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GRB Afterglow Spectra

GRB Afterglow Spectra. Daniel Perley Astro 250 19 September* 2005. * International Talk Like a Pirate Day. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy

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GRB Afterglow Spectra

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  1. GRB Afterglow Spectra Daniel Perley Astro 250 19 September* 2005 * International Talk Like a Pirate Day

  2. BackgroundGRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects The GRB Standard Model Background ISM Shocked Gas SHOCK Earth Daniel Perley GRB Afterglow Spectra 19 September 2005

  3. Background GRB Standard ModelRelativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects Relativistic Shock Background From Brian’s lecture… ISM Deceleration by factor √ 2 g = Γ √2 Γ SHOCK n′ = 4 g no E′ = 4 g2no mp c2E′/n′ = g mp c2 number densityno energy densityEo = no mp c2 energy per particleEo/no = mp c2 >Compression< by 4 g Energy Increase by factor g Daniel Perley GRB Afterglow Spectra 19 September 2005

  4. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects E′/n′ = g mp c2 energy per particleEo/no = mp c2 Energy Increase by factor g Energy Deposition Energy Deposition Where does the energy go? • Protons • Electrons • Magnetic field • Other particles? Ep = εp E′ Ee = εe E′ B = εB E′ Daniel Perley GRB Afterglow Spectra 19 September 2005

  5. Background GRB Standard Model Relativistic Shock Energy DepositionProton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects ge Proton/Electron Energy Energy Deposition Particle energy deposited in random motions. Shocked Gas ISM SHOCK g Γ Bulk motion of shocked gas relative to observer Extreme (relativistic) ‘temperature’ of shocked gas described by gp, ge Daniel Perley GRB Afterglow Spectra 19 September 2005

  6. Background GRB Standard Model Relativistic Shock Energy DepositionProton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects Proton Energy Energy Deposition Not particularly interesting on its own. Protons necessarily drag electrons with them at the same bulk velocity. Share energy with electrons: electron g factors necessarily much higher. Daniel Perley GRB Afterglow Spectra 19 September 2005

  7. Background GRB Standard Model Relativistic Shock Energy Deposition Proton EnergyElectron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects Electron Energy Energy Deposition Faster-moving electrons will radiate more efficiently by all important processes. ge Daniel Perley GRB Afterglow Spectra 19 September 2005

  8. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron EnergyElectron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects Electron Energy Distribution Energy Deposition Q: How is electron energy distributed? A: … … … ? Hypothesis: Power-law? (Seen in SNe, NR shocks) Daniel Perley GRB Afterglow Spectra 19 September 2005

  9. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron EnergyElectron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects Electron Energy Distribution Energy Deposition Model as power-law: N α[Complicated] N αg -p Log N Logg Daniel Perley GRB Afterglow Spectra 19 September 2005

  10. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron EnergyElectron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects N α[Complicated] Ngαg -p Log Ng Logg gm Electron Energy Distribution Energy Deposition Simplify: cut-off power law at minimum energy Minimum energy Daniel Perley GRB Afterglow Spectra 19 September 2005

  11. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron EnergyElectron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects ge-p Ng n gm ge 1-p 1 1 1-p 2-p 2-p p-2 p-1 Electron Energy Distribution Energy Deposition Mimimum energy determined by total energy density: ge1-p geNg E gm ge Infinite if p<2 n =∫ Ngedge Ee= me c2∫ geNgedge = me c2 C gm2-p = C gm1-p = me c2gm n C = (1-p) gmp-1 n Ee mp p-2 gm = g g εe = ≈ 610 εe g nmec2 me p-1 Daniel Perley GRB Afterglow Spectra 19 September 2005

  12. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron DistributionMagnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects Magnetic Energy Energy Deposition Strong post-shock magnetic field expected from equipartition. Generation mechanism unknown/complicated – various plasma effects B B2 = εB E′ 8π = εB 4 g2no mp c2 = 32πεBg2no mp c2 B2 = 32πεB no mp g c B no ≈ (0.4 gauss)εB1/2 ( )1/2g cm-3 Daniel Perley GRB Afterglow Spectra 19 September 2005

  13. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled SynchrotronEmission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects 4 4 3 3 Uncooled Synchrotron Emission Mechanisms How does it cool? Bremsstrahlung Pαge3/2 n2 Inverse Compton P= σTcβ2ge2Uph Synchrotron P =σTcβ2ge2UB Daniel Perley GRB Afterglow Spectra 19 September 2005

