Gamma-Ray Bursts A Puzzle Being Resolved Tsvi Piran HU, Jerusalem (also Columbia and NYU) During the last years one of the longest open mysteries in Astrophysics is being resolved.

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Relativity in Action Gamma Ray Bursts Tsvi
Piran HU, Jerusalem
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• THE DISCOVERY
• Gamma-Ray Bursts (GRBs) Short (few seconds)
  bursts of
• 100keV- few MeV were discovered accidentally by
• Klebesadal Strong and Olson in 1967
• using the Vela satellites
• (defense satellites sent to monitor
• the outer space treaty).
• The discovery was reported for the
• first time only in 1973.

• There was an invite prediction. S. Colgate was
  asked to predict GRBs as a scientific excuse for
  the launch of the Vela Satellites

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GRBs

• Duration 0.01-100s
• Two populations (long and short)
• 1 BATSE burst per day
• - (a local rate of 2 Gpc-3 yr-1 )
• 100keV photons
• Non thermal Spectrum(very high energy tail,
• up to GeV, 500GeV?)
• Rapid variability (less than 10ms)
• Cosmological Origin
• The brightness of a GRB is comparable to the
  brightness of the rest of the Universe combined.

Compton-GRO
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GRB 971214
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GRBs and Relativity
GRBs are the brightest and most luminous objects
known today.
GRBs involve the fastest macroscopic relativistic
motion observed so far (?gt100)
GRBs signal (most likely) the formation of
newborn black holes.
Sources of GRBs (merging NS or Collapsars) are
also sources of Gravitational radiation
GRBs are the best cosmological indicators known
today for the early (z5-10) universe.
GRBs are the most relativistic objects known
today.
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1991 GRBs are Cosmological

• BATSE on Compton -
• GRO (Fishman et. al.)
• discovered that the
• distribution of GRBs
• is isotropic

• The flux distribution (paucity of weak bursts)
  shows that the bursts cannot be very nearby in
  the disk
• ? GRBs are Cosmological
• By now there are redshift measurements for the
  afterglow of two dozen bursts.

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Revised Energy Estimates

• The observed fluences are 10-7 - 10-5 ergs/cm2

Cosmological corrections.

• z1 ? E1052ergs ? GRBs are the
  (electromagnetically) most luminous objects in
  the Universe.
• For a few second the luminosity of a GRB is
  comparable to the luminosity of the rest of the
  Universe.

(E)
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Implications of 1052ergs

• Need ultrarelativistic motion to get 1052erg
  out from a compact source within such a short
  time scale.
• The
• FIREBALL
• MODEL

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Implications of 1051 ergs -The Compactness
Problem ggee-

• dT .1 sec ? R cdT 3 109 cm.
• E _at_ 1051ergs.
• ? tgg ngsT R ³ 1015
• ? Expect No Photons above 500keV!
• BUT

Need New Physics?
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The Solution

• Relativistic Motion
• R cg2dT
• Eph (obs) g Eph (emitted)
• tgg g-(22a) ngsT R ³ 1015/g(22a)
• g ³ 100 (a
  _at_ 2)

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• Relativistic effects can influence the observed
  time scale in GRBs (Ruderman, 75 Krolik Pier,
  89).
• High Energy Density in a Small Region A
  Fireball
• Pure radiation fireball thermal radiation
  (Goodman, 86 Paczynski 86).
• BUT Baryonic load relativistic Baryonic flow
  (Shemi Piran, 90).
• SHOCKS Extraction of the kinetic energy of the
  Baryons by External shocks (Meszaros and Rees,
  1992) or internal shocks (Narayan, Paczynski
  Piran 1992 Paczynski and Xu, 1992 Meszaros and
  Rees, 1994).

