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. 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 Relativistic effects in extragalactic jets: Outline of the talk

3. Introduction: Morphology and dynamics from classical simulations I 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. Morphology and dynamics governed by the interaction with the external medium. Supersonic beam Cocoon (backflow) Terminal shock Contact discontinuity Bow shock Shocked ambient medium

4. Introduction: Morphology and dynamics from classical simulations II Two parameters define the initial setup and control the morphology and dynamics of jets: the beam density,  b the internal beam Mach number, M b (or the beam flow velocity, v b ) Head advance speed: 1D estimate from ram pressure equilibrium between jet and ambient in the rest frame of the jet working surface Scaling parameters: R b : Beam radius  a : ambient density c a : ambient sound speed Strong backflow in jets with large (p hs - p a ) and p hs  M b 2 v b - v h vhvh Cocoon dominates in jets with large (v b - v h ) (i.e.,  b <<  a 

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

6. Relativistic hydrodynamic equations Mass conservation: Momentum conservation: Energy conservation: Relativistic rest-mass density: Relativistic momentum density: Relativistic energy density: Flow Lorentz factor: Fluid rest-frame quantities:  : proper-rest mass density  : specific internal energy p: pressure : specific enthalpy Relativistic effects in a Boltzmann gas: e + /e - : T ~ 10 10 K e - /p : T ~ 10 13 K Relativistic effects:

7. Relativistic effects I First relativistic simulations: van Putten 1993, Martí et al. 1994, 1995, 1997; Duncan & Hughes 1994 Relativistic, hot jet models  b = 0.01  a, W b = 7.26,  b = 100 c 2 Relativistic, cold jet models  b = 0.01  a, W b = 7.26,  b = 0.01c 2 Density + velocity field vectors Thin cocoons without backfkow (v h ~ v b ; ballistic propagation); no cavity Little internal structure (stable beam) Stable terminal shock 3C273 Extended cocoons (  v b - v h ); overpressured cavities Beams with prominent internal structure (shocks) Dynamical working surface (vortex shedding) Cyg A Three parameters define the initial set up: Beam proper rest-mass density,  b Beam bulk Lorentz factor, W b (or the beam flow velocity, v b ) Beam specific internal energy,  b (not scaled to c a but to c;  b ~ c 2 : “hot jets”) Scaling parameters: R b : beam radius  a : ambient density

8. Relativistic effects II Cavity evolution: dynamics governed by the momentum,  j, and energy, L j, fluxes through the terminal shock (which are roughly proportional to h b W b 2 ); cocoon temperature depends also on the particle flux, J j, through the ratio L j / J j (proportional to h b W b ) Head advance speed: 1D ram pressure equilibrium in the reference frame of the working surface v’ a v’ b For models with same  b /  a : v h,R > v h,C (less prominent cocoons in relativistic jets) Internal beam structure: governed by the relativistic beam Mach number, M b,R : Mean flow follows relativistic Bernoulli’s law: For models with same v b, c b, stronger internal shocks and hot spots in relativistic jets Hot jets: adiabatic expansion down the jet: h b  W b  Cold jets: h b ~  W b  ~  constant

9. Classical versus relativistic jet models 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 BUT different rest mass fluxes Different cocoon temperature, particle number densities 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 Relativistic simulations needed to compute Doppler factors Komissarov & Falle 1996, 1998 Rosen et al. 1999

10. Long-term evolution of large-scale relativistic jets: FRII jets 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, L j, 1D jet advance estimate (equivalent to jet thrust,  j ) Scheck et al. 2002 Evolution followed up to T = 6 10 6 yrs Computational domain: 70 kpc x 100 kpc (6 cells/R b ) Log density [  a ]

11. Long-term evolution of large-scale relativistic jets: FRII jets Log Density vhvh 1D phase Extended B&C model: (Scheck et al.) 1D phase:  ~ 0 (B&C model) Long term evolution:  ~ -1/3 ljlj RcRc PcPc Cocoon/cavity dynamics: Similar evolution in the three models (confirms equivalence between models with same kinetic luminosity / thrust) Two phase evolution l j / R c x 0.1 x 0.01

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

13. Long-term evolution of large-scale relativistic jets: 3C31 Perucho & Martí 2007, submitted Jet injected according to Laing & Bridle (2002a,b) model at 500 pc from the core r m = 7.8 kpc Axisymmetric simulation of a purely leptonic jet with L j ~ 10 44 erg/s. 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 10 6 yrs ambient medium conditions from Hardcastle et al. 2002

