# Is Thermal Emission in Gamma-Ray Bursts Ubiquitous?

###### Abstract

The prompt emission of gamma-ray bursts has yet defied any simple explanation, despite the presence of a rich observational material and great theoretical efforts. Here we show that all the types of spectral evolution and spectral shapes that have been observed can indeed be described with one and the same model, namely a hybrid model of a thermal and a non-thermal component. We further show that the thermal component is the key emission process determining the spectral evolution. Even though bursts appear to have a variety of, sometimes complex, spectral evolutions, the behaviors of the two separate components are remarkably similar for all bursts, with the temperature describing a broken power-law in time. The non-thermal component is consistent with emission from a population of fast cooling electrons emitting optically-thin synchrotron emission or non-thermal Compton radiation. This indicates that these behaviors are the fundamental and characteristic ones for gamma-ray bursts.

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^{†}slugcomment: Date: July 10, 2021

## 1 Introduction

It was early recognized that the spectra of gamma-ray bursts (GRBs) have a non-thermal character, with emission over a broad energy range (e.g. Fishman & Meegan (1995)). This typically indicates emission from an optically-thin source and an initial proposal for GRBs was therefore an optically-thin synchrotron model from shock-accelerated, relativistic electrons (e.g. Katz (1994); Tavani (1996)). The number density of the radiating electrons is assumed to be typically a power law as a function of the electron Lorentz factor above a minimum value, , with index . Such a distribution gives rise to a power-law photon spectrum with index below a break energy and a high-energy power-law with index . However, this model has difficulties in explaining the observed spectra of GRBs which show a great variation in and (Preece et al., 2000). In particular, a substantial fraction of them have , which is not possible in the model in its simplest form, since is the power-law slope of the fundamental synchrotron function for electrons with an isotropic distribution of pitch angles (Pacholczyk, 1970). The problem becomes even more severe for the case when the cooling time of the electrons is shorter than the typical dynamic timescale. In the typical setting of GRBs having a relativistic outflow with a bulk Lorentz factor , the time scales for synchrotron and inverse Compton losses are s (Ghisellini et al., 2000b), which is much shorter than both the dynamic time scale

The peak energy from the above distribution of electrons is given by . In the external shock model and are proportional to the bulk Lorentz factor, which makes , which poses a problem in explaining the relative narrowness of the observed distribution of peak energies (Preece et al., 2000), even including the X-ray flashes. Similarly, for the internal shock model , the relative Lorentz factor between the two shells that collide, and , expected to give a larger scatter as well.

A third complication arises in explaining the observed correlation between the burst’s peak-energy and luminosity, also known as the Amati relation (e.g. Lloyd-Ronning et al. (2000); Amati et al. (2002); Ghirlanda et al. (2004)); the peak energy is correlated with the isotropically equivalent energy . For the synchrotron, internal-shock model one expects (e.g. Zhang & Mészáros (2002)), where is the typical variability time scale. This requires that both and have to be quite similar for all bursts, which is difficult to imagine. In addition, assuming a typical (e.g. Kobayashi et al. (2002)) would even lead to an anti-correlation (see also Ramirez-Ruiz & Lloyd-Ronning (2002)). Additional assumptions are needed to explain the positive correlation.

Other variations of the synchrotron or/and inverse Compton model have been suggested (see e.g. Baring & Braby (2004); Lloyd-Ronning & Petrosian (2000); Stern & Poutanen (2004)), however, none have been able to describe all aspects of the observations in a convincing manner. To account for these aspects, I argue that GRBs, in general, have a strong thermal component, which is accompanied by a non-thermal component of similar strength.

