Jets: particle acceleration and entrainment

1
Jets particle acceleration and entrainment

• Mark Birkinshaw
• University of Bristol

2
Outline

• Jets general physics issues
• Deceleration through entrainment the Laing
  Bridle analysis of 3C31
• Instabilities, turbulence, intermittency
• Associated particle acceleration critical
  energies and sites

3
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?

4
Jets and losses

• Detectable jets are intrinsically lossy amount
  of loss influences nature of flow.
• Energy of jets in two components
• internal energy density relativistic/non-relativ
  istic 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

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Entrainment

• Jets 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.

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Transport properties of plasmas

• The key transport coefficients (dynamical
  viscosity, thermal conductivity) are

?e and ?p are the electron and proton collision
times. For pure Coulomb interactions, these are
These give the Spitzer conductivity and
Braginskii viscosity but undoubtedly
underestimate the true values
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Transport properties of plasmas

• The Coulomb logarithm is the increased
  effectiveness of Coulomb interations due to
  many-particle effects

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
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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.

v
jet
external gas
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Kelvin-Helmholtz instability

• Jets 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
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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
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Kelvin-Helmholtz instability
Many possible modes dont 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.
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Jet modification

• Kelvin-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?

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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.
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Viscosity

• Effects of viscosity will also blur the edge of
  flow by sharing momentum across the boundary
• Classical viscosity of hydrogenic plasma is tiny

Take 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
Flow should be turbulent in vicinity of jet
boundary.
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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

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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

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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)
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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 F and
momentum flux ?, can solve for p(z) and ?(z)
then see how mass flux varies with z
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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.
15'
Laing Bridle (2002)
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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
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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
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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-1
Laing Bridle (2002)
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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
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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.

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3C31 optical and IR
Residual R map, after subtracting galaxy profile.
11 ?Jy feature to N is counterpart of the
brighter radio jet. Core structure from AGN and
disk. Croston et al. (2000) More convincing in
Spitzer 8 ?m data Bliss et al.
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Particle acceleration

• Turbulence/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.

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Particle acceleration

• Standard 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

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Particle acceleration

• Other 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 shocks
• Geometry 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.

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3C 66B
10 kpc

• Radio, IR, optical, X-ray jets similar, but
  details differ

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3C 66B
Spitzer 4.5 ?m image, galaxy subtracted. Narrow
mid-jet IR feature plus broad plume Bliss et al.
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M 87 and 3C 66B knot SEDs

• Break 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 (a ? 0.5) steepening to a ? 1.3.

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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

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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 cant 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?

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

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Spectra between knots

• In more distant objects these spectral
  distinctions wouldnt 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
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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

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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?

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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.