DETECTION OF GAMMA-RAY POLARIZATION IN PROMPT EMISSION OF GRB 100826A

Gamma-ray bursts (GRBs) are the most energetic explosions in the universe, and the isotropic luminosity reaches 10⁵⁴ erg s⁻¹ for the brightest bursts. Since the discovery of X-ray afterglow of GRBs by BeppoSAX (Costa et al. 1997) and the identification of optical counterparts at cosmological distance, many observational facts and theoretical works have led us to understand the nature of GRBs. However, a crucial issue that still remains to be answered is how to release such a large energy as γ-ray photons. In spite of extensive discussions using the spectral and light curve information collected, there are still several possible models of GRBs (Mészáros 2006). The polarimetric observations provide us with completely different information. A firm detection of linear polarization of γ-ray photons will further constrain the emission models (Lazzati 2006; Toma et al. 2009).

The polarization measurement of GRBs has been performed in the late optical afterglows at first (Covino et al. 1999, 2004; Wijers et al. 1999; Rol et al. 2000; Gorosabel et al. 2004). All of these results show a polarization degree (Π) of a few percent level. Mundel et al. (2007) set an upper limit of Π < 8% for the early optical afterglow. Detailed observations are performed for the optical afterglow of GRB 030329, and time variations of the polarization degree and polarization angle (PA) were reported (Greiner et al. 2003). Recently, a polarization degree of Π = 10% ± 1% was reported for the early optical afterglow of GRB 090102, at hundreds of seconds since the burst trigger (Steele et al. 2009).

On the other hand, there are controversies on polarization detections in the prompt γ-ray emission of GRBs. The first report was the detection of a high linear polarization of Π = 80% ± 20% at a confidence level of >5.7σ by RHESSI from GRB 021206 (Coburn & Boggs 2003), although independent groups could not confirm any polarization signals by reanalyzing the same data (Rutledge & Fox 2004; Wigger et al. 2004). The second reports also showed high degree of polarization for GRB 041219A with Π = 98% ± 33% (Kalemci et al. 2007) and Π = 63⁺³¹_{− 30}% (McGlynn et al. 2007) for the brightest pulse in the 100–350 keV energy band of the International Gamma-Ray Astrophysics Laboratory (INTEGRAL)-Space Platform Interferometry (SPI) at 2σ confidence level for two parameters of interest (Π and PA). Götz et al. (2009) also reported more significant detection for time-resolved analyses⁷ and suggested possible variable polarization properties for the same GRB 041219A in the 200–800 keV energy band observed with INTEGRAL-IBIS. However, Götz et al. (2009) set a strict upper limit of Π < 4% for the same brightest pulse showing high Π in the INTEGRAL-SPI data (Kalemci et al. 2007; McGlynn et al. 2007). (Götz et al. 2009 explained that the null net polarization degree results from the superposition of signals with different PAs. However, this interpretation cannot explain the positive detection by INTEGRAL-SPI simultaneously.) These inconsistent results between SPI and IBIS has led to confusion again, and the existence of γ-ray polarization is still in debate. As the authors themselves pointed out in their reports, these results are with low statistics of ∼2σ level and may be strongly affected by the instrumental systematics uncertainties (Kalemci et al. 2007; McGlynn et al. 2007; Götz et al. 2009). These controversies and conflicts indicate difficulties in detecting the γ-ray polarization.

In this Letter, we report the detection of γ-ray polarization and also the change of PA for the extremely bright GRB 100826A using the newly developed GRB polarimeter. Our polarimeter is completely designed for the polarization measurement of prompt GRBs and well calibrated during the developing phase before launch. Specifically, using a detector of proto-flight model, we experimentally and numerically understand the response for polarized γ-ray with low systematic uncertainties. In the following sections, we show the observation (Section 2), data analysis (Section 3), and discussion of the emission mechanism of prompt GRBs (Section 4).

