SWIFT GRB GRB071010B: OUTLIER OF THE E^src_peak − E_γ AND  E_iso − E^src_peak − t^src_jet CORRELATIONS

A few tight correlations linking several properties of gamma-ray bursts (GRBs), namely the spectral peak energy, the total radiated energy, and the afterglow break time, have been discovered with pre-Swift GRBs. Amati et al. (2002) found the empirical relation between the rest-frame spectral peak energy of prompt emission E^src_peak (here, we use the E^src_peak, E^obs_peak for the values in the rest and observer frames, respectively) and the isotropic-equivalent energy released during the prompt phase E_iso. Ghirlanda et al. (2004a) showed a tight empirical relation between the E^src_peak and the collimation-corrected energy E_γ based on a jet interpretation of the temporal break in the optical afterglow light curve. Liang & Zhang (2005) found the three-dimensional correlation in the E_iso − E^src_peak − t^src_jet plane. The existence of these correlations could uncover crucial properties of GRB physics which are not yet fully understood. Recently, there have been studies of outliers to these relations (e.g., Campana et al. 2007; Sato et al. 2007; Ghirlanda et al. 2007). Using Swift/XRT observations, Sato et al. (2007) showed that there are cases with continuous X-ray afterglow light curves where no jet break is seen at the expected break time derived from the E^src_peak − E_γ relation. However, some X-ray afterglow light curves may not show jet breaks together with the optical afterglow at the expected time, because there is a possibility that X-ray and optical emission come from different regions and mechanisms even in the normal decay phase (e.g., Urata et al. 2007a; Liang et al. 2007; Huang et al. 2007; Ghisellini et al. 2009). Therefore, it is critical to check the aforementioned relations by combining prompt γ-ray wide-band spectroscopy and optical long-term monitoring.

In this Letter, we present joint spectral analysis of the prompt gamma-ray and systematic optical follow-up results for GRB 071010B. This event was detected and localized by Swift (Markwardt et al. 2007a). The Suzaku/Wide-band All-sky Monitor (WAM; Yamaoka et al. 2009) and Konus/WIND (Golenetskii et al. 2007) also detected this main burst. Thanks to the wide energy band of the Suzaku/WAM (Yamaoka et al. 2009), the joint spectral fittings between the Swift/Burst Alert Telescope (BAT) and the Suzaku/WAM data yield better constraint for the determination of E_peak. The optical afterglow was discovered by Oksanen (2007) and observed by many telescopes from the early stage (e.g., Wang et al. 2008). The redshift was determined to be z = 0.947 by Cenko et al. (2007) using the Gemini North telescope. In the framework of EAFON (Urata et al. 2003, 2005), we have performed long-term monitoring to determine the jet break time. Therefore, GRB071010B is one of the most suitable event to evaluate E^src_peak − E_iso, E^src_peak − E_γ, and E_iso − E^src_peak − t^src_jet in Swift era. All the errors are quoted at the 90% statistical confidence level in this paper.

2.1. Swift/BAT

The Swift/BAT triggered and located GRB 071010B (trigger ID = 293795) at 20:45:47 (T₀) UT on 2007 October 10. The on-board localization was distributed 13 s after the trigger and its position was reported as R.A. = $10^{\rm h}02^{\rm m}07^{\rm }.5$, decl. = +45°44'0'', with an uncertainty of 3'. The spacecraft did not slew promptly to the burst position because automated slewing was disabled due to ongoing recovery from a gyro anomaly (Markwardt et al. 2007a). After 6800 s of the trigger, Swift/XRT started observing the field and detected a bright X-ray counterpart at R.A. = $10^{\rm h}02^{\rm m}09^{\rm }.2$, decl. = +45°43'522, with an uncertainty of 5''. Markwardt et al. (2007b) reported the mask-weighted light curve which shows a pre-trigger pulse starting at T₀ ∼ −45 s, peaking at T₀ ∼ −20 s, and returning almost to background at T₀ ∼ −8 s. The main FRED pulse started at T₀ ∼ 2 s and ended around T₀ ∼ 60 s. A small third soft peak started at T₀ + 95 s and was terminated by the planned spacecraft slew (Markwardt et al. 2007b). The two peaks at T₀ − 45 s and T₀ + 95 s are much weaker than the main peak, thus they are not visible in Figure 1.

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2.2. Suzaku/WAM

2.3. Optical Follow-ups

3.1. Swift/BAT Prompt Emission

3.2. Suzaku/WAM Prompt Emission

3.3. BAT and WAM Joint Analysis

In order to better constrain the spectral peak energy, we perform joint fitting between Swift/BAT and Suzaku/WAM. Figure 1 shows the overlapping time regions (from T₀ − 0.780 to T₀ + 24.2 s) for this fitting. As shown in Figure 2, the spectrum is well fitted with the Band function (Band et al. 1993). The fitting yields a low-energy photon index of 1.19^+0.29_−0.23, a high-energy photon index of 2.30^+0.06_−0.07, and E^src_peak of 86.5^+6.4_−6.3 keV (χ²/ν = 0.59 for ν = 87). This result is consistent with that of Konus/WIND (Golenetskii et al. 2007). We have also estimated the E_iso as 2.25^+0.19_−0.16 × 10⁵² erg, assuming cosmological parameters: H₀ = 71 km s^-1 Mpc⁻¹, Ω_m = 0.27, and Ω_Λ = 0.73.

