simulations of astrophysical jets

SIMULATIONS OF SIMULATIONS OF

ASTROPHYSICAL JETSASTROPHYSICAL JETS

Gianluigi Bodo, Claudio Zanni, Attilio Ferrari, Gianluigi Bodo, Claudio Zanni, Attilio Ferrari, Silvano Massaglia, A. Mignone, P. RossiSilvano Massaglia, A. Mignone, P. Rossi

INAF - Osservatorio Astronomico di TorinoINAF - Osservatorio Astronomico di Torino

Università di Torino Università di Torino

Collimated, supersonic outflows (jets)are generated in many astrophysicalenvironments

AGN

YSOX-ray transients

pulsars

Wide range of scales and velocities

Scales from below the pc up to Mpc

Highly relativistic velocities (AGN, GRB)

Mildly relativistic velocities (X-ray transients – galactic superluminals, SS433)

Few hundreds km/s (YSO)

YSO jets HST images HH 30

1"10''

AGN Jets

Scales up to MpcNon-thermal synchrotron radiationCollimation angle can be few degrees

Observed at differentenergies

time scales 10 yrs7

• Launching Launching phase: acceleration fromdisk and collimation• Propagation Propagation phase: confinement,stability, entrainment• Termination Termination: interaction with external medium

BASIC PROBLEMS

THE TOOL: PLUTO OUTLINE• Explicit, compressible code (FV):

– Shock capturing– High-mach number flows

• Works in 1, 2, 3-D• Modular structure:

– Physics– Time stepping– Interpolations– Riemann Solvers

• HD, MHD, RHD (Mignone, Plewa, Bodo 2005, HLLC Mignone & Bodo 2005) , RMHD (HLLC Mignone & Bodo 2005)

• Geometry support (Cart, Cyl, Spher)• Radiative losses

Algorithms

Time Stepping

Fwd Euler (Split/Unsplit) RK 2nd (Split/Unsplit) RK 3rd (Split/Unsplit) Hancock (Split/CTU) Characteristic Tracing

(Split/CTU)

Interpolation Prim. TVD-limited (II order) Characteristic TVD-limited Piecewise-Parabolic Multi-D Linear Interpolation 2nd and 3rd order WENO

Riemann Solvers Riemann (non-linear)

TVD/ROE HLL HLLC TVDLF

(split) (split)

HD RHD MHD RMHD

Stability of jets

Kelvin-Helmholtz instability

Transfer of momentum, entrainment

Effects on the jet evolution

Consider first a simple case, simple planar shearlayer

Velocity profileVx = tanh y

AGN: relativistic case

Linear stability: different regimes depending on the Mach number, monotonic instability at low Mach, overstability at high Mach

Nonlinear evolution dominated by vortices or by waves

Layer width velocity Layer width tracer

Relativistic cases: correspondence at equal Mr = v/s cs

we showed in linear analysis (Bodo, Mignone & Rosner 2004)that the stability limits (vortex sheet) are the same if expressed in Mr

We introduced a tracer passively advected to distinguish the material on the two sides

JET STABILITYJET STABILITY

Linear phase

Acousticphase

Mixingphase

Bodo et al. 1998

Fanaroff-Riley classificationFanaroff-Riley classification

FR II or lobe dominated “classical doubles”

FR I or jet dominated

Cygnus AVLA

3C 449VLA

Jet velocitiesNo direct velocity measures Evidences for relativistic motions on pc scale come from:

Superluminal motions

Jet one-sidedness

Rapid variabilities

High brightness temperatures

In FRI radiosources jets on kpc scale become symmetric

Brightness ratio between jetand counterjet in 3C31

3C272.1

VLBI one-sided jet VLA

AGN jets: deceleration of FRI jets

Mass entrainment

Injection from stellar winds (Komissarov 1994; Bowman, Leahy, Komissarov 1996)

Entrainment through the instability evolution

Simulations of a propagating jet perturbedat the inlet

Physical parameters

j j

e

Jet Mach number

Lorentz factor

Density ratio

Mach 3, 30Density ratio (lab frame) 10 1000Lorentz factor 10

Low resolution 12 points over radiusHigh resolution 25 points over radius

Stretched grid in the transverse directionIncreasing grid size

Parameters values

3D Numerical Simulation 3D Numerical Simulation

Grid: 300x800x300

Jet injection+perturbation

outflow

outflow

outflow

1) M=3 =1000 =10 t=760

1)

The entrainment is mediated by the cocoon

M=30 =10 =10 t=265

1)

2)

1) M=3 =1000 =10 t=760

2) M=30 =10 =10 t=265

Faster decelerationStrong pinching due to high pressure cocoonShort wavelength mode more efficient for entrainment

Helical mode

Jet mass External mass

Jet mass

External mass

Jet-IGM interaction from the point of view of IGM

Observational consequences of the interaction: X-ray observations

From the observations can we deduce information on jet parameters?

Heating of IGM

CHANDRA

HYDRA A X-RAY

HYDRA AX - RADIO

CHANDRA

Perseus AX - radio

Perseus A X-ray

OBSERVATIONS

X-ray cavities corresponding to radio lobes Shells surrounding the cavities Shell temperature equal or lower than the surrounding medium

Weak shocks

L-T relation for cluster gas

NUMERICAL SIMULATIONS

reflecting

outflow

outflow

refl

ecti

ng

0 2.6

2.6Initial density distribution

Uniform temperature

1024x1024 grid points

Jet inlet

UNITS

RESULTS

M

Subsonic jet lc = 0.5

lc = 1lc = 2

Strongly overpressured

Weakly overpressured

Similar setup as before

Larger grid, Longer integration times,longer than the lifetime of the radiosource

Three cases withcluster of different scales:

T 0.5 keV 1 keV 2 keV

Entropy and dissipated energyEntropy and dissipated energy

Efficiency Efficiency Borgani et al. (2002)Borgani et al. (2002)

Hydrostatic equilibriumHydrostatic equilibrium

Lloyd-Davies et al. (2000)Lloyd-Davies et al. (2000)

L-T relationL-T relation

Entropy per particleEntropy per particle(at )(at )

First stage, future: insert heatingat z > 0 on protoclusters and follow the evolution with a cosmological simulation

Summary

Single shear KH instability

Deceleration of relativistic jets

Heating of external medium by jets