The Interplanetary Kite-craft Accelerated by Radiation Of the Sun (IKAROS; Kawaguchi et al. 2008; Mori et al. 2009) is a small solar-power-sail demonstrator that was successfully launched on 2010 May 21. IKAROS has a large polyimide membrane 20 m in diameter, which translates the solar radiation pressure into the thrust of the spacecraft. Since the deployment of the sail on 2010 June 9, IKAROS has started solar-sailing toward Venus.

The Gamma-Ray Burst Polarimeter (GAP; Yonetoku et al. 2006, 2011; Murakami et al. 2010) on board IKAROS is fully designed to measure the degree of linear polarization in the prompt emission of GRBs in the energy range of 70–300 keV. The detection principle is the anisotropy of Compton scattered photons. If the incident γ-rays are linearly polarized, the distribution of scattered photons is due to the Klein–Nishina effect which approximately shows sin ²ϕ curves, where ϕ is the scattering angle.

The GAP consists of a central plastic scatterer 17 cm in diameter and 6 cm in thickness, and the surrounding 12 CsI(Tl) scintillators 5 mm in thickness. The coincidence events within a gate time of 5μs between the signal from any CsI and that from the plastic are accepted for polarization analysis. The GAP's high axial symmetry in shape and the high gain uniformity are key to reliable measurement of polarizations, and to avoid a fake modulation due to background γ-rays. There are no external parts of the spacecraft inside the GAP field of view. Moreover, the detector cases (chassis), except for the detector top, are covered by thin lead sheets with 0.5 mm thickness. Therefore, the effects of background γ-rays scattered by the spacecraft body are negligible.

The GAP detected GRB 100826A on 2010 August 26 at 22:57:20.8 (UT) on the way to Venus at about 0.21 AU away from the Earth. The light curve of the prompt emission is shown in Figure 1. This burst was also detected by several satellites and was localized by an interplanetary network (IPN; Hurley et al. 2010). Combining the GAP data with the published IPN information, the direction of this burst is derived as (α, δ) = (279.6 ± 0.2, −22.3 ± 0.5), which corresponds to 20.0 deg off-axis from the center of the GAP field of view. An energy fluence of this burst is (3.0 ± 0.3) × 10⁻⁴ erg cm⁻² in the 20 keV–10 MeV band by KONUS (Golenetskii et al. 2010), which is the top 1% of the brightest events listed in the BATSE catalog. The low- and high-energy photon indices are reported as α_B = −1.31^+0.06_{− 0.05} and β_B = −2.1^+0.1_{− 0.2}, respectively, and the νF_ν peak energy as E_p = 606⁺¹³⁴_{− 109} keV (Golenetskii et al. 2010). An optical afterglow of this GRB was not reported, so its redshift is unknown.

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We divided the entire data into two time intervals, labeled Interval-1 and -2 in the light curve in Figure 1. The total numbers of γ-ray photons after subtracting the background are 32,924 and 19,007 photons for each interval, respectively. The first part of this burst shows a large flare lasting 47 s since the trigger, and the following 53 s consists of multiple spikes. Although Interval-2 has several spikes, we combined all of them to keep photon statistics.

We used the background modulation curve obtained by the 36.7 hr integration just before and after the GRB trigger time. In this case, the averaged coincidence background rate is quite stable at 5.6 counts s⁻¹ CsI⁻¹, and its modulation curve can be described as constant with the standard deviation at 0.1% level. After subtracting the background modulation, the total numbers of the coincidence γ-rays (polarization signals) are 4,821 and 2,733 for Interval-1 and -2, respectively.

3.1. Model Functions

3.2. Systematic Uncertainty

3.3. Fitting the Polarization Data

First, we performed the polarization analysis for the whole data set of time interval 0–100 s. Then we obtained an acceptable result with the model of the non-polarized modulation curve and set only an upper limit of Π < 30% (2σ confidence level). We consider the possibility that the polarization degree may be weak if the polarization angle changes during the entire burst duration, as suggested by Götz et al. (2009). Therefore, we performed time-resolved polarization analyses for the data sets of Interval-1 and -2. In Figure 2, we show the observed source modulation curves as a function of scattering angle for both time intervals after subtraction of background. The error bars shown in Figure 2 include not only the statistical uncertainty but also the 1.8% systematical one as estimated in the preceeding subsection.

