GammaRay Bursts GRBs and collisionless shocks Ehud Nakar
Gamma-Ray Bursts (GRBs) and collisionless shocks Ehud Nakar Krakow Oct. 6, 2008
Gamma-Ray Bursts Flash of g-rays that last several seconds – the prompt emission NASA web site long lasting decaying radiooptical-X-ray emission – the afterglow Fox et. al. , 05
Longs & shorts Kouveliotou et al. 1993 ? Short GRBs Unknown – possibly NS-NS or BH-NS coalescence Long GRBs collapse of a massive star
Prompt emission - observations (long GRBs) u Duration 1 -1000 s u 1052 -1054 erg (isotropic equivalent) 1050 -1052 erg/s (isotropic equivalent) u ~0. 01 -2 Me. V photons Non-thermal spectrum; very high energy tail (at least up to Ge. V) u Rapid variability (less than 10 ms)
Prompt emission in the fireball model G>100 Inner Engine g-rays Relativistic Wind (p-e- or p-e+-eor EM) 106 cm Internal dissipation 1013 -1016 cm
Prompt emission - theory (long GRBs) The emission source is internal dissipation within a relativistic outflow, G>100! Radiation process – Unknown Leading candidates are synchrotron and IC Outflow composition and magnetization – Unknown Unmagentized pair plasma is unlikely Collisionless shocks ? – only if the outflow is baryonic mildly relativistic internal shocks
Afterglow - Observations Peaks in X-ray first (minutes-hour) , then in optical (hours-days) and finally in radio (days-years) Fn B, V, R, I Temporal & spectral structure: Broken power law n t (days) Stanek et al. 99 Galama et al. 99
The internal-external fireball model g-rays Inner Engine Relativistic Wind (p-e- or p-e+-eor EM) 106 cm Internal dissipation 1013 -1016 cm Afterglow External Shock 1016 -1018 cm
External shock afterglow model Hydrodynamics: A relativistic blast-wave that propagates into a perfect fluid (shocked fluid energy concentrated in – DR ~ R/g 2) g Shocked plasma pressure R/g 2 upstream pressure • Blast wave decelerates while shoveling mass - g R-3/2 (for a constant external density). • The burst emission ionize and destruct dust in the circum-burst medium upstream is ionized, unmagnetized, p-e plasma.
Radiation modeling: • Shock crossing electron acceleration N(g) g-p for g>gm • ee - fraction of electrons energy out of the internal energy at the shock crossing • e. B - fraction magnetic field energy out of the internal energy at any time synchrotron + Synchrotron Self-Compton radiation The model fit for five free parameters: Ek, n, p, ee and e. B
The basic (slow cooling) Synchrotron Afterglow Spectrum and its time evolution: t 0 t-3/2 t-1/2 Sari et al 1998 Synch self Absorption Observations Model Fn Low energy Fn n-1/3 Galama et al. 99 High Energy Fn n-p/2 n
The typical parameters that fit the data ee ~ 0. 1 e. B ~ 0. 01 -0. 001 p = 2 -2. 7 Ek, iso = 1052 -1054 erg (Comparable to Eg, iso) n ~ 0. 01 -10 cm-3 (expected in ISM)
Typical scales G~100 @ t=100 s G~10 @ t=1 day G~2 @ t=1 month (t – observer time since the burst) shock Lorentz factor - B Downstream B Upstream Bd~ m. G-G Bu~ m. G (e. B, up~10 -9) Width of shocked plasma ~1012 cm @ t=100 s ~1016 cm @ t=1 week Skin depth ~107 cm
Main microphysical assumptions in the basic model: • The shock is thin compared to the emitting region. • Electrons are coupled to the protons just through the shock. • All Electrons are accelerated – relaxing this assumption can change the best fit parameters by a factor f<mp/me (Eichler & Waxman 05) • ee and e. B are constant in time and space – e. B cannot drop significantly far in the downstream (Rossi & Rees 02)
Afterglow observations strongly suggest that weakly magnetized relativistic collisionless shocks: • Generate magnetic field with ~10 -4 -10 -2 of equipartition. • This magnetic field survives long after crossing the shock (>107 skin depths). • Polarization indicate that the magnetic field is anisotropic on large scales with ratio ~2: 1 • Efficiently accelerate electrons (in equipartitoin with protons energy) at least up to Te. V Note: External shock is the most popular and successful afterglow model. But, it is not the only model and it cannot explain all afterglow observations in all bursts.
Short GRBs • Prompt emission is similar to long GRBs • About dozen observed afterglows (mostly in X-ray) suggest a similar mechanism and physical properties as in long GRB afterglows • The progenitor is an old stellar system and therefore the expected circum burst medium is the interstellar medium – unaffected by massive stellar wind. The ability of collisionless shocks to generate field an accelerate particles is not unique to upstream which is shaped by stellar wind (e. g. , with high density clumps) Nakar 07
Magnetic field generation in GRB external shocks Equipartion field on a skin depth scale is thought to be generated in unmagnetized shocks by the Weibel instability (Moiseev & Sagdeev 63; Kazimura et al 98; Medvedev & Loeb 99, …) But … without sustaining process it is expected to decay over a similar scale (Gruzinov 01; Chang et al. , 08) How can the shock generate strong magnetic field that survives over ~109 skin depths?
Suggested processes: • Interaction of thermal plasma (upstream and/or downstream) with accelerated particles via kinetic instabilities (e. g. , recent numerical results by Keshet et al. 08 and Spitkovsky 08) • Amplification of the downstream field via downstream vorticity generated by • Density inhomogeneity in the upstream (e. g. , Sironi & Goodman 07) • Angular energy anisotropy of decelerating blast wave (Milosavljevic, Nakar & Zhang 07) • Interaction between streaming protons and the upstream plasma via nonresonant streaming instability (e. g. , Bell 2004, Milosavljevic & Nakar 06, Reville et al 06, …)
Generation of upstream density inhomogeneies by streaming protons (Couch, Milosavljevic & Nakar 2008) ` assumption: protons are accelerated in the shock by Fermi process shock frame Upstream frame ~R/G 2 ~R/G G e upstream p p e p upstream IC cooling grantee that if protons are accelerated to gp>103 then protons stream farther upstream then electrons
• Nonresonant streaming instability amplifies the magnetic field and produces density inhomogeneities (e. g. , Bell 04) • Even if the field is not amplified by orders of magnitude (e. g. , Pelletier et al 08), density contrast of order unity is generated. Such contrast is enough in order to amplify the downstream field to the observed levels by generating downstream vorticity. • In GRB external shocks there is enough time to generate order unity density contrast even if the seed field is the pre-existing m. G field
Summary • GRB prompt emission may be a result of mildly relativistic collisionless shocks (if GRB jets are baryonic). • GRB external shocks are unmagnetized ultra-relativistic collisionless shocks and are the prime candidates to be the source of the observed afterglows, in which case these shocks: • Generate long lasting magnetic field to sub-equipartition level • Efficiently accelerate electrons at least to Tev energies • Several processes were suggested as the source of the generated magnetic field in these shocks. None of which is confirmed yet.
Thank!
Are all the electrons need to be accelerated? g dn/dg ee fee e. B fe. B E E/f n n/f g If only a fraction me/mp<f<1 is accelerated the above mapping results in similar fit to f=1 (Eichler & Waxman 05).
Can the magnetic field decay after the shock? No decay Decay after crossing 1% A decay of the magnetic field after the plasma crosses much less than 1% of the shocked shell is hard to explain by the observations (Rossi & Rees 02)
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