1. Recent Advances in our Understanding of GRB emission mechanism Pawan Kumar Outline † Constraints on radiation mechanisms ♪ High energy emission from GRBs and our understanding of Fermi data. ♪ My goal is to generate a good discussion of this topic Moscow, October 9, 2013

2. central engine relativistic outflow Make point 1 ONLY: 2. Central engine is completely hidden from our view so the progress that is being made is via numerical simulation of core collapse and other very interesting works (woosley et al. Quataert et al…)‏ 1. The relativistic jet energy produced in these explosions is dissipated at some distance from the central engine and then a fraction of that energy is radiated away as gamma-rays. CONSIDERING OUR LACK OF UNDERSTANDING OF GRB JET COMPOSITION IT IS BEST TO TREAT JET DISSIPATION AND GAMMA-RAY PRODUCTION SEPARATELY. DO NOT seond more than 30d on this slide. Jet energy dissipation and γ-ray generation External shock radiation central engine  jet   -rays A good fraction of >10 2 MeV photons appear to be generated in external shock; (photo-pion & other hadronic processes might also contribute for ~30s or so) Understanding the radiation mechanism for ~10keV – 10 MeV band is one of the most challenging problems in GRBs. Emission in this band lasts for <10 2 s, however it carries a good fraction of the total energy release in GRBs. And it offers the best link to the GRB central engine.

3. Internal/external shocks, magnetic reconnection etc. Conversion of jet energy to thermal energy Radiation mechanism (sub-MeV photons) 1. Synchrotron 2. SSC (or IC of external photons) 3. photospheric mechanism… Piran et al. ; Rees & Meszaros; Dermer; Thompson; Lyubarsky; Blandford, Lyutikov; Spruit… Papathanassiou & Meszaros, 1996; Sari, Narayan & Piran, 1996; Liang et al. 1996; Ghisellini et al. 2000; Thompson (1994); Lazzati et al. (2000); Medvedev (2000); Meszaros & Rees 1992-2007; Totani 1998; Paczynski & Xu 1994; Zhang & Meszaros 2000; Meszaros & Rees 1994; Pilla & Loeb 1996; Dermer et al. 2000; Wang et al. 2001 & 06; Zhang & Meszaros 2001; Sari & Esin 01’; Granot & Guetta 2003; Piran et al. 2004; Fan et al. 2005 & 08; Beloborodov 2005; Fan & Piran 2006; Galli & Guetta 2008; Pe’er et al. 06; Granot et al. 08; Bošnjak, Daigne & Dubus 09; Katz 1994; Derishev et al. 1999; Bahcall & Meszaros 2000; Dermer & Atoyan 2004; Razzaque & Meszaros 2006; Fan & Piran 2008; Gupta & Zhang 2008; Granot et al. 08; Daigne, Bošnjak & Dubus 2011 …

4. Energy dissipation: internal shocks (current paradigm) Gehrels et al. (2002); Scientific American (Prof. Bosnjak will talk about this model in detail)

5. Distance (R s ) of γ-ray source from the center of explosion 1.Steep decline of flux at end of GRB prompt phase suggests: R s ≈ 2c  2 δt ~ 10 16 cm suggests: R s ≈ 2c  2 δt ~ 10 16 cm (Lyutikov; Lazzati & Begelman; Kumar et al.) ( R s can be smaller if the steep decline is due to central engine activity ) engine activity ) 2. Prompt bright optical flash from GRBs: (GRB 080319B – Zou, Piran & Sari 2009 ) R s 10 16 cm (GRB 080319B – Zou, Piran & Sari 2009 ) ~ > t -5 (Too steep to be RS) (RS) Kumar & Panaitescu, 09 GRB 080319B: x-ray & optical LCs Prompt  -ray emission from GRB 080319B also suggests ; R s 10 16 cm; Kumar & Narayan; Racusin et al. 2008 ~ > ~ > Shen & Zhang (2009) provide a limit on R s from prompt optical for a number of GRBs. (This would help determine if radiation mechanism is photospheric or not)

6. 3. Detection of high energy  -ray photons by Fermi/LAT (GRB 080916C…)   10 3  R s = 2cΓ 2 δt 10 16 cm~ > ~ > However, Zou, Fan & Piran (2011), Hascoet et al. (2012) suggest Γ~300 This implies R s ~10 15 cm, and that is still much larger than photospheric radius (~10 12 cm) – this is for MeV photon emission and δt ~ 0.1 s. So the photospheric radiation is not the correct mechanism for MeV γ-rays at least for some GRBs GRB 080916C, a very bright Fermi burst, had a very stringent upper limit on thermal component (Zhang & Pe’er, 2009). Incidentally, Γ>10 3 would rule out baryonic and leptopic thermal fireball model for GRBs since Γ max ~ 850 L 52 1/4 R 0,7 -1/4 ; where R 0 the jet launching radius.

