SYNCHROTRON SELF-INVERSE COMPTON RADIATION FROM REVERSE SHOCK ON GRB 120326A

Gamma-ray bursts (GRBs) are among the most powerful explosions in the universe and are observationally characterized by intense short flashes primarily in a high-energy band (so-called prompt emission) and long-lived afterglows observed from X-ray to radio wavelengths. The GRB afterglow is believed to involve a relativistically expanding fireball (e.g., Meszaros & Rees 1997). Interstellar matter (ISM) influences the fireball shell after it has been collected and considerable energy is transferred from the shell to the ISM. The energy transfer is caused by two shocks: a forward shock propagating into the ISM and a reverse shock propagating into the shell. It is also believed that the forward shock produces long-lived afterglows and the reverse shock generates short-lived bright optical flashes (e.g., Akerlof et al. 1999) and/or intense radio afterglows (e.g., Kulkarni et al. 1999).

A number of afterglows have been densely monitored in X-ray and optical bands since the launch of the Swift satellite (Gehrels et al. 2004), and a significant number of afterglows showed the different temporal evolutions in X-ray and optical bands. These results indicated that the simple forward shock model cannot explain their behavior altogether and additional processes are required (e.g., Panaitescu et al. 2006; Huang et al. 2007; Urata et al. 2007; Li et al. 2012). Inverse Compton scattering and/or reverse shocks may play an important role in solving the problem. Panaitescu & Vestrand (2011) suggested local inverse Compton scattering to describe the X-ray band's faster decay compared with that of the optical. Kobayashi et al. (2007) introduced a synchrotron self-inverse Compton radiation from a reverse shock to explain the X-ray flare and its early afterglows. Thus, confirming the existence of reverse shocks at particularly longer wavelengths and ascertaining their typical occurrence conditions is critical. Because the expected lifetime of reverse shocks at longer wavelengths is substantially longer than the lifetime of those at optical wavelengths, decoding radiations into forward and reverse shock components is possible. In addition, numerous rapid optical follow-ups are missing the reverse shock components; however, several successful detections at optical wavelengths have been made.

The possible reason for the missing reverse shock component could be that the typical reverse shock synchrotron frequency is far below the optical band. Submillimeter observations are the key elements used to catch reverse shock and to understand the emission mechanism of GRB afterglows. Searching for reverse shock emission in the submillimeter wavelength would test this possibility. These submillimeter observations also provide clean measurements of source intensity, unaffected by scintillation and extinction. However, no systematic submillimeter observational studies in the early afterglow phase exist. This has remained the case in reverse shock studies for some time. One of the main reasons for this is the absence of dedicated submillimeter telescopes and strategic follow-ups with rapid response which involve employing open-use telescopes for these challenging observations. In addition, it is nearly impossible to have rapid (several hours after the burst) follow-ups with current open-use telescopes which require manual preparation of the observational scripts. In addition to this technical problem, the sensitivities of current submillimeter telescopes, except for the Atacama Large Millimeter/submillimeter Array (ALMA), are not good enough to detect the number of afterglows in the submillimeter band (e.g., de Ugarte Postigo et al. 2012). Hence, rapid careful target selections are required to conduct effective submillimeter follow-up observations using open-use resources.

GRB 120326A was detected and localized using Swift (Siegel et al. 2012). The Suzaku/Wide-band All-Sky Monitor (Suzaku/WAM) and the Fermi Gamma-ray Burst Monitor (Fermi/GBM) also detected this burst, and quick-look spectral analyses were reported (Iwakiri et al. 2012; Collazzi 2012). The optical afterglow was discovered by Klotz et al. (2012) and observed at the early stage by using several telescopes. The optical afterglow also exhibited remarkable rebrightening (Walker et al. 2012). The afterglow at submillimeter and radio bands was also detected using an Submillimeter Array (SMA; Urata et al. 2012), the Combined Array for Research in Millimeter-wave Astronomy (Perley et al. 2012), and the Expanded Very Large Array (Laskar et al. 2012). The SMA observation provided the fastest afterglow detection (about 4.6 × 10⁴ s after the burst) among seven submillimeter afterglows at 230 GHz, which are mostly detected about 1 × 10⁵ s (∼1 day) after the bursts. Although numerous follow-ups in various wavelengths have been conducted, submillimeter afterglow monitoring from the earlier phase (<1 × 10⁵ s) is still rare and essential to understand the puzzle of afterglow radiation. The redshift was determined to be z = 1.798, according to a series of metal absorption features (Tello et al. 2012). We used f(t, ν)∝t^αν^β to express the afterglow properties.

