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