## 2 Spectral Modelling

Recently, in Ryde (2004) I identified bursts which are dominated by quasi-thermal emission throughout their duration. The temperature of the emitting matter exhibits a similar behavior for all of them, with an initially constant, or weakly decreasing, temperature ( keV, power-law index to ) and a distinct break into a faster power-law decay with an index of approximately to . I also suggested that bursts that are observed to be initially thermal, are similar to these but have an additional non-thermal component that varies in spectral slope and grows in relative strength with time. This category of bursts is illustrated in this paper by GRB980306 (all bursts discussed here were recorded by the BATSE detector on the Compton Gamma-ray Observatory). Spectra from three different times are shown in the lower-most panels in Figure 1. The model shown consists of a power law , representing the non-thermal emission, combined with a Planck function , where , is Boltzmann’s constant and is the temperature. It is clear that the relative strength of the non-thermal component increases with time and that the index varies, in this particular burst from to (see Figure 2). This leads to the apparent softening below the peak energy. Figure 2 also shows that the temperature of the black body, for this burst, exhibits a similar evolution like the purely quasi-thermal bursts discussed by Ryde (2004), with a distinct break in the cooling curve. There is a total of 10 bursts that have been discussed in the literature from this category (Ghirlanda et al., 2003; Ryde, 2004).

We will now study the spectra of more typical bursts, bursts which do not have any exceptionally hard -values, nor have any conspicuous spectral evolution, and therefore a thermal component is not required in a first appraisal. For this purpose we analyze the sample of the 25 strongest pulses in the catalogue of Kocevski, Ryde, & Liang (2003), which comprise a complete sample of pulses with a varying spectral shapes and evolution. We compare the results of the fits of the hybrid model to those of the most commonly used Band et al. (1993) model, which is an empirical function consisting of a low-energy power-law with index , exponentially connected to a high-energy power-law with index at an energy . We note that these two models have the same number of parameters; , , and two amplitudes, compared to , , , and one amplitude. The reduced values and the residuals of the fits indicate equally good fits for both models; the -values are in most cases indistinguishable statistically. The hybrid model was formally better (had a lower value) in 10 of the cases. The largest differences were for GRB950211 for 540 degrees of freedom (d.o.f.) and GRB960530 for 2071 d.o.f. and finally for GRB950818 for 1819 d.o.f. If a hybrid model with a sharply broken power law with say and (motivated in §3) is used instead, the of the latter fit becomes lower: . This illustrates the obvious fact that the simple power-law model is an approximation of the actual non-thermal emission if the break energy is within the studied window for a significant fraction of the burst duration. In comparing the two models it should also be noted that the hybrid model is a physical model rather than an empirical model and that the fit results are reasonable from a theoretical point-of-view (see §3). Figure 2 shows three of the studied bursts; GRB921207, GRB950624, which illustrate the most common behavior in which evolves from to , and GRB960530 for which is consistent of being constant even though a weak hardening is indicated. For all the cases the temperature again has a distinct break in its evolution. Three spectra from GRB950624 are also shown in Figure 1, illustrating the non-thermal character of the summed spectrum through out the pulse.

In conclusion, the spectral evolution is very similar from burst to burst and is independent of the relative strength of the thermal component. This is in stark contrast to the variety of apparent spectral behaviors found by using the Band function, for instance, with strong variation in . This fact is a strong indication that the thermal emission, combined with a non-thermal component, is ubiquitous and that the behavior of these components are the characteristic signatures of GRBs.

## 3 Discussion and Conclusion

It is argued above that thermal radiation is the key feature during the prompt phase of most GRBs. Apart from the actual fits presented above and the similarity in behaviors among bursts, such an interpretation is attractive for several reasons. First, the value of the low-energy power-law index, , that would be found if the Band function were to be used is now only a result of the relative strength of the thermal component and the slope of the non-thermal component. If the thermal component is strong and/or the non-thermal component is hard, the resulting spectrum will have a hard and vice versa. This gives a new interpretation of the observed distribution which has been a puzzle. Second, the peak of the spectrum is now determined by and is less sensitive to the bulk Lorentz factor, motivating the narrow dispersion of peak energies. In fact, if the photosphere occurs during the acceleration phase it is practically independent of . Third, the Amati correlation has a natural explanation since for a thermal emitter the luminosity and the temperature are correlated. Rees & Mészáros (2005) show that, somewhat depending on the details of the dissipation processes, a positive correlation close to the observed one arises naturally.

