ipam05

1
José Mª Martí
Departamento de Astronomía y Astrofísica
Universidad de Valencia (Spain)
Astrophysical Fluid Dynamics, April 4-9, 2005
2
Outline of the talk

• Motivation. Extragalactic jets
• Discovery and observational status
• Standard model
• The jet/outflow family
• Extragalactic jets open questions
• General relativistic hydrodynamics
• RHD eqs. as a hyperbolic system of conservation
  laws
• Numerical methods AV, HRSC,
• Simulations of extragalactic jets
• Large scale jets
• Compact jets
• Jet formation mechanisms
• Relativistic Magnetohydrodynamics
• Summary, conclusions,

3
Motivation. Extragalactic jets
General relativity and relativistic hydrodynamics
play a major role in the description of many
astrophysical scenarios. Extragalactic jets
(present in radio-loud AGNs) are a paradigmatic
example. 1918 Discovery of the optical jet in
M87 1940-50 Radio source Virgo A associated with
M87 and its jet 1970-80 Models of continuous
supply to interpret double lobed extragalactic
radio sources (obtained with aperture synthesis
techniques)
M87, HST
Scheuer 1974
Cygnus A, Cambridge 5km array Hardgrave Ryle
1974
Blandford Rees 1974
1980- with the advent of VLA, routine detection
of jets
Very Large Array Socorro, NM
4
Extragalactic jets Observational status I
Nowadays, jets are a common ingredient of
radio-loud AGNs detected and imaged at very
different spatial scales with different arrays
(kpc scales VLA, Merlin pc scales VLBA, VLBI,
VSOP)
VLBA
5
Extragalactic jets Observational status II
Kpc scales Morphological dichotomy based on jet
power
Pc scales Superluminal motion, one-sidedness
Subpc scale Collimation
Cyg A, VLA (6cm), Carilli et al. 1996
3C120, VLBA Gómez et al. 2000
M87, VLA/VLBA Junor et al. 1999
3C31, VLA (20cm), 1999
6
Extragalactic jets Observational status III
Radio polarization information about the
topology of magnetic fields at both pc and kpc
scales
1055018, Attridge et al. 1999
Hints on jet internal structure shocks, shear
layers
3C120 X-ray dips/component ejection correlations
3C31, Laing Bridle 2002 (ticks show the
orientation of magnetic field
Variability time scales and correlations between
variations in different continuum/line components
Nature and location of the different components
at the central regions of AGNs (e.g., narrow and
broad line regions) and on their
interdependencies (e.g., jet/disc connection)
Marscher et al. 2002
7
Extragalactic jets Observational status IV
Imaging of the central regions of AGNs anatomy
(narrow line region, obscuring torus) and
dynamics (rotation) of the central engine
NGC5728
NGC4261
Hubble Space Telescope
Multiwavelength imaging of the jets and spectra
emission models, spectral evolution of the
high energy electron distribution, reacceleration
sites,
3C273, radio (MERLIN), optical (HST) and X-ray
(CHANDRA) with optical contours Marshall et al.
2001
Bertsch (NASA/GSFC)
8
Extragalactic jets the standard model

• The production of jets is connected with the
  process of accretion on supermassive black holes
  at the core of AGNs (see, e.g., Celotti
  Blandford 2000)
• Hydromagnetic acceleration of disc wind in a BH
  magnetosphere (Blandford-Payne mechanism)
• Extraction of rotational energy from Kerr BH by
  magnetic processes (Blandford-Znajek mechanism,
  magnetic Penrose process)

• Emission synchrotron (responsible of the
  emission from radio to X-rays) and inverse
  Compton (g-ray emission) from a relativistic
  (e/e-, ep) jet (e.g., Ghisellini et al. 1998).
  Target photons for the IC process
• Self Compton synchrotron photons
• External Compton disc, BLR, dusty torus