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• The Fireball Model

g - rays
Relativistic Particles ?gt100 or Poynting flux
compact source
107 cm
Shocks
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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Gamma-Ray Burst 3 Stages

• 1) Compact Source, Egt1052erg
• 2) Relativistic Kinetic Energy
• 3) Kinetic Energy to Internal Energy to
  RadiationGRB

The Compact Source is Hidden
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Temporal Variability- the Second Clue

• Variability - a measure of the luminosity
  (Fenimore et al, 99 Riechart et al, 00)
• Distance indicator!
• External shocks cannot produce the observer
  variability in the light curves (Sari Piran,
  97, Fenimore et al, 97).

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Relativistic Time Scales
C
R
A
q1/g
D
B
R
D
R
tD-tA D/c
tC-tA R(1-cos q)/c R/2g2c
tB-tA R (1-b) / c R/2g2c
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External vs. Internal Shocks

• External shocks are shocks between the
  relativistic ejecta and the ISM - just like in
  SNRs.

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Internal Shocks

• dT R/cg2
• d/c D /c T
• The observed light curve reflects the activity of
  the inner engine. Need TWO time scales.
• Quiescent Periods within long bursts suggest
  that the source is inactive for of dozen seconds
  within
• long bursts
• (Nakar and Piran, 2000).

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Quiescent Periods

• Quiescent Periods within long bursts suggest
  that the source in in active for periods of dozen
  seconds within long bursts (Nakar and Piran,
  2000).

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(most) GRBs cannot originate from an EXPLOSION.

• This rules out many models
• Evaporating mini black holes.
• NS -gt BH
• NS -gt strange star
• Vacuum Instability
• .
• Highly variable (there is a small group of
  smooth bursts which can be explosive)

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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.

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Gamma-Ray Burst4 Stages

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

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The Internal-External Fireball Model
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GRB - The Movie
Four Initial shells
GRB - yellow flash
ISM
Afterglow - other colors
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Afterglow The Second Revolution

• The Italian/Dutch
• satellite BeppoSAX
• discovered x-ray afterglow
• on 28 February 1997
• (Costa et. al. 97).
• Immediate discovery of Optical afterglow (van
  Paradijs et. al 97).

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The Radio Afterglow of GRB970508 (Frail et.
al, 97).

• Variability
• Scintillations (Goodman, 97 Frail et al 97)
• Size after one month _at_1017cm.
• Rising Spectrum at low frequencies
• Self absorption (Katz Piran, 97 Frail et al
  97) Size after one month _at_ 1017cm.
• Relativistic Motion!!! (but g _at_ 2 since this is
  a long time after the explosion).

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A crash Course in Scintillations
Scintillations determine the size of the source
in a model independent way. The size (1017cm)
is in a perfect agreement with the prediction of
the Fireball model.
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Relativistic Hydrodynamics of the Fireabll Model
Tsvi PiranHU, Jerusalem ISRAEL

• Ehud Cohen (Hebrew U)
• Jonathan Granot (Hebrew U)
• Philip Hughes (Michigan U)
• Pawan Kumar (IAS, Princeton)
• Mark Miller (Washington U)
• Ehud Nakar (Hebrew U)
• Ramesh Narayan (Harvard) Reem Sari (Caltech)
• Amotz Shemi (Tel Aviv U)
• Wai Mo Suen (Washington U)

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The Acceleration Phase
Consider a dense spherical concentration of
energy in the form of radiation and some matter
a Fireball.
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Afterglow Theory

• Hydrodynamics deceleration of the
• relativistic shell by collision with the
  surrounding medium (Blandford McKee 1976)
• (Meszaros Rees 1997, Waxman 1997, Sari 1997,
  Cohen, Piran Sari 1998)
• Radiation synchrotron IC (?)
• (Sari, Piran Narayan 98)
• Clean, well defined problem.
• Few parametersE, n, p, ee, eB

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• Adiabaticity
• Arrival time
• Energy densities
• Electron distribution

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The Blandford McKee solutionA relativistic
analog of Sedov Taylor
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Radiation Processes

• Synchrotron radiation from a power law electron
  distribution E-p, (p 2.5)
• nsyn(g) eBg2/(mec) nm nsyn(gmin)

n-1/3
E-p
Emin
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Fast and Slow Cooling

