Relativistic effects in the structure and dynamics of extragalactic jets

1. Relativistic effects in the structure and dynamics of extragalactic jets José Mª Martí Departamento de Astronomía y Astrofísica Universidad de Valencia (Spain) Extragalactic Jets Girdwood, 21-24 May 2007

2. Relativistic effects in extragalactic jets: Outline of the talk • Introduction • Morphology and dynamics from classical simulations • Basic relativistic effects • Relativistic hydrodynamical equations • Relativistic effects in the morphology and propagation of jets • Classical versus relativistic jet models • Long term simulations of large scale jets • FRII jets • FRI jets • Compact jets • Hydrodynamical shock-in-jet model and superluminal sources • Transversal structure in relativistic jets • Relativistic Kelvin-Helmholtz instabilities • Summary

3. Cocoon (backflow) Supersonic beam Terminal shock Contact discontinuity Bow shock Hydrodynamical non-relativistic simulations(Rayburn 1977; Norman et al. 1982) verified the basic jet model for classical radio sources (Blandford & Rees 1974; Scheuer 1974) and allowed to identify the structural components of jets. Introduction: Morphology and dynamics from classical simulations I Shocked ambient medium Morphology and dynamics governed by the interaction with the externalmedium.

4. vh vb - vh Introduction: Morphology and dynamics from classical simulations II Scaling parameters: Rb : Beam radius ra : ambient density ca: ambient sound speed Two parameters define the initial setup and control the morphology and dynamics of jets: the beam density, rb the internal beam Mach number, Mb (or the beam flow velocity, vb) Head advance speed: 1D estimate from ram pressure equilibrium between jet and ambient in the rest frame of the jet working surface Cocoon dominates in jets with large (vb - vh) (i.e., rb << ra) Strong backflow in jets with large (phs - pa) and phs µ Mb2

5. Sideways expansion: Cavity evolution (light, powerful sources; Begelman & Cioffi 1989) Introduction: Morphology and dynamics from classical simulations III Lj : Jet kinetic luminosity (assumed constant) Ac: cavity’s cross section, Cavity pressure: (strong shock limit) From the previous equations: (assuming vh constant) Density and temperature evolution in the cocoon (Kino et al. 2007) [assuming no mixing with shocked ambient medium!] Jj : mass flux through the terminal shock (assumed constant) (ideal gas)

6. Mass conservation: Momentum conservation: Energy conservation: Fluid rest-frame quantities: Relativistic rest-mass density: r: proper-rest mass density e: specific internal energy Relativistic momentum density: p: pressure Relativistic energy density: : specific enthalpy Flow Lorentz factor: Relativistic effects: Relativistic effects in a Boltzmann gas: e+/e- : T ~ 1010 K e-/p : T ~ 1013 K Relativistic hydrodynamic equations

7. Relativistic effects I Three parameters define the initial set up: Beam proper rest-mass density, rb Beam bulk Lorentz factor, Wb (or the beam flow velocity, vb) Beam specific internal energy, eb (not scaled to ca but to c;eb ~ c2: “hot jets”) Scaling parameters: Rb : beam radius ra : ambient density First relativistic simulations: van Putten 1993, Martí et al. 1994, 1995, 1997; Duncan & Hughes 1994 Relativistic, hot jet models rb = 0.01ra , Wb = 7.26 , eb = 100 c2 Relativistic, cold jet models rb = 0.01ra , Wb = 7.26, eb = 0.01c2 Density + velocity field vectors Thin cocoons without backfkow (vh ~ vb;ballistic propagation); no cavity Little internal structure (stable beam) Stable terminal shock 3C273 Extended cocoons (µ vb - vh); overpressured cavities Beams with prominent internal structure (shocks) Dynamical working surface (vortex shedding) Cyg A