  14. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission MechanismsRelativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects e B ωcyc = g m c Uncooled Synchrotron Relativistic Cyclotron Relativistic modification to cyclotron frequency: Most emission is not at this frequency. Daniel Perley GRB Afterglow Spectra 19 September 2005

  15. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic CyclotronSynchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects e B ωcyc = g m c E t Uncooled Synchrotron Synchrotron Beaming Emission is highly pulsed – we see emission for only 1/g2 of total emission time. - One factor of g from beaming angle- Additional factor of g from "Doppler" boost 1/g 1/g 1/ωcyc 1/g2ωcyc Daniel Perley GRB Afterglow Spectra 19 September 2005

  16. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects δ(t-n/ωcyc) E t 1/ωcyc E 1/g2ωcyc t Uncooled Synchrotron 1e- Synchrotron Spectrum = =

  17. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects Uncooled Synchrotron 1e- Synchrotron Spectrum Fourier transformed: g2ωcyc ^ E t = δ(ω-nωcyc) ^ E t ωcyc g2ωcyc g2ωcyc g2ωcyc

  18. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects 4 3 Uncooled Synchrotron 1e- Synchrotron Spectrum More precisely… e-n/ωcycn 1/2 n 1/3 log Pn log n npk Shocked frame: Total Power: P = σTcβ2ge2UB Peak Freq.: npk ≈ge2ωcyc / 2π Peak Power: Pnpk≈ P / npk αge2 αge2 αconst Daniel Perley GRB Afterglow Spectra 19 September 2005

  19. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects 4 3 Uncooled Synchrotron 1e- Synchrotron Spectrum e-n/ωcycn 1/2 n 1/3 log Pn log n npk npk Shocked frame: Total Power: P = σTcβ2ge2UB Peak Freq.: npk ≈ge2ωcyc / 2π Peak Power: Pnpk≈ P / npk αge2 αge2 αconst Daniel Perley GRB Afterglow Spectra 19 September 2005

  20. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects 4 3 Uncooled Synchrotron 1e- Synchrotron Spectrum e-n/ωcycn 1/2 n 1/3 log Pn log n npk npk Observer frame: Total Power: P = σTcβ2ge2g2UB Peak Freq.: npk ≈ge2gωcyc / 2π Peak Power: Pnpk≈ P / npk αge2g2 αge2g αg Daniel Perley GRB Afterglow Spectra 19 September 2005

  21. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- SpectrumMulti-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects -p log Ng exp 1/3 log Pn log ge gm log n npk Uncooled Sychrotron Uncooled Multi-e- Spectrum Material contains many electrons at different velocities (ge) – true spectrum is a combination of individual spectra, according to electron energy distribution. Electron distribution Electron spectrum Daniel Perley GRB Afterglow Spectra 19 September 2005

  22. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- SpectrumMulti-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects -p log Ng dn dg dn dg log ge gm Uncooled Synchrotron Uncooled Multi-e- Spectrum Can just do a weighted sum (convolution) – but need to convert x-axis from ge to npk. -(p-1)/2 log Nn From before, npkαge2 log npk nm ge α Electron distribution e- distribution: Ngα ge-p Solve: Nn= Ng(n) αge-pge-1αn-(p+1)/2 Sign error?? Daniel Perley GRB Afterglow Spectra 19 September 2005

  23. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- SpectrumMulti-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects exp 1/3 log Pn log n npk Uncooled Synchrotron Uncooled Multi-e- Spectrum -(p-1)/2 log Nn log npk nm Electron spectrum Electron distribution Total Spectrum Daniel Perley GRB Afterglow Spectra 19 September 2005

  24. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- SpectrumMulti-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects -(p-1)/2 log Nn log npk nm Daniel Perley GRB Afterglow Spectra 19 September 2005 Uncooled Synchrotron Uncooled Multi-e- Spectrum exp 1/3 log Pn log n npk 1/3 -(p-1)/2 log Pn nm

  25. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- SpectrumMulti-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects Daniel Perley GRB Afterglow Spectra 19 September 2005 Uncooled Synchrotron Uncooled Multi-e- Spectrum 1/3 -(p-1)/2 log Pn log npk nm "Broken" Power law: • Below nm, emission dominated by low-g e- • Above nm, emission from electrons withnpeak(g) = nm

