Universal Scaling Law in Long Gamma-Ray Bursts

LETTER PASJ: Publ. Astron. Soc. Japan 65, L3, 2013 June 25 c 2013. Astronomical Society of Japan.  Universal Scaling Law in Long Gamma-Ray Bursts Ryo T SUTSUI and Toshikazu S HIGEYAMA Research Center for the Early Universe, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Received 2013 March 5; accepted 2013 March 31) Abstract The overwhelming diversity of long gamma-ray bursts (LGRBs), discovered after the launch of the Swift satellite, is a major obstacle to LGRB studies. Recently, it was shown that the prompt emission of LGRBs can be classified into three subclasses: Type I and Type II LGRBs, populating separate fundamental planes in a 3D space defined by the peak luminosity, the duration, and the spectral peak energy, and outliers belonging to none of these planes. Here, we show that Type I LGRBs exhibit different shapes of light curves from that of Type II LGRBs. Furthermore, we demonstrate that this classification has uncovered a new scaling law concerning the light curve of Type II LGRBs, over a span of 8 orders of magnitude ranging from the prompt emission to the late X-ray afterglow one. The scaled light curve has four distinct phases. The first phase has a characteristic time-scale, while the three subsequent phases exhibit power-law behaviors with different exponents. We attempt a new interpretation in terms of the emission from an optically thick fireball propagating in the cricumstellar matter at relativistic speed, and argue that the four observed phases correspond to its hydrodynamical phases. Our classification scheme succeeds in pinning down intrinsic luminosities of Type II LGRBs through the scaling law with a sample of polymorphic GRBs. Further refinements of this scheme and scaling law will make it possible to use a subclass of LGRBs as new standard candles with the same reliability and accuracy as Type Ia supernovae in more distant universe than the light from supernovae can reach. Key words: gamma rays: observations — methods: statistical — radiation mechanisms: non-thermal 1. Introduction A gamma-ray burst (GRB) is the most energetic explosion known in the universe. A GRB the prompt emission of which lasts longer than 2 s is classified as a long GRB (LGRB). Prompt gamma-ray emission is followed by afterglow emission at longer wavelengths. LGRBs are thought to come from the death of massive stars. The discovery of supernova 2003dh, associated with a LGRB 030329 (Stanek et al. 2003), was thought to confirm such a hypothesis. However, observational success after the launch of the Swift satellite (Gehrels et al. 2004) casted doubt on the bimodal classification based on the duration of the prompt emission. In spite of its extremely long duration ( 102 s), GRB 060614 (Gehrels et al. 2006) could result from a neutron-star merger because of no associated supernova. Even if associated supernovae are observed, many of them, e.g., GRBs 980425 and 060218, are far dimmer than ordinary GRBs. In addition to these mysteries, the diversity of the early X-ray afterglow discovered with the X-ray telescope (XRT) aboard the Swift satellite is another major obstacle in the field of GRB studies. Though all of these observations indicate the limitation of the dichotomy between the short GRB (SGRB) and the long GRB, until now there was no successful classification scheme to take into account all of these observational properties consistently. Well-known correlations between the observed quantities in prompt emission, such as the spectral peak energy (Ep )–the isotropic energy (Eiso ), Ep –the peak luminosity (Lp ), and the spectral lag (tlag )–Lp (Amati et al. 2002; Yonetoku et al. 2004; Norris et al. 2000), are sometimes used as discriminators of GRBs (Lü et al. 2010; Gehrels et al. 2006). These correlations that divide GRBs into SGRBs, LGRBs, and some low-luminosity GRBs have not always held; there has been a large dispersion in the correlation of each class. Though the dispersion had been implicitly assumed to follow a single Gaussian distribution in many studies before Swift and Fermi, recent observations of the supernova that is not associated with an apparent LGRB and diversity in the X-ray afterglow might have indicated that this is not the case. Recent observations, by Swift, Fermi, etc., provide plenty of data so that this implicit assumption can be tested. Thanks to thorough studies on the reduction of systematic errors in Ep , Lp , Eiso , and the duration of GRBs (Kaneko et al. 2006; Yonetoku et al. 2010; Kocevski 2012), criteria for the gold sample of GRBs were established as follows (Tsutsui et al. 2010, 2011, 2012): 1. Band models to reduce any systematic errors due to different choices of spectral models must be fitted to time-integrated spectra. 2. Light curves must have a time resolution of 64 ms to derive the peak luminosities with a common time resolution in the GRB rest frame by rebinning the fluxes. 3. Peak photon counts must be 10 times larger than the background fluctuation for secure estimations of the duration and Eiso . The gold sample compiled by Tsutsui et al. (2012) had the smallest systematic error, and made it possible to find a generalized correlation between Ep , TL ( Eiso =Lp ), and Lp . Furthermore, the correlation succeeded in discriminating, at R. Tsutsui and T. Shigeyama [Vol. 65, b Counts/64 ms 0.0 0.8 Cumulative Counts c 0.4 1.0 10 Type I Type II outlier 0.0 0.0 −1.0 Residual 990506 081222 0.4 1053 1052 51 Lp [erg/s] 0.8 a 1054 L3-2 10−2 10−1 100 101 0.0 (Ep 102.71[keV])1.84(TL 100.86[sec])0.29 0.2 0.4 0.6 0.8 1.0 Normarized Time Fig. 1. Classification scheme of prompt emission of LGRB. a: Ep –TL –Lp diagram for 36 LGRBs in the gold sample in Tsutsui et al. (2012) with a residual plot in the bottom panel. Three subclasses based on the distribution in this plot are indicated by different colors: Type I (blue), Type II (red), and outlier (black). The same color is used for the same subclass in the other panels. The solid black line indicates the fundamental plane for Type I LGRBs. b: Examples of normalized light curves. c: Normalized cumulative light curves. The black solid line indicates a constant count rate. least, three subclasses in LGRBs (Tsutsui et al. 2011, 2012): Type I, Type II, and outliers. This new classification was verified from the temporal properties of the prompt emission (Tsutsui et al. 2012). Figure 1a shows an Ep –TL –Lp diagram of the gold sample along with the classification given in Tsutsui et al. (2012). Blue squares indicate Type I LGRBs populating a fundamental plane plotted with the solid line, red circles Type II LGRBs on another slightly misaligned fundamental plane, and black triangles outliers. Type I and Type II LGRBs are also discriminated from the shape of their prompt-emission light curves. Figure 1b shows typical light curves for Type I LGRB (990506) and Type II (081222). As exemplified in this figure, Type I LGR (...truncated)