Probing the GRB Prompt Emission
Mechanism through the γ- and X-ray
polarimetry(Toma 2013, in preparation)
JAPANKenji Toma
(Osaka Univ → Tohoku Univ)
Supernovae and Gamma-Ray Bursts in Kyoto, Nov 11-15, 2013

Prompt Emission Mechanism©NASA• In spite of extensive light-curve and spectral
observations in the keV-MeV band as well as
in the GeV band with Fermi, the GRB
emission mechanism is still open.
• Polarimetric observations can give us somecritical information for solving the problem©MIT(e.g. Lazzati 2006; KT 2013)

Internal shocksPhotosphere

Quasi-thermal

Synchrotron

Relativistic Jet©NASAGamma-ray Polarization• GAP aboard IKAROS (See Yonetoku’s talk)• 70-300keV• Π𝐿𝐿 = 27 ± 11% (GRB 100826A),
Π𝐿𝐿 > 30% at 2𝜎𝜎 (110301A, 110721A)• These are three brightest bursts observedby GAP• Favor synchrotron emission model withordered magnetic field (Yonetoku, Murakami,IKAROS©JAXAGunji, Mihara, KT et al. 2011; 2012; KT, Mukohyama,
Yonetoku et al. 2012; KT 2013)• INTEGRAL-IBIS observations of GRB
041219A & 061122 are consistent (Gotz et al.
2009; 2013)

GAP detector (Compton-type)Photospheric Emission Model?
• If the fluid is matterdominated at thephotosphere, high Π𝐿𝐿 arises(Compton scattering ofanisotropic radiation)• High Π𝐿𝐿 from 𝜃𝜃~1/Γ(intensity relatively weak)• Unlikely that all the brightbursts have high net Π𝐿𝐿• Appear to be inconsistent
with the GAP data

Angular distribution of radiation
intensity in the fluid frame(Beloborodov 2011)(see also Lundman, Pe’er & Ryde2013)

Faraday Rotation in the Source• Detections of high linear polarization → synchrotron, B field structure• Detections of Faraday effects in the source → B field strength

Left-mode

𝐵𝐵＋Right-mode＝Δ𝜃𝜃Gradual rotation oflinear polarization
direction𝑒𝑒 3−2Δ𝜃𝜃 =𝑛𝑛𝐵𝐵cos𝜃𝜃𝜈𝜈
Δ𝑙𝑙2 2𝜋𝜋𝑚𝑚𝑒𝑒 𝑐𝑐(Rybicki & Lightman 1979)

Faraday Depolarization𝑒𝑒 3−2 Δ𝑙𝑙 ≫ 1Δ𝜃𝜃 =𝑛𝑛𝑛𝑛cos
𝜃𝜃𝜈𝜈
𝜋𝜋𝑚𝑚𝑒𝑒2 𝑐𝑐 2Emission Region

𝐵𝐵• Linear polarizations withdifferent rotation angles
are canceled out• Net Π𝐿𝐿 decreases atenergy range Δ𝜃𝜃 𝜈𝜈 ≫ 1

Π𝐿𝐿Δ𝜃𝜃Δ𝜃𝜃′Δ𝜃𝜃′′Δ𝜃𝜃(𝜈𝜈) = 1

𝜈𝜈Relativistically-Hot Plasma𝑒𝑒 3ln 𝛾𝛾𝑒𝑒 −2Δ𝜃𝜃 =2 2 𝑛𝑛𝑛𝑛 cos 𝜃𝜃2 𝜈𝜈 Δ𝑙𝑙𝜋𝜋𝑚𝑚𝑒𝑒 𝑐𝑐𝛾𝛾𝑒𝑒(Sazonov 1969; Melrose 1980)• The Faraday rotation effect by relativistically-hot
plasma is much smaller than that by cold plasma• Not remarkable in the source where all the electrons
keep accelerated

Cool Electrons in Prompt Emission Region
Predicted peak energy
𝐸𝐸𝑝𝑝 =(e.g. Meszaros 2006)

3ℎ𝑒𝑒𝑒𝑒 2
1/2 1/2 −1−2 2𝛾𝛾𝑚𝑚 Γ ≃ 600𝑓𝑓−1𝜖𝜖𝑒𝑒,−1 𝜖𝜖𝐵𝐵,−1 𝐿𝐿52 𝑟𝑟13keV
4𝜋𝜋𝑚𝑚𝑒𝑒 𝑐𝑐• Dissipation energy has to beconverted into only a small fractionof electrons.
• A large fraction of electrons are justisotropized by shock, remaining cool.

Electron energy distribution withacceleration efficiency < 100%

Cool electrons(Eichler & Waxman 2005)𝑓𝑓

Radio Afterglow
Electron energy distribution withacceleration efficiency < 100%𝐹𝐹𝜈𝜈𝜈𝜈𝑎𝑎

Cool electrons(Eichler & Waxman 2005)

Π𝐿𝐿 (𝜈𝜈)Predicted late-time polarization spectrum(KT, Ioka & Nakamura 2008)

𝜈𝜈𝑚𝑚Faraday Depolarization in Prompt
Emission• High Π𝐿𝐿 detection → Ordered B field model• Prompt emission models usually predict a large amount ofcold electrons → Strong Faraday rotationΔ𝜃𝜃 𝜈𝜈𝑉𝑉 = 1

1/4 3/4 −1 −1𝜈𝜈𝑉𝑉 ≃ 100 𝜖𝜖𝐵𝐵 𝐿𝐿52 𝑟𝑟12 Γ2.5 keV• High Π𝐿𝐿 detection by GAP ⇒ 𝜈𝜈𝑉𝑉 ≲ 70 keV
12𝑟𝑟 ≳ 10

1/4 3/4 −1𝜖𝜖𝐵𝐵 𝐿𝐿52 Γ2.5 cm

Future X-ray polarimetry (identification of 𝜈𝜈𝑉𝑉 ?) would
constrain the emission radius more strongly.

Case Study (1)••••Synchrotron
Ordered B fieldCold electrons
𝑟𝑟~1013 cm(𝐸𝐸𝑝𝑝 ~1MeV)𝐹𝐹𝜈𝜈𝐸𝐸𝑝𝑝

GAP energy range

Π𝐿𝐿𝜈𝜈𝑉𝑉𝜈𝜈• If Faraday depolarization detected in X-rays ⇒Disfavor the quasi-thermal emission modelCase Study (2)• Synchrotron + quasi-thermal ?
𝜈𝜈𝐹𝐹𝜈𝜈

(e.g. Vurm, Beloborodov, &Poutanen 2011)

GAP energy range
X-rays𝐸𝐸𝑝𝑝• If high X-ray Π𝐿𝐿 in many bright bursts ⇒ Ordered B field• If Faraday depolarization detected ⇒ A small fraction ofpositrons (strong constraint on the model)

Summary• Detections of linear polarization by GAP inbright bursts favor the synchrotron modelwith ordered B field• Detection of Faraday depolarization in X-rays
would imply [ordered B field], [electronproton plasma], [existence of cool electrons]• More quantitative calculations are in progress

Gamma-ray Polarization• Three GRBs are among the brightest bursts
observed by GAP