active galactic nuclei 4c15 - high energy astrophysics [email protected]
TRANSCRIPT
Introduction
• Apparently stellar
• Non-thermal spectra
• High redshifts
• Seyferts (usually found in spiral galaxies)
• BL Lacs (normally found in ellipticals)
• Quasars (nucleus outshines its host galaxy)
Quasars - Monsters of the Universe
Artist’s impression
AGN Accretion
Believed to be powered by accretion onto supermassive black hole
high luminosities
Eddington limit => large mass
highly variable
small source size
Accretion onto supermassive black hole
Quasars - finding their massThe Eddington Limit
Where inward force of gravity balances the outward ‘push’ ofradiation on the surrounding gas.
LEdd mass
So a measurement of quasar luminosity gives the minimum mass – assuming radiation at the Eddington Limit
Measuring a Quasar’s Black Hole
Light travel time effects
A B
d = c x t
If photons leave A and B at the same time, A arrives at the observer
a time t ( = d / c ) later.
If an event happens at A and takes a time t, then we see a change over
a timescale t+t. This gives a maximum value for the diameter, d, because we know that our measured
timescale must be larger than the light crossing time.
c = speed of lightd = diameter
Accretion Disk and Black Hole• In the very inner regions, gas is believed to form
a disk to rid itself of angular momentum
• Very hot towards the centre (emitting soft X-rays) and cool at the edges (emitting optical/IR).
• Disk is about the size of our Solar System
• Geometrically thin, optically-thick and radiates like a collection of blackbodies
Quasars
• Animation of a quasar
This animation takes you on a tour of a quasar from beyond the galaxy, right up to the edge of the black hole.
It covers ten orders of magnitude, ie the last frame covers adistance 10 billion times smaller than the first.
Accretion Rates
Calculation of required accretion rate:
sJL /1040
28
40
21031.0
10
c
LM
.
yrMyrkgskg Sun /10/103/10 3124
More about Accretion DisksDisk self-gravitation is negligible so material in differential or
Keplerian rotation with angular velocity K(R) = (GM/R3)1/2
Q
Q
If is the kinematic viscosity for rings of gas rotating, the viscous torque exerted by the outer ring on the inner will be
Q(R) = 2R R2 (d/dR) (1)
where the viscous force per unit length is acting on 2R and = His the surface density with H (scale height) measured in the z direction.
More about Accretion Disks (Cont.)
The viscous torques cause energy dissipation of Q dR/ring
Each ring has two plane faces of area 4RdR, so the radiative dissipation from the disc per unit area is from (1):
D(R) = Q(R) /4R = ½ R)2 (2)
and since K = (G M/R3)1/2
differentiate and then
D(R) = 9/8 Q(R) M/R3 (3)
•
• •
More about Accretion Disks (Cont.)
From a consideration of radial mass and angular momentumflow in the disk, it can be shown (Frank, King & Raine, 3rd ed., sec 5.3/p 202, 2002) that
= (M/3 [1 – (R*/R)1/2]
where M is the accretion rate and from (2) and (3) we thenhave
D(R) = (3G M M/8R3) [1 – (R*/R)1/2]
and hence the radiation energy flux through the disk faces is independent of viscosity
•
•
•
Accretion Disk StructureThe accretion disk (AD) can be considered as
rings or annuli of blackbody emission.
R
5.0
*3
18
3
R
R
R
MGM
Dissipation rate, D(R) is
= blackbody flux
)(4 RT
Disk TemperatureThus temperature as a function of radius
T(R): 4/15.0
*3
18
3)(
R
R
R
MGMRT
then for *RR 4/3** / RRTT
4/1
3*
* 8
3
R
MGMT
and if
Disk SpectrumFlux as a function of frequency, -
Log
Log
*F
Total disk spectrum
Annular BB emission
Black Hole and Accretion DiskFor a non-rotating spherically symetrical BH, the innermost stable orbit occurs at 3rg or :
2min
6
c
GMr
and when *RR 4/3** / RRTT
High Energy Spectra of AGNSpectrum from the optical to medium X-rays
Log
Log
(F
14 15 16 17 18
optical UV EUV soft X-rays X-rays
high-energy disk tail
Low-energy disk tail
Comptonized disk
Balmer cont, FeII lines
Fe K LineFluorescence line observed in Seyferts – from
gas with temp of at least a million degrees.
X-ray
e-
FeK
Source of Fuel
• Interstellar gas
• Infalling stars
• Remnant of gas cloud which originally formed black hole
• High accretion rate necessary if z cosmological - not required if nearby
The Big Bang and Redshift
• All galaxies are moving
away from us.
• This is consistent with
an expanding Universe,
following its creation
in the Big Bang.
Cosmological Redshift• Continuity in luminosity from Seyferts to
quasars
• Absorption lines in optical spectra of quasars with emabs zz
1abz1abz
2abz
2abz3abz3abz
emzemz
flu
x
Alternative Models
• Supermassive star - 10 solar mass star radiating at 10 J/s or less does not violate Eddington limit. It would be unstable however on a timescale of approx 10 million years.
• May be stabilized by rapid rotation => ‘spinar’ - like a scaled-up pulsar
8 39
• Also, general relativity predicts additional instability and star evolves into black hole.
• Starburst nuclei - a dense cluster of massive, rapidly evolving stars lies in the nucleus, undergoing many SN explosions.
