radio galaxies in the chandra era jets: particle acceleration and entrainment mark birkinshaw...

Radio galaxies in the Chandra era

Jets: particle acceleration and entrainment

Mark Birkinshaw

University of Bristol

08 July 2008 Mark Birkinshaw, U. Bristol 2


Outline

1. Jets – general physics issues

2. Deceleration through entrainment – the Laing & Bridle analysis of 3C31

3. Instabilities, turbulence, intermittency

4. Associated particle acceleration: critical energies and sites



Jet questions• What are the structures of the jets?• What are the jet speeds and compositions?• How are the jets launched?• On what scale do jets slow, and what structure does

slowing cause the jets to adopt?• What fractions of jet momentum and energy survive to

the large scale? • What processes cause particle acceleration, and what is

the resulting electron spectrum?



Jets and lossesDetectable jets are intrinsically lossy – amount of loss influences

nature of flow.

Energy of jets in two components:• internal energy density – relativistic/non-relativistic particles, fields, internal

random motions• bulk energy density associated with the flow itself

Loss processes:• radiation (synchrotron, inverse-Compton, etc.) – by which we visualize the

flows – changes in internal energy density• transport of energy to the external medium – both internal energy and bulk

kinetic energy



EntrainmentJets also gain material• gas near the jets can be dragged along by magnetic stresses or

viscosity• material can be brought into the jets by turbulence and

instabilities

Relative importance of (time-dependent) instabilities and (possibly steady) drag depends on transport properties (viscosity, thermal and electrical conductivity, diffusion coefficient, etc.) of the plasmas involved.

Disruption of flow if too unstable or too lossy.



Transport properties of plasmasThe key transport coefficients (dynamical viscosity, thermal

conductivity) are

eBe

Bp

p

B Tnkm

k

m

Tk 2

5

e and p are the electron and proton collision times. For pure Coulomb interactions, these are

pp

ee

p

m

m

nT

2/1

11342/34 )20/(ln)m10/()keV/(107

These give the “Spitzer conductivity” and “Braginskii viscosity” but undoubtedly underestimate the true values



Transport properties of plasmasThe Coulomb logarithm is the increased effectiveness of Coulomb

interations due to many-particle effects

2/1

2034lnln

en

Tkn

e

BDD

Transport will be vastly different from this because of the effects of magnetic fields and turbulence, which cause particle energy and momentum exchanges mediated by magnetic fields



Vortex sheet bounded jet

Issue of what defines a jet if we consider also the flow in the surrounding material.

Simplest model of jet: jet with vortex sheet boundary.

jet external gas

v



Kelvin-Helmholtz instabilityJets of this type are unstable to the Kelvin-Helmholtz instability• ripple in boundary causes flow velocity in jet to change• changing flow velocity causes changing pressure• changing pressure causes ripple to grow• non-linear growth takes on large-scale eddy pattern “cats-eyes”• leads to mixing, jet spreading – entrainment

Van Dyke (1982): shear flow experiment



Kelvin-Helmholtz instability

Scale of instability: look for fastest growth, as a function of perturbation wavelength.

Jet flow: dispersion relation solve numerically.

Fast, light, jet – here the wavelength is 80R, the exponentiation length is 10R

i.e., grows on scale small compared with wavelength, never see ripple pattern



Kelvin-Helmholtz instability

Many possible modes – don’t predict single simple pattern.

Expect boundary to become turbulent on scales of order the sound crossing time of the beam.

Adding magnetic field can give much stabilization if field is properly oriented, but generally expect instability.



Jet modificationKelvin-Helmholtz instability will convert a sharp

boundary into a turbulent shear layer, with velocity and density structure.

Shear layer will spread outwards into external medium, and inwards to jet core.

Final state will be a fully-turbulent flow, still with some bulk motion, but with reduced velocity because of momentum sharing with external material

Question:Where in this new structure are the relativistic particles and fields? Most likely spread out into a diffuse plume of emitting material. But where is the entrained gas?



Sheared beam model

More generally, may expect the beam to have a core region and a sheared layer connecting with the external medium.

This free shear layer will take up a form that depends on the transport properties of the plasma.

A crude model of that type is shown here.



ViscosityEffects of viscosity will also blur the edge of flow by sharing momentum across

the boundaryClassical viscosity of hydrogenic plasma is tiny

1112/516 s cm g)20/(ln)/(10 KTTake gas temperature near jets as 106 K, density as 1 particle cm-3,

jet radius as 10 pc, jet speed as 0.5c, then Reynolds number

7105v

Re r

Flow should be turbulent in vicinity of jet boundary.