7. MeV γ-ray radiation mechanism Synchrotron 1. Synchrotron Synchrotron peak at ~10 2 kev  B  i 2  ~ 2x10 13 Electron cooling t cool = ~ (7x10 −7 s)  i3 3  2 «  t ~ 0.1s 6  m e c(1+z) —————  T B 2  i   f   −1/2 (or α = −1.5) which holds for only a small fraction of GRBs This is basically Ghisellini et al. (2000) argument; Sari & Piran 1997 Note: 1. Synchrotron solutions with α = −2/3 is possible provided that R s >10 16 cm, and Γ> 300 –– Kumar & McMahon (2008), Beniamini & Piran (2013) –– but in this case the variability time can’t be smaller than a few sec. 2. IC cooling in KN regime (Nakar, Ando & Sari, 2009; Bosnjak et al.; Barniol Duran et al.) helps but not enough.. 3. Continuous acceleration of electrons can fix the low energy spectral index problem.

8. 2. Synchrotron-self-Compton solutions It can be shown that for SSC solutions E e α R 3 and E B α R −4  emission must be produced within a narrow range of R (factor ~2) and that seems unlikely -- especially for the IS model. and that seems unlikely -- especially for the IS model. No reason that jet energy should dissipate at the minimum of E e +E B There is another problem with the SSC solution: A lack of an excess in the Fermi/LAT band (100 MeV to 100 GeV), and absence of a bright optical flash severely constrains the SSC model (e.g. Piran, Sari and Zou, 2009). The spectral peak (E p ) for SSC: α γ i 4 so one would expect a broad distribution for E p but that is not what GRB observations find Bosnjak et al. (2013) INTEGRAL: black BATSE: violet Fermi/GBM: red

9. 3. Thermal radiation + IC Thompson (1994 & 06); Liang et al. 1997; Ghisellini & Celloti 1999; Meszaros & Rees (2001); Daigne & Mochkovitch (2002); Pe’er et al. (2006), Beloborodov (2009)… (for prompt  -rays) Low energy spectrum should be f ν  ν—ν 2 which is rarely seen. Photospheric radius ~ 10 12 cm  3 −3 L j53 ; Photospheric radius ~ 10 12 cm  3 −3 L j53 ; so the IC of thermal radiation is expected to take place at a much smaller radius than R s ~ 10 16 cm we are finding. Observational constraints However, recent work of Burgess et al. (arXiv:1304.4628) claims to see a thermal component for 5 out of 8 Fermi GRBs they analyzed. Vrum et al. (2013) & Asano & Meszaros (2013) provide general constraints on photospheric models for MeV emission (Vrum’s talk on Monday) They find that a large fraction of jet energy should be dissipated at a radius of 10 10 –10 11 cm –– optical depth ~10 –– and jet LF at this radius should be order a few 10s, i.e. the dissipation should take place at a high but not too large optical depth, i.e. some fine tuning needed. Theoretical constraints

10. ★ Consider a baryonic jet consisting of n  p +. Neutrons accelerate with the fireball expansion as long as they collide frequently with protons. Eventually at some radius (R np ) n & p + decouple & hereafter n  are no longer accelerated whereas p + Lorentz factor could continue to increase with R as long as Γ(R np ) < η. The resulting differential velocity between n & p + result in their collision and conversion of a fraction of jet KE to thermal energy below the photosphere. ★ ★ ★ Since GRB spectra are largely non-thermal, there are many different proposals as to how to modify the photospheric radiation so that the emergent spectrum is non-thermal. Let us consider one particular photosphere model – n-p collision

11.  n–p decoupling radius is given by – or For n – p to develop differential velocity: R np < R s = R 0 η Thus, GRB jets consisting of n  & p  & terminal Lorentz factor > 400 will undergo n  – p  collisions below the Thomson photosphere & convert a fraction of jet kinetic energy to radiation & e ± thermal energy (Beloborodov 2010; Vurm et al. 2011 & Meszaros & Rees 2011)

