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**INAF - Osservatorio Astronomico di Torino**

SIMULATIONS OF ASTROPHYSICAL JETS Gianluigi Bodo, Claudio Zanni, Attilio Ferrari, Silvano Massaglia, A. Mignone, P. Rossi INAF - Osservatorio Astronomico di Torino Università di Torino

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**Collimated, supersonic outflows (jets)**

are generated in many astrophysical environments AGN pulsars YSO X-ray transients

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**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)

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YSO jets HST images HH 30 1" 10''

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**AGN Jets Scales up to Mpc Non-thermal synchrotron radiation**

Collimation angle can be few degrees Observed at different energies 7 time scales 10 yrs

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BASIC PROBLEMS Launching Launching phase: acceleration from disk and collimation • Propagation Propagation phase: confinement, stability, entrainment • Termination Termination: interaction with external medium

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**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

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**Algorithms Time Stepping HD RHD MHD RMHD Riemann Solvers Interpolation**

Fwd Euler (Split/Unsplit) RK 2nd (Split/Unsplit) RK 3rd (Split/Unsplit) Hancock (Split/CTU) Characteristic Tracing (Split/CTU) (split) (split) Riemann Solvers Riemann (non-linear) TVD/ROE HLL HLLC TVDLF Interpolation Prim. TVD-limited (II order) Characteristic TVD-limited Piecewise-Parabolic Multi-D Linear Interpolation 2nd and 3rd order WENO

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Stability of jets Kelvin-Helmholtz instability Transfer of momentum, entrainment Effects on the jet evolution Consider first a simple case, simple planar shear layer Velocity profile Vx = tanh y AGN: relativistic case

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**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

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**Relativistic cases: correspondence at equal Mr = gv/gs 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 Layer width tracer Layer width velocity

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**JET STABILITY Bodo et al. 1998 Linear phase Acoustic phase Mixing**

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**Fanaroff-Riley classification**

VLA FR I or jet dominated Cygnus A VLA FR II or lobe dominated “classical doubles”

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**Jet velocities No direct velocity measures**

Evidences for relativistic motions on pc scale come from: Superluminal motions Jet one-sidedness Rapid variabilities High brightness temperatures

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**In FRI radiosources jets on kpc scale become symmetric**

VLBI one-sided jet VLA Brightness ratio between jet and counterjet in 3C31

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**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 perturbed at the inlet

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**Physical parameters Jet Mach number Lorentz factor G Density ratio h**

M G r j r e Jet Mach number Lorentz factor G Density ratio h

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Parameters values Mach , 30 Density ratio (lab frame) Lorentz factor Low resolution 12 points over radius High resolution 25 points over radius Stretched grid in the transverse direction Increasing grid size

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**3D Numerical Simulation**

Grid: 300x800x300 Jet injection+ perturbation outflow

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

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1) The entrainment is mediated by the cocoon

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M=30 h=10 G=10 t=265

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1) 2)

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**1) M=3 h=1000 G=10 t=760 2) M=30 h=10 G=10 t=265 Faster deceleration**

Strong pinching due to high pressure cocoon Short wavelength mode more efficient for entrainment 2) M=30 h=10 G=10 t=265 Helical mode

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Jet mass External mass Jet mass External mass

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**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

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CHANDRA HYDRA A X - RADIO HYDRA A X-RAY

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CHANDRA Perseus A X - radio Perseus A X-ray

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**OBSERVATIONS X-ray cavities corresponding to radio lobes**

Shells surrounding the cavities Shell temperature equal or lower than the surrounding medium Weak shocks

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**L-T relation for cluster gas**

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**NUMERICAL SIMULATIONS**

outflow Initial density distribution 2.6 Uniform temperature reflecting outflow 1024x1024 grid points Jet inlet reflecting 2.6

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UNITS

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RESULTS

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**Subsonic jet Strongly overpressured Weakly overpressured M n lc = 2**

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Similar setup as before Larger grid, Longer integration times, longer than the lifetime of the radiosource Three cases with cluster of different scales: T keV 1 keV 2 keV

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**Entropy and dissipated energy**

Borgani et al. (2002) Efficiency

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**Hydrostatic equilibrium**

Lloyd-Davies et al. (2000)

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**L-T relation Entropy per particle First stage, future: insert heating**

at z > 0 on protoclusters and follow the evolution with a cosmological simulation

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Summary Single shear KH instability Deceleration of relativistic jets Heating of external medium by jets

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