8. Relativistic effects II Head advance speed: 1D ram pressure equilibrium in the reference frame of the working surface v’b v’a For models with same rb/ra : vh,R > vh,C (less prominent cocoons in relativistic jets) Internal beam structure: governed by the relativistic beam Mach number, Mb,R : For models with same vb, cb, stronger internal shocks and hot spots in relativistic jets Mean flow follows relativistic Bernoulli’s law: Hot jets: adiabatic expansion down the jet: hbßß, Wb ˝˝ Cold jets: hb ~ 1, Wb~constant Cavity evolution: dynamics governed by the momentum, Pj, and energy, Lj, fluxes through the terminal shock (which are roughly proportional to hbWb2); cocoon temperature depends also on the particle flux, Jj, through the ratio Lj / Jj (proportional to hbWb)

9. Classical versus relativistic jet models Komissarov & Falle 1996, 1998 Rosen et al. 1999 Equivalence between classical and relativistic models with the same values of: • Inertial mass density contrast: • Internal beam Mach number: For equivalent models, classical and relativistic jet models: • have almost the same power and thrust Same jet advance speed (similar cocoon prominence) similar cocoon/cavity dynamics Different cocoon temperature, particle number densities • BUTdifferent rest mass fluxes Relativistic simulations needed to compute Doppler factors • AND the velocity field of nonrelativistic jet simulations can not be scaled up to give the spatial distribution of Lorentz factors of the relativistic simulations

10. Scheck et al. 2002 • Axisymmetric simulations of powerful jets with: • different jet composition and energy per particle(BC: baryonic cold model; LC: leptonic cold; LH: leptonic hot) • fixing kinetic luminosity, Lj, 1D jet advance estimate (equivalent to jet thrust, Pj) Long-term evolution of large-scale relativistic jets: FRII jets Log density [ra] Evolution followed up to T = 6 106 yrs Computational domain: 70 kpc x 100 kpc (6 cells/Rb)

11. Cocoon/cavity dynamics: • Similar evolution in the three models • (confirms equivalence between models with same kinetic luminosity / thrust) • Two phase evolution Long-term evolution of large-scale relativistic jets: FRII jets lj lj / Rc Rc Extended B&C model: (Scheck et al.) Log Density vh 1D phase • 1D phase: a ~ 0 (B&C model) Pc • Long term evolution: a ~ -1/3 x 0.1 x 0.01

12. Long-term evolution of large-scale relativistic jets: FRII jets Log Temperature [K] Beam temperature: for jets with same kinetic luminosity and similar flow Lorentz factors, Tb inversely proportional to the number of particles Lower temperature in model LC cocoon / cavity beam shell Shell temperature: governed by bow shock dynamics Similar in the three cases according to the extended B&C model Cocoon/cavity temperature: particles from the ambient medium must be taken into account: Nc b Nc a Model LC: Nc b > Nc a (and internal energy dominated by beam particles): isothermal cocoon and isothermal evolution (as in Kino et al. 2007 model) Models LH and BC: Nc b < Nc a (and internal energy dominated by beam particles): large spatial and temporal variations of T

13. rm = 7.8 kpc Perucho & Martí 2007, submitted Long-term evolution of large-scale relativistic jets: 3C31 Axisymmetric simulation of a purely leptonic jet with Lj ~ 1044 erg/s. • Jet injected according to Laing & Bridle (2002a,b) model at 500 pc from the core • ambient medium conditions from Hardcastle et al. 2002 Physical domain: 18 kpc x 6 kpc [Resolution: 8 cells/R_j (axial) x 16 cells/R_j (radial)] Evolution followed up to T = 7 106 yrs

14. Perucho & Martí 2007, submitted Long-term evolution of large-scale relativistic jets: 3C31 pressure density Mach number recollimation shock and jet expansion Simulation adiabatic expansion jet disruption and mass load L&B model • As in Laing & Bridle’s model, the evolution is governed by adiabatic expansion of the jet, recollimation, oscillations around pressure equilibrium, mass entrainment and deceleration. • Simulations confirm the FRI paradigm qualitatively, but • jet flare occurs in a series of shocks • comparison wth L&B model is difficult as the jet has not reached a steady state jet deceleration

