Radiative processes in GRB (prompt) emission. Asaf Pe er (STScI)

Transcription

1 Radiative processes in GRB (prompt) emission Asaf Pe er (STScI) May 2009

2 Outline Historical approach Synchrotron: pro s and co s Compton scattering in prompt emission (and why it is different than in afterglow) The importance of production & annihilation Thermal emission

3 Trying to make some sense out of what we see.

4 We see photons. Q: where do these photons originate? High energy γ-rays Non-thermal spectra

5 By mid 90 s: > 118 different theoretical models! (So, people didn t really know what was going on!!?) Nemiroff, 1993

6 Photons must originate Somehow. Why synchrotron?? A very efficient way of producing non-thermal spectrum believed Known to exist in many astronomical objects Well understood Ingredients: Energetic electrons Magnetic field Known (at least ) from the 60 s (e.g., Ginzburg & Syrovatskii, 1965, 1969)

7 Why synchrotron (2) Getting a power law spectrum is straightforward - only need power law distribution of electrons In (very) good agreement with Afterglow observations Theory (Sari, Piran & Narayan, 1998) Afterglow observations (Wijers & Galama, 1998)

8 So, basically the problem is 1. Produce B field reduced to: 2. Produce energetic electrons 3. Produce Power law distribution Non is really known. However, it is Believed, that shock waves can make all of this Introduce ignorance parameters : ε e, ε B

9 Variability in the prompt - often interpreted as due to internal shock waves! Afterglow - Interpreted as due to external shock! Shock waves are expected all over! (well, maybe )

10 But can shock waves do the trick? Particle-in Cell (PIC) simulations: Trace particles tracks & evolution of E, B fields when plasma collide. Solve Maxwell eqs. in 3D Spitkovsky, 2006 Nishikawa+ 2005, 2006 collisionless shocks : Particle interact with each other via E, B fields

11 Magnetic fields are predicted to occur due to 2-stream instability Weibel, 1959 Medvedev & Loeb, 1999 And are seen in PIC simulations Density B 2 But decay on a very short scale. Research on-going Spitkovsky, 2006

12 Can synchrotron be used to explain the prompt emission? Prompt spectrum: Historically described by the Band function (broken power law) (Band et. al., 1993) 4 free parameters: E peak ~0.1-1 MeV α, Low energy spectral slope β, high energy spectral slope A, Overall normalization Preece et. al., 1998, 2000

13 Lets look at the data: Preece et. Al. 98, 00 Kaneko et. Al. 06 <α>=-1 (νf ν ~ ν 2+α ν +1 ) <E peak >=250 kev <β>=-2.33

14 Compare theory and data I. High energy spectral slope Theory: Emission from power law dist. of electrons: dn el /dγ ~γ -p F ν ~ν -(p-1)/2 (slow cooling) F ν ~ν -p/2 (fast cooling) Data: F ν ~ν 1+β ~ν <β>=-2.33 Slow cooling: (p-1)/2 = 1.33 p=1.66 Fast cooling: p/2 = 1.33 p=2.66 (Theory of relativistic Fermi acceleration: 2.0 p 2.4)

15 Compare theory and data II. <E peak > = 250 kev Lets put some numbers: Observed energy - Energy density - Magnetic field - Characteristic elec. L.F. - ob E peak u = = h 3 2 qb m e c " 2 # el (1+ z) L 4$r 2 # 2 c = 3%108 L 51 r &2 &2 13 # 2.5 B = 8$' B u (10 4 1/ L 2 51 r &1 13 # &1 1/ ' B,&2 ) m " el = ' p, e +. / 200' e,&1 * - m e erg cm -3 G ob E peak = 15 (1+ z) L 1/ 2 51 r " # e,"1 1/ 2 # B,"2 = 650 (1+ z) L 1/ 2 51 r " # e,"1/ 2 1/ 2 # B,"1/ 2 kev kev (values of ε e, ε B referred from afterglow) (But high values of ε e, ε B )

