Lecture 2 Relativistic Shocks in GRBs 2 Shiho Kobayashi (Liverpool JMU) We have discussed a blast wave. the dynamics: simple: single parameter E /" Blast wave model: applicable to any central engine model as long as relativistic outflow involved. Insensitive to the properties of the initial fireball (e.g. gamma, B fields ) 1
Blast wave: deceleration phase applicable well after the deceleration of a fireball & E ) E " #R 3 c 2 $ 2 % R " ( ' #c 2 $ 2 + * 1/ 3 t obs " R c$ " & E ) 2 ( ' #c 5 $ 8 + * 1/ 3 " a few hundred sec The behavior of flow at earlier time is more complicated, but the emission could reflect the properties of the initial fireball. Evolution of a Fireball (3)Coasting:GRBs (2)Acceleration (4) energy transfer fireball to ambient Lorentz factor (5)Afterglow Blast Wave!3/ 2 # " R (1)Energy release Shell/Shock radius R [cm] (S.K., Piran & Sari 1999) 2
ejecta ISM " Reverse Shock Shocked ejecta Forward Shock Shocked ISM R # of particles in ejecta much larger than in forward shock ISM. lower temperature: lower frequency (optical) E = M ejecta c 2 " # M ISM c 2 " 2 " syn #$% e 2 B " syn,rs & " syn,fs /$ 2 Once reverse shock crosses, no electron acceleration any more: Short-lived emission 3
Optical Flash : GRB 990123 ROTSE GRB 9mag! (z=1.6) (Akerlof et al. 1999; Meszaros&Rees 1997; Sari & Piran 1999; S.K 2000) Light Curves of early optical afterglow Melandri et al. LT/FTN/FTS 4
Fireball model predicts early optical emission from reverse shocks A large fraction of events: No optical flash Emitted at even lower frequencies? Dust extinction in host galaxies? Poynting flux dominated outflow? Jet break " #1/$ LOS Arc length: R" 0 Side Expansion: local sound speed ~ c Time is shorter in local frame: R /c" " = (R" 0 + c R ) /R = " c# 0 +1/# 5
Jet break: afterglow light curve GRB990510 optical prompt emission & internal shocks 6
Prompt Emission highly variable: both long and short bursts the variability plays a major role in the understanding how GRBs operate. photon counts light curve time T /"T #100 prompt emission 7
We are going to show that Blast waves (external shock) can not produce a GRB Blast wave (external shock) characteristic three timescales: Photon arrival time: line-of-sight at R and 2R Curvature timescale " R /c# 2 Width of a blast wave 1/" GRB duration? R 2R Sari&Piran1997 8
variability: small regions (blobs) in the blast wave? e.g. blast wave slowed down by small external clumps S ~ R 2 /" 2 In comoving frame, the shell width: #" = R /$ the visible volume of the shell: V " # $ " ( ) 3 1/" l e " $ #/% Blob size should be less than to produce pulses with the short timescale. Variability parameter: " = T /#T =100 The number of blobs: (#") 3 /l 3 e = $ 3 Since the number of pulses in GRB: " 2 #10 4 " only one out of blobs radiates 99.99% of the fluid is silent It is highly unlikely that GRB energy is localized inside just "10 #4 of the volume of the fluid. If energy uniformly distributed, the process is extremely inefficient. Sari&Piran1997 9
Blast wave can not produce variable GRBs Early X-ray afterglow shows flare activity X-ray fares: not due to blast wave 3) X-ray Flares (Burrows et al. 2005; Falcone et al. 2005; Piro 2005) Flares in X-ray afterglow 1/3-1/2 bursts contains detectable flares sometimes as late as 10^5sec after GRB Sharp structure : "T /T <1 Intensity varies by a large factor Flare increases by A factor of 500 Chincarini et al. Falcone et al. 10
Internal-External Shock model Internal Shocks: within relativistic outflow External Shocks: Outflow impacts on the surrounding medium GRB Afterglow X O R Internal shocks invokes a long-lived central engine to explain the longer time scale: GRB duration inhomogeneity in the outflow cases shocks inside the flow itself prduces pulses with short timescales 11
T = engine operation time collisions cause shocks, and pulses the same timescales associated with each collisions the photon arrival time: line-of-sight at R and 2R the angular spreading time the width of inhomogeneity (or each shell) " R /c# 2 (" # /c) 1/" R 2R 12
each collision produces a pulse shock crossing time : ~ " /c curvature timescale :~ R/c" 2 ~ L /c sk,piran&sari1997 initial separation between shells the superposition of the pulses from collisions the whole duration: the central engine activity 13
t Ultra-relativistic outflow propagates with photons Photons produced in outer shells come first Temporal profile of GRB directly reflects central engine activity T obs R steep decay and t0 14
Swift Collaboration (Tagliaferri et al.) XRT BAT Extrapolation to XRT band Steep decay in early X-ray afterglow (Tagliaferri et al. 2005) prompt emission tail smoothly connected with early X-ray afterglow very steep decay: alpha > 5-6: F " t #$ the tail of the last internal shock pulse 15
High Latitude emission once internal shocks cross shells, no newly accelerated electrons anymore. on-axis emission dies off emission from high latitude elements begins to dominate smaller and smaller blue-shift factors LoS Kumar & Panaitescue 2000; Fenimore et al 1995; sk,piran&sari 1997; Liang et al. 2007) High latitude emission F " t #(2+$ ) ~ #t #3 Observed decay is much steeper. Why? F " t #6 16