• Jets are relativistic, as indicated by
• Superluminal motions at pc scales (due to the
  finite speed of propagation of light)
• One-sidedness of pc scale jets and brigthness
  asymmetries between jets and counterjets at kpc
  scales (due to Doppler boosting of the emitted
  radiation)

Jets Relativistic collimated ejections of
thermal (e/e-, ep) plasma ultrarelativistic
electrons/positrons magnetic fields
radiation, generated in the vicinity of SMBH
(GENERAL) RELATIVISTIC MHD ELECTRON TRANSPORT
RADIATION TRANSFER
9
The jet/outflow family

• X-ray binaries
• 20
• vjet lt 0.9c
• Ljet 1038- 1040 erg/s
• Size 10-3 10-1 pc
• Collimation few degrees
• Central engine stellar BH/NS disc

• Active galactic nuclei
• 10 AGN (radio-loud AGN)
• vjet 0.995c
• Ljet 1043- 1048 erg/s
• Size 0.1-1 Mpc
• Collimation few degrees
• Central engine SMBH disc

• Gamma-ray bursts
• vjet/wind 0.99995-0.999999995c
• LGRB 1052 erg/s (T 1s)
• Size 1 pc (late afterglow evolution)
• Collimation few tens of degrees
• Central engine stellar BH torus

• Young stellar objects
• vjet 10-3 c
• Ljet 1035 erg/s
• Size 10-3 10-2 pc
• Collimation few degrees
• Central engine YSO inflow

And more (pulsars, proto-planetary nebulae,
cataclismic variables,)
10
Extragalactic jets open questions
Jet formation hydromagnetic acceleration of disc
wind ? extraction of
rotational energy from rotating BH
Influence of radiative acceleration
Influence of hydrodynamic
acceleration Origin of the
poloidal magnetic field
Connection with jet composition ep, ee-
Acceleration present numerical simulations fail
to generate highly relativistic, steady jets
(several arguments point to
Lorentz factor few-20 IDV Lorentz factor 100)
Jet composition
Origin of the ultrarelativistic particle
distribution
Nature of the radio components relativistic
shocks ?
instabilities ?
Kiloparsec scale parsec scale
miliparsec scale
Structure and kinematics of jets magnetic field
topology role of the magnetic fields in the jet
dynamics and emission
Stability on large scales
FRI/FRII morphological dichotomy environment?
Jet power? Composition? Formation

mechanism?
Accretion regime? Magnetic field?

KH instabilities?
Role in galaxy and cluster evolution heating
11
RHD equations for a perfect fluid
The fluid is characterized by a four-velocity um
and a stress-energy tensor Tmn. The space-time in
which the fluid evolves is characterized by a
metric tensor whose components are gmn.

• The equations of relativistic hydrodynamics are
  conservation laws
• Conservation of mass
• r proper rest-mass density
• Conservation of energy and momentum
• For a perfect fluid
• e specific internal energy p pressure
• Equation of state

Approaches Full GRHD Components of the metric
as a function of coordinates from Einstein eqs.
( ) (Numerical Relativity
consistent scenarios of jet/GRB production)
Test GRHD Fluid evolving in a given space-time
(simplified scenarios of jet formation) SRHD
Flat space-time (propagation of jets at parsec
and kiloparsec scales)
12
Relativistic hydrodynamics SRHD equations

13
Relativistic hydrodynamics hyperbolicity

RHD equations form a non-linear, hyperbolic
system of conservation laws for causal EoS (e.g.,
Anile 1989)

• For hyperbolic systems,
• The Jacobians of the vectors of fluxes,
  , have real eigenvalues and a complete
  set of eigenvectors.
• Information about the solution propagates at
  finite velocities (characteristic speeds) given
  by the eigenvalues of the Jacobians.
• Hence, if the solution is known (in some spatial
  domain) at some given time, this fact can be used
  to advance the solution to some later time
  (initial value problem).
• However, in general, it is not possible to
  derive the exact solution for this problem.
  Instead, one has to rely on numerical methods
  which provide an approximate to the solution.
• Moreover, these numerical methods must be able
  to handle discontinuous solutions, which are
  inherent to non-linear hyperbolic systems.

