1. 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

2. Collimated, supersonic outflows (jets)
are generated in many astrophysical
environments
AGN
pulsars
YSO
X-ray transients

3. 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)

4. YSO jets
HST images
HH 30
1"
10''

5. 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

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

7. 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

8. 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
   
   
   
   

9. 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

10. 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

11. 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

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

14. Fanaroff-Riley classification
VLA
FR I
or jet dominated
Cygnus A
VLA
FR II
or lobe dominated
“classical doubles”

15. 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

16. In FRI radiosources jets on kpc scale become symmetric
VLBI
one-sided
jet
VLA
Brightness ratio between jet
and counterjet in 3C31

17. 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

18. 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

19. 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

20. 3D Numerical Simulation
Grid: 300x800x300
Jet
injection+
perturbation
outflow

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

22. 1)
The entrainment is mediated
by the cocoon

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

24. 1) 2)

25. 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

26. Jet mass
External mass
Jet mass
External mass

28. 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

29. CHANDRA
HYDRA A
X - RADIO
HYDRA A
X-RAY

30. CHANDRA
Perseus A
X - radio
Perseus A
X-ray

31. OBSERVATIONS X-ray cavities corresponding to radio lobes
Shells surrounding the cavities
Shell temperature equal or lower than
the surrounding medium
Weak shocks

32. L-T relation for cluster gas

33. NUMERICAL SIMULATIONS
outflow
Initial density distribution
2.6
Uniform temperature
reflecting
outflow
1024x1024 grid points
Jet inlet
reflecting
2.6

34. UNITS

35. RESULTS

37. Subsonic jet Strongly overpressured Weakly overpressured M n lc = 2

38. 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

39. Entropy and dissipated energy
Borgani et al. (2002)
Efficiency

40. Hydrostatic equilibrium
Lloyd-Davies et al. (2000)

41. L-T relation Entropy per particle First stage, future: insert heating
at z > 0 on protoclusters and
follow the evolution
with a cosmological simulation

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