GRB : Modeling of Multiwavelength Data
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1 GRB : Modeling of Multiwavelength Data Soeb Razzaque NRC-NRL, Washington, DC Gamma Ray Bursts Workshop, Nov 8-12, GSFC
2 Detection of GRB Fermi GBM and LAT observations Trigger on 2009 May 10 at 00:22:59 UT Fluence of the burst : (T( T ) ) s erg cm -2 (10 kev - 30 GeV) ; erg cm -2 (15 kev GeV) Swift BAT observations Trigger on 2009 May 10 at 00:23:00 UT (RA, DEC) = ( ο, ο ) Duration : T 90 = 0.3 ± 1 s Fluence of the burst : (T( T ) ) s erg cm -2 (15 kev GeV) Spectroscopic redshift (3.5 days) from VLT/FORS ± erg isotropic-equivalent gamma-ray energy release! Most luminous short GRB detected to-date!! 2
3 GBM and LAT Light Curves Ackermann et al Photon arrival info. GBM triggered on a weak precursor Main GBM emission starts at ~T sec >100 MeV emission starts at ~T s >1 GeV emission starts at ~T s 31 GeV photon at ~T s Highest from a SGRB Extended HE emission 3
4 Duration of GRB Duration varies across the instruments in different energy ranges Compare with Swift kev duration Done here at GSFC! Ackermann et al
5 Spectroscopy of GRB Band function fit to the BGO-0, NaI-6, NaI-7 and BAT data Done here at GSFC! s interval Band α = Band β = -10 E pk = 1907 kev A = /kev/cm 2 /s 5
6 Spectroscopy of GRB PL component in addition to phenomenological Band Spectrum Band Power-law Band-only fit Band α = Band β = E pk = 4.1 MeV A = /kev/cm 2 /s E max =30.5 GeV E max =3.43 GeV Time-resolved spectra: emergence of a hard power-law component 6
7 GRB Jet and Emission Model Rees, Meszaros, Piran and others standard GRB model Synchrotron emission by shocked electrons for prompt and afterglow emission 7
8 γγ Opacity and Bulk Lorentz Factor Numerical calculation of opacity for e + e pair production opacity Assumption: High-energy and target photons from the same internal shocks with radius R ~ Γ 2 ct v Minimum bulk Lorentz factor target photon distribution " ## (E = E max ) =1 $ % = % min Gould & Shreder 1966 Band spectrum Analytic calculation with a delta-function approximation for the cross-section and for Band spectrum 8
9 Γ min for GRB Ackermann et al
10 Extended Emission from GRB Multi-wavelength light curves in γ ray, x ray and UV Smooth power-law evolution of the fluxes are compatible with afterglow model t 0.5±0.1 t t -1.38±0.07 Afterglow De Pasquale et al t -0.74±0.03 Earth occultation t
11 GRB Blast Wave Evolution Coasting blast wave with roughly constant Γ 0 until total kinetic energy of the spherical blast wave = swept-up material (constant density medium n cm -3 ) E k = 4 3 " R3 nm p c 2 # 2 With relationship R = 2" 2 act(1+ z) #1 a = 1 coasting Deceleration time: % 3E t dec " (1+ z) k ' 32#nm p c 5 8 & $ 0 ( * ) 1/ 3 ~ 1.9(1+ z)(e 55 /n) 1/3 $ 3 +8 / 3 s Subsequent evolution in the self-similar phase Blandford-McKee 1976 a = 4 after deceleration (adiabatic( adiabatic) a = 7 after deceleration (radiative( radiative) Focus on Adiabatic case Bulk Lorentz factor: Blast wave radius: % 3E "(t) # k (1+ z) 3 ( ' * &' 32$ nm p c 5 a 3 t 3 )* $ 3E R(t) " k at ' & ) %& 2# nm p c(1+ z) () 1/ 4 1/ 8 ~ 763(1+ z) 3 / 8 (E 55 /n) 1/8 t s +3 / 8 ~ 1.4 *10 17 (1+ z) +1/ 4 (E 55 /n) 1/4 t s 1/ 4 cm 11