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At the first step, we investigated the polarization degrees, Π, and the PA (ϕ_p), measured counterclockwise from the north, separately for Interval-1 and -2. Then, the response of GAP for irradiation from 20.0 deg off-axis is modeled using the Monte Carlo method with the Geant 4 simulator. The gray solid lines are the best-fit functions for Interval-1 and -2. The best values are Π₁ = 25% ± 15% with ϕ_p1 = 159 ± 18 deg for Interval-1 and Π₂ = 31% ± 21% with ϕ_p2 = 75 ± 20 deg for Interval-2, respectively. Hereafter the quoted errors are at 1σ confidence for two parameters of interest. The significance of the polarization detection is rather low at 95.4% and 89.0% for Interval-1 and -2, while the difference of the PAs is significant at the 99.9% (3.5σ) level.

In the next step, we performed a combined fit for the two intervals, assuming that the polarization degree for Interval-2 is the same as that for Interval-1. This means that we treat Π as one free parameter to improve the statistics with the reduction of the model parameters. Here the two PAs were still free parameters for both intervals, because the change in angle is apparent. The best-fit polarization degree is Π = 27% ± 11% with χ² = 21.8 for 19 degrees of freedom. We show a Δχ² map in the (Π, ϕ_p) plane in Figure 3, where we represent ϕ_p = ϕ_p1. The significance of detection of polarization is at the 99.4% (2.9σ) confidence level.

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Gamma-ray detectors on board RHESSI and INTEGRAL have complex geometry, and the polarization analysis may be highly affected by the instrumental systematics as several other researchers have mentioned (Kalemci et al. 2007; McGlynn et al. 2007). In contrast to these, GAP is developed for the purpose of GRB polarimetry with high axial symmetry in shape. The systematic uncertainty is quantitatively estimated and found to be as small as 1.8% of the total polarization signals, as described above. Of course, GAP is well calibrated for polarized γ-rays before launch (Yonetoku et al. 2011). Therefore, for the prompt emission of GRBs, we conclude that this is probably the most convincing detection of polarization degrees and angles so far.

The emission mechanisms of GRBs that are being actively discussed using the spectral and light curve information collected so far includes synchrotron emission of electrons at the optically thin regions of relativistic jets and quasi-thermal emission from the photospheres of jets (for a review, see Mészáros 2006). Our reliable polarimetric observations may help further constrain the emission mechanisms as well as the structure of the emission sites and the magnetic fields. The main results of our polarimetric observation of GRB 100826A are the following: (1) the polarization degree averaged over the burst duration is Π = 27% ± 11% in the energy range of 70–300 keV below E_p ∼ 600 keV and (2) the PA significantly varies from Interval-1 to -2.

It has been theoretically shown that sizable net polarizations can be obtained both in the synchrotron and photospheric emission mechanisms. The synchrotron mechanism involves several different types of models with respect to magnetic field structure (for reviews, see Lazzati 2006; Toma et al. 2009): (a) synchrotron in a globally ordered toroidal field (SO model; Granot 2003; Lyutikov et al. 2003; Zhang & Yan 2011), (b) in random fields on plasma skin depth scales (SR model; Granot 2003; Nakar et al. 2003), and (c) in random fields on hydrodynamic scales (SH model; Inoue et al. 2011; Gruzinov & Waxman 1999). In the SR model, the magnetic field directions are assumed to be random not isotropically but mainly in the plane perpendicular to the local expansion direction. In this case a high degree of polarization can be obtained only when the observer sees the jet slightly off-axis, i.e., θ_v ∼ θ_j + Γ⁻¹, where θ_v is the angle between the line of sight and the jet axis, and θ_j and Γ are the opening half angle and the bulk Lorentz factor of the jet, respectively. On the other hand, (d) in the photospheric emission model (Ph model), we also expect strongly polarized radiation when the radiation energy is comparable to or smaller than the baryon kinetic energy at the photosphere (Beloborodov 2011). Around the photosphere, the photon distribution is highly anisotropic, which can lead to high levels of polarization through the last electron scatterings (see also Eichler & Levinson 2003; Lazzati et al. 2004 for the other Comptonization models). We also need the condition θ_v ∼ θ_j + Γ⁻¹ in this model to have a high net polarization. The above four models can be consistent with our result (1).

