GRB

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GRB

• Theory and observations

Useful reviews Waxman astro-ph/0103186 Ghisellini
astro-ph/0111584 Piran astro-ph/0405503 Meszaros
astro-ph/0605208 Useful links http//www-astro.ph
ysics.ox.ac.uk/garret/teaching/ http//www.cv.nra
o.edu/course/astr534/
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Progenitor Long GRBs Collapsar model Mgt30 M?
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Modelli per un GRB
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Leading model for short GRBs Progenitors
NS-NS merging primordial DNS
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Modelli per un GRB
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Spectrum well described by a broken power
law Band approximation
E? EltE0

• Nontermal Spectrum N(E) ?

E? EgtE0
BATSE (20 keV-1 MeV) 0.1 MeV lt E0lt 1 MeV ?? -2, ?
-1, -0.5
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The compactness problem

• ?t 1-10 ms

Compact sources R0? c ?t 3 107 cm

• Cosmological sources (D3 Gpc) L?
  fD21052 erg/s

R of our galaxy 30 kpc extragalactic objects
??1 ??2 (mec2)2 ??? ee-
??? ?p R0n??T?TL?/4?R0c ??1015
?? 1 MeV
?p fraction of photons above the thereshold of
pair production
?T6.25x10-25cm2
Optical depth ??? (??? ee-) gtgt1
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Implications The fireball
How can the photons escape the source?
Relativistic motion A plasma of e e- ?, a
Fireball, which expands and accelerate to
relativistic velocities, optical depth reduced by
relativistic expansion with Lorentz factor ?

• The reasons
• In the comoving frame ? below the thereshold for
  pair production ????/? ??1 ??2
  (mec2)2
• Number of photons above the threshold reduced by
  ?2(? -1) (?2 high-energy photon index)
• Emitting region has a size of ?2R0

??? reduced by a factor ? 22? ?? 6. ??? lt 1 for
? 100
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Propagation effect
Zhang Mészàros, IJMPA A19, 2385 (2004)
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• Finally,
• dt, comoving time of the shell

where D is the Doppler factor.
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Fireball evolution

• Fireball expands and cools pairs annihilate and
  photons may escape, quasi-thermal emission
  against observations!!!
• Therefore a small barion loading (10-8M?) is
  needed and the radiation energy is converted to
  kinetic energy.

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The Lorentz factor

• As the fireball shell expands, the baryons will
  be accelerated by radiation pressure.
• The fireball bulk Lorentz factor increases
  linearly with radius.
• ?0?? ? E/M0c2, M0 total baryon mass of the
  fireball

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Fireball Model Prediction vs. Postdiction

• Prediction (from Latin prae- before dicere
  to say) A foretelling on the basis of
  observation, experience or scientific reasoning.
• Postdiction (from Latin post- after dicere
  to say) To explain an observation after the
  fact.
• If your model predicts all possible outcomes,
  it is not a prediction. This merely states that
  you can not constrain the answer with your
  current model.

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Fireball Model
From IXth International Symposium on
Particles, Strings and Cosmology Tata Institute
of Fundamental Research, Mumbai, Inda Tsvi
Piran http//theory.tifr.res.in/ pascos/Proceedin
gs/Friday/ Piran/index.html
The Fireball model Assumes a relativistic
Outburst and works With a variety of
Mechanisms. We rely heavily on A review by
Tsvi Piran.

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• The Fireball Model

Relativistic Particles ?gt100 or Poynting flux
compact source
107 cm
Goodman Paczynski
Shemi Piran, Narayan, Paczynski
Piran Meszaros Rees
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Supernova Remnants (SNRs) - the Newtonian Analogue

• 10 solar masses are ejected at 10,000 km/sec
  during a supernova explosion.
• The ejecta is slowed down by the interstellar
  medium (ISM) emitting x-ray and radio for 10,000
  years.

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External Shocks

• External shocks are shocks between the
  relativistic ejecta and the ISM - just like in
  SNRs. Can be produced by a single explosion.