12. n  – p  differential motion can also arise in internal shocks Beloborodov, 2010 ★

13. c Γ 2 δt Radius where internal collisions occur: R col = c Γ 2 δt And the radius where the probability of n-p collisions drop below 0.5 is: R np α Γ -3  R col /R np α Γ 5 For an efficient conversion of outflow kinetic energy to thermal energy via n–p collisions these radii should be approximately equal, and that requires: 50 < Γ < 10 2 ★ ★ ★ Which does not appear to be consistent with GRB data.

14. Origin of high energy photons (>100 MeV) Prompt phase : high energy photons during this phase might have a separate origin than photons that come afterwards if rapid fluctuations and correlation with MeV lightcurve is established. Observers need to quantify the statistical significance of this! Hadronic processes: proton synchrotron, photo-meson … Inefficient process – typically requires several order more energy than we see in the MeV band (unless Γ were to be small, of order a few hundred, which few people believe is the case for Fermi/LAT bursts), e.g. Razzaque et al. 2010, Crumley & Kumar 2013. Bottcher and Dermer, 1998; Totani, 1998; Aharonian, 2000; Mucke et al., 2003; Reimer et al., 2004; Gupta and Zhang, 2007b; Asano et al., 2009; Fan and Piran, 2008; Razzaque et al. 2010; Asano and Meszaros, 2012; Crumley and Kumar, 2013…. Internal shock and SSC : e.g. Bosnjak et al. 2009, Daigne et al. 2011

15. Afterglow: external shock synchrotron, IC in forward or reverse shock of prompt radiation or afterglow photons; IC of CMB photons by e ± in IGM; pair enrichment of external medium and IC… Dermer et al., 2000; Zhang and Meszaros, 2001; Wang et al. 2001; Granot and Guetta, 2003; Gupta and Zhang, 2007b; Fan and Piran, 2008; Zou et al., 2009; Meszaros and Rees 1994; Beloborodov 2005; Fan et al., 200; Dai and Lu 2002; Dai et al. 2002; Wang et al. 2004; Murase et al. 2009; Beloborodov 2013….

16. GRB 130427A (Perley et al. arXiv:1307.4401) MeV duration (T 90 ) = 138s, LAT duration (T GeV ) > 4.3x10 3 s; T GeV /T 90 > 31 Highest energy photon (95 GeV) detected 242s after T 0 ; z=0.34; E γ,iso = 7.8x10 53 erg

17. GRB 110731A (Ackermann et al. 2013)

18. Kumar & Barniol Duran (2009) and Ghisellini, Ghirlanda & Nava (2010) showed that high energy γ-ray radiation from GRBs, after the prompt phase, are produced in the external-forward shock via the synchrotron process. The reasoning for this will be described in the next several slides. Gehrels, Piro & Leonard: Scientific American, Dec 2002

19. Flux above ν c is independent of density and almost independent of ε B Consider GRB circumstellar medium density profile: Blast wave dynamics follows from energy conservation: Observer frame elapsed time: Comoving magnetic field in shocked fluid: Synchrotron characteristic frequency: Observed flux at ν m : Synchrotron cooling frequency: Observed flux at ν:..

20. The flux from the external shock above the cooling frequency is given by: Note that the flux does not depend on the external medium density or stratification, and has a very weak dependence on ε B. 0.2 mJy E 55 (p+2)/4 ε e p-1 ε B (p-2)/4 (1+z) (p+2)/4 f ν = d L28 2 (t/10s) (3p-2)/4 ν 8 p/2 (1+Y) _______________________________________ Y << 1 due to Klein-Nishina effect for electrons radiating 10 2 MeV photons.

21. Temporal decay index in Fermi/LAT band; Ackermann et al. 2013 The expected decline of the >100 MeV lightcurve according to the external shock model is t -(3p-2)/4. For p=2.2 the expected decline is t -1.1 which is in agreement with Fermi/LAT observations.

