TP Vancouver I1 Relativity in Action – Gamma Ray Bursts Tsvi Piran HU, Jerusalem

TP Vancouver I2 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 There was an “invite prediction”. S. Colgate was asked to predict GRBs as a scientific excuse for the launch of the Vela Satellites There was an “invite prediction”. S. Colgate was asked to predict GRBs as a scientific excuse for the launch of the Vela Satellites

TP Vancouver I3GRBsCompton-GRO  Duration s  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.

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TP Vancouver I5 GRBs and Relativity GRBs involve the fastest macroscopic relativistic motion observed so far (  >100) 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 (z~5-10) universe. GRBs are the brightest and most luminous objects known today. GRBs are the most relativistic objects known today.

TP Vancouver I6  BATSE on Compton - GRO (Fishman et. al.) GRO (Fishman et. al.) discovered that the discovered that the distribution of GRBs distribution of GRBs is isotropic: 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. 1991: GRBs are Cosmological 1991: GRBs are Cosmological

TP Vancouver ITsvi Piran HU7 Revised Energy Estimates The observed fluences are ~ ergs/cm 2 Cosmological corrections. Galactic Halo models “standard candles ?” (E)  z~1  E~10 52 ergs  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.

TP Vancouver I8 Implications of ergs Need ultrarelativistic motion to get erg out from a compact source within such a short time scale. Need ultrarelativistic motion to get erg out from a compact source within such a short time scale.  The FIREBALL FIREBALL MODEL MODEL

TP Vancouver I9 Implications of ergs - The Compactness Problem:  e + e -   sec  R  c  = cm.  E  ergs.    = n    R   Expect No Photons above 500keV!  Expect No Photons above 500keV! BUT: BUT: Need New Physics?

TP Vancouver I10 The Solution Relativistic Motion Relativistic Motion  R  c     E ph (obs) =  E ph (emitted)    =   n    R       

TP Vancouver I11 Relativistic effects can influence the observed time scale in GRBs (Ruderman, 75; Krolik & Pier, 89). Relativistic effects can influence the observed time scale in GRBs (Ruderman, 75; Krolik & Pier, 89). High Energy Density in a Small Region A Fireball: High Energy Density in a Small Region  A Fireball:  Pure radiation fireball thermal radiation (Goodman, 86; Paczynski 86).  Pure radiation fireball  thermal radiation (Goodman, 86; Paczynski 86).  BUT Baryonic load relativistic Baryonic flow: (Shemi & Piran, 90).  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). 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).

TP Vancouver I12 The Fireball Model The Fireball Model compact source compact source Relativistic Particles  >100 or Poynting flux Shocks    rays ~ 10 7 cm Goodman; Paczynski; Shemi & Piran, Narayan, Paczynski & Piran; Meszaros & Rees,

TP Vancouver I13 Supernova Remnants (SNRs) - the Newtonian Analogue n ~ 10 solar masses are ejected at ~10,000 km/sec during a supernova explosion. n The ejecta is slowed down by the interstellar medium (ISM) emitting x-ray and radio for ~10,000 years.

TP Vancouver I14 Gamma-Ray Burst: 3 Stages 1) Compact Source, E>10 52 erg 2) Relativistic Kinetic Energy 3) Kinetic Energy to Internal Energy to Radiation=GRB The Compact Source is Hidden

TP Vancouver I15 Temporal Variability- the Second Clue  T<1sec, T~100 N=T/  T>100 Variability - a measure of the luminosity (Fenimore et al, 99; Riechart et al, 00)Variability - a measure of the luminosity (Fenimore et al, 99; Riechart et al, 00) Distance indicator!  Distance indicator! External shocks cannot produce the observer variability in the light curves (Sari & Piran, 97, Fenimore et al, 97). External shocks cannot produce the observer variability in the light curves (Sari & Piran, 97, Fenimore et al, 97).

TP Vancouver I16 Relativistic Time Scales A C B D R R R  ~1/   t B -t A ~ R (1-  ) / c ~ R/2  2 c t C -t A ~ R(1-cos  )/c ~ R/2  2 c t D -t A ~  /c

TP Vancouver I17 External vs. Internal Shocks  External shocks are shocks between the relativistic ejecta and the ISM - just like in SNRs.  Internal shocks occur between different between different shells within the shells within the relativistic ejecta. relativistic ejecta.