Recall, the first GRB model (Colgate 1968)
Invoked SN Shocks to power GRBs!
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External Shock Predictions For GRBs

• The burst of gamma-rays should be accompanied by
  a burst of optical photons (within 1 second of
  the explosion).
• Based on these predictions, fast slewing optical
  telescopes were developed (e.g. ROTSE, LOTUS).

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GRB070228 Optical Burst Seen! But observed
much later than expected. This spelled the
beginning of the end for the external shock
model!(Although some claimed this as a
prediction!)
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A NO GO THEOREM

• External shocks cannot produce a variable light
  curve!!!
• (Sari Piran 97)

Fireball Theorists then found a lot Wrong with
the external shock model!
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Time to Revise the Theory

• Gamma-rays and Afterglow arise from different
  sources
• Birth of the Internal Shock Model

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Internal Shocks Shocks between different shells
of the ejected relativistic matter

• dTR/cg2 d/c D/cT
• The observed light curve reflects the activity of
  the inner engine. Need TWO time scales.
• To produce internal shocks the source must be
  active and highly variable over a long period.

dT
T
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Internal Shocks ?Afterglow

• Internal shocks can convert only a fraction of
  the kinetic energy to radiation
• (Sari and Piran 1997 Mochkovich et. al.,
  1997 Kobayashi, Piran Sari 1997).
• It should be followed by additional emission.
• It ain't over till it's over (Yogi Berra)

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Gamma-Ray Burst 4 Stages

• 1) Compact Source, Egt1051erg
• 2) Relativistic Kinetic Energy
• 3) Radiation due to Internal shocks GRBs
• 4) Afterglow by external shocks
• The Central Compact Source is Hidden

Plus burst of optical emission!
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The Internal-External Fireball Model
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THE FIREBALL MODEL PREDICTED GRB AFTERGLOW (late
emission in lower wavelength that will follow the
GRB)
Postdicted

• Rhodes Paczynksi, Katz, Meszaros Rees,
  Waxman, Vietri, Sari Piran

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Fireball Model History

• External Shock model relativistic ejecta from
  very energetic explosion shocks with the
  interstellar medium. Synchrotron radiation in
  shock produces gamma-rays and optical burst.
• Optical burst appeared late theorists move to
  internal shocks to explain gamma-rays.

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How the energy is dissipated

• In order to have some emission from the firebal
  the energy must be dissipated somehow.
• Observed GRB produced by dissipation of the
  kinetic energy of this relativistic expanding
  fireball regardless the nature of the underlying
  source.
• Possible dissipation mechanism Internal shocks
  collisions between different parts of the plasma

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The internal/external shock scenario
Rees Meszaros 1992, 94
ISM
? 1016cm
? 1013cm
? ray phase
X-ray, Opt.-IR, Radio
Efficient! Guetta Spada Waxman 2001
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The radiation mechanisms
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The efficiency of internal shocks

• Shells collide and merge in a single shell with

The conversion efficiency of kinetic energy into
internal energy
To get high efficiency ?1gtgt ?2 and M1M2 only a
fraction ?e radiated max 20 can be radiated
(Guetta et al. 2001) But the total afterglow
energy burst energy! (Freedman and Waxman 2001)
Problem 1 Low efficiency of internal shocks
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Internal shock radius

Lets assume that a faster shell (2) impacts on a
slower the leading shell (1)
If ?ttv is the average interval between two
pulses (interval between shells ejection)
Emission properties determined by ris
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Light curves from internal shocks
Rapid variability and complexity of GRB
lightcurves result of emission from multiple
shocks in a relativistic wind
?t (interval between ejected shells) determines
the pulse duration and sepration
IS reproduce the observed correlation between the
duration of the pulse (tp) and the subsequent
interval (?tp)
Numerical simulations reproduce the observed
light curves
(Spada et al. 2000)
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Spectrum of the prompt emission
Prompt emission observed has most of energy in
0.1-2 MeV Generic phenomenological photon
spectrum a broken power law

