The Fireball Model and Internal Shocks

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The Fireball Model and Internal Shocks

• Connecting the Inner Engine (whatever that is) to
  the Afterglow

Brad Hagan
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General Outline

• Basics of Fireballs
• Radiation dominated era
• Matter dominated era
• Timescales and important radii
• Where does the variability come from?
• Shocks external vs. internal
• What internal shocks can tell us about the
  central engine

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What should you get out of this?

• Understand the general picture of the middle
  part of the GRB
• Be able to connect my talk with Brians on
  relativistic blast waves
• Know the relevant radii and where they come from
• Understand the timescales at work
• Be able to argue to your best friend as to why
  GRBs come from internal shocks
• Be aware of shortcomings and some challenges in
  understanding these processes

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Fireballs The Definition

• An optically opaque radiation plasma where the
  initial energy is much greater than its rest mass
• Plasma accelerates up to relativistic velocity,
  propelled by its internal energy
• The gained kinetic energy in the baryons and
  electrons gets converted into ??rays through
  internal shocks

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The General Picture
The Fireball is in this region
GRB
(not sure what this is)
(afterglow)
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Fireballs The Timeline

• Central Engine releases 1051 erg, (107 cm)
• Relativistic wind is radiation-dominated plasma,
  T r-1 internal energy accelerates the plasma
  ?? r
• Transition to matter-dominated wind baryons
  decouple and coast with constant ??(1010?cm)
• Temperature drops and the wind becomes optically
  thin (1013 cm)
• Internal collisions between shells with slightly
  different ? convert kinetic energy to radiation ?
  GRB (1012-14 cm)

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Deriving the Scaling Laws

• One can easily write down the relativistic
  conservation equations for baryon number density
  (?), energy density (e), and momentum density
  (?Pe?(4/3)e)
• Evaluate these along characteristics labeled by s
  (light cones ct - r s)
• Do radial derivatives along the characteristic
  (holding s constant)

Note c 1
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Scaling Laws (contd)

• Our assumptions
• Baryons, leptons, photons are highly coupled
  and move together
• This will break down when the soup becomes
  optically thin
• Rest-frame temp of radiation 1/r (cools as it
  expands)
• After a short time, the flow becomes highly
  relativistic
• The characteristics are then individual shell
  trajectories (they move at c)
• u (?2-1)1/2 ?, a large quantity
• Thus, the RHS (with ? in the denominator) can be
  set to zero to O(???)
• Then our governing equations become
• r2?????const., r2e3/4? const., r2(???????e??2
  const.
• Can be easily solved in the different regimes
  (matter- and radiation- domination)

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Radiation Dominated Regime

• Occurs when E/Mc2gtgt1
• Valid between r 107 and 109
• One can also see that from the scaling relations
  (assume egtgt??r2?????const., r2e3/4? const.,
  r2(???????e??2 const.
• So, we get the following result
• Note similarity to early universe
• An interesting result Tobsconstant

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Matter Dominated Regime

• The transition occurs when E/Mc2lt1 (that is, the
  fluid cools to the point where rest mass
  dominates the energy)
• This happens at about 109 cm
• Essentially, the internal energy isnt large
  enough to continue accelerating the baryons ?
  they coast with constant ?
• Scaling relations show that when eltlt???
• This is when shells start slamming into each other

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When does it become optically thin?

• The transition can occur if E0/mc2 ???is below
  ?thin (and we are)
• The radius at this time (Re, the emission radius)
  is
• Note ?f E0/mc2 ??
• Any radiation emitted before will not escape
• After this time, we need to be on the look-out
  for emission that we can see

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PART II

• Comparing the shock models and fitting the
  observed temporal variation

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How do we explain the temporal structure of a GRB?
?t
T

• Need to explain the long duration
• Need a mechanism for the rich structure that is
  consistent with causality, etc.
• T/?t 100
• What about the quiescent periods that
  occasionally occur?

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Relevant timescales

• Radial timescale Trad ?Re/2?e2c
• Angular timescale (due to relativistic beaming)
  Tang Re/2?e2c
• (since Re ? ?Re, TanggtTrad)
• Intrinsic duration T ??c OR Tang
• for an explosion, T Ri/c (lt1 second)
• for a wind, T can range from seconds to 10s of
  seconds
• Variation timescale ?t ??c T/100
• This must hold
• Two cases for the observed total duration
• Type 1 T Tang Re/2?e2c, if ??Re/2?e2
• Type 2 T ??c, if ??Re/2?e2

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Type 1 T Tang

• The shock is thin (??lt Re/2?e2)
• GRB is due to plowing into the ISM (giving rise
  to external shocks)
• Time signature comes from viewing the same shock
  at different angular positions
• Variability comes from broken spherical symmetry
  (a jagged shock)
• Relativistic beaming means that the observer
  zooms in on a small angular scale ???
• Thus, we need 100 variations on this small scale
  (angle 10-4)

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Problems with Type 1

• Might be able to get this with a tiny opening
  angle
• The angle we see is 1/? 0.01
• We see 100 subpulses ? it must be even narrower
  0.0001
• Too narrow!! Must be extremely cold (in rest
  frame) to prevent spreading
• Maybe the ISM that gets shocked is highly
  irregular ? no need for a narrow jet
• Extremely inefficient emitting regions must be
  tiny compared to the size of the shock
• Thus, energy output of the centralengine must be
  even LARGER
• This makes us uneasy
• Adding more emitting regionswill just smooth out
  the variations
• Peaks get wider as time goes on
• External Shocks are not the answer!!

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Type 2 T ??c

• Thick wind ????Re/2?e2
• T, the total length of time we see the GRB, is
  essentially the length of time the central engine
  operates
• Temporal structure comes from multiple shells
• Angular timescale becomes the pulse width because
  it smooths out all variation operating on shorter
  timescales
• Good news for people trying to figure out the
  central engine variations give a clue as to how
  the source emits energy
• Where does the GRB come from if not from an
  external shock?

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Internal Shocks!

• Shells assigned random Lorentz factors
• They collide in the matter-dominated regime (once
  its optically thin)
• R 2???, ? width of the shell
• Using ? ?????, this is approx. 1012 cm
• This radius corresponds to the optically thin
  region!
• How much energy is released?

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Simulated light curves
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Do models with Internal Shocks work?

• Simulated light curves look pretty good
• Efficiency could be a problem, but it could be as
  high as 60 (m??)
• Models still making post-dictions the
  distribution of ? had to be dialed a certain way
• Standard estimate of efficiency (Kumar 1999)
• Electrons are in equipartition with p, B-field
  ?1/3
• Radiated energy 1/3 of total
• Hydro efficiency 1/10

Kobayashi Sari 2001
?
1 efficiency
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What about external Type 2?

• Not possible!
• In brief, the emission radius, Re, will always be
  too large (i.e. larger than ?/?e2) ? T Tang
• Re decreases as ? increases, but only to a
  point eventually a reverse shock develops
  that gives rise to an actual ? that is less
  than the incoming value
• Kind of complicated

Piran (1999)
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Internal shocks tell us something

• We often observe quiescent periods (10 seconds)
  between bursts
• If we believe that all GRBs are due to the same
  mechanism, this rules out some ideas for GRB
  central engines (that involve explosions)
• Neutron star ? Black hole
• Neutron Star ? Strange star
• Vacuum instability
• Evaporating mini-black holes

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The End