14. Long-term evolution of large-scale relativistic jets: 3C31 Perucho & Martí 2007, submitted 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 recollimation shock and jet expansion jet disruption and mass load jet deceleration pressuredensityMach number Simulation L&B model adiabatic expansion

15. Long-term evolution of large-scale relativistic jets: 3C31 Perucho & Martí 2007, submitted Last snapshot (T = 7 10 6 yrs ~ 10 % lifetime of 3C31) beam cavity/cocoon shocked ambient 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. Long-term evolution of large-scale relativistic jets: 3C31 Perucho & Martí 2007, submitted Extended B&C model: (Perucho & Martí)  ~  0.1,  ~  1 Cocoon evolution: t  1.3 t 1t 1 ~ constant for negligible pollution with ambient particles (N c b ~ 20 - 200 N c a ), and assuming selfsimilar transversal expansion N c b N c a PsPs PcPc cc TcTc RsRs vbsvbs

17. Pc-scale jets: Hydrodynamical shock-in-jet model and superluminal sources Shock-in-jet model: steady relativistic jet with finite opening angle + small perturbation (Gómez et al. 1996, 1997; Komissarov & Falle 1996, 1997) Pressure-matched jet Overpressured jet standing shocks Radio emission (synchrotron) standing shocks steady jet Relativistic perturbation 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 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) PM jetOP jet

18. Pc-scale jets: interpreting the observations with the hydrodynamical shock-in-jet model 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) Combining both (hydro)dynamical and radiation transport effects, simulations can explain most of the phenomenology often observed in parsec scale jets: However… the capability of the model to constrain the physical parameters in specific sources is very limited…

19. Transversal structure in extragalactic jets 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, …) Two component jet models (fast jet spine + slower layers with different magnetic field structure) Koide et al. 1998 3C31, Laing & Bridle 2002 FRIIs (3C353, Swain et al. 1998: low polarization rails; limb brightening) I, P intensities in J1-J4 region IPIP Pc-scale jets (1055+018, Attridge et al. 1999) top /down asymmetrylow polarization rails

20. Stratified jets: 3D RHD + emission simulations 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 Aloy et al. 1999 jet spine shear layer Lorentz factor specific internal energy Synchrotron emission Intensity across the jet IP 10 deg to the LOS 90 deg to the LOS top/down asymmetry 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. Local variation of apparent motions Aloy et al. 2000 M87 Zhou et al. 1995 Low polarization rails

21. Kelvin-Helmholtz instabilities and extragalactic jets KH stability analysis is currently used to probe the physical conditions in 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) Lobanov & Zensus 2001 3C273 (Lobanov & Zensus 2001): double helix inside the jet fitted with elliptical/helical body/surface modes at 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

22. K-H instabilities for relativistic sheared jets I: Linear regime Goal: study the effects of shear in the (non-linear) stability of relativistic jets Perucho et al. 2005 Perucho, Martí et al. 2007 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 Vortex sheet approx. Sheared jet (d=0.2Rj) Overall decrease of growth rates 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 width that maximizes the effect Widening of the shear layer causes the absolute growth rate maximum to move towards smaller wavenumbers and lower order modes Vortex sheet dominant mode (low order mode) Dominant mode for the sheared jet (high order mode) Perturbation growth from hydro simulation (linear regime) Numerical simulations confirm the dominance of resonant modes in the perturbation growth

23. 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 Present results validate the interpretation of several observational trends involving jets with transversal structure (e.g., Aloy et al. 2000) Perucho et al. 2005 Perucho, Martí et al. 2007 Sheared jet (d=0.2 Rj) Lorentz factor 20 jet Sheared jet (d=0.2 Rj) Lorentz factor 5 jet Shear layer resonant modes suppress the growth of disruptive long wavelength instability modes Specific internal energy TIME

24. Summary Basic relativistic effects in the morphology and propagation of jets from large flow Lorentz factors (W b ) and/or relativistic enthalpies (h b ) in the beam 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 (  h b W b 2 ). 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 (  h b W b ). 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 Non linear (hydrodynamical) KH instability studies: role of shear layers and shear layer resonant modes Equivalence between classical and relativistic jet models with the same power and thrust Parsec scale jets: success of the relativistic hydrodynamical shock-in-jet model in interpreting the phenomenology of pc-scale jets and superluminal sources and observational signatures of jet stratification (However, observations dramatically affected by relativistic radiation transport effects)