Recent Advances in our Understanding of GRB emission mechanism Outline Pawan Kumar 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 May 6, 2013
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. Jet energy dissipation and γ-ray generation relativistic outflow central engine External shock radiation central engine jet -rays
Conversion of jet energy to thermal energy Internal/external shocks, magnetic reconnection etc. Piran et al. ; Rees & Meszaros; Dermer; Thompson; Lyubarsky; Blandford, Lyutikov; Spruit Radiation mechanism (sub-mev photons) Synchrotron, SSC, IC of external photon field, thermal radiation, jitter radiation 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 2001
GRB: current paradigm (internal shock model) Gehrels et al. (2002); Scientific American This paradigm has several problems. We don t know what replaces it though
GRB 080319B: x-ray & optical LCs 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 (Lyutikov; Lazzati & Begelman; Kumar et al.) (R s can be smaller if the steep decline is due to central engine activity) 2. Prompt bright optical flash from GRBs: R s > 10 16 cm (GRB 080319B Zou, Piran & Sari 2009)) ~ t -5 (Too steep to be RS) (RS) Kumar & Panaitescu, 09 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.
3. Detection of high energy -ray photons by Fermi/LAT (GRB 080916C, 090510 ) 10 3 R s = 2cΓ 2 δt 10 16 cm Abdo et al. 2009; Greiner et al. 2009; Kumar & Barniol-Duran 2009 (R s is close to the deceleration radius for such a high ) > ~ > ~ R s > ~ 10 16 cm is larger than expected for internal shocks (10 13 10 15 cm) Large R s is a problem for the internal shock model; internal shocks are less efficient at larger distances. Large R s is expected for a poynting jet: Lyutikov & Blandford
Radiation mechanism Synchrotron, IC or SSC in internal shocks, RS or FS, or hadronic collision or photo-pion process... 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
Let us turn to γ-ray radiation mechanism 1. Synchrotron Synchrotron peak at ~10 2 kev B i2 ~ 2x10 13 Electron cooling 6m e c(1+z) t cool = ~ (7x10 7 s) 3 i3 2 «t ~ 0.1s 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 can be found for R s >10 17 cm; IC cooling in KN regime (Nakar, Ando & Sari, 2009; Bosnjak et al.) helps but not enough.. 2. It an be shown that for the Jitter process Y»10 3 ; recent PIC simulation of Sironi & Spitkovsky (2009) casts doubt on Jitter 3. Small pitch angle radiation ( < i -1 ) can give f +ve (Lloyd & Petrosian, 2000); but shock accelerations don t produce small distribution. angle between e - momentum and B
Continuous acceleration of electrons can fix the low energy spectral index problem. Recently Uhm & Zhang (2013) suggested an interesting idea that the magnetic field downstream of the shock front decays with distance and that can prevent synchrotron cooling and flatten the emergent spectrum to α ~ 1. The field should decay on a length scale of order ct`cool = 2x10 6 cm γ 3 i3 Γ 2 2 << R/Γ for the mechanism to work. This requires some degree of fine tuning However, if γ i ~10 5 then ct`cool ~ R/Γ, and no fine tuning is needed. This is in fact the value of γ i Uhm & Zhang considered in their work. The question then is how do you get such a large γ i in internal shocks? If 1 in 10 2 electrons are accelerated in shocks, then there should be a large population of electrons with γ e ~ 10 2 which would radiate in the optical band and produce a bright flash (~10 mag).
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. sharp minimum of E e + E B ; Kumar & Narayan (2009) 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 mode (e.g. Piran, Sari and Zou, 2009).
3. Thermal radiation + IC (for prompt -rays) Thompson (1994 & 06); Liang et al. 1997; Ghisellini & Celloti 1999; Meszaros & Rees (2001); Daigne & Mochkovitch (2002); Pe er et al. (2006), Beloborodov (2009) Observational constraints 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. GRB 080916C for which there was excellent data from 8keV to ~20 GeV showed no thermal component Zhang and Pe er (2009) and that provides a severe constraint on this mechanism & baryonic jet model. Low energy spectrum should be f ν ν ν 2 which is rarely seen. The presence of a thermal component in GRB prompt emission is unclear Ryde (2004, 05) finds evidence for thermal spectrum, but Ghirlanda et al. (2007) do not. Recent work of Burgess et al. (arxiv:1304.4628) claims to see a thermal component for 5 out of 8 Fermi GRBs they analyzed.
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. The basic idea behind all these proposals is to dissipate a fraction of the energy of GRB relativistic outflow & produce non-thermal seed photons, and mildly relativistic electrons (or e ± ). Seed photons are IC scattered by e ± multiple times, at the photosphere, to produce the observed non-thermal spectrum. The dissipation below the photosphere could be a result of magnetic reconnection (Meszaros & Rees) or n-p collisions (Beloborodov 2010, 2011; Meszaros & Rees, 2011).
Vrum, Lyubarsky and Piran (2013) derive general constraints that should be satisfied by photospheric models for GRB prompt radiation. They find that a large fraction of jet energy should be dissipated at a radius of 10 10 10 11 cm and jet LF at this radius should be order a few 10s, i.e. the dissipation should take place at a high optical depth. We will consider one particular photosphere model n-p collision in some detail.