The Swift Burst Alert Telescope (Swift/BAT) triggered and located GRB 120326A at 01:20:29 (T₀) UT on 2012 March 26. Swift immediately slewed to the burst and the X-Ray Telescope (XRT) initiated follow-up observations at 59.5 s after the burst. The X-ray afterglow was identified and localized at R.A. $=18^{\rm h}15^{\rm m}36\buildrel{\mathrm{s}}\over{.}47$, decl. =+69°15'370, with an uncertainty of 41. The X-ray afterglow was observed using the XRT until ∼5 × 10⁵ s. UVOT also obtained images by using the White filter starting 67 s after the burst and no counterpart in the band was observed.

The Suzaku/WAM also triggered the burst at 01:20:31.9 (T₀ + 2.9 s) UT on 2012 March 26. The WAM (Yamaoka et al. 2009) is a lateral shield of the Hard X-ray Detector (Takahashi et al. 2007) on board the Suzaku satellite (Mitsuda et al. 2007) and is a powerful GRB spectrometer covering an energy range of 50–5000 keV to determine prompt spectral energy peaks, E_peak (e.g., Ohno et al. 2008; Tashiro et al. 2007; Urata et al. 2009). As shown in Figure 1, the prompt X-ray and γ-ray light curves observed using the Swift/BAT and Suzaku/WAM exhibited a single fast rise and exponential decay structure.

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We performed the optical afterglow observations using the Lulin 1 m telescope (LOT; Huang et al. 2005) and the LOAO robotic 1 m telescope (Han et al. 2005; Lee et al. 2010) within the framework of the EAFON (Urata et al. 2003). Four color observations were made with LOT on the night of March 26. The LOAO data were obtained in the R-band filter from 2013 March 26 to April 2. The afterglow was also observed with Camera for Quasars in the Early Universe (Park et al. 2012; Kim et al. 2011; Lim et al. 2013) on the 2.1 m Otto-Struve Telescope of the McDonald observatory, Texas, USA. The data were obtained in g, r, i, z, and Y filters, starting at 2013 March 26, 10:09:22 (UT) and continued until April 2. The logs for both observations are summarized in Table 1.

We also triggered the submillimeter continuum follow-up observations by using the seven 6 m antennas of SMA (Ho et al. 2004). The first continuum observation at 230 GHz (with an 8 GHz bandwidth) was conducted at 10:15:05 on 2012 March 26, about 4.6 × 10⁴ s after the BAT trigger. As Urata et al. (2012) reported, the submillimeter counterpart was observed at the location of the X-ray and optical afterglow. The continuous monitoring using the SMA was also performed at the same frequency setting on March 27, 29, 31, and April 6 and 11. Table 2 summarizes the scientific observations that were conducted for four nights, because of weather conditions and antenna reconfiguration. Figure 2 shows submillimeter light curves of all the GRB afterglows detected at the 230 GHz to date. Among all seven events, we successfully detected the earliest submillimeter afterglow on GRB 120326A. A possible reason for this successful submillimeter monitoring was the target selection using the quick optical follow-ups.

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Table 2. Log of SMA Observations

Instruments	Observing Period	T−T0	Band	Beam Size	Flux Density
	(UT)	(s)	(GHz)		(mJy)
SMA	2012 Mar 26 13:00–15:00	45571	230	174 × 114	2.84 ± 0.86
SMA	2012 Mar 26 15:10–17:30	53971	230	169 × 102	3.56 ± 0.75
SMA	2012 Mar 26 18:00–20:15	64171	230	203 × 096	3.36 ± 1.04
SMA	2012 Mar 27 13:25–19:15	138480	230	162 × 111	2.38 ± 0.51
SMA	2012 Mar 29 12:45–18:50	310290	230	062 × 037	1.76 ± 0.50
SMA	2012 Apr 11 15:50–21:10	1377571	230	055 × 042	<1.44 (3σ)

