Transcript GRB jets and their interaction with the progenitor star

Gamma-Ray Burst Jets:
dynamics and interaction
with the progenitor star
Davide Lazzati, Brian Morsony,
and Mitch Begelman
JILA - University of Colorado
Evidence for SN association
SN1998bw
Galama et al. 1998
SN2003dh
Stanek et al. 2003
Hjorth et al. 2003
Phases of jet propagation
Confined Jet
Shocked jet
Shock breakout
Unshocked jet
I: confined jet
Lazzati & Begelman 2005
Jet reacts to cocoon pressure with
internal and ram pressure terms.
Acceleration ~p-1/4.
Jet head
propagates
under ram
pressure
equilibrium
Cocoon is over-pressured and drives shock
into stellar material. Shock expands under
Kompaneets approximation
vsh~(pcocoon/star)1/2. Cocoon cools
adiabatically (relativistic EOS).
No mixing
between shocked
jet and star
material
I: confined jet
In a monolithic jet the pressure
scales with working surface
P~-1/2
Simulations show the monolithic
approximation to be inaccurate. A
boundary layer develops. Jet free
inside, the velocity is parallel to the
boundary in the layer
z
[ ( )
pcocoon  pjet  4 pjet sin tan
2
r

j 
 2j
1 
2
j
h
1
( )]
dz
1 z
 tan
dr
r
 
2
j
Lj
c 3 
II: Shock breakout
Is the first radiative
phase: hot nonrelativistic material is
released on the stellar
surface
Ramirez-Ruiz et al. 2002
MacFadyen et al. 1999
Zhang et al. 2003
III: Shocked Jet
The jet in this phase is heavily
affected by the transversal
collimation shocks.
IV: Unshocked Jet
The evolution can be computed
analogously to the confined jet
geometry but now the cocoon
pressure decreases with time.
dQ
cocoon

dt
cs
2
1 dz
1 z
pcocoon  pjet  4 pjet sin tan
 tan
dr
r
[ ( )


j 
( )]
0
1 Kpcocoon
The opening angle of the
jet grows with time
Analytic vs. Numeric
Analytic vs. Numeric
Analytic vs. Numeric
Cocoon pressure and
breakout time are very
well reproduced.
Jet opening angle
works better for jet
initially out of causal
contact (due to hyperrelativistic
approximations).
Energy stored in the
cocoon:
8x1050 vs. 9x1050
Analytic Results
A jet with initial
opening angle of
10o and =10 is
propagated
through polytropic
stars of varying
mass and radius.
PopIII
The break-out
opening angle is
smaller for more
massive and large
stars
WR
Analytic Results
A jet with initial
opening angle of
10o and =10 is
propagated
through polytropic
stars of varying
mass and radius.
The break-out time
depends very
mildly on the
mass, so too the
energy deposited
into the star
PopIII
WR
Analytic Results
Assuming =0.3 is
a good
approximation in
most cases.
As a consequence
massive compact
stars will NOT
explode due to the
jet propagation
GRBs without SN?
Exploding Stars
Non exploding (no SN?)
Numerical
: movies
Numerical
: movies
Numerical Results
Numerical Results
Different observers see
GRBs dominated by a
different phase
Small angles are
dominated by shocked
jet.
Intermediate angles are
dominated by
unshocked jet
Large angles are
dominated by cocoon
Numerical Results
Precursor
X-ray flash
Dead times
X-ray flash
Summary
 A simple pressure balance explains some features of
the jet/cocoon/star interaction and allows quantitative
computations
 Jet can propagate fast in very massive stars if
compact (~0.3 robust). PopIII GRBs?
 Jet propagation takes place in 4 phases: 3 radiative
 Cocoon = Precursor but we do not see shocked or
un-shocked jet. Different observers are however
dominated by different phases.
 Even a constant luminosity at the base can produce
very complex time histories at the stellar surface.