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3.4. Optical Afterglow

A standard routine including bias subtraction and flat-fielding corrections was employed to process the data using the IRAF package. The DAOPHOT package was used to perform aperture photometry of the GRB images. For the photometric calibration of the afterglow, several calibration stars reported by Henden (2007) were chosen. In Figure 3, we plot the Rc-band light curve of the GRB071010B afterglow based on our photometry. The data contain our LOAO measurements, TAOS observations (Wang et al. 2008) with the re-calibrated GCN measurements (Oksanen 2007; Kann et al. 2007a, 2007b, 2007c; Kocevski et al. 2007; Klunko et al. 2007). The light curve between 0.02 and 10.6 day is well fitted by a single power law with index α = −0.60 ± 0.02 (χ²/ν = 0.89 for ν = 37), defined by F(t) ∝ t^α, where F(t) is the flux in the Rc band at time t after the BAT trigger time T₀. The single power-law index is consistent with that of the TAOS measurement (α ∼ −0.51) reported by Wang et al. (2008). This fitting also excludes the possible 3.4 days temporal break reported by Kann et al. (2007a, 2007b) and Im et al. (2007) based on GCN data point measurements. We have also confirmed that the host-galaxy brightness (i' = 23.63 mag, z' = 22.73 mag) derived by the CFHT observations is insufficient to affect this fitting. We consider both red and typical host-galaxy colors to evaluate R-band brightness. Although the late-time light curve could be fitted by a single power law, it is interesting to note that a possible temporal break occurred at around 9 days after the burst. We tried to fit the 0.02–10.6 days light curve with a broken power-law function expressed as

$$\begin{equation} F_{\nu }(t) = {F_{\nu }^{\ast } \over [(t/t_b)^{\alpha _1}+(t/t_b)^{ \alpha _2}]}, \end{equation} \tag{ 1 }$$

where α₁ and α₂ are the power-law indices before and after the break, F*_ν is the flux at the break, and t_b is the break time. The fitting yields α₁ = −0.54 ± 0.03, α₂ = −3.03 ± 1.15, and t_b = 9.81 ± 1.00 (χ²/ν = 0.52 for ν = 35). When we fix α₂ as −2, the fitting provides the break time of t_b = 9.61 ± 1.49. Therefore, these results imply that the temporal break should be around or later than 9.8 days after the burst.

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Spectral parameters of the prompt emission of GRB071010B are well constrained by our joint fitting of Swift/BAT and Suzaku/WAM. The measured values of current event (E^src_peak = 86.5^+6.4_−6.3 keV and E_iso = 2.25^+0.19_−0.16 × 10⁵² erg) well follow the E^src_peak − E_iso relation. Furthermore, our systematic long-term (10 days) optical monitoring observation suggests a possible jet break at later than ∼9.8 days after the burst. The wealth of the multi-wavelength data with a good temporal coverage makes GRB071010B one of the best targets to evaluate the E^src_peak − E_γ and the E_iso − E^src_peak − t^src_jet relations which studies have been in stagnation due to the lack of the E^src_peak estimation and long-term optical monitoring.

In order to evaluate the E^src_peak − E_γ relation for the optical light curve, we invert this relation to predict the jet break time as described in Sato et al. (2007). The expected jet break time is expressed as

$$\begin{eqnarray} t_{\rm jet} &=& 389\left(1+z\right)\left(\frac{n}{3\; {\rm cm^{-3}}}\right)^{-\frac{1}{3}}\left(\frac{\eta _{\gamma }}{0.2}\right)^{-\frac{1}{3}} \nonumber \\ && \times \, {\rm {{\it E}_{iso,52}}^{-1}}\left(\frac{{\ E^{\rm src}_{\rm peak}}}{A}\right)^{1.89} {\rm day}, \end{eqnarray} \tag{ 2 }$$

where n and η_γ are the number density of the ambient medium and the efficiency of the shock, respectively. Here, we use the Ghirlanda relation as E^src_peak = AE_γ,52^0.70, allowing A to vary within the 3σ level. The value of n is in general within 1<n<30 cm⁻² (Panaitescu & Kumer 2001, 2002). Following the assumption made by Ghirlanda et al. (2004a) for most of their sample GRBs, we initially assume n = 3 cm⁻² and η_γ = 0.2. As shown in Figure 3, the optical light curve is well described with a single power law during the expected jet break time. We also tried to fit the optical light curve by fixing the jet break time as t_j = 1.25 days expected from Equation (2). The fitting yields α₁ = −0.30 ± 0.06 and α₂ = −0.91 ± 0.04(χ²/ν = 0.72 for ν = 36). Although this fitting is acceptable in terms of the χ²-fitting, an F-test indicates that this broken power-law model with t_j = 1.25 days over the single power law is not significant at the 90% confidence level. These temporal decay indices are inconsistent with those of typical jet break events. The temporal (α_x = 0.67) and spectral (β_x = 1.10) relation of X-ray afterglow also supports the sphere phase (α = 3/2β − 1 ∼ 0.65). These X-ray values come from UK's X-ray afterglow repository (Evans et al. 2009). Thus, these results imply that GRB071010B is an outlier of the tight E^src_peak − E_γ relation.

