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 Mark Birkinshaw, U. Bristol

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? Mark Birkinshaw, U. Bristol

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-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 Mark Birkinshaw, U. Bristol

5. 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. Mark Birkinshaw, U. Bristol

6. 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 Mark Birkinshaw, U. Bristol

7. 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 Mark Birkinshaw, U. Bristol

8. 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 Mark Birkinshaw, U. Bristol

9. 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 Mark Birkinshaw, U. Bristol

10. 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 Mark Birkinshaw, U. Bristol

11. 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. Mark Birkinshaw, U. Bristol

12. 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? Mark Birkinshaw, U. Bristol

13. 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. Mark Birkinshaw, U. Bristol

14. 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. Mark Birkinshaw, U. Bristol

15. 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 Mark Birkinshaw, U. Bristol

16. 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 Mark Birkinshaw, U. Bristol

17. 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) Mark Birkinshaw, U. Bristol

18. 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 Mark Birkinshaw, U. Bristol

19. 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) Mark Birkinshaw, U. Bristol

20. 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 Mark Birkinshaw, U. Bristol

21. 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 Mark Birkinshaw, U. Bristol

22. 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) Mark Birkinshaw, U. Bristol

23. 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 Mark Birkinshaw, U. Bristol

24. 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. Mark Birkinshaw, U. Bristol

25. 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. Mark Birkinshaw, U. Bristol

26. 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 Mark Birkinshaw, U. Bristol

27. 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. Mark Birkinshaw, U. Bristol

28. 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 (α 0.5) steepening to α 1.3. Mark Birkinshaw, U. Bristol

29. 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 Mark Birkinshaw, U. Bristol

30. 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? Mark Birkinshaw, U. Bristol

31. 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) Mark Birkinshaw, U. Bristol

32. 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 Mark Birkinshaw, U. Bristol

33. 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 Mark Birkinshaw, U. Bristol

34. 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 Mark Birkinshaw, U. Bristol

35. 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? Mark Birkinshaw, U. Bristol

36. 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. Mark Birkinshaw, U. Bristol