• Internal shocks are mildly relativistic, ?sha
  few, particle acceleration in subrelativistic
  shocks. Electrons are accelerated to a power law
  with energy distribution

with p2 and ?egt ?m
Electrons accelerated in magnetic field
synchrotron emission? i.e. emission from
relativistic electrons gyrating in random
magnetic fields
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Fermi acceleration at shock

• Suppose to have a shock wave propagating in a
  medium where energetic particles are already
  present.
• Shock is a wave propagating with vgtvsound
• Density after (downstrem) and before (upstream)
  the shock is ?2/?1?1/?-1
  where ? is the politropic index of the gas. For a
  gas completely ionized ?5/3 and ?2/?14, v1/v24

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Shocks
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Shocks
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Fermi acceleration at shocks
Uvu

• e-
• Unshocked gas vd1/4vu

Hot shocked gas vu
Consider the case of a shock propagating into
cold gas at speed vu. In the shock frame we see
the unshocked gas ahead of us approaching at
speed vu and the hot shocked gas streaming behind
us at speed vd1/4 vu. Consider now electrons
initially at rest in the unshocked gas frame.
They see the shock approaching at vu but they
also see the hot shocked gas approaching at 3/4
vu. As they cross the shock they are accelerated
to a mean speed of 3/4 vu, as viewed from the
frame of the unshocked gas, and are also
thermalized to a high temperature. The clever
part is next consider what would happen if, as a
result of its thermal motion, an electron is
carried back over the shock front. With respect
to the frame it has just come from the shocked
gas frame it is once again accelerated by 3/4 vu.
The particle gain energy from the gas behind the
shock. Let us say the fractional change in
kinetic energy at each crossing is ß. After n
crossings, a particle with initial energy E0 will
have energy E E0ßn. The particles will not
continue crossing the shock indefinitely the net
momentum flux of the shocked gas downstream will
carry them away in due course. So let us call the
probability of remaining in the shock-crossing
region after each crossing P . Then after n
crossings there will be N N0Pn of the original
N0 electrons left.
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Fermi acceleration at shocks
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Fermi acceleration at shocks

• Now we want to find k-1logP/log?

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Fermi acceleration at shock
1 Pre-shock
2 Post-shock
vu
vd
p,E
X0
Vvu-vd velocity of shocked material in the
particle frame
In 2 E?(EpVcos?) p?(pcos?VE/c2)
In 1 E?2(E2 vVcos?/c2V2/c2)
Energy gain lt?E/Egt?V/c Energy distribution
dN/dEk E-p p2
N dominated by low energy particles but Etot
dominated by high energy particles.
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Synchrotron emission

• Both prompt emission and afterglow emission are
  clearly non-thermal, and most natural process is
  synchrotron emission, i.e. emission from
  relativistic electrons gyrating in random
  magnetic fields.
• For an electron with comoving energy ?emec2 and
  bulk Lorentz factor ? the observed emission
  frequency is
• ???e2(eB/2? mec)

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Motion of a particle in a magnetic field

• Gyro radiation is produced by electrons whose
  velocities are much smaller than the speed of
  light vltltc.
• Mildly relativistic electrons(kinetic energies
  comparable with rest massXc2) emit cyclotron
  radiation.
• Ultrarelativistic electrons (kinetic energies gtgt
  rest massXc2) produce synchrotron radiation.

a v v v-
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Motion of a particle in a magnetic field
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Synchrotron emission
We can use Larmor's formula to calculate the
synchrotron power and synchrotron spectrum of a
single electron in an inertial frame in which the
electron is instantaneously at rest, but we need
the Lorentz transform of special relativity to
transform these results to the observer frame.
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Synchrotron emission
me?
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Synchrotron emission
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Synchrotron spectrum

• Our next problem is to explain how the
  synchrotron mechanism can yield radiation at
  frequencies much higher than ??L/?. To solve it,
  we first calculate the angular distribution of
  the radiation in the observer's frame.
• In the non relativistic case P goes like sin2?,
  where ? is the angle between the direction of the
  acceleration and the direction of the photons.
• In the relativistic case, relativistic
  aberration causes the Larmor dipole pattern in
  the electron frame to become beamed sharply in
  the direction of motion as v approaches c. This
  beaming follows directly from the relativistic
  velocity equations implied by the differential
  form of the Lorentz transform. For an electron
  moving in the x direction