TP Vancouver I18  = R/c   =  = R/c   =  /c  /c =T  /c  /c =T The observed light curve reflects the activity of the “inner engine”.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 withinQuiescent Periods within long bursts suggest that the source is inactive for of dozen seconds within long bursts long bursts (Nakar and Piran, 2000). (Nakar and Piran, 2000).  =cT ==cT==cT Internal Shocks

TP Vancouver I19 Quiescent Periods n Quiescent Periods within long bursts suggest that the source in in active for periods of dozen seconds within long bursts (Nakar and Piran, 2000).

TP Vancouver ITsvi Piran HU20 (most) * GRBs cannot originate from an EXPLOSION. This rules out many models: Evaporating mini black holes.Evaporating mini black holes. NS -> BHNS -> BH NS -> strange starNS -> strange star Vacuum InstabilityVacuum Instability ………….…………. * Highly variable (there is a small group of smooth bursts which can be explosive)

TP Vancouver I21 Internal shocks can convert only a fraction of the kinetic energy to radiationInternal shocks can convert only a fraction of the kinetic energy to radiation (Sari and Piran 1997; Mochkovich et. al., 1997; Kobayashi, Piran & Sari 1997). (Sari and Piran 1997; Mochkovich et. al., 1997; Kobayashi, Piran & Sari 1997).  It should be followed by additional emission. D =cT =d=cdT=d=cdT Internal Shocks  Afterglow

TP Vancouver I22 1) Compact Source, E>10 51 erg 2) Relativistic Kinetic Energy 3) Radiation due to Internal shocks = GRBs 4) Afterglow by external shocks Gamma-Ray Burst: 4 Stages

TP Vancouver I23 Inner Engine Relativistic Wind The Internal-External Fireball Model There are no direct observations of the inner engine. The  -rays light curve contains the best evidence on the inner engine’s activity. External Shock Afterglow Internal Shocks  -rays

TP Vancouver I24 GRB - The Movie Four Initial shells ISM Afterglow - other colors GRB - yellow flash

TP Vancouver I25 Afterglow – The Second Revolution  The Italian/Dutch satellite BeppoSAX satellite BeppoSAX discovered x-ray afterglow discovered x-ray afterglow on 28 February 1997 on 28 February 1997 (Costa et. al. 97). (Costa et. al. 97).  Immediate discovery of Optical afterglow (van Paradijs et. al 97).

TP Vancouver I26 The Radio Afterglow of GRB (Frail et. al, 97).  Variability:  Scintillations (Goodman, 97; Frail et al 97)  ® Size after one month  cm.  Rising Spectrum at low frequencies:  Self absorption (Katz & Piran, 97; Frail et al 97) ® Size after one month  cm.  Relativistic Motion!!! (but  since this is a long time after the explosion 

TP Vancouver I27 A crash Course in Scintillations Scintillations determine the size of the source in a model independent way. The size (~10 17 cm) is in a perfect agreement with the prediction of the Fireball model.

TP Vancouver I28 Relativistic Hydrodynamics of the Fireabll Model Ehud Cohen (Hebrew U)Ehud Cohen (Hebrew U) Jonathan Granot (Hebrew U)Jonathan Granot (Hebrew U) Philip Hughes (Michigan U)Philip Hughes (Michigan U) Pawan Kumar (IAS, Princeton)Pawan Kumar (IAS, Princeton) Mark Miller (Washington U)Mark Miller (Washington U) Ehud Nakar (Hebrew U)Ehud Nakar (Hebrew U) Ramesh Narayan (Harvard) Re’em Sari (Caltech)Ramesh Narayan (Harvard) Re’em Sari (Caltech) Amotz Shemi (Tel Aviv U)Amotz Shemi (Tel Aviv U) Wai Mo Suen (Washington U)Wai Mo Suen (Washington U) Tsvi Piran HU, Jerusalem ISRAEL

TP Vancouver I29 The Acceleration Phase Consider a dense spherical concentration of energy in the form of radiation and some matter – a Fireball.

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TP Vancouver I37 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 parameters: E, n, p,  e,  B initialshell ISM

TP Vancouver I38 n Adiabaticity: n Arrival time: n Energy densities: n Electron distribution:

TP Vancouver I39 The Blandford McKee solution A relativistic analog of Sedov Taylor initialshell ISM

TP Vancouver I40 Radiation Processes Synchrotron radiation from a power law electron distribution E -p, (p  2.5) syn (  ) = eB  2 /(m e c) m = syn (  min ) E min E -p -1/3

TP Vancouver I41 Fast and Slow Cooling Fast Cooling EcEc Slow Cooling P syn =(4/3)  T c U B  2  c = (3 m e c)/(4  T U B t) c = syn (  c ) c = syn (  c )

