Stability and evolution of parsec and kiloparsec-scale jets

Manuel Perucho i Pla

Departament d’Astronomia i AstrofísicaUniversitat de València

Spain

VLBI GroupMax-Planck-Institut für Radioastronomie

Germany

December 14th 2005

OUTLINE OF THE TALK

• Jet stability.• Vortex sheet limit.• Sheared flows.

• Application to extragalactic jets.• Parsec-scale: 3C 273.• Kiloparsec-scale: 3C 31.

• Recent developments and future prospects.• Relativistic Magnetohydrodynamics.

JETS AND KELVIN-HELMHOLTZ INSTABILITIES (i)

• Kelvin-Helmholtz instabilities grow in the interface between two flows in relative motion.

• They may grow after any small perturbation, generating observable structures and eventual mass loading and disruption of the flow.

• In 2D: – Cylindrical jets: pinching

modes.– Slab jets: pinching and

helical modes.

Birkinshaw (1991)

JETS AND KELVIN-HELMHOLTZ INSTABILITIES (ii)• KH modes might be present in:

– Kiloparsec scale structures:• Knots in radio jets.• Responsible of mass entrainment

in decelerated jets: FRI-FRII dichotomy (e.g., Komissarov 1994, Bicknell 1994).

– Parsec scale structures: Helical patterns (Lobanov & Zensus 2001, Hardee et al. 2005), trailing components (Agudo et al. 2001).

• Linear analysis has proven to be a powerful tool to extract information from observations and numerical simulations (e.g., Hardee 2000, 2003, Hardee et al. 2005).

• Observations can provide us with wavelengths and transversal structure which could be interpreted using linear perturbation theory (Lobanov & Zensus 2001) and numerical simulations (Perucho et al. 2005) in order to obtain physical parameters of the jet.

OBJECTIVES OF THE WORK

• Our purpose was to study the transition of KH instabilities in relativistic jets from the linear to the non-linear regimes and to perform a systematic study in terms of the jet/ambient parameters.

• From this study, we could gain insight in– the mechanisms of jet disruption, – the long term stability properties of jets in terms of the

physical parameters,– the formation of observed structures in relativistic jets (knots,

helices, shear layers,...).

JET STABILITYVORTEX SHEET LIMIT

VORTEX SHEET STABILITY (i)– Linear regime (Perucho et al.

2004a)– Initial setup of simulations.

• Solve the dispersion relation – frequencies and growth rates in

terms of wavelength.

• Select first body mode at maximum growth rate.

• Parameters:– Lorentz factor (velocity).– Rest mass density contrast.– Specific internal energy.– Pressure equilibrium.

• Performed simulations sweeping beam specific internal energy (0.07-60 c^2), and Lorentz factor (from 5 to 20).

Axial velocity pert. Pressure pert.

Perp. velocity pert.

-The numerical code reproduces linear growth (temporal view, high resolution).-KH instabilities saturate when the amplitude of the perturbation of axial velocity (in the jet reference frame) reaches the speed of light (Hanasz 1995, 1997).

VORTEX SHEET STABILITY (ii)

• Evolution of Kelvin-Helmholtz instabilities in relativistic flows:– PHASES: LINEAR, SATURATION, NON-LINEAR

VORTEX SHEET STABILITY (iii)

• Evolution of Kelvin-Helmholtz instabilities in relativistic flows:– PHASES: LINEAR, SATURATION, NON-LINEAR

VORTEX SHEET STABILITY (iv)

• Evolution of Kelvin-Helmholtz instabilities in relativistic flows:– PHASES: LINEAR, SATURATION, NON-LINEAR

VORTEX SHEET STABILITY (v)

We followed the non-linear evolutionof the instabilities (Perucho et al. 2004b) and characterised it with two criteria:

- Transfer of axial momentum.- Width of the shear/mixing layer.

Results show faster, cold/warm jets as the most stable, and slower, colder jets as the most unstable (high momentum transfer and wide mixing layers).

During the transition to the non-linear regime, the formation of a shock wave in the jet/ambient boundary (mainly in colder and slower jets) is previous to jet disruption.

JET STABILITYSHEARED FLOWS

STABILITY OF SHEARED FLOWS (i, see poster)• Simulations perturbing several helical and pinching modes in slab jets with shear

layer (Perucho et al. 2005).

• Linear stability solutions reveal the presence of fast growing, small wavelength resonances, mostly important in faster jets.

• The code – develops those small scale structures as harmonics of the longer excited wavelengths.– reproduces the growth rates of perturbed modes in the simulations, excepting for the

resonances, where non-linear effects might be taking place.

Theoretical representationof a non-resonant mode

Theoretical representationof a resonant mode

Snapshot of a simulation in the linear phase

STABILITY OF SHEARED FLOWS (ii)• Non linear regime

– Resonant modes are crucial in the non-linear evolution. They appear in higher Lorentz factor and relativistic Mach number jets.

STABILITY OF SHEARED FLOWS (iii)

• UST1 models: mixed and slowed down after shock.• UST2 models: progressive mixing and slowing.• ST models: resonant modes avoid disruption and generate a

hot shear layer which protects the fast core.• Separation of models is observed in the evolution of axial

momentum, final shear layer structure (next slide) and in a relativistic Mach number-Lorentz factor plot:

STABILITY OF SHEARED FLOWS (iv)• Shear layer (mean profiles of variables).