In the y direction perpendicular to the electron
velocity, the velocity formula gives
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Synchrotron spectrum
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Synchrotron spectrum
Relativistic beaming transforms the dipole
pattern of Larmor radiation in the electron frame
(dotted curve) into a narrow searchlight beam in
the observer's frame. The solid curve is the
observed power pattern for ?5. The observed
angle between the nulls of the forward beam 2/
?, and the peak power gain 2 ?. For example, a
10 Gev electron has ?20000 so 2/? 20 arcsec!
The observer sees a short pulse of radiation
emitted during only the tiny fraction
of the electron orbit, when the electron is
moving directly toward the observer.
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Synchrotron spectrum
t1 1/?
t2
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Synchrotron spectrum
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Synchrotron spectrum
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Spectrum Power Law Self Absorption
Extrapolating the power law at low frequency the
energy density would will increase until a
thermodinamic equilibrium will set, I.e. energy
equipartition 3/2KT?mc2 . The electron
temperature will be proportional to ? and
?(?c/?L)1/2 and therefore at each frequency
there will be a temperature T (?c/?L)1/2 . Lets
define the brightness temperature TbFc2/ ?2,
the temperature for which if F is given by the RJ
formula (FKT?2) TTb. But we are in this
situation and therefore the spectrum at low
frequency is the RJ spectrum. The difference with
the BB is that in the BB Tconst, while in this
case T (?c/?L)1/2 and therefore F ? 5/2.
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Spectrum of the prompt emission
Characteristic frequency of synchrotron emission
is determined by ?m and B, Ebh?mh??m2eB/mec
The strength of the magnetic field is unknown,
but its energy density B2/8? is a fraction ?B
of the internal energy.
B1016-17 G more than a magnetar
As observed!
ris
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GRBs 2 additional Constraints with n(ge)
gge2qeB/(2pmec) Below some frequency, we are
below the minimum electron Lorentz
factor gmee(p-2)/(p-1) mp/meg Above a critical
frequency, the electron loses a significant
fraction of its energy to radiation gc6pmec/(sTg
B2t)
Sari, Piran, Narayan 1998
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GRBs 2 phases gmgtgc All the electrons cool
down to gc fast cooling. gcgtgm Only
electrons with gegtgc can cool slow cooling.
Sari, Piran, Narayan 1998
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Time Evolution
(17Et)1/4/ (4pmpnc)1/4

• R(t)
• g(t)

adiabatic
(4ct/L)1/7L
radiative
Sari, Piran, Narayan 1998
(17E)1/8/ (1024pmp nc5t3)1/8
adiabatic
(4ct/L)-3/7
radiative
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Time Evolution
nc2.7x1012eB-3/2E52-1/2n1-1td-1/2Hz
nm5.7x1014eB1/2ee2E521/2td-3/2Hz
Fn,max1.1x105eB1/2E52n11/2 D28-2mJy
Sari, Piran, Narayan 1998
nc1.3x1013eB-3/2E52-4/7g24/7
n1-13/14td-2/7Hz
nm1.2x1014eB1/2ee2E524/7g2-4/7
n1-1/14td-12/7Hz
Fn,max4.5x103eB1/2E528/7n15/14
g2-8/7D28-2td-3/7mJy
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The Early Afterglow and the Optical Flash

• The late afterglow observations confirmed
  relativistic motion.
• But what is the value of g during the GRB
  phase?
• 100 lt g0 E0/M0 lt 105
• dirty clean
• This could be tested
• by early afterglow
• observations (Sari
• Piran Rome, Oct 1998
• Astro-ph/11/1/1999)

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The Internal-External Fireball Model
g-rays
Internal Shocks
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Optical Flash Revisited

• Do internal shocks also predict prompt bursts?