  26. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled SynchrotronCooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects 4 3 B gauss Daniel Perley GRB Afterglow Spectra 19 September 2005 Cooled Synchrotron Characteristic Cooling Time 1/3 -(p-1)/2 log Pn log npk nm This analysis is too simplistic for GRBs. Calculate characteristic cooling time: Potentially much shorter than time since GRB (shock passage) tcool = E / P = gmec / σTcβ2g2UB ≈ 4 × 10-3 s ( )-2g-1

  27. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects 4 3 Cooled Synchrotron Cooling e- Spectrum If an electron's energy changes significantly over the time since the energy injection, use an "averaged" spectrum for that electron. ge = Initial electron energy (at injection) gc≡ Final electron energy (after cooling)≈ Energy of the highest-g e- that hasn't cooled Determined by observational timescale: tobs= gcmec / σTcβ2gc2UBgc = 6πmec σTB2tobs Daniel Perley GRB Afterglow Spectra 19 September 2005

  28. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects exp 1/3 log Pn log n npk Cooled Synchrotron Cooling e- Spectrum Electron radiates as it cools, with a simple synchrotron spectrum corresponding to the instantaneous energy gi . ge = Initial electron energy gc≡ Final electron energy gi Instantaneous spectrum Daniel Perley GRB Afterglow Spectra 19 September 2005

  29. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects Cooled Synchrotron Cooling e- Spectrum Peak power radiated at each gi is the same: ge = Initial electron energy gc≡ Final electron energy gi P(gi) = const Electron evolution Instantaneous spectrum exp 1/3 log Pg log Pn log gi log n gc ge npk(gi) Daniel Perley GRB Afterglow Spectra 19 September 2005

  30. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects dn dg dn dg Cooled Synchrotron Cooling e- Spectrum Another convolution -need to transform ge to npk. -1/2 log Pn From before, npkαge2 nc ne ge α Electron evolution Power distribution: Pg= const const Solve: Pn= Pg(n) = g-1 = n-1/2 log Pg log gi gc ge Daniel Perley GRB Afterglow Spectra 19 September 2005

  31. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects exp 1/3 log Pn log n npk Cooled Synchrotron Cooling e- Spectrum -1/2 log Pn nc ne Instantaneous spectrum Electron evolution Daniel Perley GRB Afterglow Spectra 19 September 2005

  32. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects Cooled Synchrotron Cooling e- Spectrum -1/2 exp 1/3 log Pn log Pn nc log n ne npk Instantaneous spectrum Electron evolution 1/3 -1/2 log Pn Daniel Perley GRB Afterglow Spectra 19 September 2005

  33. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects Cooled Synchrotron Cooling e- Spectrum -1/2 1/3 log Pn log n nc ne Broken power law: •n > ne : Exponential cut-off (model as no emission) •nc < n < ne : Instantaneous emission when electron passed through appropriate g • n < nc : Post-cooling emission Daniel Perley GRB Afterglow Spectra 19 September 2005

  34. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects Cooled Synchrotron Cooling e- Spectrum -1/2 1/3 log Pn log n nm ne Higher initial energy simply extends the curve to higher frequencies. Daniel Perley GRB Afterglow Spectra 19 September 2005

  35. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- SpectrumCooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects Daniel Perley GRB Afterglow Spectra 19 September 2005 Cooled Synchrotron Cooling Regimes Two possibilities for multi-electron spectra: gc < gm -p log Ng ALL electrons will cool on given timescale :Fast cooling log ge gc gm gc > gm -p log Ng SOME electrons will cool on given timescale :Slow cooling log ge gm gc

  36. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling RegimesFast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects Daniel Perley GRB Afterglow Spectra 19 September 2005 Cooled Synchrotron Fast Cooling gc < gm -p log Ng ALL electrons will cool on given timescale :Fast cooling log ge gc gm

  37. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling RegimesFast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects Daniel Perley GRB Afterglow Spectra 19 September 2005 Cooled Synchrotron Fast Cooling Sum for multi-e- using the new spectrum: -1/2 1/3 -(p-1)/2 log Nn log Pn log ne nc ne nc nm Cooled synchrotron spectrum Electron distribution 1/3 -1/2 Fractionof Nn > n n-1/2 log Pn -p/2 -(p-2)/2 ?? log n nc nm

  38. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling RegimesFast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects Cooled Synchrotron Fast Cooling 1/3 -1/2 log Pn -p/2 log n nc nm Broken power law: •n > nm : Emission from electrons with ge > g(n) , during passage through appropriate g •nc < n < nm : Emission from all electrons, during passage through appropriate g • n < nc : Emission from all electrons at all times Daniel Perley GRB Afterglow Spectra 19 September 2005