TP Vancouver I42 The Simplest Synch Spectrum (I) (Sari Piran & Narayan 1998) Fast Cooling ( c < m ) Low energy Low energy F n -1/3 F n -1/3 a: n e  n a ( a ) L = 1 a: n e  n a ( a ) L = 1 Synch self Synch self Absorption Absorption Fast Cooling during the High Energy F  -p/2 early afterglow (first half hour) n

TP Vancouver I43 The Simplest Synch Spectrum (II) Slow Cooling during most of the afterglow (after half hour) ( c > m ) Low energy Low energy F n -1/3 F n -1/3 a: n e  a ( a ) L = 1 a: n e  a ( a ) L = 1 Very low energy Very low energy Synch self Absorption Synch self Absorption High Energy F n -p/2 High Energy F n -p/2

TP Vancouver I44 Light Curves and Spectrum of the BM-Synch Afterglow F    F    n For spherical expansion:  For  c  =(p-1)/2 ;  =(3p-3)/4 ;  =3   For  c  = p/2 ;  =(3p-2)/4 ;   ‚ For GRB970508:  =1.12,  consistent with  =1.12,  consistent with p= and with  c. p= and with  c.

TP Vancouver I45 Comparison with Observations (Sari, Piran & Narayan 98; Wijers & Galama 98; Granot, Piran & Sari 98) Radio observations

AFTERGLOW SLOPES

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TP Vancouver I48Complications n Wind (Chavalier & Li 99, Panaitescu and Kumar,00) : (still a spherical cow). (still a spherical cow). n Sideway Expansion (an expanding jet) (Rhoads 99, Sari Piran Halpern 99, Panaitescu and Meszaros 99) :

TP Vancouver I49 Further Complications n A jet into a wind (Panaitescu and Kumar 00) n A collimated jet n Inverse Compton (Panaitescu and Kumar 00, Esin and Sari,00)

TP Vancouver I50 Generalized hydro relations This relation is now plugged into the frequencies and fluxes estimate and one obtains an asymptotic light curce R~const for q=1 (jet)

TP Vancouver I51 JETS and BEAMING Jets with an opening angle  expand forwards until   and then expand sideways rapidly lowering quickly the observed flux (Piran, 1995; Rhoads, 1997; Wijers et al, 1997; Panaitescu & Meszaros 1998). lowering quickly the observed flux (Piran, 1995; Rhoads, 1997; Wijers et al, 1997; Panaitescu & Meszaros 1998).  

TP Vancouver I52 Schematic Jet Expansion Four Initial shells ISM Afterglow - other colors GRB - yellow flash

TP Vancouver I53 Light Curves from a Jet Fast expansion Fast expansion Slow expansion

TP Vancouver I54 The Synchrotron - Power Law Afterglow Model from a Jet F     F     n For spherical expansion:  For  c  =(p-1)/2 ;  =(3p-3)/4 ;  =3   For  c  = p/2  =(3p-2)/4 ;  n For a jet expanding sideways (Rhoads, 1997, Sari Piran Halpreen, 1999):   =p  For  c  =(p-1)/2 ;  =2   For  c  = p/2 ;  =2 

TP Vancouver I55 GRB Another Jet!  1     t break = 1.2 days  jet angle = 4 o From Harrison et al 1999

TP Vancouver I56 Redshift and Energy Determination GRBZ E (× ) c

TP Vancouver ITsvi Piran HU57 The Energy Crisis? (E) Totani’s prediction for the energy of GRBs

TP Vancouver I58 The Resolution of the Energy Crisis The Resolution of the Energy Crisis  E tot - The total energy  E  iso  -  Observed (iostropic)  ray energy Beaming:  E  - Actual  ray energy The two most powerful BeppoSAX bursts are jets (Sari, Piran & Halpern; 1999).

TP Vancouver ITsvi Piran HU59 The Energy Crisis? (E) Prediction for the energy of GRBs What goes up must go down e.g. NASDAQ

TP Vancouver I60 Constant ENERGY E    erg (Frail et al, 01; Panaitescu and Kumar 01)

TP Vancouver I61 Numerical Simulations Jonathan Granot (Hebrew U), Mark Miller (Washington U) Wai Mo Suen (Washington U), Philip Hughes (Michigan U) n Why is it not trivial? u A flying pancake. u Extremely relativistic motion. u Because of the time dependance it is much more difficult than “standard” relativistic “jet” simulations.