15. Perucho & Martí 2007, submitted Long-term evolution of large-scale relativistic jets: 3C31 Last snapshot (T = 7 106 yrs ~ 10 % lifetime of 3C31) shocked ambient cavity/cocoon beam bow shock Bow shock Mach number ~ 2.5, consistent with recent X-ray observations by Kraft et al. 2003 (Cen A) and Croston et al. 2007 (NGC3081)

16. ~ constant Perucho & Martí 2007, submitted Long-term evolution of large-scale relativistic jets: 3C31 Extended B&C model: (Perucho & Martí) a ~ -0.1, b ~ -1 Ps t-1 t -1.3 Rs Nc b vbs Nc a Pc rc Cocoon evolution: Tc for negligible pollution with ambient particles (Nc b ~ 20 - 200 Nc a), andassuming selfsimilar transversal expansion

17. Relativistic perturbation Pressure-matched jet steady jet Overpressured jet standing shocks standing shocks Shock-in-jet model: steady relativistic jet with finite opening angle + small perturbation (Gómez et al. 1996, 1997; Komissarov & Falle 1996, 1997) Pc-scale jets: Hydrodynamical shock-in-jet model and superluminal sources Radio emission (synchrotron) PM jet OP jet Synthetic radio maps must account for the relativistic effects in the radiation transport (Doppler boosting and light travel time delays) (see next talk by C. Swift) • Convolved maps (typical VLBI resolution; contours): core-jet structure with superluminal (8.6c) component • Unconvolved maps (color scale): • Steady components associated to recollimation shocks • dragging of components accompanied by an increase in flux

18. Pc-scale jets: interpreting the observations with the hydrodynamical shock-in-jet model Combining both (hydro)dynamical and radiation transport effects, simulations can explain most of the phenomenology often observed in parsec scale jets: • Isolated(3C279, Wehrle et al. 2001) and regularly spaced stationary components(0836+710, Krichbaum et al. 1990; 0735+178, Gabuzda et al. 1994; M87, Junor & Biretta 1995; 3C371, Gómez & Marscher 2000) • Variations in the apparent motion and light curves of components(3C345, 0836+71, 3C454.3, 3C273, Zensus et al. 1995; 4C39.25, Alberdi et al. 1993; 3C263, Hough et al. 1996) • Coexistence of sub and superluminal components(4C39.25, Alberdi et al. 1993; 1606+106, Piner & Kingham 1998) and differences between pattern and bulk Lorentz factors(Mrk 421, Piner et al. 1999) • Dragging of components(0735+178, Gabuzda et al. 1994; 3C120, Gómez et al. 1998; 3C279, Wehrle et al. 1997) • Trailing components(3C120, Gómez et al. 1998, 2001; Cen A, Tingay et al. 2001) • Pop-up components (PKS0420-014, Zhou et al. 2000) However… the capability of the model to constrain the physical parameters in specific sources is very limited…

19. I, P intensities in J1-J4 region I P Transversal structure in extragalactic jets • Twocomponent jet models (fast jet spine + slower layerswith different magnetic field structure) • Appeared in some models of jet formation(e.g., Sol et al. 1989: inner relativistic e+/e- jet + thermal disk wind) and numerical simulations(e.g., Koide et al. 1998: slow magnetically driven jet + fast gas pressure driven jet) • Are invoked to fit the brightness distributions of FRI jets(3C31, M87, …) Koide et al. 1998 3C31, Laing & Bridle 2002 • FRIIs(3C353, Swain et al. 1998: low polarization rails; limb brightening) • Pc-scale jets(1055+018, Attridge et al. 1999) top /down asymmetry low polarization rails

20. jet spine shear layer specific internal energy Lorentz factor Stratified jets: 3D RHD + emission simulations Aloy et al. 1999 • Transversal structure of the jet • High specific internal energy • Relativistic, sheared flow • Magnetic field structure • Jet spine: toroidal + radial (shocks) + random • Shear layer: toroidal + aligned (shear) + random Synchrotron emission top/down asymmetry Aloy et al. 2000 10 deg to the LOS • Low polarization rails • Limb brightening • Top/down asymmetry: the angle to the LOS (in the fluid frame) of the helical magnetic field has a top/down asymmetry affecting the synchrotron emission/absortion coeffs. Intensity across the jet I P Low polarization rails 90 deg to the LOS Local variation of apparent motions M87 Zhou et al. 1995

