Transcript Magnetohydrodynamic Effects in Gamma

Magnetohydrodynamic Effects in
(Propagating) Relativistic Ejecta
Yosuke Mizuno
Center for Space Plasma and Aeronomic Research
University of Alabama in Huntsville
Collaborators
B. Zhang (UNLV), B. Giacomazzo (MPIG, AEI),
K.-I. Nishikawa (NSSTC/UAH), P. E. Hardee (UA), S. Nagataki (YITP, Kyoto Univ.),
D. H. Hartmann (Clemson Univ.)
Mizuno et al. 2009, ApJ, 690, L47
High Energy Phenomena in Relativistic Outflows II, Oct. 26-30, Buenos Aires
Role of Magnetic Field in Propagating
Relativistic Jet/Ejecta
• The magnetic fields play an important role in relativistic
jets/ejecta (e.g., jet formation)
• The degree of magnetization (quantified by s; magnetic to kinetic energy
flux ratio) is poorly constrained by observations.
• GRB afterglow modeling indicates GRB ejecta are more
magnetized than the ambient medium (e.g., Zhang et al. 2003, Gomboc et
al. 2008)
• possibly important dynamic role for magnetic fields in GRB jet/ejecta
• Useful diagnostic for jet magnetization can be obtained from
interaction between decelerating jet/ejecta and ambient medium
• Addition of magnetic field in the jet changes the condition for formation
and strength of a reverse shock (RS) (e.g., Kennel & Coroniti 1984)
Role of Magnetic Field in Propagating
Relativistic Jet/Ejecta (cont.)
• Analytical studies of the deceleration
of a GRB flow with magnetic field
(Zhang & Kobayashi 2005) suggest some
new behavior that does not exist in
pure hydrodynamic model (e.g., Sari &
Piran 1995)
• However, a consensus as to the
conditions for the existence of the RS
has not yet been achieved (e.g., Zhang
& Kobayashi 2005; Giannios et al.
2008)
GRB blast wave model
Purpose of This Study
• We investigate the interaction between magnetized
relativistic jet/ejecta and unmagnetized external
medium
• For GRB case, the interaction with external medium
takes place after acceleration, collimation, and prompt
emission phase are over
• A Riemann Problem is solved both analytically and
numerically over a broad range of magnetization
(s=magnetic to kinetic energy flux ratio).
The Riemann Problem
• Consider a Riemann problem consisting of two uniform initial states
• Right (external medium): cold fluid with constant rest-mass density and
essentially at rest.
• Left (jet/ejecta): higher density, higher pressure, relativistic velocity
normal to the discontinuity surface
• To investigate the effect of magnetic fields, put toroidal (By) components
of magnetic field in the jet region (left state)
• Typical case
–
–
–
–
–
Density: rho_L=100.0, rho_R=1.0
Pressure: p_L=1.0, p_R=0.01
Velocity: Vx_L=0.995c (g=10), Vx_R=0.0c
Adiabatic index: 4/3
Calculation box:0.8-1.2 (transition at 1.0)
• To solve the Riemann problem, RMHD exact solution calculation code
developed by Giacomazzo & Rezzolla (2006) is used
Ejecta-Medium Interaction
s: magnetization
parameter =Emag/Ekin
In Riemann profile,
S: shock, C: contact discontinuity
R: rarefaction wave
• s=0.1 (black)
• SCS profile, reverse shock (RS) propagate
in the ejecta
• s=1.0 (red)
• SCS profile, RS becomes weaker and
propagate faster than s=0.1 case
• These features are expected from analytical
work (Zhang & Kobayashi 05)
• s=10.0 (green)
•RCS profile, reverse rarefaction wave (RR)
propagate in the ejecta
• Density, pressure in the ejecta decrease
• Flow velocity increases (accelerated)
• s=20.0 (blue)
• RCS profile, jet is more accelerated
• s=2.7 (yellow)
• Critical sigma value, neither reverse shock
nor a rarefaction wave is established
Solid: Gas pressure
Dashed: Mag pressure
density
Lorentz factor
Physical Conditions for Reverse Shock
or Magnetic Acceleration
Four regions:
(1) unshocked medium, (2) shocked medium,
(3) shocked ejecta, (4) unshocked ejecta