TP Vancouver I62 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

TP Vancouver I63 The Initial Data - A slice from a BM solution:  =0.2; E 52 =n 0 =1 The Initial Data - A slice from a BM solution:  =0.2; E 52 =n 0 =1 

TP Vancouver I64 The Density Profile and the Velocity Field t=0 t=0 t=100 t=100 t=200 t=200 t=300 t=300 t=400 t=400 t=500 t=500

TP Vancouver I65 Conditions at the end of the computation Emisivity Lorentz Factor Density Velocity Field

TP Vancouver I66 Emissivity Lorentz Factor Density

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TP Vancouver I68 Slow Sideways Expansion

TP Vancouver I69 A refined BM-Synch Model Granot, Piran & Sari 98a,b; Waxman & Gruzinov 98 Emission is from an “egg” shaped object with an opening angle  -1 Smooth Spectrum Smooth Spectrum Images at different frequencies Images at different frequencies

TP Vancouver I70 But a Sharp (Not Achromatic) Break! * synch emission does not include the effects of cooling.

TP Vancouver I71 Orphan Afterglows – Non observed so far Orphan Afterglow

TP Vancouver I72 Uniform Structured Jet? (Rossi et al 02) If E(   we will also see a jet break but now the interpreted angle will correspond to  obs the observer viewing angle relative to the center of the jet. If E(   we will also see a jet break but now the interpreted angle will correspond to  obs the observer viewing angle relative to the center of the jet. n This implies much more energy and much fewer bursts. It also implies different and fewer “orphan afterglows”.

TP Vancouver I73 GRB Remnants (GRBRs) Ayal & Piran Ap J GRB involves ejection of ~10 51 ergs in kinetic energy into the ISM. GRB involves ejection of ~10 51 ergs in kinetic energy into the ISM. This is similar to supernovae that produce SNRs This is similar to supernovae that produce SNRs How will a GRB Remnant (GRBR) look thousands of years AB (after burst)? How will a GRB Remnant (GRBR) look thousands of years AB (after burst)? Can we distinguish a GRBR from a SNR? Can we distinguish a GRBR from a SNR? Search for the signature of GRB beaming in the GRBR. Search for the signature of GRB beaming in the GRBR.

TP Vancouver I74 The GRB and the Afterglow

TP Vancouver I75 The Newtonian Phase Newtonian transition. Newtonian transition. Sedov regime (energy of ejecta and ISM mass dominates (self similar in the spherical case). Sedov regime (energy of ejecta and ISM mass dominates (self similar in the spherical case). Shells merge Shells merge Spherical Remnant Spherical Remnant

TP Vancouver I76 DEM L316 a GRBR or a Double SNR?

TP Vancouver I77 Initial conditions In the Sedov regime the late time results are insensitive to uncertainties in the initial conditions. We need only approximate initial conditions.  rad (0.3rad-3rad) Unknown energy and density distribution within the ejecta.Unknown energy and density distribution within the ejecta. R0R0R0R0 

TP Vancouver I78 The  parameter Define :

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TP Vancouver I84 Results: Shells collide at  ~(1-5)  t ~ (50-250) yr (E 51 /n) 1/3 R~4pc (E 51 /n) 1/3 Shells collide at  ~(1-5)  t ~ (50-250) yr (E 51 /n) 1/3 R~4pc (E 51 /n) 1/3 GRBR becomes spherical at  ~10 5. t ~ 3  10 3 yr (E 51 /n) 1/3 R~12pc (E 51 /n) 1/3 GRBR becomes spherical at  ~10 5. t ~ 3  10 3 yr (E 51 /n) 1/3 R~12pc (E 51 /n) 1/3 The expected number of non-spherical GRBRs is 0.5 (f b /0.002) -1 (E 51 /n) 1/3 per galaxy The expected number of non-spherical GRBRs is 0.5 (f b /0.002) -1 (E 51 /n) 1/3 per galaxy ~ 20 non spherical GRBRs up to 10 Mpc with angular sizes ~1.2marcsec. ~ 20 non spherical GRBRs up to 10 Mpc with angular sizes ~1.2marcsec.

TP Vancouver I85 A Spherical Underlying SN v= dR/dt ~2(pc/yr)  -2/3. v= dR/dt ~2(pc/yr)  -2/3. A SN shell with v~10 4 km/sec will catch the GRBR shell at A SN shell with v~10 4 km/sec will catch the GRBR shell at  ~ 3000 ;  ~ 3000 ; t~150 yr (E 51 /n) 1/3 ; t~150 yr (E 51 /n) 1/3 ; R~4pc (E 51 /n) 1/3. R~4pc (E 51 /n) 1/3. Namely around the time of the two shell collision. Namely around the time of the two shell collision. The non spherical structure will be destroyed. 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 E SN  E GRB.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 E SN  E GRB.