– Upper panels: thermodynamical variables.– Lower panels: dynamical variables.

tracer rest mass densityspecific internal energy

Norm. Lorentz factor Norm. Axial momentum Axial velocity

UST1 UST2 ST

STABILITY OF SHEARED FLOWS (v)• Mean velocities and structures found

point towards the following:– UST1 models

• Disrupted, thick shear layers: FRI’s? (e.g., Laing and Bridle 2002a,b).

– ST models • Stable: FRII’s? • hot shear layers: observed? (kpc,

Swain et al. 1998; pc, Attridge et al. 1999).

• Relativistic thin (~2Rj) hot shear layers confirm results found in 3D simulations of Aloy et al. (1999, 2000)

I, P intensities in J1-J4 region

I

P

1055+018, Attridge et al. 19993C 353, Swain et al. 1998

3C31, Laing & Bridle 2002

PARSEC-SCALE JETS3C 273

Parsec scale jets: 3C 273 (see poster) • High resolution observations with space VLBI

resolve transversal structure of jets, allowing for interpretation of structures in terms of KH instabilitites (e.g., 3C 273, Lobanov and Zensus 2001, LZ01).

• Consistency of the linear approach.– Are the observed structures linear KH

instabilities? Are the approximations used in the linear approach valid?

• We have shown that numerical codes reproduce the linear regime.

• We have tested in two simulations whether the structures found in 3C 273 by LZ01 are due to KH instabilities or to the periodicities of precession and ejection of fast components (Abraham et al. 1996, Krichbaum et al. 2000).

• Our results reinforce the interpretation in LZ01 of KH instabilities as the origin of the structures.

– Source periodicities have difficulties in generating observed wavelengths.

KILOPARSEC-SCALE JETS 3C 31

Observations and modelling (Laing and Bridle 2002a,b)Laing and Bridle (2002a,b) compare VLA data of total intensity and polarization of 3C 31 with theoretical one-dimensional models.

Models:- Axisymmetric, time-stationary, relativistic jet.- Parametrized distributions of velocity, emission and magnetic field.- Apply conservation of mass, momentum and energy to infer variations of pressure, density, Mach number and entrainment rate.

- External density and pressure from Hardcastle et al. (2002). - Pressure equilibrium with the external medium in the outermost studied region.

Results:- Jet axial structure: inner, flaring, outer.- 52º to line of sight.- Transversal structure (spine+shear layer).- Spine velocity decreasing due to entrainment after the steady shock (from 0.9 to 0.25 c).

3C31, Laing & Bridle 2002

I F O

THE MODEL THE OBSERVATION

Observations and modelling (Laing and Bridle 2002a,b)

FRI paradigm: free expansion, recollimation at shock, mass entrainment and deceleration to transonic speeds.

Dynamics:- The jet is overpressured at the inlet and expands rapidly.- Recollimation occurs when the jet becomes underpressured.

-Recollimation is accompanied by a peak in the entrainment rate.- The jet is slowly entrained and decelerated outwards.- Jet composition is probably purely leptonic, but picks up thermal plasma.

Numerical simulations (i)• The jet is injected with the values at 500 pc from injection.• Jet Lkin~ 10^44 erg/s (FRI).• Implemented Synge equation of state in the code, which allows for

two families of particles (electron/positron and proton, following Scheck et al. 2002, Falle & Komissarov 1996).

• 2D simulations (axisymmetric jet):• Resolution: 8 cells/R_j axially and 16 cells/R_j radially

– A: 2880x1800 cells, 18 kpc x 6 kpc (v=0.87 c).– B: 672x480 cells, 4.2 x 1.8 kpc (v=0.5 c).

rm=7.8kpc

μ=0.5 mass p.p.X=1. H abundance

External medium (Hardcastle et al. 2002) Initial set of parameters

Numerical simulations (ii)evolution

~ constant advance speed (A: ~ 0.007c)(B: ~ 0.0025c)

self-similar evolution (A: L/r ~2.5)(B: L/r ~1.6)

A: The bow shock is still supersonic by the end of the simulation M~2-3B: the bow shock is only slightly supersonic.

A

B

Numerical simulations

(iii)

jet expansion

jet disruption, mass loadand deceleration

growth of instabilities

recollimation shock

SIMULATION B

Numerical simulation (results v)

SIMULATION A SIMULATION B

Recollimation shock Mass loading Oscillations around pressureequilibrium

THE FUTURERELATIVISTIC

MAGNETOHYDRODYNAMICS

Relativistic Magnetohydrodynamics (see poster Roca-Sogorb et al.)

• An RMHD code developed in València and the MPA in Garching (Antón et al. 2005, Leismann et al. 2005) is now available for our work.

• This code has been parallelised for the use in share memory machines and adapted to our needs in the last weeks. Work still in progress…– 3D version.– Relativistic equation of state (realistic atmospheres).

• Combination of these elements along with the use of two dimensional analysis of high resolution VLBI observations (e.g., Lobanov & Zensus 2001) will allow us to reconstruct in detail the physical conditions in jets and to interprete emission patterns and transversal structure in terms of physical facts.

• In Roca-Sogorb et al. we show our first results on the emission and polarization of magnetised jets.

Relativistic Magnetohydrodynamics (see poster Roca-Sogorb et al.)

Helical magnetic field withpitch angle of 20º.

vj=0.99 Mj=15.05 Pj/Pa=2.0 Γ=4/3 ρj/ρa=0.001

Θ=43.8 º

Θ=8.1 º Θ=1.4 º