Spectral evolution in gamma-ray bursts: predictions of the internal shock model and comparison to observations

Several trends have been identified in the prompt gamma-ray burst (GRB) emission: e.g. hard-to-soft evolution, pulse width evolution with energy, time lags, hardness-intensity/-fluence correlations. Recently Fermi has significantly extended the spectral coverage of GRB observations and improved the characterization of this spectral evolution. We study how internal shocks can reproduce these observations. In this model the emission comes from the synchrotron radiation of shock accelerated electrons, and the spectral evolution is governed by the evolution of the physical conditions in the shocked regions. We present a comprehensive set of simulations of a single pulse and investigate the impact of the model parameters, related to the shock microphysics and to the initial conditions in the ejecta. We find a general qualitative agreement between the model and the various observations used for the comparison. All these properties or relations are governed by the evolution of the peak energy and photon indices of the spectrum. In addition, we identify the conditions for a quantitative agreement. We find that the best agreement is obtained for (i) steep electron slopes (p>~2.7), (ii) microphysics parameters varying with shock conditions so that more electrons are accelerated in stronger shocks, (iii) steep variations of the initial Lorentz factor in the ejecta. When simulating short GRBs by contracting all timescales, all other parameters being unchanged, we show that the hardness-duration correlation is reproduced, as well as the evolution with duration of the pulse properties. Finally, we investigate the signature at high energy of these different scenarios and find distinct properties - delayed onset, longer emission, and flat spectrum in some cases - suggesting that internal shocks could have a significant contribution to the prompt LAT emission. [abridged]

Prompt thermal emission in gamma-ray bursts

GRB spectra appear non-thermal, but recent observations of a few bursts with Fermi GBM have confirmed previous indications from BATSE of the presence of an underlying thermal component. Photospheric emission is indeed expected when the relativistic outflow emerging from the central engine becomes transparent to its own radiation, with a quasi-blackbody spectrum in absence of additional sub-photospheric dissipation. However, its intensity strongly depends on the acceleration mechanism - thermal or magnetic - of the flow. We aim to compute the thermal and non-thermal emissions produced by an outflow with a variable Lorentz factor, where the power injected at the origin is partially thermal (fraction epsilon_th) and partially magnetic (fraction 1-epsilon_th). The thermal emission is produced at the photosphere, and the non-thermal emission in the optically thin regime. Apart from the value of epsilon_th, we want to test how the other model parameters affect the observed ratio of the thermal to non-thermal emission. If the non-thermal emission is made by internal shocks, we self-consistently obtained the light curves and spectra of the thermal and non-thermal components for any distribution of the Lorentz factor in the flow. If the non-thermal emission results from magnetic reconnection we were unable to produce a light curve and could only compare the respective non-thermal and thermal spectra. In the different considered cases, we varied the model parameters to see when the thermal component in the light curve and/or spectrum is likely to show up or, on the contrary, to be hidden. We finally compared our results to the proposed evidence for the presence of a thermal component in GRB spectra. Focussing on GRB 090902B and GRB 10072B, we showed how these observations can be used to constrain the nature and acceleration mechanism of GRB outflows.

The origin of the late rebrightening in GRB 080503

GRB 080503, detected by Swift, belongs to the class of bursts whose prompt phase consists of an initial short spike followed by a longer soft tail. It did not show any transition to a regular afterglow at the end of the prompt emission but exhibited a surprising rebrightening after one day. We aim to explain this rebrightening with two different scenarios - refreshed shocks or a density clump in the circumburst medium - and two models for the origin of the afterglow, the standard one where it comes from the forward shock, and an alternative one where it results from a long-lived reverse shock. We computed afterglow light curves either using a single-zone approximation for the shocked region or a detailed multizone method that more accurately accounts for the compression of the material. We find that in several of the considered cases the detailed model must be used to obtain a reliable description of the shock dynamics. The density clump scenario is not favored. We confirm previous results that the presence of the clump has little effect on the forward shock emission, except if the microphysics parameters evolve when the shock enters the clump. Moreover, we find that the rebrightening from the reverse shock is also too weak when it is calculated with the multi-zone method. On the other hand, in the refreshed-shock scenario both the forward and reverse shock models provide satisfactory fits of the data under some additional conditions on the distribution of the Lorentz factor in the ejecta and the beaming angle of the relativistic outflow.