14
Relativistic hydrodynamics characteristic
structure I

Donat et al. 1998 Martí et al. 1991, Eulderink
1993, Font et al. 1994
15
Relativistic hydrodynamics characteristic
structure II

16
Numerical relativistic hydrodynamics AV methods I
May Whites code (May White 1966,
1967) Lagrangian (1D) finite difference scheme
artificial viscosity (AV) for spherically
symmetric, relativistic, stellar collapse

Space-time metric
m total (barionic) rest-mass up to radius R
Mass, energy and momentum conservation
Einstein equations
EoS
Richtmyer von Neumanns (1950) AV
AV produces dissipation at shocks that reduces
post-shock oscillations
17
Numerical relativistic hydrodynamics AV methods
II
Wilsons approach (Wilson 1972, 1979) Eulerian 2D
finite difference scheme artificial viscosity
(AV) for test GRHD (31formalism)

Mass conservation
Momentum conservation
Energy conservation
EoS

• Extension to Full GRHD Smarr Wilson code
  (Wilson 1979) Wilsons formulation built on a
  vacuum numerical relativity code for the head-on
  collision of two black holes (Smarr 1975)
• Smarr Wilsons approach allowed to simulate
  complex relativistic scenarios for the first
  time
• Axisymmetric stellar core collapse (Wilson 1979,
  Dykema 1980, Nakamura et al. 1980, Bardeen
  Piran 1983, Evans 1984, )
• Issues on Numerical Cosmology inflation,
  primordial nucleosynthesis, microwave anisotropy,
  evolution of primordial gravity waves,(Centrella
  Wilson 1983, 1984, )
• Accretion onto compact objects (Hawley et al.
  1984a,b, )
• Heavy ion collisions (Wilson Mathews 1989, )

18
Numerical relativistic hydrodynamics AV methods
III
Wilsons approach. Numerical method (Wilson 1972,
1979 see the recent book by Wilson Mathews
2003) Eulerian 2D finite difference scheme
artificial viscosity (AV) for test GRHD
(31formalism)

Model equation in 1D
(transport equation with source terms)
Discretization (Donnor cell or Leleviers
method upwind, first order)
Newer developments Consistent AV artificial
viscosity as a bulk scalar viscosity (Norman
Winkler 1986)
Non-consistent AV artificial viscosity added to
the pressure in some terms of the hydro eqs.
Large innacuracies in mildly relativistic flows
Very accurate increase of coupling
19
High-Resolution Shock-Capturing methods
see LeVeques 1992 book
HRSC methods deal with hyperbolic systems of
conservation laws. Model equation in 1D

HRSC methods finite difference (volume) schemes
in conservation form. Integrating the PDE over a
finite space-time domain

Lax-Wendroff theorem (LW 1960) conservation form
ensures the convergence of the solution under
grid refinement to one of the weak solutions of
the original system of equations
Numerical fluxes

• exact or approximate Riemann solvers
  (Godunov-type methods)
• standard finite-difference methods local
  conservative dissipation terms (e.g., symmetric
  schemes)

• High-order of accuracy
• Total variation stable (TVD, TVB) algorithms

Stability (no spurious oscillations) and
convergence

• Standard approach Conservative monotonic
  polynomials as interpolant functions within zones
  (slope limiter methods also flux limiter methods)

• MINMOD (van Leer 1977 second order)
• PPM (Colella Woodward 1984 third order)
• ENO (Harten et al. 1987)

20
HRSC methods in Relativistic Hydrodynamics
See Martí Müller, Numerical Hydrodynamics in
Special Relativity,Living Reviews in Relativity,
http//www.livingreviews.org/Articles/lrr-2003-7