21. KH stability analysis is currently used to probe the physical conditions in extragalactic jets Kelvin-Helmholtz instabilities and extragalactic jets • Linear KH stability theory: • Production of radio components • Interpretation of structures (bends, knots) as signatures of pinch/helical modes • Non-linear regime: • Overall stability and jet disruption • Shear layer formation and generation of transversal structure • FRI/FRII morphological jet dichotomy Linear KH stability analysis: physical parameters in pc scale jets 3C120 (Hardee 2003, Hardee et al. 2005): wavelike helical structures with differentially moving and stationary features can be fitted by precession and wave-wave interactions (Hardee 2000, 2001) 3C273 (Lobanov & Zensus 2001): double helix inside the jet fitted with elliptical/helical body/surface modesat their respective resonant wavelengths 0836+710 (Lobanov et al. 1998, Perucho & Lobanov 2007): jet structure reproduced by the helical surface mode and a combination of helical and elliptical body modes of the sheared KH instability Lobanov & Zensus 2001

22. Perucho et al. 2005 Perucho, Martí et al. 2007 K-H instabilities for relativistic sheared jets I: Linear regime Goal: study the effects of shear in the (non-linear) stability of relativistic jets More than 20 models analyzed by varying jet specific internal energy, Lorentz factor and shear layer width Growth rate vs. long. wavenumber for antisymmetric fundamental and body modes of a hot, relativistic (planar) jet model Shear layer resonances (peaks in the growth rate of high order modes at maximum unstable wavelength) • Resonant modes dominate in large Lorentz factor jets • Increasing the specific internal energy causes resonances to appear at shorter wavelengths • Widening of the shear layer reduces the growth rates and the dominance of shear layer resonances optimal shear layer widththat maximizes the effect • Widening of the shear layer causes the absolute growth rate maximum to move towards smaller wavenumbers and lower order modes Overall decrease of growth rates Sheared jet (d=0.2Rj) Vortex sheet approx. Numerical simulations confirm the dominance of resonant modes in the perturbation growth Vortex sheet dominant mode (low order mode) Dominant mode for the sheared jet (high order mode) Perturbation growth from hydro simulation (linear regime)

23. Perucho et al. 2005 Perucho, Martí et al. 2007 K-H instabilities for relativistic sheared jets II: Nonlinear regime Shear layer resonant modes dissipate most of their kinetic energy into internal energy close to the jet boundary generating hot shear layers Shear layer resonant modes suppress the growth of disruptive long wavelength instability modes Specific internal energy TIME Present results validate the interpretation of several observational trends involving jets with transversal structure (e.g., Aloy et al. 2000) Sheared jet (d=0.2 Rj) Lorentz factor 20 jet Sheared jet (d=0.2 Rj) Lorentz factor 5 jet

24. Summary • Basic relativistic effects in the morphology and propagation of jets from large flow Lorentz factors (Wb) and/or relativistic enthalpies (hb) in the beam • Equivalence between classical and relativistic jet models with the same power and thrust • Long term evolution (perfect fluid, pure hydrodynamic, no radiative losses): • dynamics of the cocoon/cavity + shell (FRIIs)/shocked ambient(FRIs) governed by energy flux and thrust through the terminal shock (µhbWb2). Described by B&C model or simple extensions • shell/shocked ambient temperature governed by the dynamics of the bow shock. B&C model or simple extensions • cocoon/cavity temperature depend on the quotient of energy and particle fluxes across the terminal shock (µhbWb). Pollution with shocked ambient particles must be taken into account • Mildly relativistic simulations of light jets through density decreasing atmospheres confirm the FRI paradigm qualitatively • Parsec scale jets: success of the relativistic hydrodynamical shock-in-jet model in interpreting the • phenomenology of pc-scale jets and superluminal sourcesandobservational signatures of jet • stratification (However, observations dramatically affected by relativistic radiation transport effects) • Non linear (hydrodynamical) KH instability studies: role of shear layers and shear layer resonant modes