Do Fermi-LAT observations imply very large Lorentz factors in GRB outflows ?

Recent detections of GeV photons in a few GRBs by Fermi-LAT imply huge bulk Lorentz factors to avoid a large gamma gamma optical depth at high energy. Estimates can be as high as Gamma ~ 1000 in the most extreme cases. This puts severe constraints on models of the central engine and the jet acceleration in GRBs. These estimates are however obtained from a simplified single zone model. We present here a more realistic calculation which takes into account the time, space and direction dependent photon field existing in an outflow with several relativistically moving emitting zones. The formalism is general and can be applied to many models of the prompt GRB emission. We present results obtained for a numerical implementation in the framework of the internal shock model. We show that (i) the minimum Lorentz factor Gamma_min in bright LAT GRBs is reduced by a factor ~ 2-3 compared to previous estimates if the GeV and MeV emission are produced in the same region, and by an additional factor ~ 2-8 if the GeV emission is produced at larger radii. We provide an improved approximate formula for Gamma_min which is in good agreement with our numerical results and can be directly applied to LAT GRB data; (ii) a delayed GeV onset can be due to the time evolution of the opacity. As an illustration of these two first results, we present a synthetic GRB that reproduces most features of GRB 080916C with a mean Lorentz factor of ~ 340, an optically thin regime for gamma gamma opacity at 3GeV in bin b, a variability timescale of 0.5s in the MeV lightcurve and a delayed onset of ~ 5s of the GeV emission; (iii) the gamma gamma opacity can smooth the short timescale variability in the GeV lightcurve. This last result implies that the observed variability at high energy is not necessarily a good test to distinguish between an internal and an external origin for the GeV emission in GRBs. [abridged]

Reconciling observed GRB prompt spectra with synchrotron radiation ?

(abridged)Prompt GRB emission is often interpreted as synchrotron radiation from high-energy electrons accelerated in internal shocks. Fast synchrotron cooling predicts that the photon index below the spectral peak is alpha=-3/2. This differs significantly from the observed median value alpha approx -1. We quantify the influence of inverse Compton and adiabatic cooling on alpha to understand whether these processes can reconcile the observations with a synchrotron origin. We use a time-dependent code that follows both the shock dynamics and electron energy losses. We investigate the dependence of alpha on the parameters of the model. Slopes between -3/2 and -1 are reached when electrons suffer IC losses in the Klein-Nishina regime. This does not necessarily imply a strong IC component in the Fermi/LAT range because scatterings are only moderately efficient. Steep slopes require that a large fraction (10-30%) of the dissipated energy is given to a small fraction (<~1%) of the electrons and that the magnetic energy density fraction remains low (<~ 0.1%). Values of alpha up to -2/3 can be obtained with relatively high radiative efficiencies (>50%) when adiabatic cooling is comparable with radiative cooling (marginally fast cooling). This requires collisions at small radii and/or with low magnetic fields. Amending the standard fast cooling scenario to account for IC cooling naturally leads to alpha up to -1. Marginally fast cooling may also account for alpha up to -2/3, although the conditions required are more difficult to reach. About 20% of GRBs show spectra with slopes alpha>-2/3. Other effects, not investigated here, such as a thermal component in the electron distribution or pair production by HE photons may further affect alpha. Still, the majority of observed GRB prompt spectra can be reconciled with a synchrotron origin, constraining the microphysics of mildly relativistic internal shocks.

The GRB luminosity function in the internal shock model confronted to observations

We compute the expected luminosity function of GRBs in the context of the internal shock model. We assume that GRB central engines generate relativistic outflows characterized by the respective distributions of injected kinetic power Edot and contrast in Lorentz factor Kappa = Gamma_max/Gamma_min. We find that if the distribution of contrast extends down to values close to unity (i.e. if both highly variable and smooth outflows can exist) the luminosity function has two branches. At high luminosity it follows the distribution of Edot while at low luminosity it is close to a power law of slope -0.5. We then examine if existing data can constrain the luminosity function. Using the log N - log P curve, the Ep distribution of bright BATSE bursts and the XRF/GRB ratio obtained by HETE2 we show that single and broken power-laws can provide equally good fits of these data. Present observations are therefore unable to favor one form of the other. However when a broken power-law is adopted they clearly indicate a low luminosity slope ~ -0.6 +- 0.2, compatible with the prediction of the internal shock model.