12 Forward Shock in the GRB Blast Wave Forward shock evolves as Γ(t) Energy injection rate in the forward shock: e shock = 4" nm p c 2 # 2 A fraction ε B =u B /e shock is converted to magnetic field /e shock Magnetic field in the FS: B "(t) # $(t) 32%& B nm p c 2 ~ 300(1+ z) 3 / 8 1/ & 2 B (E 55 n 3 ) 1/8 '3 / t 8 s G A fraction ε e of e shock is injected in shocked electrons forming a non- thermal spectrum above # m,e " (t) =$ e (m p / m e )%(t) k %1 1% (' " e = # e $ m,e & /' sat,e & ) k%2 e ;k ( 2 k%1 k % 2 1% (' m,e & /' sat,e & ) n e =n p in the pre-shocked fluid ξ e is the fraction accelerated dn d " # e Electron spectrum $k # e " m " p e # #" m sat,e e # e " 12
13 Synchrotron Afterglow Model - I Synchrotron radiation by shock-accelerated electrons in the FS Synchrotron cooling time for electrons: t syn " (# e " ) = 6$ m ec % T B " 2 " Equate cooling time to dynamic time t dyn =tγ/(1+ /(1+z) and solve for γ e Synchrotron cooling break: # c,e " (t) ~ 12(1+ z) $1/ 8 % $1 B (E 3 55 n 5 ) -1/8 1/ 8 t s Fast cooling - all electrons cool within dynamic time: γ c,e < γ m,e Slow cooling - high-energy electrons cool within dynamic time: γ c,e > γ m,e # e Cooling causes a break in the electron spectrum: (and a break in synchrotron spectrum) & n( # e " ) $ #" %k ; # e " < " ' (# " %k%1 ; # e " > " # c,e # c,e Synchrotron frequency: h" = 3 2 B # eh m e c $ e # 2 % 1+ z 13
14 Synchrotron Afterglow Model - II Synchrotron flux normalization Total number of emitting electrons in the blast wave: N e (t) = 4 3 " R3 (t)# e n Synchrotron power from each electron: P e (# e " ) = c$ T 6% B " 2 2 # e " Total synchrotron flux at maximum from the blast wave at ν m,e F max ",e = N e (t) 2 4# d L P e (% m,e $ ) & 2 (t) h" m,e (1+ z) ~ 52 ' e E 55 (( B n)1/ 2 Jy 2 2 (1+ z) d 28 Fast-cooling spectrum: ν c,e < ν m,e ; Slow-cooling spectrum: ν c,e > ν m,e Transition time from fast-to-slow ν c,e = ν m,e : t 0,e ~ 1.5 "10 10 (1+ z)(# B $ e ) 2 ne 55 s Synchrotron break frequencies and flux evolve with time Different parts of the spectra evolve differently closure relations 14
15 GRB Afterglow - Synchrotron Spectra Fast cooling : ν m > ν c F ν ν β t α closure relations " c < " < " m : F " #" $1/ 2 t $1/ 4 " > " m > " c : F " #" $ p / 2 $(3 / 4)( p$2 / 3) t Sari, Piran & Narayan 1998 p-particle particle spectral index : Slow cooling : ν c > ν m dn de " E# p F ν ν β t α closure relations " m < " < " c : F " #" $( p$1)/ 2 $(3 / 4)( p$1) t " > " c > " m : F " #" $ p / 2 $(3 / 4 )( p$2 / 3) t 15