• Based on Riemann solvers (upwind methods)
• Linearized solvers based on local
  linearizations of the Jacobian matrices of the
  vector of fluxes
• Roe-type Riemann solvers (Roe-Eulderink
  Eulderink 1993 LCA Martí et al. 1991)
• Falle-Komissarov (Falle Komissarov 1996)
  based on a primitive-variable formulation of the
  eqs.
• Marquina Flux Formula (Donat Marquina 96)
• Solvers relying on the exact solution of the
  Riemann problem (Martí Müller 1994 Pons, Martí
  Müller 2000)
• rPPM (Martí Müller 1996)
• Random choice method (Wen et al. 1997)
• Two-shock approximation (Balsara 1994 Dai
  Woodward 1997)

HRSC METHODS DESCRIBE ACCURATELY HIGHLY
RELATIVISTIC FLOWS WITH STRONG SHOKS AND THIN
STRUCTURES

• Symmetric TVD, ENO schemes with nonlinear
  numerical dissipation
• LW scheme with conservative TVD dissipation
  terms (Koide at al. 1996)
• Del Zanna Bucciantini 2002 Third-order ENO
  reconstruction algorithm spectral-decomposition-
  avoiding RS (LF, HLL)
• NOCD (Anninos Fragile 2002)

21
Exact Riemann solver in RHD I
(Martí Müller 1994 Pons, Martí Müller 2000)

Riemann Problem IVP with initial discontinuous
data L, R
W shock / rarefaction (self-similar expansion)
C contact discontinuity
1. The compressive character of shock waves
allows as to discriminate between shocks (S) and
rarefaction waves (R)
pressure ahead and behind the wave
2. The functions Wg, Wf allow one to determine
the functions and ,
respectively.
RS(p) / SS(p) family of all states which can be
connected through a rarefaction / shock with a
given state S ahead the wave.
3. The pressure p and the velocity vx in the
intermediate states are then given by the
condition across the contact discontinuity
22
Exact Riemann solver in RHD II
Solution of the Riemann problem in the pressure
normal flow velocity diagram

(Martí Müller 1994, Pons, Martí Müller 2000)
The wave-pattern (RR, SR, SS) of the solution can
be predicted in terms of the relativistic
invariant relative velocity between the initial
left and right states (Rezzolla Zanotti
2001,Rezzolla, Zanotti Pons 2002)
changing initial tangential speeds
S
Relative velocity between L, R initial states
S
R
S
23
Algorithms for Numerical RHD I upwind HRSC
methods

24
Algorithms for Numerical RHD II central HRSC
methods

Harten-Lax-van Leer Flux
25
Algorithms for Numerical RHD III other approaches

26
Special relativistic Riemann solvers in GR
Pons et al. 1998
According to the Equivalence Principle, physical
laws in a local inertial frame of a curved
spacetime have the same form as in Special
Relativity

free falling frames
The solution of the Riemann problem in GR
coincides (locally) with the one in SR if
described in a LIF

• 1. Perform at each numerical interface, , a
  coordinate transformation to locally Minkowskian
• coordinates, , according to
• where are the coordinates of the center
  of the interface and is given by
• 
  
• where is the orthonormal basis attached
  to , with orthogonal to .
• 2. Set up the Riemann problem at the two sides of
  by transforming the velocity
• components to the new basis, .
• 3. Solve the Riemann problem as in special
  relativity and compute numerical fluxes
• 4. Transform numerical fluxes to the coordinate
  basis, .

This procedure has been used with success in
numerical GRMHD and force-free degenerate
electrodynamics in the context of jet formation
scenarios (Komissarov 2001, 2004, 2005)
27
Simulations of relativistic jets Kiloparsec
scale jets 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). Two
parameters control the morphology and dynamics of
jets the beam to external density ratio and the
internal beam Mach number

Morphology and dynamics governed by interaction
with the external (intergalactic) medium. The
simulations have allowed to identify the
structural components of radio jets
First relativistic simulations van Putten 1993,
Martí et al. 1994, 1995, 1997 Duncan Hughes
1994
Relativistic, hot jet models
Relativistic, cold jet models
Density velocity field vectors
featureless jet thin cocoons without backflow
stable terminal shock naked quasar jets (e.g.,
3C273)
knotty jet extended cocoon dynamical
working surface FRII radio galaxies and lobe
dominated quasars (e.g., Cyg A)
28
Simulations of relativistic jets Kiloparsec
scale jets II

