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Radio Galaxies
Lecture 1: Physical processes
Geoff Bicknell
Research School of Astronomy & Astrophysics, ANU
1 What is a radio galaxy?
Example of a powerful radio galaxy
• PKS 2356-61 is a classical double-lobed radio galaxy and is typical of many powerful radio galaxies
• This image shows the radio emission in red-yellow overlaid on the optical field
• The corresponding elliptical galaxy is the large blue “blob” in the centre
• The radio power emitted by PKS
2356-61 at 1.4 GHz is The radio power emitted over the range 10 MHz – 10 GHz is approxi-mately
5 26×10 W Hz 1–
1036 W
• There is also another nearby interacting galaxy (to the north)
• The optical point sources in the field are stars
Cygnus A - the prototype high-powered radio galaxy
Low-powered radio galaxies
• 3C 31 is an example of a low-pow-ered radio galaxy
• Note the “plumes” of radio emission emanating from the galactic core
Fanaroff-Riley classification
• FR1 radio galaxies have the brightest emitting region less than half of the distance from the core to the extremity of the radio source (e.g. 3C31)
• FR2 radio galaxies have the brightest emitting region more than half of the distance from the core to the extremity of the radio source (e.g. PKS2356-61)
Optical morphology
• Almost all radio galaxies are elliptical or S0 galaxies
• Some powerful galaxies have associated emission line gas possibly associated with a merger in the recent past
Owen-Ledlow diagram
FR1 and FR2 radio galaxies delin-eated by sharp division in optical/radio luminosity plane
-21.0 -22.0 -23.0 -24.0
23.0
24.0
25.0
26.0
27.0
28.0
MR
log
P14
15
(W
Hz
-1)
2 Emission mechanism
Radio emission results fromthe synchrotron mecha-nism, involving highly rela-tivistic particles in amagnetic field
B
B1 γ⁄
α
v
Pitch angle
The critical frequency of synchro-tron emission is:
Radio frequencies in a magnetic field re-
quire electrons
Non-thermal distributions of electrons
The “zeroth order” spectrum for a distribution of electrons is fre-quently represented as a power-law
νc3
4π------- q Bm----------γ2 αsin=
1 nT 10µG=
γ 104∼
N γ( )dγ No. density of particles in the interval γ γ dγ+→
Kγ a– dγ= =
Power-law in energy => pow-er-law in frequency
Typically:
1e+03 1e+04 1e+05 1e+061e-01
1e+00
1e+01
1e+02
Frequency (MHz)
Flu
x de
nsity
(Jy
)
Cygnus A hot spots A and D
N γ( ) Kγ a–= jν ν α–∝⇒
α a 1–2-----------=
α 0.6 0.8–≈
Origin of particle spectrum
• Shock waves in relativistic plasma give rise to power-law distribution of electrons
• Repeated scatterings of electrons across the shock front. At each scattering the particle gains energy
• Particles with the most scatterings gain the most energy
• There is a finite probability, in the post-shock region that a particle will escape downstream
• The combination of scatterings plus escape leads to power-law in energy
v1 v2
Scattering centre
Scattering centre
ShockParticle
3 The energy involved in radio galaxies
• Measurements of the emission from an astrophysical object involve the flux density:
• For optically thin emission, this is related to the emissivity and the luminosity distance of the source by:
Fν Watts m 2– Hz 1–= at telescope
Fν1
DL2-------- jν Vd
V∫=
• The emissivity is defined as
• In the case of synchrotron emission
jνPower emitted per unit volume
per unit frequency per steradian=
jν εeBa 1+
2------------ν
a 1–2-----------
–∝
εe Energy density of electrons= B Magnetic field=
• Hence the flux density of a synchrotron emitting source gives us information on
but not and individually.
• However, we can estimate the minimum energy
subject to the constraint provided by the flux density
εeBa 1+
2------------Vd
V∫
εe B
Emin εeB22µ-------+
VdV∫=
• The minimum energy is defined by:
Bminmee-------
a 1+2------------ 1 cE+( )C2
1– a( )c
me-------
FνDL2να
V----------------------
f a γ1 γ2, ,( )
2a 5+-------------
=
εe min,4
a 1+------------
Bmin2
2µ0------------
=
Emin εe min,
Bmin2
2µ------------+ V=
Characteristic values of minimum energy parametersCygnus A:
Bmin 9 9–×10 T 9 5–
×10 G= =
εe,min 4 11–×10 J m 3–=
Emin 3 52×10 J≈
4 Radio galaxies - the smoking gun for black holes
What can we learn from the minimum energy?
Of order solar masses has to be accreted into a black hole toachieve Cygnus A type minimum energies. It is not surprising then thatwe contemplate black holes comprising ~ solar masses
M˙acc Mass accretion rate=
Power released from accretiononto black hole
αM˙accc2=
α 0.1∼
Total energy released Etot αMaccc2= =
MaccEtotαc2----------- 5.6 6
×10E
1053 J------------------- α
0.1------- 1–
solar masses= =
2 6×10
108 9–
5 Relativistic jet physics
Description of the radiation fieldDefine:
As the name surface brightness implies the spe-cific intensity measures the brightness of an in-dividual region of a source/object
It is related to the flux density of a given region by:
i.e. the flux is obtained by integration of the surface brightness oversolid angle
n dΩ
dA
Iν Surface brightness Specific intensity= =
Energy per unit time per unit frequencyper unit solid angle per unit area
=
Fν Iν θ Ωdcos∫=
Surface brightness and emissivityFor optically thin emission (i.e. emission in which no absorption ispresent), the surface brightness is determined by the contributionfrom the emissivity over each part of the ray, i.e.