In Figure 4, we also plotted the E^src_peak − E_γ relation together with GRB041006, GRB050904, and others reported by Ghirlanda et al. (2007). According to the detailed optical analysis of the GRB041006 afterglow (Urata et al. 2007b), this pre-Swift era event shows a chromatic optical plateau phase around 0.1 ∼ 0.2 days after the burst. Since Ghirlanda et al. (2007) regarded this chromatic plateau in the GRB041006 optical light curve as the jet break, we updated E_γ for this event. As shown in Figure 4, GRB071010B is a clear outlier of the tight correlation with more than 3σ deviation. GRB041006 is also a possible outlier at the 2σ level. We have also tested the wind case. The estimated E_γ, _w>2.8 × 10⁵0 erg from the jet break limit is inconsistent with Ghirlanda et al. (2007) by over 3σ level. According to Sugita et al. (2009), GRB050904 is also an outlier of the E^src_peak − E_γ relation, but it follows the E^src_peak − E_iso relation.

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These three events including a high-redshift GRB050904 imply the E^src_peak − E_γ relation could have larger scatter than originally suggested. Since the E^src_peak − E_γ correlation requires a small scatter to be used to standardize GRBs in a way similar to Type Ia supernovae (Ghirlanda et al. 2004b), these three events pose a problem to the cosmological application of the E^src_peak − E_γ relation. Another implication is that these outliers have the relevant role of the circumburst environments for different origins (e.g., long and short bursts). In the GRB050904 case, the gap can be explained by a higher circumburst density which implies a massive stars origin. The required density is consistent with the estimations by optical and radio observations (Sugita et al. 2009). However, GRB071010B requires a 2 or 3 order smaller circumburst density ($n\sim 5.9 \times 10^{-3} \rm {cm^{-3}}$) to be consistent with the tight correlation. This lower density environment implies the origin of GRB071010B is of short GRB, where typical circumburst density is $n=10^{-2}\; \rm {cm^{-3}}$ (e.g., Nakar 2007), even though the prompt duration of GRB071010B is longer than 2 s (T₉₀ = 36.0 ± 2.3 s).

We also tested the empirical E_iso − E^src_peak − t^src_jet relation (Liang & Zhang 2005) expressed as

$$\begin{equation} {\ E_{\rm iso}}/10^{52} = (0.85\pm 0.21)\!\left(\frac{E^{\rm src}_{\rm peak}}{100\; {\rm keV}} \right)^{\!\! 1.94\pm 0.17} \!\!\! \left(\frac{t^{\rm src}_{\rm jet}}{1\; {\rm day}} \right)^{\!\! -1.24\pm 0.23}\!\!\!\!, \end{equation} \tag{ 3 }$$

where t^src_jet is the jet break time in the rest frame. As shown in Figure 5, this relation yields the expected upper limit of isotropic total energy as E_iso < 0.11 × 10⁵²erg with the jet break time t_jet>9.8 day. Therefore, GRB071010B is also an outlier of this model-independent relation at more than the 3σ level.

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Since the tight correlations E^src_peak − E_γ and E_iso − E^src_peak − t^src_jet might indicate a crucial property of GRB physics (e.g., Thompson (2006) and Thompson et al. (2007) for the E^src_peak − E_γ relation), GRB071010B might be classified as a new category. However, there is also the possibility that these relations simply have larger dispersion than previous studies. Therefore, further study is required with large volume of good samples which can be built up by the joint analysis of Swift/BAT, Suzaku/WAM, Konus/WIND, Fermi/GBM, and future missions such as the Space Variable Objects Monitor (SVOM) (Basa et al. 2008) with ground-based optical follow-ups.

We thank Bing Zhang for useful comments and discussions. M.I. and I.L. acknowledge the support by the Creative Research Initiatives grant R16-2008-015-01000-0 of MOST/KOSEF. This work is partly supported by grants NSC 98-2112-M-008-003-MY3 (Y.U.), NSC 96WFA0700264 (W.H.I.), the Ministry of Education under the Aim for Top University Program NCU (W.H.I.), the National Natural Science Foundation of China (No. 10673014), and the National Basic Research Program of China (No. 2009CB824800). Access to the CFHT was made possible by the Ministry of Education and the National Science Council of Taiwan as part of the Cosmology and Particle Astrophysics (CosPA) initiative.