Photosphere deathline and GRB 110721A

# GRB 110721A: photosphere “death line” and the physical origin of the GRB “Band” function

Bing Zhang11affiliation: Department of Physics and GXU-NAOC Center for Astrophysics and Space Sciences, Guangxi University, Nanning 530004, China 22affiliation: On leave from Department of Physics and Astronomy, University of Nevada, Las Vegas, NV 89154, USA , Rui-Jing Lu11affiliation: Department of Physics and GXU-NAOC Center for Astrophysics and Space Sciences, Guangxi University, Nanning 530004, China , En-Wei Liang11affiliation: Department of Physics and GXU-NAOC Center for Astrophysics and Space Sciences, Guangxi University, Nanning 530004, China , Xue-Feng Wu33affiliation: Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008, China
###### Abstract

The prompt emission spectra of gamma-ray bursts (GRBs) usually have a dominant component that is well described by a phenomenological “Band” function. The physical origin of this spectral component is debated. Although the traditional interpretation is synchrotron radiation of non-thermal electrons accelerated in internal shocks or magnetic dissipation regions, a growing trend in the community is to interpret this component as modified thermal emission from a dissipative photosphere of a GRB fireball. We analyze the time dependent spectrum of GRB 110721A detected by Fermi GBM and LAT, and pay special attention to the rapid evolution of the peak energy . We define a “death line” of thermally-dominated dissipative photospheric emission in the plane, and show that of GRB 110721A at the earliest epoch has a very high MeV that is beyond the “death line”. Together with the finding that an additional “shoulder” component exists in this burst that is consistent with a photospheric origin, we suggest that at least for some bursts, the “Band” component is not from a dissipative photosphere, but must invoke a non-thermal origin (e.g. synchrotron or inverse Compton) in the optically thin region of a GRB outflow. We also suggest that the rapid “hard-to-soft” spectral evolution is consistent with the quick discharge of magnetic energy in a magnetically-dominated outflow in the optically thin region.

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## 1. Introduction

The prompt emission spectrum of a gamma-ray burst (GRB) is usually well described by a phenomenological function known as the “Band” function (Band et al. 1993). This model, which is essentially a broken power law function with a smooth (exponential) transition, was traditionally invoked to model spectra of GRBs detected by BATSE on board the Compton Gamma-Ray Observatory. The function is found successful to describe most GRB spectra detected by later missions as long as the spectral band is wide enough (e.g. Abdo et al. 2009; Zhang et al. 2011).

The physical origin of this phenomenological Band function is not identified. The traditional model is synchrotron emission of non-thermal electrons in an optically thin region, e.g. internal shocks or internal magnetic dissipation regions (Mészáros et al. 1994; Tavani 1996; Daigne & Mochkovitch 1998; Lloyd & Petrosian 2000; Bosnjak et al. 2009; Zhang & Yan 2011). Alternatively, a matter-dominated outflow (fireball) can have a bright photosphere (Paczýnski 1986; Goodman 1986; Mészáros & Rees 2000; Mészáros et al. 2002), which may be enhanced by kinetic or magnetic dissipation processes near the photosphere (Thompson 1994; Rees & Mészáros 2005; Pe’er et al. 2006; Giannios 2008; Beloborodov 2010; Lazzati & Begelman 2010; Ioka 2010). It has been argued that due to geometrical and/or physical broadening, this quasi-thermal component may be modified to mimic a Band function (e.g. Beloborodov 2010; Lazzati & Begelman 2010; Pe’er & Ryde 2011; Lundman et al. 2012). The scalings of a non-dissipative photosphere model are argued to be able to interpret various empirical correlations (Fan et al. 2012).