Slow Cooling

• Fast Cooling

Ec
Psyn(4/3)sT c UB g2 gc (3 me c)/(4 sT UB
t) nc nsyn(gc)
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The Simplest Synch Spectrum (I)(Sari Piran
Narayan 1998)

• Fast Cooling
• (nc lt nm)
• Low energy
• Fn n -1/3
• na ne sna(na) L 1
• Synch self
• Absorption
• Fast Cooling during the High Energy Fn
  n -p/2
• early afterglow (first half hour)

n
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The Simplest Synch Spectrum (II)

• Slow Cooling during most of the afterglow
  (after half hour)
• (nc gt nm)
• Low energy
• Fn n -1/3
• na ne sna(na) L 1
• Very low energy
• Synch self Absorption
• 
  High Energy Fn n
  -p/2

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Light Curves and Spectrum of the BM-Synch
Afterglow

• Fn n-b t-a
• For spherical expansion
• For nltnc b(p-1)/2 a(3p-3)/4 a3b/2
• For ngtnc b p/2 a(3p-2)/4 a(3b-1)/2
• For GRB970508
• a1.12, b1.14 consistent with
• p2.2-2.5 and with ngtnc .

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Comparison with Observations(Sari, Piran
Narayan 98 Wijers Galama 98 Granot, Piran
Sari 98)
Radio observations
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AFTERGLOW SLOPES
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BUT
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Complications

• Wind (Chavalier Li 99, Panaitescu and Kumar,00)
  
• (still a spherical cow).
• Sideway Expansion (an expanding jet) (Rhoads 99,
  Sari Piran Halpern 99, Panaitescu and Meszaros
  99)

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Further Complications

• A jet into a wind (Panaitescu and Kumar 00)
• A collimated jet
• Inverse Compton (Panaitescu and Kumar 00, Esin
  and Sari,00)

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Generalized hydro relations
Rconst for q1 (jet)
This relation is now plugged into the frequencies
and fluxes estimate and one obtains an asymptotic
light curce
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JETS and BEAMING
g q -1
Jets with an opening angle q expand forwards
until g q-1 and then expand sideways rapidly
lowering quickly the observed flux (Piran, 1995
Rhoads, 1997 Wijers et al, 1997 Panaitescu
Meszaros 1998).
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Schematic Jet Expansion
Four Initial shells
GRB - yellow flash
ISM
Afterglow - other colors
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Light Curves from a Jet
Fast expansion
Slow expansion
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The Synchrotron - Power Law Afterglow Model from
a Jet

• Fn n-b t-a
• For spherical expansion
• For nltnc b(p-1)/2 a(3p-3)/4 a3b/2
• For ngtnc b p/2 a(3p-2)/4 a(3b-1)/2
• For a jet expanding sideways (Rhoads, 1997, Sari
  Piran Halpreen, 1999)
• ap
• For nltnc b(p-1)/2 a2b1
• For ngtnc b p/2 a2b

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GRB 990510 - Another Jet!

• a1 0.85 a22.18
• tbreak 1.2 days Þ jet angle 4o

From Harrison et al 1999
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Redshift and Energy Determination
GRB Z E ( 1051)
970228 0.695 22.4
970508 0.835 5.46
970828 0.958 220
971214 3.412 211
980613 1.096 5.67
980703 0.967 60.1
990123 1.6 1440
990506 1.3 854
990510 1.619 178
990705 0.84 270
990712 0.433 5.27
991208 0.706 147
991216 1.02 535
000131 4.5 1160
000131c 2.034 46.4
000418 1.119 82.0
000926 2.037 297
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The Energy Crisis?
(E)
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The Resolution of the Energy Crisis

• Etot - The total energy
• Eg iso - Observed (iostropic) g-ray energy

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The Energy Crisis?
(E)
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Constant ENERGY
E q2 ? 1051 erg (Frail et al, 01 Panaitescu and
Kumar 01)
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Numerical SimulationsJonathan Granot (Hebrew U),
Mark Miller (Washington U)Wai Mo Suen
(Washington U), Philip Hughes (Michigan U)

• Why is it not trivial?
• A flying pancake.
• Extremely relativistic motion.
• Because of the time dependance it is much more
  difficult than standard relativistic jet
  simulations.

