Gamma-Ray Burst Jets: dynamics and interaction with the progenitor star Davide Lazzati, Brian Morsony, and Mitch Begelman JILA - University of Colorado.

Gamma-Ray Burst Jets:

dynamics and interaction with the

progenitor star

Gamma-Ray Burst Jets:

dynamics and interaction with the

progenitor starDavide Lazzati, Brian Morsony, and Mitch

BegelmanJILA - University of Colorado

Davide Lazzati, Brian Morsony, and Mitch

BegelmanJILA - University of Colorado

Evidence for SN association

Evidence for SN association

SN2003dhStanek et al. 2003Hjorth et al. 2003

SN1998bwGalama et al. 1998

Phases of jet propagation

Phases of jet propagationConfined Jet Shock breakout

Shocked jet Unshocked jet

I: confined jetI: confined jet

Jet head propagates under ram pressure equilibrium

No mixing between shocked jet and star material

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).

Jet reacts to cocoon pressure with internal and ram pressure terms. Acceleration ~p-1/4.

Lazzati & Begelman 2005

I: confined jetI: confined jetIn 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

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pcocoon = pjet + 4 pjetΓ 2 sin[tan−1( dzdr⊥

)− tan−1( zr⊥)]

€

β j =ηΓ j

2

1+ ηΓ j2β h

€

ηj2 =

L jρ∗c

3Σ

z

r

II: Shock breakoutII: Shock breakoutIs the first radiative phase: hot non-relativistic material is released on the stellar surfaceRamirez-Ruiz et al. 2002

MacFadyen et al. 1999Zhang et al. 2003

III: Shocked JetIII: Shocked JetThe jet in this phase is heavily affected by the transversal collimation shocks.

IV: Unshocked JetIV: Unshocked JetThe evolution can be computed analogously to the confined jet geometry but now the cocoon pressure decreases with time.

€

dQ

dt= −ρ cocoonΣ

cs

€

pcocoon = pjet + 4 pjetΓ 2 sin[tan−1( dzdr⊥

)− tan−1( zr⊥)]

€

θ j =θ0

1+Kpcocoon

The opening angle of the jet grows

with time

Analytic vs. Numeric

Analytic vs. Numeric

Analytic vs. Numeric

Analytic vs. Numeric

Analytic vs. Numeric

Analytic vs. NumericCocoon pressure

and breakout time are very well reproduced.Jet opening angle works better for jet initially out of causal contact (due to hyper-relativistic approximations).Energy stored in the cocoon:

8x1050 vs. 9x1050

Analytic ResultsAnalytic Results

The break-out opening angle is smaller for more massive and large stars

A jet with initial opening angle of 10o and =10 is propagated through polytropic stars of varying mass and radius. WR

PopIII

Analytic ResultsAnalytic ResultsA jet with initial opening angle of 10o and =10 is propagated through polytropic stars of varying mass and radius. WR

PopIIIThe break-out time depends very mildly on the mass, so too the energy deposited into the star

Analytic ResultsAnalytic ResultsAssuming β=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:

movies

Numerical:

movies

Numerical ResultsNumerical Results

Numerical ResultsNumerical ResultsDifferent observers see GRBs dominated by a different phaseSmall angles are dominated by shocked jet.

Intermediate angles are dominated by unshocked jetLarge angles are dominated by cocoon

Numerical ResultsNumerical Results

Precursor

Dead times

X-ray flash

X-ray flash

SummarySummary 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 (β~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.

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 (β~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.