• 3D simulations (Nishikawa et al. 1997, 1998
  Aloy et al. 1999 Hughes et al. 2002, )
• Simulations too short (mean jet advance speed
  too high poorly developed cocoons)
• Two-component jet structure fast (LoF 7)
  inner jet slower (LoF 1.7) shear layer with
  high specific internal energy

8.6 Mcells
3.6 Mcells
Aloy et al. 1999

• Long term evolution and jet composition (Scheck
  et al. 2002)
• Evolution followed up to 6 106 y (10 of a
  realistic lifetime).
• Realistic EoS (mixture of e-, e, p)
• Long term evolution consistent with that
  inferred for powerful radio sources
• Relativistic speeds up to kpc scales
• Neither important morphological nor evolutionary
  differences related with the plasma composition

29
Simulations of relativistic jets RMHD sims of
kpc jets
(Nishikawa et al. 1997, 1998 Komissarov 1999
Leismann et al. 2005)
Relativistic jet propagation along aligned and
oblique magnetic fields (Nishikawa et al. 1997,
1998)

• Relativistic jets carrying toroidal magnetic
  fields (Komissarov 1999)
• Beams are pinched
• Large nose cones (already discovered in
  classical MHD simulations) develop in the case of
  jets with Poynting flux
• Low Poynting flux jets may develop magnetically
  confining cocoons (large scale jet confinement by
  dynamically important magnetic fields)

• Models with poloidal magnetic fields (Leismann et
  al. 2005)
• The magnetic tension along the jet affects the
  structure and dynamics of the flow.
• Comparison with models with toroidal magnetic
  fields
• The magnetic field is almost evacuated form the
  cocoon. Cocoons are smoother.
• - Oblique shocks in the beam are weaker.

30
Simulations of relativistic jets pc-scale jets
and superluminal radio sources
Shok-in-jet model steady relativistic jet with
finite opening angle small perturbation (Gómez
et al. 1996, 1997 Komissarov Falle 1996, 1997)
Radio emission (synchrotron overpressured jet)

• Convolved maps (typical VLBI resolution
  contours) core-jet structure with superluminal
  (8.6c) component
• Unconvolved maps (grey scale)
• Steady components associated to recollimation
  shocks
• dragging of components accompanied by an
  increase in flux
• correct identification of components (left
  panel) based on the analysis of hydrodynamical
  quantities in the observers frame

3D hydroemission sims of relativistic precessing
jets (including light travel time delays) Aloy
et al. 2003
31
Relativistic hydrodynamics and emission models
In order to compare with observations,
simulations of parsec scale jets must account for
relativistic effects (light aberration, Doppler
shift, light travel time delays) in the emission

• Basic hydro/emission coupling (only synchrotron
  emission considered so far! Gómez et al. 1995,
  1997 Mioduszewski et al. 1997 Komissarov and
  Falle 1997)
• Dynamics governed by the thermal (hydrodynamic)
  population
• Particle and energy densities of the radiating
  (non-thermal) and hydrodynamic populations
  proportional (valid for adiabatic processes
• (Dynamically negligible) ad-hoc magnetic field
  with the energy density proportional to fluid
  energy density
• Integration of the radiative transfer equations
  in the observers frame for the Stokes parameters
  along the line of sight
• Time delays emission ( ) and absortion
  coefficients ( ) computed at retarded times
• Doppler boosting (aberration Doppler shift)

• Further improvements
• Compute relativistic electron transport during
  the jet evolution to acount for adiabatic and
  radiative losses and particle accelerations of
  the non-thermal population (e.g., Jones et al.
  1999, non-relativistic MHD sims.)
• Include inverse Compton (scattering process!)
• Include emission back reaction on the flow
  (important at high frequencies)