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• AMR (Adaptive Mesh Refinement) Relativistic hydro
  code.

A test with a BM profile
Density profile with a high level mesh structure
Convergence test by comparing different refinment
levels
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The Initial Data - A slice from a BM solution
q0.2 E52n01.
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The Density Profile and the Velocity Field
t0
t100
t200
t300
t400
t500
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Conditions at the end of the computation
Emisivity
Lorentz Factor
Density
Velocity Field
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Emissivity
Lorentz Factor
Density
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Slow Sideways Expansion
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A refined BM-Synch Model

• Granot, Piran Sari 98a,b
• Waxman Gruzinov 98
• Emission is from an egg
• shaped object with an
• opening angle g-1
• Smooth Spectrum
• 
  Images at different frequencies

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But a Sharp (Not Achromatic) Break!
synch emission does not include the effects of
cooling.
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Orphan Afterglows Non observed so far
Orphan Afterglow
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Uniform Structured Jet?(Rossi et al 02)

• If E(q)q-2 we will also see a jet break but
  now the interpreted angle will correspond to
  qobs the observer viewing angle relative to the
  center of the jet.
• This implies much more energy and much fewer
  bursts. It also implies different and fewer
  orphan afterglows.

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GRB Remnants (GRBRs)Ayal Piran Ap J. 2001

• GRB involves ejection of 1051ergs in kinetic
  energy into the ISM.
• This is similar to supernovae that produce SNRs
• How will a GRB Remnant (GRBR) look thousands of
  years AB (after burst)?
• Can we distinguish a GRBR from a SNR?
• Search for the signature of GRB beaming in the
  GRBR.

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The GRB and the Afterglow
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The Newtonian Phase

• Newtonian transition.
• Sedov regime (energy of ejecta and ISM mass
  dominates (self similar in the spherical case).
• Shells merge
• Spherical Remnant

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DEM L316 a GRBR or a Double SNR?
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Initial conditions
R0
q

• In the Sedov regime the late time results are
  insensitive to uncertainties in the initial
  conditions. We need only approximate initial
  conditions.
• q 1 rad (0.3rad-3rad)
• Unknown energy and density distribution within
  the ejecta.

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The m parameter
Define
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Results
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Results

• Shells collide at m(1-5)?103.
  t (50-250) yr (E51/n)1/3 R4pc
  (E51/n)1/3
• GRBR becomes spherical at m105.
  t 3?103 yr (E51/n)1/3 R12pc
  (E51/n)1/3
• The expected number of non-spherical GRBRs is
  0.5 (fb/0.002)-1 (E51/n)1/3 per galaxy
• 20 non spherical GRBRs up to 10 Mpc
  with angular sizes 1.2marcsec .

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A Spherical Underlying SN

• v dR/dt 2(pc/yr) m-2/3.
• A SN shell with v104 km/sec will catch the GRBR
  shell at
• m 3000
• t150 yr (E51/n)1/3
• R4pc (E51/n)1/3 .
• Namely around the time of the two shell
  collision.
• The non spherical structure will be destroyed.
• The number of non spehrical GRBRs is smaller by a
  factor of 10 and the size is smaller by a factor
  of 3 if there is an underlying spherical SNR
  with ESN?EGRB .

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What about DEM L316?

• The closest morphology is
• at m103.
• But using the observed
• mass 5000 Mo and
• energy 5?1050ergs
• of DEM L316 we find
• m7?105.
• A GRBR would have been
• spherical at this stage

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Implications of the Fireball Model
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Clues on the Inner Engine The inner source is
hidden. The observations reflect only the
conditions at the fireball.