16 Compare theory and data III. Low energy spectral slope <α>=-1 ob E peak = 650 (1+ z) L 1/ 2 51 r " # e,"1/ 2 1/ 2 # B,"1/ 2 kev Naively: Single particle, slow cooling - <α> = -2/3 Below the self absorption freq: <α> = +1 But what is the cooling frequency? t cool (") = E p = 6#m ec $ T "B 2 ; t dyn = r %c t cool = t dyn & " c = 6#m ec 2 % $ T B 2 r ob E cool ' 0.1 (1+ z) L (3 / 2 51 r 13 % 6 (3 / ) B,(1/ 2 ev Electrons cool very rapidly! Should have <α> = -3/2 inconsistent!

17 Can this still be resolved? Need to think of new ideas: e.g., Comptonization in K-N regime (Derishev+03) Alternative: maybe the electrons don t cool so much. - magnetic field decays very rapidly (Pe er & Zhang 06) ε B as a function of Z (taken from Frederiksen et. a.l., 2004) Simulations are carried out over ~100 skin depth 10 cm; ct dyn ~10 8 cm ~ 10 9 skin depth We have no idea how the magnetic field evolves!! So maybe it does decay??

18 Summary of Synchrotron Natural - seen in many objects Explains Afterglow Efficient Well understood Consistent with the general picture of shock waves Partially consistent with the data Initiate a huge effort aimed to understand creation of B-field and particle acceleration is shock waves Xinconsistent with low energy spectral slopes XNot at all clear that there are shock waves in prompt! (inefficient way of dissipating energy)

19 ..or maybe it is something completely different! Compton scattering (eγ eγ, with energy exchange) Sari & Esin (01) Importance depends on: 1) Optical depth (=number of scatterings) 2) Photon & electron energy: Thompson regime - ε(in)γ el <=m e c 2; ε(out) ~ ε(in)γ el 2 ; At higher energies - the cross section drops, σ ~ ε -1 ( Klein Nishina suppression )

20 Lets have a look at the optical depth τ~δr n σ T Afterglow: σ T ~10-24 cm 2 R~10 18 cm ; ΔR = R/Γ n ~ 4 Γ n ISM ~ 40 Γ 1 n ISM,0 cm -3 τ ~ ; Most of the photons don t scatter at all! Note though that this fact does not mean that the Power emitted by IC is insignificant; P Every scattered photon gains ΔE/E in ~γ el2, and IC = u " P Syn u B

21 A look at the optical depth (II) Prompt: R ~ cm; "R = R/# n p = L 4$r 2 c# 2 % p m p c = 2 2 &1011 L 51 R '2 13 # '2 2.5 % '1 p,0 cm -3 ( )e ~ 10 '2 L 51 R '1 13 # '3 '1 2.5 % p,0 Marginally - most of the photons don t scatter But lets look at the electrons: n " = L 4#r 2 c$ < % " > = 5 &1016 L 51 r '2 13 $ '1 2.5 < % ",MeV > -1 cm -3 ( e" ~ 10 3 L 51 r '1 13 $ '2 2.5 < % ",MeV > -1 In the prompt phase, an electron undergo many scattering! -> Electron energy distribution is very likely to change! (complicated effect - depends on the energy of the photons)

22 Expected spectra I. Low optical depth: distinctive components Relative importance - depends on microphysics (ε e, ε B ) Sync. (Pe er & Waxman, 2004) IC ε e ~ε B ε e >>ε B

23 Expected spectra II. High optical depth: (quasi)- thermalization Pair annihilation peak (will be smeared) What happens: Electrons lose their energy; Photons undergo many scattering Spectrum becomes quasi-thermal - very different than synchrotron!