  39. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast CoolingSlow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects Daniel Perley GRB Afterglow Spectra 19 September 2005 Cooled Synchrotron Slow Cooling gc > gm -p log Ng SOME electrons will cool on given timescale :Slow cooling log ge gm gc

  40. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast CoolingSlow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects Daniel Perley GRB Afterglow Spectra 19 September 2005 Cooled Synchrotron Slow Cooling Fast-cooling electrons have fast-cooling spectrum, but with effective gm→gc(no -1/2 segment) -p log Ng log ge gm gc 1/3 log Pn -p/2 nc log n

  41. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast CoolingSlow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects Daniel Perley GRB Afterglow Spectra 19 September 2005 Cooled Synchrotron Slow Cooling Non-cooling electrons have an uncooled-population spectrum, but cut off at nc. -p log Ng log ge gm gc 1/3 -(p-1)/2 log Pn nm nc log n

  42. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast CoolingSlow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects 1/3 -(p-1)/2 -p/2 Daniel Perley GRB Afterglow Spectra 19 September 2005 Cooled Synchrotron Slow Cooling By their powers combined… -p log Ng log ge gm gc 1/3 -(p-1)/2 1/3 log Pn -p/2 nm nc log n

  43. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast CoolingSlow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects Cooled Synchrotron Slow Cooling 1/3 -(p-1)/2 log Pn -p/2 log n nm nc Broken power law: •n > nc : Emission from cooling electrons with ge > g(n) during passage through appropriate g •nm < n < nc : Emission from slow electrons with initial (constant) energy g • n < nm : Emission from slow electrons with min. gm Daniel Perley GRB Afterglow Spectra 19 September 2005

  44. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow CoolingCooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects Cooled Synchrotron Cooling Comparison 1/3 -1/2 Fast cooling log Pn -p/2 log n nc nm 1/3 -(p-1)/2 Slow cooling log Pn -p/2 log n nm nc Daniel Perley GRB Afterglow Spectra 19 September 2005

  45. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling ComparisonSelf-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects Cooled Synchrotron Synchrotron Self-Absorption Photon can be re-absorbed to excite an electron in a magnetic field (inverse of synchrotron emission.) Synchrotron emission/absorption will be in equilibrium below a certain frequency na: below this point the shocked gas is optically thick and will radiate as a blackbody (Pnαn2) 1/3 log Pn 2 log n na Daniel Perley GRB Afterglow Spectra 19 September 2005

  46. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-AbsorptionComplete Comparison Spectral Observation Observation vs. Theory Observation Parameters Intervening ISM Effects Synchrotron Summary Complete Comparison 1/3 -1/2 Fast cooling log Pn 2 -p/2 na nc nm log n 1/3 -(p-1)/2 Slow cooling 2 log Pn -p/2 nm nc na log n Daniel Perley GRB Afterglow Spectra 19 September 2005

  47. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral ObservationObservation vs. Theory Observation Parameters Intervening ISM Effects Theory vs. Observations Observing GRB970508 – Galama et al. 1998 tburst = 12.1 days 0.44 >1.1 -0.6 -1.12 Daniel Perley GRB Afterglow Spectra 19 September 2005

  48. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. TheoryObservation Parameters Intervening ISM Effects Observable Parameters Subject An instantaneous spectrum gives several key pieces of information: nancnm p Fpk z εeεB no E' Daniel Perley GRB Afterglow Spectra 19 September 2005

  49. Background GRB Standard Model Relativistic Shock Energy Deposition Proton Energy Electron Energy Electron Distribution Magnetic Energy Uncooled Synchrotron Emission Mechanisms Relativistic Cyclotron Synchrotron Beaming 1e- Spectrum Multi-e- Spectrum Cooled Synchrotron Cooling Time 1e- Spectrum Cooling Regimes Fast Cooling Slow Cooling Cooling Comparison Self-Absorption Complete Comparison Spectral Observation Observation vs. Theory Observation ParametersIntervening ISM Effects Intervening ISM Effects Subject Cosmological redshift will not affect power-law - all radiation scaled down by (1+z)Will see deviation from power-law in some frequency ranges in some cases: Galactic extinction (can be calculated/removed) Host extinction (similar to Galactic, but at higher frequencies, and cannot be estimated independently of GRB) Hydrogen absorption features (associated with high-z) Daniel Perley GRB Afterglow Spectra 19 September 2005

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