• A compact Object
• A compact Object
• Prolonged activity
• gt an accretion disk ?
• Baryonic Flow ?
• Lower energy, higher rates, orphan afterglows
• A rare phenomenon

• Etot 1051 ergs
• dt lt 10-2 sec
• T 30 sec
• g 200 (dirty)
• Jets 2o - 5o
• Rate 10-5 /yr/galaxy

Most likely powered by accretion onto a newborn
black hole
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Routes to a BH-Disk-Jet

• Different routes can lead to a Black-hole
  -disk-jet system
• NS-NS merger
• BH-NS merger
• BH-WD merger
• NS/BH-He core merger
• Collapsar

Davies et al , 94
Woosley et al, 99
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Evidence for Supernova association with GRBs
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Evidence for Supernova association with GRBs

• Association of SN98bw and GRB980425 with a
  similar type of SN in GRB030329
• Late red bumps in light curves of GRB980326 and
  GRB970228 and several other afterglows.
• Location
• Association of GRBs with star forming regions.
• Association of GRBs with central regions of
  galaxies
• Iron lines indicating large 0.5Mo of Fe.

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Jet Propagation through a stellar envelope
(MacFadyen et al. )
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Neutron star merger Rosswog et al., 03
Newtonian SPH with accurate EOS and some
neutrino transport. GW backreaction included.
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Accretion disks in GRBs

• (Narayan, Piran Kumar 2001)
• Need 1051ergs ? md 10-3 Mo
• Accretion time, tacc, is the duration of the
  burst.
• In CDAF (Convection dominated accretion flow)
  most of the matter is ejected back to infinity at
  slow velocities accretion efficiency is very
  low.
• Accretion is effective in NDAF (Neutrino
  dominated accretion flow) but NDAFs are very
  small routlt50rg

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Convection dominated accretion flow
Igumenenshev Abraowicz and Narayan
Most of the matter is ejected to infinity
(Newtonian Calculations)
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Contours of Log(tacc)
-1
1
ACCRETION TIME
CDAF to NDAF
optically thick to neutrinos
NDAF
CDAF
tacc is determined by the size of the disk.
Disk mass in units of mo
gas-pressure-dominated to degeneracy -dominated
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Implications

• Need large disks (100-1000rg) to produce long
  duration jets.
• Need small disks (10rg) to produce short bursts.

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Contours of Log(?) - Accretion efficiency
NDAF ?1
CDAF
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Implications

• Need large disks (100-1000rg) to produce long
  duration jets.
• Need small disks (10rg) to produce short bursts.

• Large disks (100-1000rg) are inefficient and
  cannot produce 1051 ergs.
• Small disks (10rg) are efficient.

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Contours of Log(?) - Accretion efficiency
Injection of mass onto a small disk by infall ?
Collapsar

NDAF ?1
CDAF
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Implications of Accretion Theory(Narayan,
Piran, Kumar 00)

• Large CDAFs are inefficient and cannot produce
  GRBs. Models with large accretion disks (He star
  NS/BH WD-NS/BH etc..) are ruled out.
• A Collapsar might produce a small NDAF disk in
  which the long duration is determined by the
  infall time and NOT by the accretion time.
• NS mergers produce small NDAF disks in which the
  duration is determined by the accretion time.

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Routes to a BH-Disk-Jet
short

• Different routes can lead to a Black-hole
  -disk-jet system
• NS/BH-NS merger
• BH-WD merger
• NS/BH-He core merger
• Collapsar

Long
Davies et al , 94
Woosley et al, 99
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NY Times May 99
Roswog et al, 99
Woosley et al., 99
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Sources of GRBs (NS mergers - short - or
Collapsars - long) are sources of Gravitaional
Radiation

• One long GRBs per 104 (?/0.1)-2 years per galaxy.
  Beaming factor
• One observed long burst per year at D600 Mpc.
• One unobserved burst per year at D135 (?/0.1)
  2/3 Mpc.
• Short bursts are most likely at zlt0.5 with one
  short burst per 103 (?/0.1)-2 years per galaxy.
• One observed short burst per year at D250 Mpc.
• One unobserved short burst per year at
  D80(?/0.1)2/3Mpc. Is this the rate of NS
  mergers?