• Explains luminosity and spectra of low-luminosity AGN
• BUT SN phase will be short (about 1 million years) then evolves to black hole
• radio observations demonstrate well-ordered motions (i.e. jets!) which are hard to explain in a model involving random outbursts
Radio Sources
• Only few % of galaxies contain AGN
• At low luminosities => radio galaxies
• Radio galaxies have powerful radio emission - usually found in ellipticals
• RG 10 - 10 erg/s = 10 - 10 J/s
• Quasars 10 - 10 erg/s = 10 - 10 J/s
38 43 31 36
43 47 36 40
Radio Galaxies and Jets
Cygnus-A →VLA radio image at = 1.4.109 Hz- the closest powerfulradio galaxy (d = 190 MPc)
← 3C 236 Westerbork radio image at = 6.08.108 Hz – a radio galaxy of very large extent (d = 490 MPc)
Jets, emanating from a central highlyactive galaxy, are due to relativisticelectrons that fill the lobes
150 kPc
Radio Lobes
5.7 MPc
Radio Lobes
Jets: Focussed Streams of Ionized Gas
energy carried out along channels
lobe
hot spot
material flows back towards galaxy
jet
Electron lifetimes
Calculating the lifetimes in AGN radio jets.
If m = 10 Hz (radio) ~ 4.17x10 E B
E B = 2.5x10 J Tesla
syn = 5x10 B E sec
For B = 10 Tesla, ~3x10 sec, ~ 1 month
For B = 10 Tesla, ~ 10 sec, ~ 3x10 yrs
syn
syn
8 36 2
2 -29 2
-13 -2 -1
-3 6
-8 14 6
For Synchrotron radiation by electrons:
Shock waves in jets
Lifetimes short compared to extent of jets => additional acceleration required. Most jet energy is ordered kinetic energy.
Gas flow in jet is supersonic; near hot spot gas decelerates suddenly => shock wave forms. Energy now in relativistic e- and mag field.
Equipartition of energy
Relative contributions of energy
What are relative contributions for minimum energy content of the source?
Energy in source
particles magnetic field
• Assume electrons distributed in energy according to power-law:
kEEN )(
2max
max
0 2)( E
kEdEENE
E
Total energy density in electrons,
Must express k and E as functions of B.max
• Assume electrons distributed in energy according to power-law:
kEEN )(
2max
max
0 2)( E
kEdEENE
E
Tot
Total energy density in electrons,
Must express k and E as functions of B.max
We observe synchrotron luminosity density:
And we know that:
dEPENLE
synmax
0
)(
22' BEkPsyn
Hence:
3
max
222
max
0 3
'' E
BkkdEBEkkEL
E
So:
3max
2'
)3(
EBk
Lk
max2')2(
)3(
EBk
LETot
and the total energy density in electrons then becomes:
Finding Emax
Find E by looking for :max max2maxmax BEconst
2/1max
2/1max '' BkE
2/32/1
max2/12 ''')2(
)3(
aBBkBk
LETot
So:
The energy density in the magnetic field is:
Thus total energy density in source is:
For T to be minimum with respect to B:
2
0
2
2bB
B
22/3 bBaBT
0
B
T
Thus:
So:
022
3 2/5 bBaB
B
T
2/7
4
3 aBb
2/32/3
4
3 aBaBT
particle magnetic field
And finally,
This corresponds to saying that the minimum energy requirement implies approximate equality of magnetic and relativistic particle energy or equipartition.
energy density in particlesenergy density in magnetic field
13
4
Equipartition in Radio Sources
• If dlobe ~ 75 kPc = 2.3.1021 m and vjet ~ 103 km/s, then
tlife ~ 2.3.1021/106 = 2.3.1015 s ~ 7.107 years
• Rlobe ~ 35 kPc = 1021 m and hence Vlobe = 4/3 Rlobe3
= 5.1063 m3
• Total energy requirement ~ 5.1037 x 2.3.1015 ~ 1053 J and energy density ~ 1053/1064 = 10-11 J/m3
• So from equipartition → B2/2o ~ 10-11 or B ~ 5.10-9 Tesla
For Cygnus A → Lradio ~ 5.1037 J/s
Maximum frequency observed is 10 Hz.11
BEm236102.4
262 105.2 BE
5102182 1010105 eVEJE1213105 EBsyn
yrs513 103sec10 Thus electron acceleration is required in the lobes.
Relativistic Beaming
Plasma appears to radiate preferentially along its direction of motion:
Thus observer sees only jet pointing towards her - other jet is invisible.
Photons emitted in a cone of radiation and Doppler boosted towards observer.
Jet collimation
• Nozzle mechanism hot gas inside large, cooler cloud which is spinning: hot gas escapes along route of least resistance = rotation axis => collimated jet
• But VLBI implies cloud small and dense and overpredicts X-ray emission
Supermassive Black Hole
• Black hole surrounded by accretion disk
• Disk feeds jets and powers them by releasing gravitational energy
• Black hole is spinning => jets are formed parallel to the spin axis, perhaps confined by magnetic field
Geometrically-thick disk
• Black hole + disk; acc rate > Eddington
• Disk puffs up due to radiation pressure
• Torus forms in inner region which powers and collimates jets
• Predicted optical/UV too high however, but still viable
ACTIVE GALACTIC NUCLEI
END OF TOPIC
Q 4.d) If the high energy electron spectrum in the galaxy is of the formN(E) E-3/2, express the ratio of Inverse Compton-produced to Synchrotron-produced X-ray intensities in terms of IC and Synch.
Ratio = (no of electrons with )
(no of electrons with )
But:
ICS 2
2
S
IC
S
IC
S
IC
N
N2
2
2
3
2
3
S
IC
S
IC
S
IC
E
E
N
N
Hence IIC/ISynch = [IC/Synch]2-3/2 = [IC/Synch]
1/2