24 Pair production, pair annihilation I. Pair production rate: n " e>me c 2 = L 4#r 2 c$ 2 m e c 2 l'= % "" &ee = L' T 4#rc$ 3 m e c 2 At l >>1, production rate of pairs is very rapid; Approximate as energy injection rate in energetic photons R "" #e ± $ u < E > t dyn ~ L 4%r 2 c& 2 m e c 2 t dyn

25 Pair production, pair annihilation R "" #e ± $ u < E > t dyn ~ II. Pair annihilation & balance: L 4%r 2 c& 2 m e c 2 t dyn For low energy pairs, " ± ~ " T # ~ " T Annihilation rate: R $ n 2 e ± "## ± c% T At steady state: R "" #e ± = R e±#"" $ n ± % l'1/ 2 Even at high compactness, large number of pairs is NOT expected r& T $ ' ± % l' 1/ 2 (Pe er & Waxman, 2004)

26 Pair production and maximum observed energy Pair production limits the maximum energy of photons: Basically, very similar calculation. Estimate the number of photons from the observed flux: dn " dtdsde = f 0E #$ N " (E>E') = 4%d 2 f 0 &t E'1#$ 1# $ ; n " = N " 4%r 2 'r ( "" )e ± = 'r* T n " ; E 1 ob E 2 ob +, 2 m e c 2 ( "" )e ± = C($)* T 4%d 2 f 0 &t 4%r 2 (1# $) - /. E ob m e c #1+$, 2#2$ Krolik & Pier (1991) Lithwick & Sari (2001) The requirement τ=1, for a given E ob limits, R, Γ

27 Example: High energy emission in GRB c GRB080916c: - energetic (E iso ~ 9 x10 54 erg) - High energy emission: 13.2 GeV - No evidence for thermal emission Zhang & Pe er, 2009

28 Summary: Compton, pair prod., pair ann. For small number of scattering - IC contributes to the high energy part For large number of scattering - Compton scattering modifies the entire spectrum Pair production limits the maximum observed energy Pair annihilation prevents very large number of pairs; Limits the contribution of pairs.

29 Thermal emission High optical depth: τ>1 Low optical depth: τ<1 Photospheric radius: r ph = 6*10 12 L 52 Γ 2-3 cm..is naturally expected in the fireball model E G -> E k -> E γ Meszaros & Rees (2000) Meszaros+ (2002) Rees & Meszaros (2005)

30 Thermal emission: additional spectral component Various components: Synchrotron, Thermal, Comptonization of thermal relatie importance depends on r, Γ, ε e, ε B. Meszaros & Rees (2000)

31 Complex spectrum due to back reaction Pe er, Meszaros & Rees 2006 Electron cool by IC, gain energy by direct Compton; Low energy elec. (in steady state), up scatter photons -> resulting spectrum is complex, depends on the optical depth Steep at low energies, flat above the thermal peak, due to IC.

32 Photosphere in relativistically expanding plasma is θ- - dependent Relativistic wind r ph (") = R & d " ( # ' sin(") $ % ) + * R d M $ & & T = 3# 10 L 4m % c p " 17! cm for " <<1;# >>1$ r ph (") % R ' d 1 2& # + " 2 * ), ( Photon emission radius Abramowicz, Novikov & Paczynski (1991) $ "t ob. # r ' ph & ) * 2 % c ( 2 = R $ d * 2 ' & ) 3+c % 2 ( 2 # 30L 52, -1 2 * 4-1 s Thermal emission is observed up to tens of seconds! Pe er (2008)

33 Summary: thermal component Naturally expected in fireball model Adds further complexity to the spectrum: additional source of photons to IC Can modify electron distribution Relative importance depends on exact flow parameters Temporal behavior - high latitude emission in optically thick expanding plasma

34 Summary I discussed radiative processes that shape the prompt emission: Synchrotron Compton scattering production & annihilation of pairs Thermal emission The complex conditions, in particular high optical depth implies a wealth of spectra that are difficult to model analytically!!