X-ray & γ-ray. Polarization in Gamma-Ray Bursts. Jonathan Granot. Institute for Advanced Study, Princeton

Transcription

1 X-ray & γ-ray olarization in Gamma-Ray ursts Jonathan Granot Institute for Advanced Study, rinceton X-ray olarimetry Workshop KIAC, February 10, 2004

2 Outline of the Talk: Short Overview of GRs Why is GR polarization interesting GR polarization: an unresolved relativistic jet olarization of the prompt γ-ray emission: theoretical expectations (relatively in detail) olarization of early X-ray afterglow (brief) Conclusions

3 Observations: rompt GR ν Variable light curve Flux ν Duration: ~ sec Time Time ν Spectrum: non-thermal νf ν peaks at E p ~0.1-1 MeV E p (E 1/2 (Amati (E γ,iso iso) 1/2 Amati et al. 03) ν Rapid variability, non thermal spectrum & z~1 relativistic source (Γ( _ ) (compactness problem: Schmidt 1978; Fenimore et al. 1993; Woods & Loeb 1995; ) νf ν ν

4 ν ν Observations: Afterglow X-ray, optical & radio emission over days, weeks & months,, respectively, after a GR Spectrum: consists of several power law segments & is well fit by synchrotron emission GR Spectrum at 12.1 days (Galama et al. 1998)

5 ν ν Light curve: power law decay; some afterglows show an achromatic steepening of the light curve ( jet break ) z ~ 1 + fluence energy output in γ-rays: υ assuming isotropic emission: Eγ,iso ~ erg υ correcting for a jet: Eγ ~1051 erg Optical light curve of GR (Harrison et al. 1999) X-ray light curves Of several GRs (iro 1999)

6 Theory: Fireball vs. oynting Flux *Meszaros & Rees 92, Katz 94, Sari & iran 95 Shemi & iran 90, Goodman 86, aczynski 86,, Compact Source Matter dominated outflow E kin _ E EM rompt GR Internal Shocks article acceleration synchrotron γ-rays ejecta Afterglow Reverse shock * Optical Radio Forward Shock (Rees & Meszaros 92) X-rays Optical Radio External medium oynting flux dominated flow EEM E kin Thopson 94, Usov 94, Meszaros & Rees 97, Katz 97, reconnection (or other EM instability) Magnetic bubble Lyutikov & landford 02,03 X-rays Optical Radio

7 Why is GR olarization Interesting It teaches us about the magnetic field structure in the GR ejecta & provides clues as to whether most of energy is in oynting flux or kinetic energy: E EM E kin ordered magnetic field is expected E kin _ E EM ordered & random fields are possible rovides a strong test for the structure of GR jets, both in the prompt GR & in the afterglow robes magnetic field structure behind afterglow shock Helps pin down cause of time variability in afterglows

8 olarization of Synchrotron Emission e Cone of angle 1/γ e rojection of the magnetic field on plane of the sky k The direction of the polarization lane of the sky ν linear polarization perpendicular to the projection of on the plane of the sky The maximal polarization is for the local emission from an ordered -field: max =(α+1 +1)/( )/(α+5/3) where F ν ν -α, -1/3 α _ % max _ 80% (Rybicki & Lightman 1979; Granot 2003)

9 Shock roduced Magnetic Field: A magnetic field that is produced at a relativistic collisionless shock, due to the two-stream instability, is expected to be tangled within the plane of the shock (Medvedev & Loeb 1999) Magnetic field tangled within a (shock) plane hoton emitted normal to plane n ph = n sh = 0 θ = max sin 2 θ/(1+cos 2 θ) = max hoton emitted along the plane (Liang 1980) n ph n sh

10 Source frame Relativistic source: Aberration of light or relativistic beaming Observer frame Γ Γ 1 The observer sees mostly emission from within an angle of 1/Γ around the l.o.s. 1/Γ 1/Γ Direction of olarization 1/Γ Direction to observer Source frame Observer frame

11 olarization in the observer frame Random field in shock plane Γ Ordered field in shock plane Γ K K Sari 99; Ghisellni & Lazzati K K K K K Granot & Königl 03 ~ max

12 olarization of rompt γ-ray emission: GR = 80% GR = 80% ± 20% Extremely bright GR, 18 from the sun favorable for measuring polarization with RHESSI 20% (Coburn & oggs 2003) hoton energy range: MeV Integration time: 5 sec Significance: > 0 at better than 5.7 σ However: this result is controvertial Rutledge & Fox (2003) claim: A factor of ~10 less relevant photon scattering events in the detector cannot be constrained There is an ongoing controversy (stay tuned for the next two talks)

