disrupted Star near BH
Fuel also could be tidally disrupted stars, which place an upper limit on
the central BH mass.
A star of mass density  near a massive body of density BH and radius
R can approach no closer than the familiar Roche limit
 BH 
Roche Radius: rR  2.4 
  
1/ 3
R

Without being tidally disrupted.
To ensure that a star is tidally disrupted before it crosses the event
horizon requires rR > RS
 3M 
rR
 2.4 
RS
 4 RS3 3  
1/ 3
1
 c 
M  0.64  3 
 G  
6
1/2
 5  10 8 1/2 M
Tidally-disrupted Star near BH
ULMER 1999
Gezari et al. 2006
Tidally-disrupted Star near BH
ULMER 1999
Disrupt Giant Stars?
AGN的连续谱
归一化
平均谱
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AGN的连续谱
SED弥散很大
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AGN的连续谱
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小篮包
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AGN的连续谱
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UV-Optical Continuum
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UV-Optical Continuum
A More correct derivation takes into account how the
energy is dissipated in the disk through viscosity
which is a consequence of work done by viscous
torques.
If r >> Ri then
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UV-Optical Continuum
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UV-Optical Continuum
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UV-Optical Continuum
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UV-Optical Continuum
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UV-Optical Continuum
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UV-Optical Continuum(SS)
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UV-Optical Continuum(ADAF)
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UV-Optical Continuum
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UV-Optical Continuum
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Free－free 发射拟合大蓝包
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Free－free 发射拟合大蓝包
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小篮包
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