Relativistic effects in the structure and dynamics of extragalactic jets

José Mª MartíDepartamento de Astronomía y Astrofísica

Universidad de Valencia (Spain)

Extragalactic JetsGirdwood, 21-24 May 2007

• 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

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 shockContact

discontinuity

Bow shock

Shocked ambient medium

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, 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

Scaling parameters:

Rb : Beam radiusa : ambient densityca : ambient sound speed

Strong backflow in jets with large (phs - pa)and phsMb

2

vb - vh

vh

Cocoon dominates in jets with large (vb - vh)(i.e., b << a

Introduction: Morphology and dynamics from classical simulations III

Cavity evolution (light, powerful sources; Begelman & Cioffi 1989)

Cavity pressure:Lj : Jet kinetic luminosity (assumed constant)Ac: cavity’s cross section,

Sideways expansion:

From the previous equations:(assuming vh constant)

(strong shock limit)

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)

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 ~ 1010 K e-/p : T ~ 1013 K

Relativistic effects:

Relativistic effects I

First relativistic simulations: van Putten 1993, Martí et al. 1994, 1995, 1997; Duncan & Hughes 1994

Relativistic, hot jet modelsb = 0.01a , Wb = 7.26 , b = 100 c2

Relativistic, cold jet modelsb = 0.01a , Wb = 7.26, b = 0.01c2

Density + velocity field vectors

Thin cocoons without backfkow (vh ~ vb; ballistic propagation); no cavityLittle internal structure (stable beam)Stable terminal shock3C273

Extended cocoons (vb - vh); overpressured cavitiesBeams 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, Wb (or the beam flow velocity, vb)

Beam specific internal energy, b (not scaled to ca but to c; b ~ c2: “hot jets”)

Scaling parameters: Rb : beam radiusa : ambient density

Relativistic effects II

Cavity evolution: dynamics governed by the momentum, j, and energy, Lj, fluxes through the terminal shock (which are roughly proportional to hbWb

2); cocoon temperature depends also on the particle flux, Jj, through the ratio Lj / Jj (proportional to hbWb)

Head advance speed: 1D ram pressure equilibrium in the reference frame of the working surface

v’av’b

For models with same b/a : vh,R > vh,C (less prominent cocoons in relativistic jets)

Internal beam structure: governed by the relativistic beam Mach number, Mb,R :

Mean flow follows relativistic Bernoulli’s law:

For models with same vb, cb, stronger internal shocks and hot spots in relativistic jets

Hot jets: adiabatic expansion down the jet: hb Wb˝˝Cold jets: hb ~Wb~constant

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, 1998Rosen et al. 1999

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, Lj, 1D jet advance estimate (equivalent to jet thrust, j)

Scheck et al. 2002

Evolution followed up to T = 6 106 yrsComputational domain: 70 kpc x 100 kpc (6 cells/Rb)

Log density [a]

Long-term evolution of large-scale relativistic jets: FRII jets

Log Density

vh1D

phase

Extended B&C model: (Scheck et al.)

• 1D phase: ~ 0 (B&C model)

• Long term evolution: ~ -1/3

lj

Rc

Pc

Cocoon/cavity dynamics: • Similar evolution in the three models (confirms equivalence between models with same kinetic luminosity / thrust)

• Two phase evolution

lj / Rc

x 0.1

x 0.01

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 temperaturefor jets with same kinetic luminosity and similar flow Lorentz factors, Tb 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: Nc b > Nc a (and internal energy dominated by beam particles): isothermal cocoon and isothermalevolution (as in Kino et al. 2007 model)

Models LH and BC: Nc b < Nc a (and internal energydominated by beam particles): large spatial and temporal variations of T

Nc bNc a

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

rm = 7.8 kpc

Axisymmetric simulation of a purely leptonic jet with Lj ~ 1044 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 = 7 106 yrs

• ambient medium conditions from Hardcastle et al. 2002

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 shockand jet expansion

jet disruption and mass load

jet deceleration

pressure density Mach number

Simulation

L&B model

adiabatic expansion

Long-term evolution of large-scale relativistic jets: 3C31

Perucho & Martí 2007, submitted

Last snapshot (T = 7 106 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)

Long-term evolution of large-scale relativistic jets: 3C31

Perucho & Martí 2007, submittedExtended B&C model: (Perucho & Martí)

~ 0.1, ~ 1

Cocoon evolution:

t 1.3

t 1

~ constant

for negligible pollution with ambient particles (Nc b ~ 20 - 200 Nc a ), and assuming selfsimilar transversal expansion

Nc b

Nc a

Ps

Pc c

Tc

Rs

vbs

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 jet OP jet

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…

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. 19983C31, Laing & Bridle 2002

• FRIIs (3C353, Swain et al. 1998: low polarization rails; limb brightening)

I, P intensities in J1-J4 region

I

P

• Pc-scale jets (1055+018, Attridge et al. 1999)

top /down asymmetry low polarization rails

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. 1999jet spine

shear layer

Lorentz factor

specific internal energy

Synchrotron emission

Intensity across the jet

I P

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

M87Zhou et al. 1995

Low polarizationrails

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

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. 2005Perucho, 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 antisymmetricfundamental 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

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. 2005Perucho, 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

TIM

E

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

• 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 (hbWb

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 (hbWb). 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 thephenomenology of pc-scale jets and superluminal sources and observational signatures of jet stratification (However, observations dramatically affected by relativistic radiation transport effects)