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(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

Lecture 3

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Rees图Rees（ 1984）

黑洞的形成

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牛顿力学：

黑洞的定义

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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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:

Fuelling RateFuelling Rate

L =dEdt

=ηM•

c2能量平衡

M•=

Lηc2 ≈1.8 ×10−3 L44

η⎛⎝⎜

⎞⎠⎟ Me yr−1

Accretion: conversion of gravitational potential energy to radiation.

L ≈dUdt

=GM

rdmdt

=GM m

•

r

To power a typical AGN requires an accretion rate

Most important !

η的计算， Soltan假设

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):

U =GMm5Rs

=GMm

10GM / c2 =0.1mc2

η0.1, which is an order of magnitude more efficient than fusion of hydrogen to helium (η=0.007).

取η 0.1， LQSO1046erg s-1

M•=

Lηc2 ≈1.8 ×10−3 L44

η⎛⎝⎜

⎞⎠⎟ Me yr−1

≈2Me 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):

U =GMm5Rs

=GMm

10GM / c2 =0.1mc2

η0.1, which is an order of magnitude more efficient than fusion of hydrogen to helium (η=0.007).

取η 0.1， LQSO1046erg s-1

M•=

Lηc2 ≈1.8 ×10−3 L44

η⎛⎝⎜

⎞⎠⎟ Me yr−1

≈2Me yr−1

ASCA (Tanaka et al. 1995)

Problem of Angular MomentumProblem of Angular Momentum

The mass accretion rate necessary to sustain the Eddington luminosity.

M•

Edd =LE

ηc2 ≈2.2M8Me yr−1

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.

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.

Problem of Angular MomentumProblem of Angular Momentum

Tidally-disrupted Star near BHTidally-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

Roche Radius: rR =2.4BH

∗

⎛

⎝⎜⎞

⎠⎟

1/3

R

Without being tidally disrupted.

To ensure that a star is tidally disrupted before it crosses the event horizon requires rR > RS

rRRS

=2.43M

4πRS33∗

⎛

⎝⎜⎞

⎠⎟

1/3

>1 M < 0.64

c6

G3∗

⎛

⎝⎜⎞

⎠⎟

1/2

≈5×108∗−1/2Me

Tidally-disrupted Star near BHTidally-disrupted Star near BH

ULMER 1999

Gezari et al. 2006

Tidally-disrupted Star near BHTidally-disrupted Star near BH

ULMER 1999

Disrupt Giant Stars?

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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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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

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

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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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