Note that along a ray in freespace,
Iν
jν
Iν jν sd∫=
Iν constant=
SidednessIn rest frame:
The quantity is a relativistic in-variant, i.e.
Both the frequencies in the lab andrest frame and the angle are relatedby the Doppler factor
:
Lab frame
Rest frame
D
D
θ
θ′
M87
Iν jν′s′ jν′Dθ′sin-------------= =
ν 3– Iν
Iνν3------
Iν′ν′3--------=
δ Γ 1– 1 β θcos–( ) 1–=
θ′sin δ θsin= ν δν′=
Also, the emissivity of synchrotron radiation is a power-law in frequen-cy:
Putting this all together gives:
jν′ jνν′ν----- α–
δαjν= =
Iν δ2 α+jνD
θsin----------- =
Non-relativistic part
Relativistic correction
The Doppler factor
is a very sensitive function of especially near .
Doppler boostingFor a highly relativistic jet , near (pole on)
e.g.
δ 1Γ 1 β θcos–( )----------------------------------=
θ θ 0=
Γ 1»( ) θ 0=
δ 2Γ≈ δ2 α+ 2Γ( )2 α+≈⇒
Γ 5= α, 0.6=( ) δ2 α+ 400≈⇒
Doppler dimmingHighly relativistic jet side-on :θ π 2⁄≈( )
δ1Γ---≈ δ2 α+ Γ 2 α+( )–≈
Γ 5= α, 0.6=( ) δ2 α+ 0.015≈⇒
Oppositely directed jetsIf the two jets are intrinsically thesame, then
e.g.
Iν θ( )
Iν π θ–( )
θ
Iν θ( )
Iν π θ–( )-----------------------
1 β θcos+1 β θcos–-------------------------
2 α+=
θ 30°= Γ, 5 β 0.9798 α,≈, 0.6= =
Iν θ( )
Iν π θ–( )----------------------- 670≈
3C219 - another example of sidedness in a relativistic jet source
6 Superluminal motion (more important for pc-scale jets)
By analysing the diagram at right, itcan be shown that the apparent veloc-ity of a “particle”-”blob”-”feature” isgiven by moving in the indicated direc-tion wrt the observer:
This velocity can be greater than 1 foracute angles and close to 1.
θ
E1E2v
βappβ θsin
1 β θcos–-------------------------=
β
βapp,max Γβ= for θ βcos 1–=
7 FR2 jets - hot spot dynamics
Non-relativistic calculation for hot-spot advance
Bow shockContact dis-
continuity
Shock
ρjetvjet2
vjet vhsρextvhs
2
Frame of contact discontinuity
CD
For a non-relativistic jet, balancing the ram pressures in the frame ofthe contact discontinuity gives
For various reasons, we know that jets are light:
so that the velocity of advance of the jet is much less than the jetspeed itself.
ρjetvjet2 ρextvhs
2= vhs⇒ρjetρext----------- 1 2/
vjet=
ηρjetρext----------- 1«=
However, it is readily shown that the Mach number of the hot-spot ad-vance is supersonic
if the jet is supersonic.
Relativistic jetThe relativistic calculation is similar. In this case we have
Mhsvhs
cs ext,---------------- 1>=
wΓ2β2 Relativistic momentum flux density=
w Relativistic enthalpy Total energy density + pressure= =
ρ0c2 ε p+ +=
Rest mass energy density
Internal energy density
Pressure
The momentum balance equation
leads to:
For extreme relativistic plasma
e.g. , gives
wjetΓjet2 βjet
2 ρextvhs2=
βhsw
ρextc2------------------ 1 2/
Γjetβjet=
w 4p=
pjet 10 10– N m 2–= next 103 m 3–=
βhs 0.07Γjetβjet≈
8 FR1 jets
Entrainment
Relativistic base
The prototype FR2 radiosource 3C 31 is used to illus-trate some of the importantfeatures of jets in low-pow-ered radio galaxies.
Entrainment is responsiblefor the spreading of jets withdistance from the core andfor a high surface brightness
The jets are relativistic nearthe base and show a surfacebrightness asymmetry result-ing from relativistic beaming
Illustration of the physics of entrainmentSome of the essential features of entrainment may be illustrated bythe simple model of an incompressible subsonic jet
When there is no pressure gradientin the surrounding atmosphere, themomentum flux is conserved:
The mass flux across the area ofthe jet is given by:
vc AR
Sheared veloc-ity profile
ρv2 AdA∫ ρvc
2A∝ constant=
M˙ρv A ρvcA∝d
A∫
ρvc2A
vc---------------= =
Hence, if the mass flux increases as a result of entrainment, then must decrease, i.e. the jet decelerates.
Self-similar flow
Frequently, turbulent flow assumes a self-similar form. In this case,this manifests itself in a linear increase of jet radius with distancefrom the point at which the turbulence becomes fully developed, i.e.
Hence,
This is a classic result for the dependence of velocity in an incompress-ible turbulent jet
vc
R α z z0–( )=
ρvc2A πρvc
2R2 πρvc2α2 z z0–( )2 constant= = =
vc1
z z0–( )--------------------∝⇒
Similar physical principles apply to transonic, compressible, variabledensity flow - as we have in FR1 sources - but the details are more com-plicated. The important features are:
• FR1 jets are decelerated from relativistic velocities close to the core
• The deceleration means that the particle energies do not decrease as quickly as they would in a constant velocity expanding jet
• The magnetic field is compressed in the axial direction
• Both of these effects lead to a slower rate of decline of surface brightness than expected for a constant velocity flow
Element of jet plasma
The giant radio galaxy NGC 315
FWHM of northern jet
Fit of surface brightness model to data
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