# Introduction Active Galactic Nuclei

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grav

e

2

p e

grav 2

### 

Gravitational Force on electron plus proton pair (medium must be neutral)

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1 38

1

4

e p

### π

sun

This is known as the Eddington limit, which can be used to establish a minimum for the mass of the BH:

For typical Seyfert galaxies L ≈ 1044 erg s−1 , so MSy ≈ 8 x 105 M QSOs L ≈ 1046 erg s−1 , so MQSO ≈ 8 x 107 M

The Eddington luminosity is the maximum luminosity emitted by a body

E

5 44 sun

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2

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### Accretion Efficiency for Non-Rotating Black Holes

In accretion onto the SMBH some of the rest-mass energy is converted into radiated energy

### L = η (dM/dt) c

2

Efficiency Mass-accretion

Through slow accretion (via an accretion disk; HEA) material

falls onto the black hole via (quasi-circular) orbits, turning potential energy into radiation through collisions with other gas particles.

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S

S

S

2

2

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2

2

2

### 

Effective potential Veff

Particle (pseudo) energy E*

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### Accretion Efficiency for Non-Rotating Black Holes

To find the circular orbit, we need to determine the extrema of Veff

m

2

2

### ]

Extrema are only found if L ≥ √12 M or rms ≥ 6 GM/c2

Hence the “innermost stable” or “marginally stable” orbit is 6 times the Schwarzschild radius. Inside that radius

NO circular orbits exist and the gas/particles plunge into the BH !

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### What does this imply for the SMBH accretion efficiency?

How much energy is lost “down the road” from infinity till 6M ? (a) Pseudo energy at 6 RS : E*(6M) = 4/9

(energy of particle)

(b) Associated E = √[2E*(6M)] = (√8)/3

(what is should be if no energy was lost)

(c) Binding energy: EB = 1 – E = 0.057

(hence this is what was lost on the way)

Hence 6% (η=0.06) of the particle restmass has been converted to (mostly radiative) energy through loosing angular momentum

(redshifting accounted for).

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### For rotating black holes the situations is more difficult (see Krolik), but the procedure is the same.

In this case: rms ~ GM/c2

and η=1-1/√3 = 0.42 for a maximally rotating (Kerr) Black Hole

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### Stellar Kinematics

• Velocity dispersion

increases to 250 km/s toward center

• Radial velocities increase to 200 km/s before

passing through center

• Kormendy (1988) derived a mass of about 107 Msun

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### Gas Kinematics

• Radial Velocity measurements using spectroscopy of

emission lines of ionized gas

• Ford et al. conclude a mass of 2.4 x 109 Msun within the inner 18 parsecs of the nucleus

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20 cm

H2O megamaser @ 22 GHz detected in 1 cm

NGC 4258 in a warped annulus of 0.14

− 0.28pc and less than 1015 cm of thickness, with a beaming angle of 11°

(Miyoshi et al. 1995, Maloney 2002).

Combining the Doppler velocities (±900km s−1) and the time to

transverse the angular distance (0.14 pc) gives the mass of the nucleus 3.9

x 10 M within r ≤ 0.012 pc

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### MCG-6-30-15: Kα Fe line

• X-ray spectroscopy in

Seyferts has revealed highly broadened iron Kα lines on the order of 104 km/s

• Future X-ray observations will give better estimate on mass of central object

• Greene et al. derived a mass of about 5 x 106 Msun

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The profile is skewed with an extended red wing due to gravitational redshift, and a prominent blue wing which is relativisticaly boosted due to

the high orbital velocities of the disk.

### MCG-6-30-15: Kα Fe line

Accretion disk

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The BLR is photoionized, since it responds to continuum variations, with a certain delay, which is a function of the BLR geometry, viewing angle, line emissivity, etc.

In general the line response is given by

### ∫

Ψ

= τ L t τ dτ

t

I( ) ( ) ( )

where Ψ is called transfer function.

The centroid of the cross-correlation function between the continuum and the line gives the mean radius of emission: CCF(τ ) =

### ∫

Ψ (τ )ACF(τ τ )dτ

where ACF is the autocorrelation function of the continuum.

### SMBH Mass Measurement

e.g., for a thin spherical shell, the BLR would respond at a delay

time τ given by the parabolid

### τ = +

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(Peterson 2001, data from Clavel et al. 1992, Peterson et al. 1992)

ACF CCF CCF CCF CCF CCF CCF

### SMBH Mass Measurement

If the kinematics of the BLR are

Keplerian, we can apply the virial theorem

2 BLR

### =

with f, a factor close to 1. Measuring the line widths (FWHM) of the emission lines, we have an estimate of

the velocity dispersion σ.

### Measure time-lag

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2 1 3

5 rms

s km 10 day

) lt 10

45 . 1

(





×

τ v M c

M (Wandel, Peterson & Malkan 1999)

τ c b

a log logvFWHM = +

b=−1/2

The masses derived by this method range from M = 107 Msun for Sy 1s (i.e., in the range of the

LINER NGC 4258) to M = 109 Msun for QSOs Different lines give you the same answer,

even if the rBLR measured is different.

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### Sagittarius A*

• An unresolved bright continuum at radio wavelengths

• Essentially at rest

• Upper limit on size from radio measurements on order of 3 x 1010 km

• Several Stars in orbital motion around Sgr A*

• In particular S2

• Deduce an enclosed mass of 3.7 x 107 Msun

• Other clues

– X-ray flares

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### Sagittarius A*

Andrea Ghez et al. (2003)

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### Evidence for massive objects (SMBH) come from:

Stellar/gas kinematics: Increasing to very small radii

Mega-masers: Keplerian velocity of gas disks

Broadened Fe lines: Relativistic accretion disks

Reverberation Mapping: BLR response to continuum variability

Sgr A* !!!: Individial stellar orbits around Galactic center

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### Based on Chapt. 4 of Krolik

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