Afterglows Theory Re em Sari - Caltech

Transcription

1 Π= Π m /3 Afterglows Theory Re em Sari - Caltech 30s 2h t -2 30m t +1/2 t Rising -1 spectrum ν 1/3 1d t d t -1.5

2 Gamma-Ray Burst: 4 Stages 1) Compact Source, E>10 51 erg 2) Relativistic Kinetic Energy 3) Radiation due to Internal Shocks = GRB 4) Afterglow by External Shocks

3 Gamma-Ray Burst: 4 Stages Coasting, IS=GRB Energy release Thermal acceleration Deceleration= Afterglow

4 4 Stages Coasting, IS=GRB Thermal acceleration Early Afterglow FS + RS Deceleration= Afterglow Late Afterglow Newtonian Energy release

5 Afterglow was Predicted! Paczyski & Rhoads 1993 Katz 1994 Vietri 1996 Meszaros & Rees 1997 Sari & Piran 1997 GRB: internal shocks afterglow: external shocks GRB proper is NOT the early afterglow

6 Simple Theory Dynamics: deceleration of the relativistic shell by collision with the surrounding medium (Blandford & McKee 1976; Meszaros & Rees 1997; Waxman 1997; Sari 1997; Cohen, Piran & Sari 1998; Rhoads 1999; Best & Sari 2000) Radiation: synchrotron & Inverse Compton (IC) (Meszaros & Rees; Katz & Piran; Waxman; Sari, Piran & Narayan; Granot Piran & Sari) Clean, well defined problem. Few parameters: E, n, p, ε e, ε B initial shell ISM Energy Density Electron distribution Electrons energy Magnetic field

7 Theoretical Spectra (Sari, Piran & Narayan 1998)

8 N(γ e ) Theoretical Spectra (Sari, Piran & Narayan 1998) N(γ e ) γ e -p +B cooling γ e ν 2 universal ν ~ B γ e 2

9 Synchrotron Radiation: Calculating n a n m n c F max Synchrotron: ν~ Γ Bγ e 2 & F ν ~ Γ B B 2 /8π ~ ε B Γ 2 n m p c 2 n m : γ e ~ 1840 ε e Γ n c : P t/ Γ = γ e m e c 2 F max ~ Γ B * 4πR 3 n/3 F ν< νa ~ 2c -2 n 2 kt (R/ Γ) 2 Γ

10 Observations vs. Theory P=2? (Galama et. al., 1998 compared to Sari, Piran & Narayan 98) Good agreement between theory and observations

11 Theory & Observations (Harrison et. al. ; Yost et. al.) Good agreement between theory and observations

12 Inferring Physical Parameters from the Observed Spectra We observe ν a, ν m, ν c, F m We infer R B γ min N 3 n ~ N/R 3 A ~ N/R With synchrotron only Pure powerlaws There is always a single solution.

13 Physical Parameters from the Observed Spectra The parameters: E, n 0, ε e, ε B, p p: the slope at high frequencies remaining parameter: Solving equations for: ν a, ν m F m, ν c (Wijers & Galama 1998) For GRB we obtained: E = 5.3x10 51 ergs n 0 = 5.3 cm -3 ε e = 0.57 ε B = observables & 4 unknowns This method is sensitive to the details of the model Can be applied at several epochs

14 Inverse Compton

15 Another 4 powerlaw segments One powerlaw segment ν c <ν<ν m extended Frequency higher by γ e 2 Inverse Compton May be observed in X-ray if n>10 Energy in IC: σ T n R γ 2 e or ε e / ε B With synchrotron + IC No Pure powerlaws There are two or no solution. C / 3 13/ 6 3/ td DL,28 η ν a,9 ν m,13 ν c,14 Fm, mjy < 1 4

16 Dynamics - Scaling Adiabatic: E ~ M c 2 γ 2 12/17 One γ for bulk motion & One γ for thermal motion t~r/γ 2 c ISM: M R 3 γ R -3/2 γ t -3/8 Wind: M R γ R -1/2 γ t -1/4 Jet: M θ 2 γ e -R/Rj γ t -1/2 θ=θ 0 +1/γ R~Const. Newtonina: β instead of γ

17 Sidewise Expansion (Rhoads; Meszaros & Rees; Sari, Piran & Halpern) Fluid frame expansion ~ c. Observer frame: R ~R/γ. Initially: θ~θ 0 After 1/γ θ 0 : θ~1/γ t jet : γ(t jet )=1/θ 0

18 Dynamics + Radiation =Light Curves (Sari, Piran & Narayan 1998) α β game

19 Adiabatic v.s. Radiative (Blandford & McKee 1976; Sari 1997; Cohen, Piran & Sari 1998) Most models assume adiabatic evolution. Strongly radiative: only if ε e ~1 and all electrons cool. Partially radiative evolution: lasts for a long time, especially if p~2. E=E 0 (t/t 0 ) -17ε/12 -> E 0 /E=2-30 Not negligible! F m E aft,x E cal

20 More Complications Pre acceleration: High energy photons fronts (Thompson & Madau; Beloborodov) Decupled Neutrons Change of external density 3/10 3/10 1/5 Termination shocks rt = 7.5 pcm& 5 ρ 24 vw,3t Additional energy Slow shells may have most of the energy - reverse shocks (Kumar & Piran; Sari & Meszaros) 2/5 6

21 Dynamics in more detail Self similar solution: BM76. Extensions Jets? Characteristic width w=r/16γ 2 Hydrodynamic profiles (1+(R-r)/w) -17/12 Partial radiative solutions: Cohen, Piran & Sari Extreme density gradients: Best & Sari Phys. Fluids 2000 Exponential density: Perna & Vietri No detailed solution. Only rough scalings Panaitescu Kumar. Hydrodynamic simulations: Granot et. al.