Within the framework of the standard fireball-shock model, a GRB prompt emission spectrum is expected to be the superposition of a quasi-thermal photosphere emission component and a non-thermal component in the optically-thin internal shock region (Mészáros & Rees 2000; Zhang & Mészáros 2002; Toma et al. 2011; Pe’er et al. 2012). Such a superposition effect has been claimed in the BATSE data archive (e.g. Ryde 2005; Ryde & Pe’er 2009), and was confirmed more robustly recently with the Fermi data (e.g. Ryde et al. 2010; Zhang et al. 2011; Guiriec et al. 2011; Axelsson et al. 2012). On the other hand, most GRB spectra (e.g. GRB 080916C) are still well described by one single Band component (Abdo et al. 2009; Zhang et al. 2011). This sharpens the debate regarding the origin of the Band function. For GRB 080916C, the non-detection of a thermal component led to the suggestion of a Poynting-flux-dominated outflow (Zhang & Pe’er 2009; see also Daigne & Mochkovitch 2002; Zhang & Mészáros 2002). Alternatively, some authors attempted to interpret the entire Band function as emission from a dissipative photosphere (e.g. Beloborodov 2010; Vurm et al. 2011; Giannios 2008; Ioka 2010). These two interpretations invoke distinct assumptions regarding the composition of the GRB jets. Finding observational clues to differentiate between them is therefore essential to unveil the physics of GRB central engine, jet composition and energy dissipation mechanisms, which are poorly constrained (e.g. Zhang 2011).

Here we show that the time-resolved spectral information of GRB 110721A holds the key to address this open question.

## 2. “Death line” of GRB baryonic photosphere emission in the Ep−L plane

For a hot fireball with total wind luminosity launched from an initial fireball radius , the initial temperature is

 T0≃(Lw/4πR20ca)1/4≃1.4×1010 K L1/4w,52R−1/20,7, (1)

where is speed of light, and is the Stefan-Boltzmann energy density constant. The observed photosphere temperature can be as high as if the fireball is clean enough so that the photosphere radius does not exceed the fireball coasting radius , but is lower than for fireballs with a heavier baryon loading when . More specifically, one has (Mészáros & Rees 2000)

 TphT0=⎧⎪ ⎪⎨⎪ ⎪⎩(RphRc)−2/3=(ηη∗)8/3,η<η∗,Rph>Rc,1,η>η∗,Rph

where is the dimensionless entropy of the fireball, and

 η∗=(LwσT4πmpc3R0)1/4≃1.04×103(Lw,52R0,7)1/4 (3)

is the critical value of . The photosphere luminosity is . For , since and , one has const. For , since , , . So the photosphere luminosity is

 LphLw=⎧⎪ ⎪⎨⎪ ⎪⎩(RphRc)−2/3=(ηη∗)8/3,η<η∗,Rph>Rc,1,η>η∗,Rph

If a GRB spectrum is dominated by the photosphere emission, for a certain observed isotropic -ray luminosity , the spectral peak energy should not exceed , where is a factor to denote the peak of the photosphere spectrum. Therefore a baryonic photosphere emission has a “death line” defined by

 Ep≤ζkT0≃1.2 MeV ζL1/452R−1/20,7. (5)

The factor is subject to the shape of the spectrum. For a strict blackbody, . For a relativistic outflow, the shape of blackbody is modified to the form (see also Li & Sari 2008 and references therein)

 Fν∝ν2c2kT∫∞hν/kTdxex−1. (6)

The spectrum has a maximum value at

 ζ∼2.82. (7)

The death line (5) is derived for a non-dissipative photosphere. For a thermally-dominated jet, dissipation via internal shocks or neutron collisional heating near the photosphere would compensate adiabatic cooling, so that the photosphere temperature would be maintained close to but never exceed the maximum temperature (Beloborodov 2012), so eq.(5) applies to a broad categories of dissipative photosphere models as well. A possible exception would be the dissipative photosphere model that invokes continued magnetic dissipation at extended radii above the photosphere (Drenkhahn & Spruit 2002), which allows to be above the death line (5) if the bulk Lorentz factor is large enough and dissipation at high optical depth is suppressed (Giannios 2012). However, in order to thermalize the jet, the required Lorentz factor is very low (Vurm et al. 2012), making it essentially impossible to exceed the death line. Also this model may not interpret the GRB 110721A phenomenology, including the existence of the shoulder thermal component and the rapid spectral softening during the rising phase of bolometric luminosity (see Sect. 3).

