Disintegrating Bullet Model for Null Periods in GRBs
Almog Yalinewich - RandoAstro -13.2.20
Also experiments!
If you've seen one GRB,
you've seen just one GRB
null periods
LGRB - SN association
SN 1998bw
GRB 980425
Collapsars
Collapsars
Illustration
Acceleration
Rayleigh Taylor Instability
Disintegrating Bullet Model
Mathematical Model
Projectile motion
Instability evolution
Newtonian Projectile Motion
Equation of motion
Velocity pressure relation? Riemann invariants
Isentropic relation
Sound speed
Riemann Invariants
Acoustic relation
Extrapolation
Ideal gas
Rayleigh Taylor Growth Rate
High k - grow fast and saturate fast
Low k - grow slow
optimal k determined by bullet width
Bullet Width Evution
x
p
contact with pressure behind
Bullet expands adiabatically after the first shock
Breakup Time
but in this case this is independent of time
Either happens in the very beginning, or never
Perturbation growth
Enter Relativity!
Relativistic Riemann Invariant
Even in spherical geometry
Acceleration Transformation
Motion with uniform acceleration
Lorentz boost to instantaneously comoving frame
Rest frame quantities
Opening Angle
Relativistic beaming
Wide jets
Narrow jets
Instability Growth
Relativistic inertia effect pm growth rate
Breakup time
Grows with time!
Application
Using typical values, breakup time in the lab frame
Observer time
disintegrating bullet
By almog yalinewich
disintegrating bullet
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