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The BAT data were analyzed using the standard BAT analysis software included in HEADAS version 6.12. The time-averaged spectrum (15–150 keV) from T₀ − 2 to T₀ + 11 s was extracted using batgrbproduct. Response matrices were generated by the task batdrmgen, using the latest spectral redistribution matrices. The WAM spectral and temporal data were extracted using hxdmkwamlc and hxdmkwamspec in HEADAS version 6.12. The background was estimated using the fitting model described in Sugita et al. (2009). Response matrices were generated by the WAM response generator as described in Ohno et al. (2008). We used three models for the joint spectral fitting: the power-law model, power law with exponential cutoff model, and the Band function model. As shown in Figure 3, the spectrum was reasonably fitted with the Band function. The fitting yielded a low-energy photon index of $1.17^{+0.53}_{-0.32}$, a high-energy photon index of $2.23^{+0.09}_{-0.11}$, and a νFν spectrum peak energy in the source frame $E^{\rm src}_{\rm peak}$ of $107.8^{+15.2}_{-15.3}$ keV (χ²/ν = 0.92 for ν = 63). Both the power law (χ²/ν = 1.55 for ν = 65) and power law with exponential cutoff models (χ²/ν = 1.38 for ν = 67) were not acceptable, leaving the curvature of the residuals around 30–40 keV at the observer frame (the second and third panels in Figure 3). We also estimated the equivalent isotropic radiated energy in the prompt phase at the 1–10,000 keV band E_iso as $3.18^{+0.40}_{-0.32}\times 10^{52}$ erg, assuming cosmological parameters: H₀ = 71 km s⁻¹ Mpc⁻¹, Ω_m = 0.27, and Ω_Λ = 0.73.

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We obtained a reduced Swift/XRT light curve with a flux density unit at 10 keV from the U.K. Swift Science Data Center (Evans et al. 2007, 2009). The light curves shown in Figure 4 were suitably fitted using the broken power-law model described in Urata et al. (2009), using the best-fitted parameters of α_X1 = 0.19 ± 0.09, α_X2 = −2.35 ± 0.15, and t_bX = (5.29  ±  0.32) × 10⁴ s. We also generated the time-averaged spectrum at a mean time of 6.47 × 10⁴ s (from 55741 to 73639 s). The spectra were suitably fitted using the power law modified by photo-electric absorptions (Galactic and intrinsic), and the photon index was estimated as $1.95^{+0.18}_{-0.17}$.

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A standard routine, including bias subtraction and flat-fielding corrections, was employed to processes the optical data by using the IRAF package. The DAOPHOT package was used to perform the aperture photometry of the GRB images. Standard star observation in one night is used to derive magnitudes of reference stars in the vicinity of the GRB afterglow, and these reference stars were used to perform photometry of the afterglow. We also made use of the Pan-STARRS1 3π catalogs (Magnier et al. 2013; Schlafly et al. 2012; Tonry et al. 2012) to calibrate our g'-, r'-, i'-, z'-, and Y-band data. As shown in Figure 4, the light curves in the g', r', i', and z' bands indicated the achromatic temporal break at ∼2.6 × 10⁵ s. We successfully fitted the broken power-law model to the g'-, r'-, i'-, and z'-band light curves. Regarding the g' band, we have obtained α_g1 = −1.01 ± 0.06, α_g2 = −2.84 ± 0.16, and t_bg = (2.58 ± 0.15) × 10⁵ s; regarding the r' band, α_r1 = −0.96 ± 0.01, α_r2 = −2.64 ± 0.09, and t_br = (2.58 ± 0.07) × 10⁵ s; regarding the i' band, α_i1 = −0.88 ± 0.02, α_i2 = −2.48 ± 0.05, and t_bi = (2.51 ± 0.10) × 10⁵ s; regarding the z' band, α_z1 = −0.89 ± 0.01, α_z2 = −2.64 ± 0.10, and t_bz = (2.63 ± 0.06) × 10⁵ s; and regarding the y' band, we fitted the light curve by using the simple power-law model, because the y'-band observations covered only before the temporal break. The light curve was fitted with the model and we obtained α_y = −0.87  ±  0.03. The decay indices before and after the break are ∼−1 and ∼−2, respectively, which is highly consistent with typical well-observed long GRB optical afterglows. In Figure 5, we plot the spectral flux distribution with the submillimeter and X-ray data. We fitted the optical data alone using a power-law function and obtained β = −1.44 ± 0.10, −1.11 ± 0.09, and −1.18  ±  0.17 at t = 6.42 × 10⁴ s, 1.38 × 10⁵ s, and 3.10 × 10⁵ s, respectively. To remove the effects of the Galactic interstellar extinction, we used the reddening map by Schlafly & Finkbeiner (2011).