22 The Contribution to the Observed Flux: Equal arrival time surface & volume

23 A Prediction: Rings (Waxman; Sari; Panaitescu & Meszaros; Granot, Piran & Sari abc; Granot & Sari) If a nearby GRB occurs it can be resolved. (redshift z<0.1) High frequency: narrow ring Low frequency: disk with brighter edges. Scintillation & Microlensing

24 Temporal Breaks with Jets jet F ν t -α Change from spherical ISM ν>ν m F ν t -p ~t -2.2 α -1.1 ν a <ν<ν m F ν t -1/3 α = -5/6 ν<ν a F ν t 0 α = -1/2 (>p1) (>p1) (>p1) The break is substantial at all frequencies.

25 Observed Jets t t jet =1.2d t -2.18

26 F ν t -α Jets Without Breaks (Sari, Piran & Halpern 1999) Two classes: α ~ 1.2 & α ~ 2 Jet candidates without breaks: α=2.05 ± α=2.10 ± 0.13 The Large L distribution is due to jets. (Based on 4 bursts, 2 without redshift)

27 3 Classes of Optical Afterglows Break No Break t -1 Jets!! Spherical t -2 probably jets

28 Wind for fast decays? Requires p=3 and slow cooling: ν c Hz BUT: IC should be accounted for! C / 3 13/ 6 3/ td DL,28 η ν a,9 ν m,13 ν c,14 Fm, mjy < : ν c Hz Wind interpretation for is difficult.

29 Distribution of θ0

30 Beaming Luminosity Relation

31 GRB Standard Candles! 4πD 2 F= Luminosity distribution is spread over a factor of 500 2πθ 2 D 2 F= After correcting for beaming, spread <10 Frail et al.

32 Direction of Polarization B >B^ B <B^

33 Direction of Polarization B <B^ Π=0 0 Π= Π m /3 0 Π=0 Π= Π m

34 Polarization Evolution Offset=0.3θ 0 Offset=0.95θ 0

35 Polarization Lightcurves

36 Radio upper limits: Observations 19% GRB (Taylor et. al.) 8% GRB (Frail et. al.) Optical upper limit: <2.3% GRB (Hjorth et. al.) First detection 1.7% for GRB (Covino et. al.; Wijerse et. al.)

37 Polarization - Summary Fluctuations occur if coherent B cells are large. For Beamed Afterglows: polarization even for small coherence length 1 or 3 peaks of polarization polarization may rotate by 90. Direction of polarization is towards the center of the jet or perpendicular to that. Together with proper motion: infer the direction of B Need observations at multiple times around t jet.

38 Confirmation of The Fireball Model? YES! BUT Most afterglow observations detect only late stage with γ< <γ 0 <10 5 M=E/γ 0 Moderately Extremely Clean Clean No direct evidence to internal or external shocks.

39 4 Stages Coasting, IS=GRB Thermal acceleration Early Afterglow FS + RS Deceleration= Afterglow Late Afterglow Newtonian Energy release

40 Initially: More complicated hydrodynamics (Sari & Piran 1995). Four critical radii: R s where shell may spread and IS may happen. R where reverse shock crosses the shell R γ where the shock had collected mass of M/γ=E/cγ 2 R N where the reverse shock turns from Newtonian to relativistic

41 Two Possible Evolutions (Sari & Piran 1995). ξ 2 R s = ξ 1/2 R = R γ = ξ -1 R N where ξ~(e/n) 1/6-1/2 γ 0-4/3 Two possible orderings: ξ>1: shell spreads (R s ), reverse shocks crosses the shell (R ) and then shell decelerate (R γ ) ξ<1, the reverse shock first becomes relativistic (R N ), R γ is no important, and the self similar stage begins (R ), there is no spreading.

42 Prediction: Transition Burst Afterglow (Sari 1997) The initial external shocks (afterglow) may overlap the internal shocks (GRB) signal. Confirmation requires very early (10-100s) afterglow observations

43 Predicted optical flash γ -rays Reverse shock forward shock X -rays optical

44 Reverse Shock in GRB optical reverse shock forward shock

45 Reverse Shock in GRB radio

46 Early Afterglow - Summary Optical: Gaps - Onset of afterglow (γ 0 + IS vs. ES) Reverse shock ejecta emission γ 0, loading. Transition reverse-forward Polarization Jet geometry ---> correct energy. X-ray: Gaps - Onset of afterglow. GRB Afterglow mismatch (IS vs. ES) Partially Radiative phase True energy E 0 Radio: Radio flares ejecta emission γ 0, loading. Winds or ISM (early value of n 0 ). SHAPE, WHERE, HOW, HOW FAST, WITH WHAT jets n int ext γ 0 Baryons or B

47 Reverse, Forward, Jets... 30s t -2 t +1/2 2h 30m Rising spectrum ν 1/3 Polarization Π 10% 1d t -1 t d t -1.5