## 3. Grb 110721a

GRB 110721A was jointly detected by the Gamma-Ray Burst Monitor (GBM; Meegan et al. 2009) and the Large Area Telescope (LAT; Atwood et al. 2009) onboard the Fermi Gamma-Ray Telescope (Axelsson et al. 2012 and references therein). A candidate optical counterpart was reported (Greiner et al. 2012). Assuming that the association is real, Berger (2012) suggested two possible redshifts or , with the former one preferred.

The time-dependent spectral evolution of GRB 110721A was reported by Axelsson et al. (2012). Two noticeable features of the burst are: 1. A thermal component is identified to be superposed on the Band component in both the time integrated spectrum and time-resolved spectra. The temperature of this “shoulder” thermal component evolves with time as a broken power law, which is consistent with the expectations of the photosphere model (Ryde & Pe’er 2009). 2. The Band component displays an extremely rapid spectral evolution. The at the earliest epoch reaches a record-breaking value MeV.

We have independently processed the Fermi data of GRB 110721A. We performed a joint spectral analysis using the data from the NaI 6, 7 and BGO 1 detectors on GBM, as well as the LAT data111http://fermi.gsfc.nasa.gov/cgi-bin/ssc /LAT/LATDataQuery.cgi. For GBM, we used the TTE event data containing individual photons with time and energy tags. Background rates are estimated by fitting the light curve before and after the burst using a one-order background polynomial model. We pretreated the LAT data using the LAT ScienceTools-v9r27p1 package and the P7TRANSIENTV6 response function (detailed informatin for the LAT GRB Analysis are available in the NASA Fermi web site222grbanalysis.html). In the diffuse response calculation, a three-component model is used: GRB 100721A with a PowerLaw2 spectrum, the Galactic diffuse model of gal2yearp7v6v0.fits, and the extragalactic diffuse power law model. We then extracted the background-subtracted light curves from the GBM and LAT and demonstrated them in Figure 1. It is obvious that higher energy photons arrive earlier than the lower energy photons.

In order to better understand the cause of such a behavior, we carry out a detailed time-dependent spectral analysis. We adjust the size of the time bins so that each time bin contains enough photons to perform a statistically significant spectral analysis. We applied the software package RMFIT (version 3.3pr7) to carry out the analyses. We confirm the conclusion of Axelsson et al. (2012) that adding a shoulder thermal component can improve the fits to the data significantly. Since the evolution of the thermal component has been presented in Axelsson et al. (2012), in this paper we focus on the Band component only in order to study its physical origin. We find that the Band model usually gives a reasonable fit to the data, with the reduced in the range . Figure 2 gives an example of the Band model fitting the data in the time interval of [-0.512, 0.064]s. This earliest epoch indeed shows an extremely high value MeV, which is consistent with MeV reported by Axelsson et al. (2012). The larger error in our fit may be because the Fermi team has included the extra LLE (LAT Low Energy) data, which is currently unavailble to the public. We also present the best fit model curves in different time intervals in Fig.3.

Figure 4 displays the rest-frame plot for time-resolved spectra of Fermi GRBs with well measured redshifts. The data are a sub-sample of Fig.9 of Lu et al. (2012), for which only the parameters during the rising phase of GRB pulses are adopted. This is because the decaying phase may be controlled by the high-latitude curvature effect, which does not directly reveal radiation physics. Two “death lines” (eq.[5]) are drawn, which correspond to cm (solid, typical value) and cm (dashed, an extreme value to allow highest death line possible). GRB 110721A at the earliest epoch [-0.512. 0.064]s is plotted for two candidate redshifts. It is clearly seen from the figure that for both redshifts, the points are way above the death lines. This rules out a wide range of dissipative photosphere models at least for this earliest epoch.

One may make one step further. Axelsson et al. (2012) showed that evolution of the Band component can be fit as a power-law decay with time, suggesting that this component might have a same physical origin during the burst. Figure 3 displays evolution of the spectral shape of the Band component, which shows a similar value with a gradually shallowing value. This suggests that the Band component should share the same physical origin in different epochs: it is not from the photosphere, but is likely from an optically thin region where non-thermal particles are accelerated.