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Predictions of the Optical Flash
Depending upon the Exact details of the
Explosion (width of Shock, structure of
Internal shocks in Addition to all of the Many
Fireball free Parameters)
Sari Piran 1999
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The Parameter space allowed for Optical Flashes
Sari Piran 1999
The amount of energy In the optical flash
Varies over many Orders of magnitude. Predictio
n depending Upon the model, you will/will not
see the flash.
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GRB 990123 - ThePrompt Optical Flash

• ROTSEs detection of a 9th magnitude prompt
  optical flash.

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Conclusions

• Internal Shocks reproduce the prompt ?-ray
  temporal structure but low efficiency problem
• Theoretical open questions on the process of the
  behaviour of the shocks, particle acceleration
  and generation of strong B
• Determination of ?b,?e, ?p that are free
  parameters of the model, still ot clear the
  physics that determines these parameters.

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Summary of GRB models
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Fireball Model - Summary

• Thusfar, the fireball model has made very few
  true predictions
• Current Favorite form of the Fireball model uses
  internal and external shocks.

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Particles in a B-field radiate

• Relativistic Particles
• Psynchrotron 2q2/3c3 g4 q2B2/(g2m2c2)vperp2
• 2/3 r02cbperp2g2B2
• where r0e2/mc2
• Psynch4/3sTcb2g2B2/(8p)
• where sT8pr02/3 is the Thompson Cross-Section

B
ltbperp2gt2b2/3
Isotropic velocities
vpar
vperp
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Fireball Model - Summary

• Basic Fireball model simple Relativistic shocks
  with synchrotron inverse Compton emission
• Internal Shocks produce optical burst and
  gamma-rays, External Shocks produce afterglow
• Jets alter the spectra in an observable way.

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Jets Make a Sharp Break in the light curve
synch emission does not include the effects of
cooling.
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Observations place several constraints on the
Engine!

• Few times 1051 erg explosions (few foe)
• Most of energy in gamma-rays (fireball model
  works if explosion relativistic)
• Rapid time variability
• Duration ranging from 0.01-100s
• Accompanied by SN-like bursts
• Occur in Star Forming Regions
• Explosion Beamed (1-10 degrees)

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With the fireball model, these constraints are
strengthened!

• Relativistic factors above 100!
• Some explosions must occur in windswept media
• Some (all?) explosions are jets

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GRB Engines

• Energy sources and conversion on earth and in
  astrophysics
• Variability constraints Compact object models
• With observational constraints, models now fall
  into two categories
• I) Black hole accretion disk models (compact
  binary merger, collapsar)
• II) Neutron Star Models (magnetar, supranova)

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Energy Sources What Powers These Explosions?
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Energy Source Gravitational Potential Energy
Hydroelectric Power
Energy from Falling Water Drives Turbines!
1-2000 MegaWatts
Hoover Dam - Arizona/Nevada
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Nuclear Energy
Diablo Canyon, CA
Breaking Bonds Within the Atom 1) Fission
1,000 MWatts
Large Atom (e.g. Uranium) Captures an Electron
Causing It to Become Unstable and Break
Apart. Some Mass is Converted to Energy
EMc2
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Nuclear Energy
II) Fusion Combining Atoms To Form A Larger
Atom Can Also Release Energy!
Atomic Bomb Can Be Fusion or Fission
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Energy Conversion
Energy released through gravitational potential,
chemical, or nuclear sources must be converted
into useful energy. Useful Electricity on
Earth (to Most of Us) Explosion
Energy (to the Astronomy Observer) This usually
requires a mediator something to transport
the energy Magnetic Fields e.g. a
Dynamo Radiation e.g. Photons (light), Neutrinos
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MagneticDynamo
Water (Accelerated by Gravity Or Thermal
Pressure) Spins Large Magnets. The Motion Of
the Magnets Drives an Electric Current --
Electricity!
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Radiation
Photons (Light) or Neutrinos Can Transport Energy
Nuclear Energy Released in the Sun Must Make Its
Way Out of the Sun Via The Transport of Light or
Neutrinos.
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Energy Sources

• Chemical rarely important in astrophysics
• Nuclear Physics Stars, Type Ia Supernovae,
  X-ray Bursts
• Gravitational Potential Energy All other
  supernovae, X-ray Binaries, Pulsars (neutron star
  spin arises from potential energy) and, for most
  theories, GRBs!