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The raw data of the SMA observations were calibrated using the MIR and MIRIAD packages and images were made with the natural weighting. Regarding the first night of observation, we split the data into three periods to describe the temporal evolution of submillimeter afterglow. Table 2 summarizes each observation period and flux density measurements (upper part). Because of adverse weather conditions during the first 1.08 × 10⁴ s, only the data recorded after 13:00 on March 26 UT were used for the scientific analysis. In the final period, we constrained the 3σ upper limit. With our SMA follow-ups, we successfully monitored the afterglow from 4.32 × 10⁴ to 3.46 × 10⁵ s as shown in Figure 4. The submillimeter afterglow exhibited a flat evolution with slight brightening between the first and second periods. To describe the temporal evolution, we fitted the submillimeter data with the single power-law function and obtained α_{submillimeter} = −0.33 ± 0.08, which was considerably flatter than those of the X-ray and optical.

4.1. Prompt Emission and Energetics Relations

The joint fitting of the Swift/BAT and Suzaku/WAM suitably constrained the spectral parameters of the prompt emission of GRB 120326A that are critical to characterize the event. As shown in Figure 6, the spectral peak energy in the source frame, $E^{\rm src}_{{\rm peak}}$, is one of the lowest events among the sample of the joint Swift/BAT–Suzaku/WAM analysis. The trend is similar to that of the νFν spectral peak energy at the observer frame $E^{{\rm obs}}_{{\rm peak}}$ in comparison to a larger set of $E^{{\rm obs}}_{{\rm peak}}$ values of 479 GRBs drawn from the Fermi/GBM catalog (von Kienlin et al. 2014); however, the Fermi/GBM measurements do not represent $E^{\rm src}_{{\rm peak}}$ due to the lack of redshift information. By comparing with the HETE-2 sample (Sakamoto et al. 2005), GRB 120326A can be categorized as X-ray-rich GRBs. Using the definition with Swift/BAT data (Sakamoto et al. 2008), we confirm that GRB 120326A with an ∼0.74 fluence ratio in the 25–50 keV and 50–100 keV bands falls into the X-ray-rich GRB family.

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The abundance of the multi-color optical light curves for estimating the jet break time suggests that GRB 120326A is a favorable target for evaluating ${E^{\rm src}_{\rm peak}\hbox{--}E_{\rm iso}}$ (Amati et al. 2002) and ${E^{\rm src}_{\rm peak}\hbox{--}E_{\rm \gamma }}$ (Ghirlanda et al. 2007) relations. Here, ${E^{\rm src}_{\rm peak}\hbox{--}E_{\rm \gamma }}$ is the correlation between the intrinsic spectrum peak energy, ${E^{\rm src}_{\rm peak}}$, and the jet collimation-corrected energy in the prompt phase, E_γ. The closure relation of the observed optical temporal decay and the spectral indices (e.g., Sari et al. 1999; Zhang & Mészáros 2004) indicates that, of all the p > 2 options, the optical results are consistent with both the fast and the slow cooling and both the wind and the ISM medium, as long as ν_{m, FS} and ν_{c, FS} lie below the optical band. Here, ν_{m, FS} and ν_{c, FS} are the characteristic synchrotron frequency and the cooling frequency based on the standard forward shock synchrotron model. Thus, the jet opening angle and the jet corrected energy are estimated using t_br as 669 ± 016 and (2.17 ± 0.10) × 10⁵⁰ erg by assuming the circumburst density, n =1.0 cm⁻³, and the energy conversion efficiency, η_γ = 0.2. To covert the measured jet break time, t_br, to the jet opening angle, we used the formulation of Sari et al. (1999) and Frail et al. (2001). As shown in Figure 7, GRB 120326A obeys the ${E^{\rm src}_{\rm peak}\hbox{--}E_{\rm iso}}$ and ${E^{\rm src}_{\rm peak}\hbox{--}E_{\rm \gamma }}$ relations within a 3σ confidence level. Therefore, GRB 120326A belongs to the typical long duration GRB family, even with a low $E^{\rm src}_{{\rm peak}}$.