32
Simulations of superluminal sources
interpreting the observations with the
hydrodynamical shock-in-jet model
Isolated (3C279, Wehrle et al. 2001) and
regularly spaced stationary components (0836710,
Krichbaum et al. 1990 0735178, Gabuzda et al.
1994 M87, Junor Biretta 1995 3C371, Gómez
Marscher 2000)
Variations in the apparent motion and light
curves of components (3C345, 083671, 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 1606106, Piner
Kingham 1998) and differences between pattern and
bulk Lorentz factors (Mrk 421, Piner et al. 1999)
Dragging of components (0735178, 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)
3C120 Gómez et al. 1998
1606106 Piner Kingham 1998
3C279 Wehrle et al. 1997
3C371 Gómez Marscher 2000
Gabuzda et al.1994 0735178
3C263 Hough et al. 1996
33
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

Interpretation of parsec scale jets
Wavelike helical structures with differentially
moving and stationary features can be produced
by precession and wave-wave interactions (Hardee
2000, 2001) used to constrain the physical
conditions in the inner jet of 3C120 (Hardee
2003, Hardee et al. 2005)
The 3C273 case
1. Emission across the jet resolved
double helix inside the jet 2. Five sinusoidal
modes are required to fit the double helix 3. The
sinusoidal modes are then identified with
instability modes (elliptical/helical
body/surface modes) at their respective resonant
wavelengths from which physical jet conditions
are derived
Lorentz factor 2.1 0.4 Mach number 3.5
1.4 Density ratio 0.023 0.012 Jet sound
speed 0.53 0.16
34
Kelvin-Helmholtz instabilities non-linear regime
Perucho et al. 2004a,b Perucho et al. 2005

• Goals of the study
• Relativistic effects on the stability of jets
• Transition from linear to nonlinear stability

• Dynamics of jet disruption
• Long term evolution (jet disruption, shear layer
  formation, )

• Numerical simulations
• Planar (2D) symmetric (pinch) / antysymmetric
  (helical) modes
• Resolution 400 zones/Rj (transversal) x 16
  zones/Rj (longitudinal)

• Initial conditions steady jet small amplitude
  perturbation (first body mode)
• Temporal approach

Lorentz factor 5 model
Initial model
Linear phase
Non-linear evolution
Evolutionary phases
Saturation
Pressure maximum
Mixing
Quasisteady
Linear
35
Simulations of jet formation (accretion/outflow,
acceleration, collimation)
Plasma acceleration in BP mechanism
Blandford-Payne mechanism hydromagnetic
acceleration of disk wind in a BH magnetosphere
(barion loaded jet GRMHD) Accretion/ejection
from Keplerian (co-rotating/counter-rotating)
cold disks around Schwarzschild (Koide et al.
1997), rapidly rotating Kerr BH (Koide et al.
2000)
Kerr BH Koide et al. 2000
Magnetic Penrose process
Schwarzschild BH Koide et al. 1997
Magnetic line twist extract energy from BH
ergosphere

• Extraction of rotational energy form Kerr BH by
  magnetic processes
• Blandford-Znajek mechanism BH as a magnetized
  rotating conductor whose rotational energy can be
  efficiently extracted by means of magnetic torque
  (Poynting flux jet force-free electrodynamics).
  Confirmed recently by Komissarov (2001 -FFDE-,
  2004 -GRMHD, rarefied plasma-) formation of a UR
  particle, Poynting dominated wind
• magnetic Penrose process magnetic field lines
  accross the ergosphere twisted by frame dragging
  line twist propagates outwards as
  torsional Alfven wave train carrying e.m. energy
  total energy of the plasma near the hole
  decrease to negative values swallowing
  of this plasma by the hole reduces the BH
  rotational energy (Poynting flux jet GRMHD).
  Koide et al. 2002, Koide 2003 controversial
  Komissarov 2005 (magnetic Penrose process does
  not operate)

Koide et al. 2002
36
Relativistic Magnetohydrodynamics

37
RMHD as hyperbolic system of conservation laws
In one spatial dimension, the system of RMHD can
be written as a hyperbolic system of conservation
laws for the unknowns
(conserved variables) subject to the constraint
along the evolution.