16 Jet break and Spectral Changes Spherical blast wave approximation is valid as long as θ jet > θ view ~1/Γ(t) Edges of the jet becomes visible at a time t = t jet when Γ(t jet ) ~1/θ jet Jet-break time: t jet "10 5 (1+ z)(e 55 /n) 1/3 8 / # 3 $1 s Sari, Piran & Halpern 1999 After jet- break time " m # t $2 [t $3 / 2 ] " c #const. [t $1/ 2 ] F " max # t $1 [const.] Modified closure relations after break " m < " < " c : F " #" $( p$1)/ 2 t $ p [t $(3 / 4)( p$1) ] " > " c > " m : F " #" $ p / 2 t $ p [t $(3 / 4 )( p$2 / 3) ] Acromatic break in Flux decay index α and β are not related Collimation-corrected absolute jet energy: E jet " 1 # 2 2 jet E k ;# jet <<1 16
17 Leptonic-Hadronic Synchrotron Model Both electrons and ions are accelerated in the Forward shock dn d " # A $k # A " 1 Ion spectrum $k # A " 2 dn d " # e Electron spectrum $k # e " " " A # # sat,a " # A " m " p e # #" m sat,e e # e " Scaling relations for proton- to ion-synchrotron radiation Crucial parameters: ε B ; η A, η e, k and k 2 are fitted from data Fraction of jet energy: ε A and ε e are calculated from required spectra 17
18 Modeling GRB Data Use closure relations F ν ν β t α to determine β and k or k 2 Note: e-synchrotron model alone cannot satisfy the closure relations XRT light curve: t -0.74±0.03 in between ~100 s and 1.4 ks Model with e-synchrotron in the fast-cooling and for ν XRT > ν m,e > ν c,e k = (4/3)α XRT + 2/3 = 1.65 ± 0.04 ; β XRT = k/2 = 0.83 ± 0.02 LAT light curve: t -1.38±0.07 in between ~0.3 s and 100 s Model with p-synchrotron in the slow-cooling and for ν m,p < ν LAT < ν c,p k 2 = (4/3)α γ + 1 = 2.84 ± 0.09 ; β γ = (k( 2-1)/2 = 0.92 ± 0.05 β γ needs to be compatible with measured LAT photon index (and it is) Parameters such as n ISM and Γ 0 are mainly constrained by t dec 0.3 s Parameters such as E k,iso,ε B, η e, η p are set to produce required fluxes Parameters ε e, ε p are calculated from other parameters and constrained <1 UVOT light curve is constrained by XRT (e-synchrotron) BAT light curve can not be fitted continued central engine activity 18
19 Leptonic-Hadronic Synchrotron Spectra Protons and electrons p - synchrotron (k 2 = 2.84) p is always slow-cooling e shifts from fast- to slow- cooling in s % "F " # " 4 / 3 % ' ;" < " " 4 / 3 ;" < " & m,p e - synchrotron ' c,e (' " 0.08 ;" $ " "F " #&" 1/ 2 ;" m,e > " $ " c,e m,p (k = 1.65) ' (" 0.18 ;" $ " m,e LAT emission is dominated by p- synchrotron with photon spectrum ν Compatible with data 19
20 Light Curves from Afterglow Modeling Multiwavelength light curves from combined leptonic-hadronic modelling Solid lines: p-synchrotron synchrotron,, Dashed lines: e-synchrotron EO E k = erg n = 3 cm -3 Γ 0 = 2400 ε B = 0.3 ε p = 0.5 ε e = 10 4 Razzaque 2010 η e = 20(m e /m p ) η p = 5000 k = 1.65±0.04 k 2 = 2.84±
21 Absolute GRB Jet Energy Ratio of gamma-ray to kinetic energy E γ,iso ~ erg E γ,iso /E k,iso ~ 0.01 Collimation-corrected energy follows from jet-break time t jet "10 5 (1+ z)(e 55 /n) 1/3 8 / # 3 $1 s Sari, Piran & Halpern 1999 Jet-break time during the Earth Occultation: 1.4 ks < t jet < 5.1 ks Jet opening angle: 1 degree < θ jet < 1.5 degree Absolute jet energy: (3-7) erg Is there an absolute maximum? erg θ jet ~6 degree 21
22 Build your own Afterglow Model and fit Multiwavelength Data 22
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