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4.2. Does the Classical Forward Shock Synchrotron Model Work?

4.3. Forward Shock Synchrotron Modeling

4.4. Reverse Shock and Synchrotron Self-Compton Radiation

We conducted multi-wavelength observations of a typical long-duration GRB 120326A, including rapid observations using SMA. Our SMA observation successfully made the fastest afterglow detection among seven submillimeter afterglows at 230 GHz and monitored from 4.32 × 10⁴ to 3.46 × 10⁵ s. The submillimeter afterglow showed considerably slower temporal evolution (α_{submillimeter} = −0.33 ± 0.08) which is not likely to be explained by the forward shock synchrotron model. Based on our dense optical observations, we found that the optical afterglows were well-fitted by the broken power-law model, and the forward shock synchrotron model is feasible to explain the properties. With the boxfit code, we also found the reasonable model function within the forward shock synchrotron model under the assumption of ISM circumburst medium. Using the simple testing method of the forward shock model with temporal decay indices of optical and X-ray afterglows, we found that the origin of the X-ray afterglow could differ from that of the optical. Our joint spectrum fitting for prompt emission using Swift/BAT and Suzaku/WAM also characterized the event and found that the current event obeys the ${E^{\rm src}_{\rm peak}\hbox{--}E_{\rm iso}}$ and ${E^{\rm src}_{\rm peak}\hbox{--}E_{\rm \gamma }}$ relations within a 3σ confidence level.

Based on the detection and the slow decay of the afterglow in submillimeter, we introduced the synchrotron self-inverse Compton radiation from reverse shock and found that this is a plausible method to explain the diversity. This successful modeling could benefit other GRBs. Similar to GRB 120326A, numerous events exhibited no apparent jet breaks in the X-ray band and different temporal evolutions between the X-ray and optical. These observational properties imply that additional components, such as reverse shock and its synchrotron self-inverse Compton radiation, cause different temporal evolution and hide obvious jet breaks in the X-ray. Because of a lack of submillimeter observations for these samples, interpretation from the same picture for these events was difficult. Thus, further rapid follow-ups and continuous monitoring with submillimeter instruments such as SMA and ALMA will enable systematic testing of the reverse shock and self-inverse Compton radiation.

We thank Glen Petitpas for various arrangements on the SMA observations and Shiho Kobayashi for useful comments. We also thank all of staff at the Lulin observatory. This work is partly supported by the Ministry of Education and the National Science Council of Taiwan grants NSC 100-2112-M-008-007-MY3(YU), 99-2112-M-002-002-MY3(KYH). M.I., J.W.K., M.J., and S.J. acknowledge support from the National Research Foundation of Korea (NRF) grant No. 2008-0060544, funded by the Korea government (MSIP). This work made use of data supplied by the UK Swift Science Data Centre at the University of Leicester. This paper includes data taken at the McDonald Observatory of the University of Texas in Austin. The PS1 Surveys have been made possible through contributions of the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its participating institutes, the Max Planck Institute for Astronomy, Heidelberg and the Max Planck Institute for Extraterrestrial Physics, Garching, The Johns Hopkins University, Durham University, the University of Edinburgh, Queen's University Belfast, the Harvard-Smithsonian Center for Astrophysics, and the Las Cumbres Observatory Global Telescope Network, Incorporated, the National Central University of Taiwan, and the National Aeronautics and Space Administration under grant No. NNX08AR22G, issued through the Planetary Science Division of the NASA Science Mission Directorate.