Power-law modeling F " t #$ early afterglow: sensitive to the choice of t=0 Piro et al.2005; Tagliaferri et al. 2005; Quimby et al. 2006 Blast wave (external shock) t=0: explosion time ~ GRB trigger time Lazzati&Begelman2006;SK&Zhang2007 Internal shocks ejection of multiple shells t=0: the ejection time of the relevant shells t t0 null obs R 17
Consider the tail of the last pulse at t=100sec logl ~ t "3 1s 10s 100s log(t " t 0 ) time since pulse contracted t 0 ~ 100s logl ~ t "3 t 0 =100s 1000s time since GRB trigger logt efficiency 18
Problem Low Efficiency kinetic energy to radiation: ~MeV Monte Carlo: ~ 10-20% SK,Piran&Sari1997;Daigne&Mochkovitch1998; Kumar&Panaitescu2000;Beloborodov2000;SK&Sari2001; Two shells collide and merger to form a single shell m r," r m s," s m s + m r + " /c 2,# m conservations: energy & momentum " m # m s " s + m r " r m s /" s + m r /" r $ =1% (m s + m r )" m (m s " s + m r " r ) Conversion efficiency kinetic energy into internal energy 19
shells with random Lorentz factors efficiency fluctuation " # A 2 /2 A 2 = $ 2 % $ 2 $ 2 " max /" min =10 # $ ~ 10 % 20% MeV? Afterglow modeling Fireball energy: 1day after the burst compared with prompt gamma-ray energy Freedman&Waxman2001 20
energy injection in the early afterglow phase? Energy budget for prompt emission ---- smaller than that evaluated in pre-swift era? flux more than 90% efficiency for some GRBs Zhang et al.2007 A few 100 sec Shallow decay: t^-0.5 " Ldt # " t $0.5 dt # t 0.5 10^3-4 sec time Generic problem in Synchrotron Shock model F " #" 1/ 3 or equivalently N " #" $2 / 3 Many events violate this limit!!! Preece et al. 1998 Thermal emission from the initial fireball Jitter radiation: mag field scales < Larmor radii of electrons Anisotropy in electron pitch angle distribution Meszaros&Rees2000;Medvedev2000;Lloy-Ronning&petrosian2002 21
>-2/3 Preece et al. 2000 Relativistic Turbulent model Alternative to internal shocks Randomly oriented relativistic emitters in a relativistically expanding shell How such macroscopic relativistic motions can be generated and sustained? Lyutikov&Blandford2002;Lazar2005;Lyutikov2006;Narayan&Kumar2009; Lazar et al.2009 22
The duration of GRBs T = R /c" 2 the scales: shell width, curvature timescale When the shell is located at R Lab time: R/c (shell expands with almost speed of light) the shell frame: R /c" the emitter frame: R /c"# " : shell's bulk expansion Lorentz factor # : emitter's random Lorentz factor in the shell frame 23
Emitters exhibit a coherent macroscopic motion Each emitter should be causally connected the size of the emitter in its own frame: r " R /#$ visible volume of the shell in the shell frame: the total number of emitters: (#"/r) 3 $ % 3 (#") 3 $ (R /%) 3 In the shell frame, an emitter has size r in a plane perpendicular to its velocity vector. assumption: each causal volume produces an emitter Emitters are confined to the shell. In the shell frame, it should make during #"/c " # /2 turn " # each emitter illuminates a total solid angle ~ 1/" " 3 1/" 2 (shell frame) ~ 1/"# 2 (obs frame) Summing over all emitters, the total solid angle: All the radiation beamed within a solid angle: each observer receives radiation from emitters " 2 " 2 /# 2 24
Relativistic turbulent model duration: shell width or curvature timescale T ~ R /c" 2 pulse width: emitter width (or curvature time of emitter) "T = R /c# 2 $ 2 the number of pulse: visible emitters " 2 out of " 3 " ~ 10 # variability parameter = T/$T =100 We observe a small fraction of emitters (~1/10) the emission highly beamed toward us Summary Internal shocks time scales, variability efficiency observations, (correlations) Relativistic turbulent model timescales, variability 25
Cepheid-like distance indicators Spectral-Energy correlations spectral peak energy fluence/peak flux of GRBs E iso " E p 2 Amati et al. 2002; Ghirlanda et al.; Yonetoku et al. Luminosity-lag peak luminosity pulse lag time between different BATSE energy channels L "#t $1 Norris et al. 2000 Luminosity-variability variable bursts:luminous L "V 3 Fenimore&Ramirez-Ruiz2000 ;Reichart et al. 2001 Ep-Eiso L-V Amati 2006 Reichart et al. 26
Variable GRBs: bright! L bright L dim t t L R = " r " s internal shock radius L $ 2% 2 s L " s # " r The pulse width: angular spreading time "t = R /2c# 2 $ L /c Pairs with small separation tend to collide at small radii and produce narrow pulses. 27
Shells are optically thick at small radii Collisions inside the photosphere do not produce pulses. Fireball optically thick below the photosphere we do not observe a large fraction of collisions, especially narrow pulses. all collisions happen outside the photosphere t t R Low gamma GRBs R High gamma GRBs (S.K., Ryde & MacFadyen 2002;Meszaros et al2002) The Correlation even more enhanced Geometrically corrected energy: constant? narrow jet: more luminous narrow jet: less baryon load? higher gamma? 28