A strong photospheric emission at ray wave lengths is predicted in most GRB scenarios, such as in kinetic models (Mészáros, & Rees, 2000; Daigne & Mochkovitch, 2002), in MHD models (Drenkhahn & Spruit, 2002), as well as in Poynting flux models (Lyutikov & Usov, 2000). In the simplest outflow models the observer-frame temperature should be constant (independent of collimation) during the acceleration phase, since the adiabatic losses are compensated by the acceleration. The typical temperature is

(1) |

for erg, cm and . After saturation (the free energy of the outflow has been transferred to kinetic energy) the temperature will follow a simple adiabatic relation, during which the outflow coasts along with a constant , where and are the luminosity and mass outflow rates. The observed emission from an optically-thick shell that expands outwards would emit according to this type of a pattern, similarly to the observed temperature drops in Figure 2. The timescale for the saturation, which according to the observed pulses should be around 1 s, leads to the necessity of very under-loaded fireballs ( M). However, the radiative efficiency is, by necessity, very low for such a scenario, due to large optical depths and that most energy is in kinetic form. On the other hand, if the outflow is indeed radiation-dominated then the saturation will naturally occur at the photosphere. This is also the typical case for electromagnetic outflows (Drenkhahn & Spruit, 2002). Furthermore, Rees & Mészáros (2005) argued that dissipation processes (magnetic reconnections, shocks) below the photosphere could radically enhance the thermal luminosity and thus the radiative efficiency (see also Pe’er & Waxman (2004)). Comptonization would convert a fraction of the dissipated kinetic energy back into thermal energy and thus re-energize the photosphere, giving typical peak energy of hundreds of keV. But to keep the spectra quasi-thermal during the evolution, as is observed, there must be sufficient photons available to keep the spectra close to those of a black-body. Grimsrud & Wasserman (1998) (see also Mészáros, Laguna, Rees (1993)) noted that the photons may still be coupled to the matter (e or baryons), ensuring a quasi-thermal distribution, beyond the radius where the optical depth has become unity. This occurs when the Compton drag time is shorter than the dynamic time. The flow then saturates when the decoupling occurs, now at a very low optical depth. The electron distribution must after this not be perturbed too much from its thermal distribution to be able to reproduce the observed spectra.

The non-thermal component could be interpreted as the synchrotron spectrum from a distribution of fast-cooling electrons. The initial values of are expected from electrons that are cooled to energies below the of the injected electrons. The change in index to could indicate that the frequency corresponding to now moves though the observed energy range and that we, at late times, are detecting the high-energy power-law of the cooling spectrum with . For instance, for a Fermi type of particle acceleration in relativistic shocks and (Mészáros, 2002).

In Figure 3, we plot the energy-flux light-curves of three of the bursts studied. The relative strengths of the thermal component vary substantially among them, with GRB980306 having a strong thermal, initial phase. The obvious correlation between the thermal and the non-thermal components is noteworthy, indicating that the emissions cannot be completely independent. Rees & Mészáros (2005) suggested that the non-thermal emission, which is superimposed on the thermal Compton-spectrum, is due to synchrotron shock-emission further out from the photosphere. Internal outflow variations, leading to the internal shocks, would be accompanied by corresponding variations in the thermal emission. An alternative scenario is that non-thermal electrons, accelerated at a shock close to the photosphere, are cooled quickly by the thermal radiation, thereby emitting a non-thermal Compton radiation, boosting every photon by a factor of . The radiation energy-density could then be comparable or larger than the magnetic energy density. An increase in thermal emission and energy density from the photosphere would lead to an increase in the Compton cooling and emission from the non-thermal electrons. This would naturally explain the close correlation between the components and that they occur approximately simultaneously. The variation in from to would then be interpreted as approaching .

The temperature is shown above to decay as during the coasting phase. The thermal energy flux goes as , where is the emitting surface. Due to relativistic abberation of light, the surface visible to an observer at infinity is . Therefore, and typical values of give

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