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  1. GRB Useful reviews: Waxman astro-ph/0103186 Ghisellini astro-ph/0111584 Piran astro-ph/0405503 Meszaros astro-ph/0605208 Useful links Theory and observations

  2. Progenitor Long GRBs: Collapsar model M>30 M

  3. Modelli per un GRB

  4. Leading model for short GRBs Progenitors NS-NS merging primordial DNS

  5. Modelli per un GRB

  6. Spectrum well described by a broken power law Band approximation EE<E0 • Nontermal Spectrum N(E)  EE>E0 BATSE (20 keV-1 MeV) 0.1 MeV< E0< 1 MeV  -2,  ~ [-1, -0.5]

  7. The compactness problem • t ~ 1-10 ms Compact sources R0 c t ~ 3 107 cm • Cosmological sources (D~3 Gpc) L~ fD2~1052 erg/s R of our galaxy ~ 30 kpc: extragalactic objects 1 2≥(mec2)2  e+e- ~ pR0nT~TL/4R0c~1015  ~ 1 MeV p fraction of photons above the thereshold of pair production T=6.25x10-25cm2 Optical depth  ( e+e-) >>1

  8. 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 2+2  6.  < 1 for  ≥100

  9. Propagation effect Zhang & Mészàros, IJMPA A19, 2385 (2004)

  10. Finally, • dt’, comoving time of the shell where D is the Doppler factor.

  11. 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.

  12. 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

  13. 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.

  14. Fireball Model From IXth International Symposium on Particles, Strings and Cosmology Tata Institute of Fundamental Research, Mumbai, Inda Tsvi Piran pascos/Proceedings/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.

  15. g- rays Shocks Relativistic Particles >100 or Poynting flux The Fireball Model compact source ~ 107 cm Goodman; Paczynski; Shemi & Piran, Narayan, Paczynski & Piran; Meszaros & Rees

  16. 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.

  17. 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!

  18. 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).

  19. 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”!)

  20. A NO GO THEOREM Fireball Theorists then found a lot Wrong with the external shock model! External shocks cannot produce a variable light curve!!! (Sari & Piran 97)

  21. Time to Revise the Theory • Gamma-rays and Afterglow arise from different sources Birth of the Internal Shock Model

  22. D=cT d=cdT Internal Shocks Shocks between different shells of the ejected relativistic matter • dT=R/cg2= d/c £ D/c=T • 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

  23. D=cT d=cdT Internal Shocks Afterglow • Internal shocks can convert only a fractionof 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)

  24. Gamma-Ray Burst: 4 Stages 1)Compact Source, E>1051erg 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!

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

  26. Postdicted THE FIREBALL MODEL PREDICTED GRB AFTERGLOW (late emission in lower wavelength that will follow the GRB) Rhodes & Paczynksi, Katz, Meszaros & Rees, Waxman, Vietri, Sari & Piran

  27. 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.

  28. 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

  29. The internal/external shock scenario [Rees & Meszaros 1992, ’94] ISM  1016cm  1013cm  ray phase X-ray, Opt.-IR, Radio Efficient! [Guetta Spada & Waxman 2001]

  30. The radiation mechanisms

  31. 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 1>> 2 and M1=M2 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

  32. Internal shock radius Let’s assume that a faster shell (2) impacts on a slower the leading shell (1); Ift=tvis the average interval between two pulses (interval between shells ejection) Emission properties determined by ris

  33. 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)

  34. 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, sh~a few, particle acceleration in subrelativistic shocks. Electrons are accelerated to a power law with energy distribution with p~2 and e> m Electrons accelerated in magnetic field: synchrotron emission? i.e. emission from relativistic electrons gyrating in random magnetic fields

  35. 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 v>vsound • 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/1=4, v1/v2=4

  36. Shocks

  37. Shocks

  38. Fermi acceleration at shocks U=vu Hot shocked gas vu • e- Unshocked gas vd=1/4vu 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 vd=1/4 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 β. After n crossings, a particle with initial energy E0 will have energy E = E0βn. 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.

  39. Fermi acceleration at shocks

  40. Fermi acceleration at shocks Now we want to find k=-1+logP/log

  41. 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emec2and bulk Lorentz factor the observed emission frequency is: =e2(eB/2 mec)

  42. Motion of a particle in a magnetic field • Gyro radiation is produced by electrons whose velocities are much smaller than the speed of light: v<<c. • Mildly relativistic electrons(kinetic energies comparable with rest massXc2) emit cyclotron radiation. • Ultrarelativistic electrons (kinetic energies >> rest massXc2) produce synchrotron radiation. av|| v v-

  43. Motion of a particle in a magnetic field

  44. 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.

  45. B Synchrotron emission me

  46. Synchrotron emission

  47. 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:

  48. Synchrotron spectrum