Based on relativistic shock jump conditions with
adiabatic index G=4/3
and
Thermal pressure generated in the forward shock region
• Constant speed across the contact discontinuity, g2=g3
• Relation between gas pressure and internal energy, p2=u2/3
The condition for existence of the reverse shock/ reverse rarefaction wave
pressure balance between forward shock (pgas, 2) and ejecta (pmag, 4)
Reverse shock: pgas,2 > pmag, 4; Rarefaction wave: pgas, 2< pmag, 4
Critical sigma value
Dependence on magnetization parameter
Pressure of shocked flow
Gas pressure in FS to magnetic
pressure in flow ratio
RS regime
RR regime
Lorentz factor of
propagating RS or
RR to Alfven
Lorentz factor
ratio
Shocked Lorentz
factor
Initial magnetization
• Magnetization, s in flow increases,
pressure ratio decreases with s and
makes smooth transition from RS to
RR regime
• Transition of RS to RR
s~0.7, 2.7, 10.6 in gL=5, 10, 20
• The critical s increases with gL, so
that a RS can exist in the high-s
regime if flow Lorentz factor is
sufficiently large
• Another condition for a RS: shock
propagation speed in the fluid frame is
higher than the speed of the Alfven
wave, g’RS,RR > g’A
• pFS/pB and g’RS,RR/g’A reach unity at
the same critical s
• Two RS conditions have intrinsically
the same physical origin (see Giannios
et al. 2008)
Terminal Lorentz factor
• The terminal Lorentz factor after magnetic acceleration can be
estimated by pressure balance between the forward shock and
shocked ejecta region
• From the definition of magnetized parameter, s=B2/gr,
this condition becomes
•This analytical estimation is good agreement with the exact
solution of the Riemann problem
Magnetic Acceleration Efficiency
•A jet with a higher initial
Lorentz factor reaches a
higher terminal Lorentz factor
•But a lower initial flow
Lorentz factor experiences a
higher acceleration efficiency
Terminal Lorentz factor
Acceleration Efficiency
RS regime
RR regime
Acceleration efficiency
Initial flow Lorentz factor
+: analytical estimation
Discussion
• The observed paucity of bright optical flashes in GRBs (e.g.,
Roming et al. 2006) may be attributed to highly magnetized ejecta
(if optical flashes are related the emission from RS)
• The magnetic acceleration mechanism suggests that s and g
are not independent parameters at the deceleration radius.
• For high-s flow, ejecta would experience magnetic
acceleration at small radii, before reaching the coasting
regime; the coasting Lorentz factor (initial Lorentz factor for
the afterglow) = terminal Lorentz factor (same mechanism also
seen in Mimica et al. 2009)
• Our results suggest the possibility of magnetic acceleration
occurring where highly magnetized jet material overtakes
more weakly magnetized jet material. It may be related to
variable emission observed in some TeV blazars which
suggests very high Lorentz factor in AGN jets (Aharonian et al.
2007)
Summery
• We
have investigated the interaction between magnetized
relativistic jet/ejecta and unmagnetized static ambient medium
• We confirm that the reverse shock propagating in the flow
becomes weak when the jet is magnetized
• We found the new acceleration mechanism by the rarefaction
wave propagating in the jet/ejecta when the flow is strongly
magnetized
• Critical magnetization for new acceleration mechanism depends
on the initial jet velocity;
– For the magnetic acceleration the jet with higher initial Lorentz factor
needs strong magnetization
• Terminal Lorentz factor depends on the magnetization of
jet/ejecta
• Recently Mimica et al. (2009) have performed 1D RMHD
simulations of radially expanding magnetized GRB ejecta and
found same acceleration mechanism has occurred when GRB
ejecta is highly-magnetized.