Our result (2) provides us with very important information, which excludes axisymmetric jets both in the synchrotron and photospheric emission models. If the emitting surface is symmetric around the jet axis, as assumed by most authors in the SO, SR, and Ph models, the direction of the net polarization in the high Π case is determined to be either parallel or perpendicular to the direction from the jet axis toward the line of sight. Therefore, we conclude that the non-axisymmetric structure of the brightness and/or the magnetic fields on the observable angular scale ∼ Γ⁻¹ are required to have a substantial change of PA (see also Lazzati & Begelman 2009).

A possible solution for results (1) and (2) is patchy emission in the SO, SR, or Ph model, or a patchy magnetic field structure, i.e., the SH model. For instance, the SH model produces net polarization as $\Pi \sim 70\%/\sqrt{N}$, where N is the number of independent patches with coherent magnetic field in the observable region. The polarization degree for N ∼ 2–50 can be consistent with the individual results for Interval-1 and -2 within 1σ confidence. The angle of the averaged polarization is statistically random, so that they can be consistent with our result (2). Similar arguments may be made for the patchy SO, SR, and Ph models. In the patchy SO model, the emission from each patch can have different PA's easily when θ_j ∼ Γ⁻¹. In the patchy SR and Ph models, we no longer require the off-axis viewing of the jet, and the emission from each of the off-axis viewed patches has high Π and different PA.

How can we further constrain the models with the analysis results of other bursts detected by GAP and the future polarimetry missions? We note that the statistical analysis results of the SO, SR and Ph models in Toma et al. (2009) are not applicable since they assume axisymmetric jets. In the Ph model, the patch scales are constrained as θ_p ≳ Γ⁻¹. Then, high local polarizations are obtained from patches with θ_v ∼ θ_p + Γ⁻¹ ≳ 2Γ⁻¹, although their brightness is much smaller than that from patches with θ_v ≲ Γ⁻¹ because of the relativistic beaming effect. Thus, it is not expected that all the bright bursts have a high net polarization in the patchy Ph model. The statistical studies of the GAP bursts might provide us with some implications for further constraining the emission mechanism.

This polarimetric observation for GRB 100826A has been performed in the energy range below E_p. In reality, the spectral indices α_B of bursts below E_p are not fully explained in the framework of synchrotron or photospheric mechanism. In the synchrotron mechanism, the radiative cooling of emitting electrons should not be so rapid as to produce a sufficiently hard spectrum below E_p, so that the emission region could be thick, unlike the thin shell emission assumed in many papers (e.g., Asano & Terasawa 2009). The photospheric models include the idea that the emission below E_p is a superposition of many quasi-thermal components with different temperatures and/or Γ (e.g., Ryde et al. 2010; Toma et al. 2011). Clearly, more studies on the energy dependence of polarization (as well as the non-axisymmetric structure of the jet) in each model are needed to discuss the observational results quantitatively.

This work is supported by the Grant-in-Aid for Young Scientists (S) No. 20674002 (DY), Young Scientists (A) No. 18684007 (DY), JSPS Research Fellowships for Young Scientists No. 231446 (KT), and also supported by the Steering Committee for Space Science at ISAS/JAXA of Japan. K.T. thanks K. Ioka for useful conversations.