22. Table of expected and observed 100 MeV flux 080916C 090510 090902B 110731A 130427A 50 9 300 8 48 67 14 220 ~5 ~40 Expected flux ♪ from ES in nJy Observed flux (nJy) Time (observer frame in s) 150 100 50 100 600 4.3 0.9 1.8 2.83 0.34 z 8.8 0.11 3.6 0.6 0.78 E γ,54 _____________________________________________________________ ♪ We have taken energy in blast wave = 3E γ, ε e =0.2, p=2.4, ε B =10 -5

23. Nava et al. 2013 -- arXiv:1308.5442 According to the external shock model the LAT flux should be proportional to E (p+2)/4 ε e p-1 or ~ (Eε e ) (E is proportional to E γ,iso and PIC simulations suggest ε e ~0.1-0.2) t -(3p-2)/4 ≈ t -1.1 t -(3p-2)/4 ≈ t -1.1 (independent of n, ε ) B

24. Abdo et al. 2009 (GRB 080916C) Long lived lightcurve for >10 2 MeV (Abdo et al. 2009) f ν α ν -1.2 t -1.2 α = 1.5β – 0.5 (FS) α = 1.5β – 0.5 (FS)

25. >10 2 MeV data  expected ES flux in the X-ray and optical band (GRB 080916C) We can then compare it with the available X-ray and optical data. Abdo et al. 2009, Greiner et al. 2009, Evans et al. 2009 Long lived lightcurve for >10 2 MeV (Abdo et al. 2009) Kumar & Barniol Duran (2009)

26. Or we can go in the reverse direction… Assuming that the late (>1day) X-ray and optical flux are from ES, calculate the expected flux at 100 MeV at early times And that compares well with the available Fermi data. X-ray Optical > 100MeV 50 - 300keV Abdo et al. 2009, Greiner et al. 2009, Evans et al. 2009 Kumar & Barniol Duran (2009)

27. The expected flux between 100 MeV and ~10 GeV due to synchrotron emission in external shock is within a factor 2 of the observed flux (as long as electrons are accelerated as per Fermi mechanism). The predicted flux is independent of ISM density and ε B. And hence the flux predictions are robust. An alternate mechanism to explain the >100 MeV flux observed by Fermi/LAT would have to make a more compelling case than the external shock model. ★ ★ A Brief Summary Let us look at one recent proposal…

28. According to the recent proposal of Beloborodov et al. (2013) – IC scattering of MeV photons by e ± produced in the external medium – when R(1+z)/2cΓ 2 (observer frame time for arrival of IC photons) exceeds a few time T 90 the GeV flux should decline sharply. 080916C 090510 090902B 110731A 130427A >7 360 23 75 >30 60 0.3 30 7.3 138 >400 120 700 550 >4300 T 90,MeV (s) T LAT (Power-law decline part) in s T LAT /T 90,MeV ___________________________________________________________ In other words this model suggests T LAT < 3 T 90,MeV ~

29. There is little evidence for high density CBM required for this model to work (A * ~ 0.5). Moreover, the high density is likely to over produce 100 keV flux at t obs < T 90,MeV The large optical flux according to this model (~1 Jy) could have escaped detection. However, its IC scattering off of e ± produces ~10 keV photons with flux ~ τ ± f opt ~ a few mJy that is harder to hide. Deceleration radius (for wind medium) R d = 2x10 15 E 55 A * -1 Γ 0,3 -2 cm

30. What about 10 GeV – 95 GeV photons detected from GRB 130427A? Highest energy photon (95 GeV) was detected 242s after the trigger (z=0.34, E γ,iso = 7.8x10 53 erg) when Γ~ 10 2. Highest possible energy for synchrotron photons is when Could these be produced by the synchrotron process? electrons lose half their energy in one Larmor time (Because electrons gain energy by a factor ~2 in shock acceleration in ~ a few Larmor time) m e γ e c qB Larmor time = Synchrotron loss rate = σ T B 2 γ e 2 c 6π Larmor time x Synchrotro loss rate < m e γ e c 2  ν max = q γ e 2 ΓB 2π m e c < 9m e c 3 Γ 16π q 2 = 50 Γ MeV ★ ★ ★ < 10GeV ~ >10GeV photons might be due to IC in external shock, however, perhaps the above limit could be violated by inhomogeneous B.

31. Summary High energy photons (>100 MeV), after the prompt phase, are produced by the simplest possible mechanism one could imagine, i.e. synchrotron in external shock. However, it is unclear how >10 GeV photons are produced. The mechanism for generation of photons of energy between ~10 keV and 10 MeV remains elusive. ✫ ✫