Turbulence• Turbulence will be on scales from R to the dissipation scale,

R Re-3/4

• Expect the process to feed some fraction of the bulk kinetic energy in the mixing layer into internal thermal energy

• Spreading of jet occurs at roughly linear rate in constant density external medium, as turbulence pulls material into flow

• Shear layer likely heated to level where turbulent speeds similar to internal sound speed

• Turbulent layer will be unsteady• Unsteady energy injections from edges will give surges in local

mass entrainment, magnetic field• Turbulence also likely to give field reconnection and particle

acceleration – probably only soft electron spectrum



Entrainment

Follow arguments of Bicknell (1994), Laing & Bridle (2002).

Conservation law analysis – uses only general ideas

• Relativistic equation of state for jet fluid throughout (so kinetic energy dissipation goes entirely into relativistic particles and field)

• Concept of control volume where conservation laws apply

• Negligible energy loss through radiation, electron conduction, plasma waves

• Quasi-1D steady flow



Control volume concept

Control volume – slow flow in at entrainment surface SE where pressures balance

Ignore turbulent energy compared with other energies

Apply linear (z axis) momentum and energy conservation within this volume

Bicknell (1994)



Conservation of energy and momentum

Laing & Bridle (2002).

Integral term describes buoyancy effects, important if the Mach number of the flow is low.

If can get run of velocity with z, and run of external pressure with z, and measure change of cross-sectional area A with z, then for assumed values of energy flux Φ and momentum flux , can solve for p(z) and (z) – then see how mass flux varies with z

dzc

pc

dz

dpAApppc

Acpc

ext22

22ext

ext222

2

)1(

)4(1)4(

4)1(



3C 31

3C 31 radio images: left at 1.4 GHz; right at 8.4 GHz.

Smooth, two-sided, straight jet allows sidedness ratio to be used to infer velocity run, if symmetry of flow is assumed.

Caution needed: light-travel time effects important for unsteady flows.

Laing & Bridle (2002)

15'



3C 31 – velocity structure

Run of velocity in 3C31 deduced from brightness and polarization: on axis, at an intermediate point, and at jet edge.

Point 1 marks the start of the flaring region in the jet, where a shock may change the jet structure

Laing & Bridle 2002



3C 31 – gas environment

Run of density and pressure inferred from X-ray imaging of 3C31.

Dashed line shows minimum energy pressure: jet likely underpressured relative to external medium everywhere. Hardcastle et al

2002; Laing & Bridle 2002



3C 31 – mass flux

Mass flux in 3C31 inferred from the conservation law analysis (for one of a set of viable models).

Mass flux = cA

Rapid mass-loading at flare region where A increases quickly.

Flux few × 10-2 M yr-1Laing & Bridle (2002)



3C 31 – entrainment and flaring

Mass entrainment rapid where the jet broadens rapidly.

Mass entrainment inferred exceeds likely mass input from embedded stars (dashed curve)

At this entrainment rate, can the turbulent energy be ignored? Laing & Bridle 2002



Entrainment Details of entrainment rate will change with changed modelling

(e.g., if some fraction of energy goes into internal motions), but the increased symmetry and decreased linearity of the flow at larger distances from the core suggests slowed flow.

It would be very instructive to repeat this in the IR, where the jet and counter-jet are also clearly detected in the same region.

Changing spectral properties from centre to edge suggest that entrainment is having an effect on the radiating particle population too.



Particle accelerationTurbulence/instabilities at edge of jet are plausible location for

energy inputs to jet.Effects usually result in thermal heating, not relativistic particle

acceleration.Difficulty is in converting bulk kinetic energy into relativistic

particles with some efficiency. Simple heat input is not enough – must develop hard tail to spectrum.

Efficient acceleration generally requires starting with particles of moderate energy: pre-accelerated particles. Others generally are thermalized.

Note – we could do with far better information on the limits to the amount of thermal plasma at the edges of jets – via far deeper X-ray data and much improved Faraday rotation information.



Particle accelerationStandard processes• Diffusive shock acceleration at a non-relativistic shock.

Resulting power spectrum with energy index depending on compression ratio of shock. Strong shocks give spectra

N() -2

• Relativistic shocks tend to give somewhat steeper power laws (Kirk et al. 2002)

N() -2.2

In either case, process involves charged particles scattering across shock fronts, and needs suprathermal particles to start the process

Maximum energy depends on size of region, scattering process



Particle accelerationOther processes• Transient electric fields from strong in-flow instabilities• Fermi acceleration from convergent flow without shock• Multiple Fermi acceleration from population of weak shocks

within jet rather than strong shocksGeometry of shocks within flow should be traceable by X-ray

structures (and variability in structures?) with sufficient resolution. Magnetic field compression at shocks (and extension at shear layers) also clue to configuration of flow, but magnetic structure hard to interpret (e.g., 3C 15; Dulwich et al. 2007)

Shear structure of jet, and possible stratification in particle populations, plus relativistic effects, complicates matters.