Garcia-Senz et al. 1999
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Energy Sources
Helium Detonation on NS

• Chemical rarely important in astrophysics
• Nuclear Physics Stars, Type Ia Supernovae,
  X-ray Bursts
• Gravitational Potential Energy All other
  supernovae, X-ray Binaries, Pulsars (neutron star
  spin arises from potential energy) and, for most
  theories, GRBs!

Zingale et al. 2001
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Energy Sources

• Chemical rarely important in astrophysics
• Nuclear Physics Stars, Type Ia Supernovae,
  X-ray Bursts
• Gravitational Potential Energy All other
  supernovae, X-ray Binaries, Pulsars (neutron star
  spin arises from potential energy) and, for most
  theories, GRBs!

Fryer Heger 1999
87
Energy Sources

• Chemical rarely important in astrophysics
• Nuclear Physics Stars, Type Ia Supernovae,
  X-ray Bursts
• Gravitational Potential Energy All other
  supernovae, X-ray Binaries, Pulsars (neutron star
  spin arises from potential energy) and, for most
  theories, GRBs!

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Energy Sources

• Chemical rarely important in astrophysics
• Nuclear Physics Stars, Type Ia Supernovae,
  X-ray Bursts
• Gravitational Potential Energy All other
  supernovae, X-ray Binaries, Pulsars (neutron star
  spin arises from potential energy) and, for most
  theories, GRBs!

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Energy Sources

• Chemical rarely important in astrophysics
• Nuclear Physics Stars, Type Ia Supernovae,
  X-ray Bursts
• Gravitational Potential Energy All other
  supernovae, X-ray Binaries, Pulsars (neutron star
  spin arises from potential energy) and, for most
  theories, GRBs!

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GRB Energy Sources
Energy Needed 1052 erg Of useful energy (not
leaked Out in neutrinos or Gravitational waves
or Lost into a black hole)! Most GRB Models
invoke Gravitational potential energy As the
energy source. Collapse to a NS or
stellar Massed BH most likely source
E G M2/r 1-10 solar masses 3-10 km
E1053-1054 erg Allowing a 1-10 Efficiency!
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Gamma-Ray Burst Durations
Two Populations Short 0.03-3s Long
3-1000s Possible third Population 1-10s
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Burst Variability
Not only must any model Or set of models
predict A range of durations, But the bursts
must also Be rapidly variable!
Burst Variability on the lt10-100 Millisecond
level
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Durations and Variabilities
Variability size scale/speed of
light Again, Neutron Stars and Black Holes
likely Candidates (either in an Accretion disk
or on the NS surface). 2 p 10km/cs .6 ms cs
1010cm/s
NS, BH
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Durations and Variabilities
Duration Rotation Period / Disk Viscosity (a
0.1-10-3) Period 2 pr3/2/G1/2MBH1/2
.3 ms near BH surface Duration for
small disks 3-300ms
NS, BH
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Harnessing the Accretion Energy
Mechanism I Neutrinos from hot disk annihilate
Above the disk Producing a Baryon-poor, High-
energy jet
Mechanism II Magnetic fields are Produced by
Differential rotation In the disk. This
Magnetic field produces a jet.
Accretion Disk
Details Lecture 5
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Neutrino Driven Jets Neutrinos from accretion
disk deposit their energy above the disk. This
deposition can drive an explosion.
Densities above 1010-1011 g cm-3 Temperatures
above a few MeV
Disk Cools via Neutrino Emission
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Neutrino Driven Jets
e,e- pair plasma
Neutrino Annihilation
Scattering
Absorption
Densities above 1010-1011 g cm-3 Temperatures
above a few MeV
Disk Cools via Neutrino Emission
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Neutrino Summary