Anile Pennisi 1987, Anile 1989 (see also van
Putten 1991) have studied the characteristic
structure of the equations (eigenvalues,
right/left eigenvectors) in the space of
covariant variables
Wavefront diagrams in the fluid rest frame
(Jeffrey Taniuti 1964)

• There are seven physical waves
• Two Alfven waves,
• Two fast magnetosonic waves,
• Two slow magnetosonic waves,
• One entropy wave,

(Deg II)
The wave propagation velocity depend on the
relative orientation of the magnetic field, q
(Deg I)
orientation of the magnetic field

• As in classical MHD there are two kinds of
  degeneracies
• Degeneracy I
• Degeneracy II

• Physically two or more wavespeeds become equal
  (compound waves)
• Numerically the spectral decomposition (needed
  in upwind HRSC methods) blows up

38
Algorithms for Numerical RMHD
(HRSCAV)
39
Numerical RMHD 1D Tests
Fast, slow shocks rarefactions Alfvén waves
shock tubes magnetic field divergence-free
condition satisfied by construction
still lacking an analytical solution!!
Antón et al. 2005 (also van Putten 1993, Balsara
2001, Del Zanna et al. 2002, De Villiers
Hawley 2003, )
Antón et al. 2005 (also Komissarov 1999, Del
Zanna et al. 2002, De Villiers Hawley 2003, )
40
Numerical RMHD 2D Tests
Cylindrical explosions Ambient (r gt1.0) p
3.e-5, r 1.e-4 Homogeneous
magnetic field, B (Bx, 0, 0) (Smooth)
transition layer (0.8 lt r lt 1.0) Bx
0.01, 0.1, 1.0 (b 1.6, 1.6e2, 1.6e4)
Cylinder (r lt 0.8) p 1.0, r 1.e-2
Antón et al. 2005 (proposed by Komissarov 1999
see also Del Zanna et al. 2002, b 8.e2)
Rotors Static ambient (r gt 0.1) p 1.0, r
1.0, B (Bx, 0, 0), Bx 1.0 (b 0.5) Rotating
disk (r lt 0.1) p 1.0, r 10.0, w 9.95
(Lorentz factor approx. 10)
Del Zanna et al. 2002
t 0.4
0.35 (w) 8.19 (b)
5.3e-3 (w) 3.9 (b)
3.8e-4 (w) 2.4 (b)
1.0 (w) 1.79 (b)
41
Summary, conclusions,

• Extraordinary advance, in the last decade, in
  numerical methods for (ultra)relativistic
  hydrodynamics, specially with RS/Sym HRSC methods

• Easy extension to (test) GRHD via local
  linearizations of the geometrical terms or local
  coordinate transformations (for RS HRSC methods
  Pons et al. 1998)

• Important advances in numerical RMHD (RS/Sym
  HRSC methods, also AV methods), however present
  numerical codes are less robust than in the
  purely hydro case

• Big impact in extragalactic jet research,
  specially parsec scale jets, superluminal sources
  and jet
• formation mechanisms

• Important advances in the understanding of the
  morphology and dynamics of large scale
  relativistic jets

• First simulations of superluminal sources
  (success of the relativistic shock-in-jet model).
  First steps in the combination of hydro
  relativistic electron transport radiation
  transfer codes

• First simulations of relativistic jet formation

• Numerical study of the non-linear regime of KH
  instabilities

• Still lacking

• RMHD sims of pc and kpc jets to elucidate the
  configuration and role of magnetic fields at
  these scales

• Jet formation mechanisms need further numerical
  study (no steady relativistic outflow yet found)
  

• Consistent simulation of all the jet components
  (thermal matter, high energy particles, radiation
  and magnetic fields) and their mutual interaction.