TP Vancouver I86 The closest morphology is The closest morphology is at  ~10 3. But using the observed But using the observed mass ~5000 M o and energy ~ 5  ergs energy ~ 5  ergs of DEM L316 we find of DEM L316 we find m~7  m~7  A GRBR would have been A GRBR would have been spherical at this stage spherical at this stage What about DEM L316?

TP Vancouver ITsvi Piran HU87 Implications of the Fireball Model

TP Vancouver I88 Clues on the Inner Engine The inner source is hidden. The observations reflect only the conditions at the fireball.  E tot ~ ergs   t < sec  T ~ 30 sec   ~ 200 (“dirty”)  Jets ~ 2 o - 5 o  Rate /yr/galaxy  A compact Object  Prolonged activity:  > an accretion disk ?  Baryonic Flow ?  Lower energy, higher rates, orphan afterglows  A rare phenomenon Most likely powered by accretion onto a newborn black hole

TP Vancouver I89 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

TP Vancouver I90 Evidence for Supernova association with GRBs

TP Vancouver I91 Evidence for Supernova association with GRBs Association of SN98bw and GRB with a similar type of SN in GRB Association of SN98bw and GRB with a similar type of SN in GRB Late red bumps in light curves of GRB and GRB and several other afterglows. Late red bumps in light curves of GRB and GRB and several other afterglows. Location: Location: Association of GRBs with star forming regions. Association of GRBs with star forming regions. Association of GRBs with central regions of galaxies Association of GRBs with central regions of galaxies  Iron lines indicating large ~0.5M o of Fe.

TP Vancouver I92 Jet Propagation through a stellar envelope (MacFadyen et al. )

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TP Vancouver I97 Neutron star merger Rosswog et al., 03 Newtonian SPH with accurate EOS and some neutrino transport. GW backreaction included.

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TP Vancouver I101 Accretion disks in GRBs (Narayan, Piran & Kumar 2001): Need ergs  m d ~ MoNeed ergs  m d ~ Mo Accretion time, t acc, is the duration of the burst.Accretion time, t acc, 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.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 r out <50r gAccretion is effective in NDAF (Neutrino dominated accretion flow) – but NDAFs are very small r out <50r g

TP Vancouver I102 Convection dominated accretion flow – Igumenenshev Abraowicz and Narayan Most of the matter is ejected to infinity (Newtonian Calculations)

TP Vancouver I103 CDAF to NDAF gas-pressure-dominated to degeneracy -dominated optically thick to neutrinos Contours of Log(t acc) 1 CDAF NDAF t acc is determined by the size of the disk. Disk size in units of r g Disk mass in units of m o ACCRETION TIME

TP Vancouver I104 Implications  Need large disks ( r g ) to produce long duration jets.  Need small disks (10r g ) to produce short bursts.

TP Vancouver I105 Contours of Log(  ) - Accretion efficiency NDAF  =1 CDAF  =.1 Disk size in units of r g Disk mass in units of m o

TP Vancouver I106 Implications  Need large disks ( r g ) to produce long duration jets.  Need small disks (10r g ) to produce short bursts.  Large disks ( r g ) are inefficient and cannot produce ergs.  Small disks (10r g ) are efficient.

TP Vancouver I107 Contours of Log(  ) - Accretion efficiency CDAF NDAF  =1  =.1 Disk size in units of r g Disk mass in units of m o Injection of mass onto a small disk by infall  Collapsar

TP Vancouver I108 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.

TP Vancouver I109 Routes to a BH-Disk-Jet Different routes can lead to a Black-hole -disk-jet system:  NS/BH-NS merger  BH-WD merger  NS/BH-He core merger  Collapsar Davies et al, 94 Woosley et al, 99 shortLong - LONG - SHORT

TP Vancouver I110 Roswog et al, 99 Woosley et al., 99 NY Times May 99

TP Vancouver I111 Sources of GRBs (NS mergers - short - or Collapsars - long) are sources of Gravitaional Radiation  One long GRBs per 10 4 (  /0.1) -2 years per galaxy. Beaming factor  One observed long burst per year at D~600 Mpc.  One unobserved burst per year at D~135 (  /0.1) 2/3 Mpc.  Short bursts are most likely at z<0.5 with one short burst per 10 3 (  /0.1) -2 years per galaxy.  One observed short burst per year at D~250 Mpc.  One unobserved short burst per year at D~80 (  /0.1) 2/3 Mpc. Is this the rate of NS mergers?