Is GRB afterglow emission intrinsically anisotropic ?

The curvature of a relativistic blast wave implies that its emission arrives to observers with a spread in time. This effect is believed to wash out fast variability in the lightcurves of GRB afterglows. We note that the spreading effect is reduced if emission is anisotropic in the rest-frame of the blast wave (i.e. if emission is limb-brightened or limb-darkened). In particular, synchrotron emission is almost certainly anisotropic, and may be strongly anisotropic, depending on details of electron acceleration in the blast wave. Anisotropic afterglows can display fast and strong variability at high frequencies (above the fast-cooling frequency). This may explain the existence of bizarre features in the X-ray afterglows of GRBs, such as sudden drops and flares. We also note that a moderate anisotropy can significantly delay the jet break in the lightcurve, which makes it harder to detect.

The origin of the prompt GRB spectrum

Using a detailed model of the internal shock phase, we discuss the origin of the prompt emission in gamma-ray bursts. We focus on the identification of the dominant radiative process (Fermi-GBM range) and propose an explanation for some features observed by Fermi-LAT at high energy in some GRB lightcurves.

Prompt high-energy emission from gamma-ray bursts in the internal shock model

The prompt GRB emission is thought to arise from electrons accelerated in internal shocks propagating within a highly relativistic outflow. The launch of Fermi offers the prospect of observations with unprecedented sensitivity in high-energy (>100 MeV) gamma-rays. The aim is to explore the predictions for HE emission from internal shocks, taking into account both dynamical and radiative aspects, and to deduce how HE observations constrain the properties of the relativistic outflow. The emission is modeled by combining a time-dependent radiative code with a dynamical code giving the evolution of the physical conditions in the shocked regions.Synthetic lightcurves and spectra are compared to observations. The HE emission deviates significantly from analytical estimates, which tend to overpredict the IC component, when the time dependence and full cross-sections are included. The exploration of the parameter space favors the case where the dominant process in the BATSE range is synchrotron emission. The HE component becomes stronger for weaker magnetic fields. The HE lightcurve can display a prolonged pulse duration due to IC emission, or even a delayed peak compared to the BATSE range.Alternatively, having dominant IC emission in the BATSE range requires most electrons to be accelerated into a steep power-law distribution and implies strong 2nd order IC scattering. In this case, the BATSE and HE lightcurves are very similar. The combined dynamical and radiative approach allows a firm appraisal of GRB HE prompt emission. A diagnostic procedure is presented to identify from observations the dominant emission process and derive constrains on the bulk Lorentz factor, particle density and magnetic field of the outflow.

The low-luminosity tail of the GRB distribution: the case of GRB 980425

(abridged) The association of GRB 980425 with SN 1998bw at z=0.0085 implies the existence of a population of GRBs with an isotropic-equivalent luminosity which is about 10^4 times smaller than in the standard cosmological case. We investigate two scenarios to explain a weak GRB : a normal (intrinsically bright) GRB seen off-axis or an intrinsically weak GRB seen on-axis. For each of these two scenarios, we first derive the conditions to produce a GRB 980425-like event and we then discuss the consequences for the event rate. If we exclude the possibility that GRB 980425 is an occurence of an extremely rare event observed by chance during the first eight years of the afterglow era, the first scenario implies that (i) the local rate of standard bright GRBs is much higher than what is usually expected; (ii) the typical opening angle is much narrower than what is derived from observations of a break in the afterglow lightcurve. In addition, we show that the afterglow of GRB 980425 in this scenario should have been very bright and easily detected. For these reasons the second scenario appears more realistic. We show that the parameter space of the internal shock model indeed allows GRB 980425-like events, in cases where the outflow is only mildly-relativistic and mildly-energetic. The rate of such weak events in the Universe has to be much higher than the rate of standard bright GRBs to allow the discovery of GRB 980425 during a short period of a few years. However it is still compatible with the observations as the intrinsic weakness of these GRB 980425-like bursts does not allow detection at cosmological redshift. We finally briefly discuss the consequences of such a high local rate of GRB 980425-like events for the future prospects of detecting non-electromagnetic radiation, especially gravitational waves.