Photospheric model involving collisions between n & p Consider a baryonic jet consisting of n & p +. Neutrons accelerate with the fireball expansion as long as they collide frequently with protons. However, as the fireball expands p + density decreases as R 2 & the collision between n & p + becomes less frequent. 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.
n p decoupling radius is given by ' t np R c 4R 2 npm p c 2 0 L R np c or R np 0 L 4m p c 3 2 For n p to develop differential velocity: R np < R s = R 0 η 0 L 4m p c 3 R 0 1 4 1/ 485 L 4 1/ 4 51 R 0,7 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)
n p differential motion can also arise in internal shocks Beloborodov, 2010
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.
Meszaro & Rees (2011) added a new element to this picture n p collisions within the core of the jet, they claim, produces γ- rays of 20 MeV (higher energy γ-rays are converted to e ± since the hadronic collisions take place below the Thomson photosphere). Neutrons from the outer part of the jet which is moving more slowly diffuse inside the core region on a longer time scale, i.e. at a larger radius, and collide with protons. These collisions produce e ± which in turn produces >10 2 MeV photons. According to this picture the few second delay we see between MeV & GeV photons is due to GeV photons being produced at a larger radius.
Poynting jet dissipation and relativistic turbulence Meszaros & Rees 97; Lyutikov & Blandford 03 ; Narayan & Kumar 09 ; Lazar, Nakar & Piran 09; Zhang and Yan (2011) The acceleration of magnetic jets is very different from a thermal fireball: Γ α r 1/3 for Poynting jets when acceleration is driven by magnetic dissipation and also for adiabatic expansion of a short magnetic pulse, e.g. Contopoulos (1995), Drenkhahn (2002), Drenkhahn and Spruit (2002), Granot et al. (2011). While inside the star: Γ α r a/4 (p α r a ) These results are easy to understand using flux conservation, causality & pressure equilibrium
Example: Γ α r a/4 due to jet collimation by star (p α r a ) Consider the jet transverse radius to increase with r as R t (r). The transverse and radial components of the magnetic field, in the rest frame of the star scale as: B ϕ α R -1 t & B r α R -2 t respectively. In jet comoving frame: B ϕ α B ϕ /Γ, B r = B r & B ϕ ~ B r (to avoid magnetic pinching) Γ α R t Pressure equilibrium: B r 2 α Γ -4 α p Γ α r a/4 The fraction of magnetic energy converted to jet kinetic energy, and the fraction into radiation are still highly uncertain. 1. 2. In magnetic dissipation/reconnection jet acceleration and radiation production are approximately equal and proceed together: γ-ray emission peaks at a radius ~ R BH σ 02 /ε; where σ 0 is jet initial magnetization parameter, and ε ~ 10 2 is the speed at which reconnection proceeds (in terms of the Alfven speed). For a Poynting jet undergoing adiabatic expansion, the radiation is produced by either reconnection, if conditions are appropriate, or by internal shocks after σ drops below unity.
ICMART (Internal Collision-induced Magnetic Reconnection and Turbulence) model of Zhang & Yan (2011) suggests that jet magnetic fields get increasingly more twisted in internal collisions and eventually reconnection is triggered. Relativistic turbulence is likely produced in the ICMART model, which can give rise to short time variability even at large radius from the central engine as shown by Lyutikov & Blandford 03 ; Narayan & Kumar 09 ; Lazar, Nakar & Piran 09. 1/ R s t Line of Sight Variability time = R s (1+z) (2c 2 ) t 2 Consistent solutions for -ray emission is found & R s ~ 10 15 cm or larger as suggested by observations.
Fermi 8 KeV to 300 GeV 6/11/2008 High energy γ-rays One of the goals for Fermi is to understand γ-ray burst prompt radiation mechanism by observing high energy photons from GRBs.
Abdo et al. 2009 1. >10 2 MeV photons lag <10MeV photons (2-5s) 2. >100 MeV radiation lasts for ~10 3 s whereas emission below 10 MeV lasts for ~30s or less!
high energy photons (>100 MeV) for t > ~ 10s are produced in the External-shock via synchrotron Gehrels, Piro & Leonard: Scientific American, Dec 2002
Long lived lightcurve for >10 2 MeV (Abdo et al. 2009) (GRB 080916C) Abdo et al. 2009
Kumar & Barniol Duran (2009) Long lived lightcurve for >10 2 MeV (Abdo et al. 2009) >10 2 MeV data expected ES flux in the X-ray and optical band (GRB 080916C) Abdo et al. 2009, Greiner et al. 2009, Evans et al. 2009 We can then compare it with the available X-ray and optical data.
Or we can go in the reverse direction Kumar & Barniol Duran (2009) Assuming that the late (>1day) X-ray and optical flux are from ES, calculate the expected flux at 100 MeV at early times > 100MeV 50-300keV Optical X-ray Abdo et al. 2009, Greiner et al. 2009, Evans et al. 2009 And that compares well with the available Fermi data.
Summary SSC is highly constrained by optical + Fermi data. Synchrotron process is very likely to contribute to the GRB prompt radiation. There are stringent limits on a thermal component for prompt γ- ray emission for some GRBs whereas at least several GRBs seem to have non-zero thermal radiation (even for these we probably need synchrotron to account for low energy index). Gamma-rays of >10 2 MeV energy, after the prompt phase, are produced in the external shock via the synchrotron process. However, their origin during the prompt phase is disputed.