• Critical Densities for most-likely accretion
  disks 104-108 g/cm3
• For Collapsars type I, this corresponds to black
  hole masses of 10-25 Msun and delays between
  collapse and jet of 30-300s. Does the
  neutrino-driven Collapsar type I model work?
• Alternatives magnetic fields, Collapsar type II
  (MacFadyen Woosley 1999)

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Magnetic Field Driven Jets

• And then the theorist raises his magic. I mean
  magnetic wand and viola, there are jets -
  Shri Kulkarni
• Lots of Mechanisms proposed, but most boil down
  to a reference to the still unsolved mechanism
  behind the jet mechanism for Active Galactic
  Nuclei (Generally the Blandford-Znajek
  Mechanism).
• We are extrapolating from a non-working model
  dangerous at best.

100
Magnetic Field Mechanism Sources of Energy

• Source of Magnetic Field Dynamo in accretion
  disk.
• Source of Jet Energy -
  I) Accretion Disk
  II) Black Hole Spin

101
Magnetic Dynamos

• Duncan Thompson (1993) High Rossby Number
  Dynamo (convection driven) Bsat(4prvconvective2
  )1/2
• Akiyama et al. (2003) Shear-driven Dynamo
  Bsat2(4prr2W2(dlnW/dlnr)2
• Popham et al. (1999) Disk Dynamo
  Bsat2h(4prvtot2)

102
Schematic Cross-Section of a black hole and
magnetosphere
The poloidal field is shown in solid lines,
typical particle velocities are shown with
arrows. In the magnetosphere, spark gaps (SG)
form
that create electron/ positron pairs.
Blandford Znajek 1977
103
Electromagnetic structure of force-free
magnetosphere with (a) radial and (b)
para- boloidal magnetic fields. For paraboloidal
fields, the Energy appears to be Focused alonge
the rotation Axis. The overall efficiency of
Electromagnetic energy Extraction from a disk
Around a black hole is Difficult to calculate
with Any precision
Blandford Znajek (1977)
104
Magnetic Jet Power

• Blandford-Znajek L3x1052 a2 dM/dt erg/s with
  B2x1015(L/1051 erg/s)1/2 (MBHa)-1
• Popham et al. 1999 (Based on BZ)
  L1050a2(B/1015G)2 erg/s, Bhrv2 where h1
• Katz 1997 (Parker Instability)
  L1051(B/1013G)(W/104s-1)5(h/106cm) (r/1013g
  cm-3)-1/2(r/106cm)6 erg/s

105
Magnetic Field Summary

• Magnetically driven jets could possibly produce
  much more energy than neutrino annihilation
  (easily enough for GRBs). If it works for AGN,
  it must work for GRBs.
• Most estimates extrapolate from an already faulty
  AGN jet model. No physics calculation or
  derivation has yet to be made.

106
Black Hole Accretion Disk Models
Collapsar (aka hypernova
Supernova explosion of a very massive (gt 25 Msun)
star
Iron core collapse forming a black hole
Material from the outer shells accreting onto the
black hole
Accretion disk gt Jets gt GRB!
107
Collapsars

• Observations Explained
• Energetics explained
• Duration and variability explained

• Observations Predicted
• SN-like explosions along with GRB outburst
• Bursts occurring in star forming regions
• GRB Beaming

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Massive Star Models

• With the observations pushing toward massive
  stars, a number of other massive star models
  appeared pushing for neutron star mechanisms!
• Explosions from Magnetars
• Supranova (neutron star which later collapses to
  a black hole)

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Supernovae/Hypernovae
Nomoto et al. (2003)
EK
Failed SN?
13M?15M?
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Supranova Model For GRBs
If a neutron star is rotating extremely rapidly,
it could escape collapse (for a few months) due
to centrifugal forces.
Neutron star will gradually slow down, then
collapse into a black hole gt collapse triggers
the GRB
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Disadvantages of the Supranova Model
Mass thing Duration cant be Longer than
3-3000ms
NS, BH
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Disadvantages of the Supranova Model
Duration Rotation Period / Disk Viscosity (a
0.1-10-4) Duration cant be Longer than
3-3000ms Current bursts with Iron lines are all
Long-duration!
NS, BH