13 olarization of prompt γ-ray emission: Theoretical Expectations ν Shock produced -field + θ obs _ θ j -1/ 1/Γ 0 ν ~ max can be achieved in the following ways: (1) ordered magnetic field in the ejecta, (2) special geometry: θ j < θ obs _ θ j +1/ 1/Γ narrow jet: θ _ j 1/Γ (works with a shock produced magnetic field) Waxman (2003)

14 Ordered Magnetic Field in the Ejecta: Total emission from jet Afterglow: instantaneous emission rompt GR: time integrated emission Granot & Königl 03 (Granot 2003) ν F ν ν -α, increases with α ν from an ordered -field is slightly larger in afterglow

15 Narrow Jet + shock produced -field High polarization + reasonable flux θ j < θ obs _ θ j +1/ 1/Γ ν A reasonable probability for such θ obs Γθ j _ a few ν Since Γ _ 100 & θ j _ 0.05, Γθ j _ 5 and is typically larger However GR was very bright, suggesting a very narrow jet: f = erg which for z~1 implies E iso ~10 54 erg & θ j ~ (10 51 erg/e iso ) 1/2 ~ 0.03 (Frail et al. 01) ν Γθ j ~ 3(Γ/100 /100) Γθ j _ a few is possible (Waxman 03) The jet must have sharp edges: Δθ j _ 1/4Γ (Nakar et al. 03) a structured jet produces low polarization (several( %)% Most GRs are viewed from θ obs < θ j and are expected to have a very low polarization in this scenario

16 Random -field in sock plane Γ (Granot 2003) y j (Γθ j ) 2 F ν ν -α ν ΔΓ ~ Γ between different shell collisions (different pulses in GR light curve) reduces by a factor ~ 2

17 ~ 80% ~ 50% ~ 25% _ 10% statistics Optical flash otential problems Ordered Field X with rnd _ ord with rnd > ord High in all GRs High - similar to the prompt GR Some rnd required for Fermi acceleration Narrow Jet X X with rnd _ low in most GRs Similar to prompt GR (low in most GRs) Γθ j _ a few, ΔΓ ~ Γ, rnd (afterglow (afterglow obs.)

18 Temporal evolution of olarization within a pulse in the GR liht curve: short pulse (ΔR<R) Ordered -field: (Nakar, iran & Waxman 2003) Random field in shock plane: long pulse (ΔR>R)

19 osition Angle in Different ulses: In the internal shocks model, the polarization position angle θ p is expected to remain constant between different pulses in the GR light curve, both for ord or narrow jet+shock produced field For the external shocks model θ p is expected to vary between different the pulses rnd in shock plane 2 Ordered field ord

20 Alternative to Synchrotron: Compton Drag (ulk Inverse Compton Scattering of External photons) (Lazzati et al. 2003; Dar & De Rujula 2003, Eichler & Levinson 2003) Requires a special geometry and/or viewing angle, θ j < θ obs _ θ j +1/ 1/Γ Similar polarization properties as a shock produced - field with one relative advantage: the local polarization =(1-cos 2 θ)/(1+cos 2 θ) can reach up to 100% while max ~ 70% for synchrotron Shares drawbacks of shock produced field + narrow jet It has additional problems, unrelated to polarization: Explaining the prompt GR spectrum Supplying external photons for all the ejected shells High photon density small radii high τ γγ

21 Afterglow olarization: Observations Linear polarization at the level of ~ 1%-3% was detected in several optical afterglows In some cases varied, but usually θp const Different from predictions of uniform or structured jet GR (Gorosabel et al. 1999) (Covino et al. 1999)

22 Afterglow olarization: Theory the polarization is usually attributed to a jet geometry Ordered -field * : t 0 Log(t) θp = const Uniform jet : Log(dE de/d /dω) ν (t t j ) ~ (t~t j ) while for jet models (t t j ) (t~t j ) * Granot & Königl 03 θ 0 t jet Log(θ) Log(t) θ p flips by 90 o at t jet (Sari 99; Ghisellini & Lazzati 99) Structured jet : Log(dE de/d /dω) θ core θ -2 Log(θ) Log(t) ostnov et al. 01; Rossi et al. 02; Rhoads 97,99; Sari et al. 99, Zhang & Meszaros 02 t jet θ p =const (Rossi et al. 2003)

23 Conclusions: Ordered magnetic field in the ejecta naturally produces ~ 30% - 65%,, for all GRs (all θ obs ) & reverse shock should increase with the spectral index α (F ν ν -α ) Narrow jet + shock produced -field or Compton drag naturally produce ~20%-30% for θ j < θ obs _ θ j +1/ 1/Γ but for most GRs θ obs _ θ j and 0 ν The temporal evolution of within a single pulse can help distinguish between ordered -field & a shock produced -field or Compton drag ν The pol. position angle θ p in different pulses can help distinguish between internal & external shocks ν olarization measurements in early X-ray afterglow can test the GR jet structure & the possible role of ordered magnetic field component: (t t jet ) ~ (t~t jet )