## 4. Summary and discussion

We have shown that the Band function component of GRB 110721A is beyond the “death line” of thermally-dominated dissipative photosphere models in the plane. Together with the fact that an additional shoulder thermal component is consistent with the photosphere model, we reach the conclusion that the so-called “Band” component is not of a photospheric origin at least for this burst, and is formed via non-thermal dissipation processes in the optically thin regions. Veres et al. (2012) interpreted this emission as synchrotron emission from a magnetically-dominated jet.

Such a finding has profound implications in understanding the origin of other Band function spectra of GRBs. Zhang et al. (2011) identified three elemental spectral components through a detailed time-resolved spectral analysis of 17 GRBs co-detected with Fermi GBM and LAT. They found that there are two types of GRBs. GRB 080916C’s spectra remain the “Band” shape even though the time interval for the spectral analysis progressively reduces, reaching s in the rest frame. GRB 090902B, on the other hand, showed a clear “narrowing” feature as time bin reduces, and spectrum is much narrower at rest-frame 1 s. The time integrated spectrum of this burst is also narrower than other Band GRBs. This burst’s “Band” component can be indeed de-composed as superposed photosphere emission (Ryde et al. 2010; Zhang et al. 2011; Pe’er et al. 2012; Mizuta et al. 2011). However, such bursts are not common. Most bursts are similar to GRB 080916C.

The spectral parameters of GRB 110721A are similar to those of GRB 080916C and many other GRBs. The conclusion that the Band component of GRB 110721A originates from the optically thin region also supports the suggestion that most Band components are non-thermal (synchrotron or SSC) emission in the optically thin region. Available data seem to suggest the following unified picture: The GRB central engine may have a range of magnetization parameter . 1. For low bursts, dissipation can occur at small radii, so that a bright photospheric emission component (such as the case of GRB 090902B) is detected. Such bursts are usually accompanied by a high energy component due to upscattering of the thermal photons (and probably also synchrotron self-Compton, Pe’er et al. 2012). 2. For intermediate bursts, the photosphere component is weaker but still detectable. Examples of this category include GRB 110721A (Axelsson et al. 2012) and GRB 100724B (Guiriec et al. 2011). The Band component of these bursts are formed in the large radii via internal shocks (IS) or internal collision-induced magnetic reconnection and turbulence (ICMART). 3. Finally, if is large enough, both the photosphere and IS components are suppressed. The Band component forms at even larger radii via the ICMART process (Zhang & Yan 2011).

Finally, very rapid hard-to-soft evolution observed in GRB 110721A (Axelsson et al. 2012 and this work) and many other GRBs (Lu et al. 2010, 2012) challenges existing models. Such a rapid evolution is not expected in the internal shock model. For the photosphere model, some moderate hard-to-soft evolution may be expected due to the intial growth of optical depth in a fireball (W. Deng & B. Zhang 2012, in preparation), but never an extreme evolution like GRB 110721A. A possible interpretion may be made within the framework of the ICMART model. According to this model (Zhang & Yan 2011), in the emission region rapidly decreases during each ICMART event, since the magnetic energy is continuously dissipated. If a good fraction of local magnetic dissipation energy is deposited to electrons, the typical electron Lorentz factor would have a -dependence, so that decreases with time as reduces. Also relativistic turbulent reconnection would lead to locally Doppler-boosted mini-jets, whose Lorentz factors would also depend on the local value (Zhang & Zhang 2012). The time dependent Doppler boosts for mini-jets would enhance the hard-to-soft evolution.

We thank the referee for helpful comments, P. Mészáros, B.-B. Zhang, and P. Veres for discussing their work with us, and A. Beloborodov, F. Daigne, D. Giannios, P. Kumar, R. Mochkovitch, A. Pe’er, and F. Ryde for useful discussion. This work was partially supported by NSF AST-0908362, National Natural Science Foundation of China (Grants No. 11025313 and 11063001), the “973” Program of China (2009CB824800), the Guangxi Natural Science Foundation (2010GXNSFA013112 and 2010GXNSFC013011), and the special funding for national outstanding young scientist (Contract No. 2011-135). XFW is supported by One-Hundred-Talent Program of Chinese Academy of Sciences.

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