M 87 and 3C 66B knot SEDsBreak frequencies in IR or optical. Using equipartition fields, implies break energy of about 300 GeV

This energy is similar in many jets.

Not simple power-law or simple aged synchrotron spectrum: flat (α 0.5) steepening to α 1.3.



Electron energies and spectra• Beq 15 nT.• Electrons at spectral breaks have E 300 GeV, break

amplitudes not consistent with ageing• Lifetimes of electrons emitting synchrotron X-rays 30 years –

much local acceleration to energies of order 10 TeV• Underlying electron energy distributions look similar in several

objects.• More complicated in detail: X-ray/radio offsets with X-rays

more upstream than radio – acceleration to highest energies can be fast, so many pre-accelerated particles in diffuse inter-knot regions



Spectra in and between knots• Systematic study comparing the inter-knot and in-knot emission

done in rather few objects – not many have quality of data needed

• Cen A about best – shows extended emission both with flatter and steeper X-ray spectra than knots (Hardcastle et al. 2008), but full SEDs not well defined so can’t study break properties

• Cen A also shows off-axis emission steeper than on-axis emission (Worrall et al. 2008)

• Infer knots not in shear layer, and particle acceleration in shear layer may only be pre-acceleration that spreads through entire jet

• In shear structure, might expect flow velocity to drop from axis to edge, so different spectra since different shock strengths?



Cen A

Knot and diffuse X-ray spectra – systematic variations down jet (left), and across jet (right). Hardcastle et al. (2007), Worrall et al. (2008)

mid-jet jet edge



Spectra in and between knots• Shear layer at edge of jet excellent location for heating plasma, turbulent

particle acceleration, energy releases from reconnection, but this cannot be entire story – X-ray emitting electrons cannot propagate to mid-jet

• Spectra at edges steeper in X-ray than spectra in middle of jet – suggests – shear layer is location of pre-acceleration, where particles are moved from high-

energy tails of thermal distribution into mildly relativistic regimes– mid-jet is location of shocks where pre-accelerated particles can be boosted to

highly Lorentz factors and so emit synchrotron X rays • No lifetime issues: shear layer particles at pre-accelerated Lorentz factors can

reach middle of jet before losing energy provided diffusion from edge of jet is sufficiently rapid (issue with magnetic field structure)

• Acceleration in bulk of jet at shocks propagating down jet and static shocks at obstructions

• Toy model: acceleration in shocks and wakes can explain offsets



Spectra between knots• In more distant objects these

spectral distinctions wouldn’t be so easy to see, but need more cases of resolved radio – IR – optical – X-ray spectra

• Turbulent acceleration tends to produce steep electron spectra (as in suggested mechanisms for radio halo sources; Dogiel et al. 2006) – process of momentum diffusion from high-energy tail of thermal distribution

time increasing



Electron energies and spectra• In 3C66B, M87, other objects, often see spectra with breaks

corresponding to electron energies of order 1 TeV• Higher than expected energy for turbulent acceleration, but

possible for reconnection or diffusive shock acceleration• Also consistent with the cyclotron instability (which should give

electron and positrons to E 1 TeV) and B = Beq (e.g., Hoshino et al. 1992; Amato & Arons 2006).

• Mechanism – ion gyromotions generate plasma waves– waves couple resonantly to electrons– accelerate electrons to energies of order 1 TeV with flat spectra



Magnetic field• Shear layer may also be good location for magnetic

field amplification• Process of converting kinetic energy density in shear

layer, via vorticity, into magnetic energy density• Shear would give mean field orientation parallel to jet

axis• Often see parallel magnetic fields at jet edges,

qualitatively consistent with field amplification• On-axis fields often perpendicular to jet: compression

of tangled fields diffusing/advected in from shear layer?



Summary• Shear layer at edge of jet probably provides significant jet heating, mass

entrainment, turbulent particle acceleration, magnetic field amplification• Entrainment probably not efficient at generating relativistic material (despite

Bicknell/Laing & Bridle analysis). Information on fate of entrained matter is sparse (Cen A evidence of intrusions in NML, Kraft et al.; different knot types in main jet, Hardcastle et al.)

• Particle acceleration to sub-TeV energies with different spectrum from higher energies: two (or more) processes?

• Radio, optical, X-ray offsets: particle acceleration through several processes? Acceleration to high energies possible even between knots.

• Likely we see average of unsteady behaviours – need time and spatial resolution.

radio galaxies in the chandra era jets: particle acceleration and entrainment mark birkinshaw...

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