The properties of gamma-ray bursts (GRBs) that are inferred from observations depend on the value of the bulk Lorentz factor, Γ. Consequently, accurately estimating it is an important aim. In this work, we present a method of measuring Γ based on observed photospheric emission, which can also be used for highly dissipative flows that may lead to nonthermal spectral shapes. For the method to be applicable, two conditions need to be met: the photon number should be conserved in the later stages of the jet, and the original photon temperature must be inferred from the data. The case of dissipation via subphotospheric shocks is discussed in detail, and we show that the method is particularly efficient when a low-energy spectral break is identified. We demonstrate the capabilities of the method by applying it to two different GRB spectra. From one of the spectra, we obtain a value for Γ with statistical uncertainties of only ∼15%, while for the other spectrum we only obtain an upper limit.

Gamma-ray burst (GRB) spectra are typically non-thermal, with many including two spectral breaks suggestive of optically thin emission. However, the emitted spectrum from a GRB photosphere, which includes prior dissipation of energy by radiation-mediated shocks (RMSs), can also produce such spectral features. Here, we analyse the bright GRB 211211A using the Kompaneets RMS Approximation (KRA). We find that the KRA can fit the time-resolved spectra well, significantly better than the traditionally used Band function in all studied time bins. The analysis of GRB 211211A reveals a jet with a typical Lorentz factor (Γ∼300), and a strong RMS (upstream dimension-less specific momentum, γuβu∼3) occurring at a moderate optical depth (τ∼35) in a relatively cold upstream (θ_u = k_B T_u /m_e c^2∼10^(−4)). We conclude that broad GRB spectra that exhibit two breaks can also be well explained by photospheric emission. This implies that, in such cases, the spectral shape in the MeV-band alone is not enough to determine the emission mechanism during the prompt phase in GRBs.

In many astrophysical systems, photons interact with matter through thermal Comptonization. In these cases, under certain simplifying assumptions, the evolution of the photon spectrum is described by an energy diffusion equation such as the Kompaneets equation, having dependencies on the seed photon temperature, theta(i), the electron temperature, theta e, and the Compton y-parameter. The resulting steady-state spectrum is characterized by the average photon energy and the Compton temperature, which both lack analytical dependencies on the initial parameters. Here, we present empirical relations of these two quantities as functions of theta(i), theta(e), and y, obtained by evaluating the steady-state solution of the Kompaneets equation accounting for energy diffusion and electron recoil. The relations have average fractional errors similar to 1 per cent across a wide range of the initial parameters, which make them useful in numerical applications.

The early steep decay, a rapid decrease in X-ray flux as a function of time following the prompt emission, is a robust feature seen in almost all gamma-ray bursts with early enough X-ray observations. This peculiar phenomenon has often been explained as emission from high latitudes of the last flashing shell. However, in photospheric models of gamma-ray bursts, the timescale of high-latitude emission is generally short compared to the duration of the steep decay phase, and hence an alternative explanation is needed. In this paper we show that the early steep decay can directly result from the final activity of the dying central engine. We find that the corresponding photospheric emission can reproduce both the temporal and spectral evolution observed. This requires a late-time behaviour that should be common to all gamma-ray burst central engines, and we estimate the necessary evolution of the kinetic power and the Lorentz factor. If this interpretation is correct, observation of the early steep decay can give us insights into the last stages of central activity, and provide new constraints on the late evolution of the Lorentz factor and photospheric radius.

Photons that decouple from a relativistic jet do so over a range of radii, leading to a spreading in arrival times at the observer. Therefore, changes to the comoving photon distribution across the decoupling zone are encoded in the emitted signal. In this paper, we study such spectral evolution occurring across a pulse. We track the radiation from the deep subphotospheric regions all the way to the observed time-resolved signal, accounting for emission at various angles and radii. We assume a simple power-law photon spectrum injection over a range of optical depths and let the photons interact with the local plasma. At high optical depths, we find that the radiation exists in one of three characteristic regimes, two of which exhibit a high-energy power law. Depending on the nature of the injection, this power law can persist to low optical depths and manifest itself during the rise time of the pulse with a spectral index β ≈ α − 1, where α is the low-energy spectral index. The results are given in the context of a gamma-ray burst jet, but are general to optically thick, relativistic outflows.

The debate regarding the emission mechanism in gamma-ray bursts has been long-standing. Here, we study the spectral signatures of photospheric emission, accounting for subphotospheric dissipation by a radiation-mediated shock. The shocks are modeled using the Kompaneets RMS approximation (KRA). We find that the resulting observed spectra are soft, broad, and exhibit an additional break at lower energies. When fitting a collection of 150 mock data samples generated by the model, we obtain a distribution of the low-energy index α that is similar to the observed one. These results are promising and show that dissipative photospheric models can account for many of the observed properties of prompt gamma-ray burst emission.

Emission from the photosphere in gamma-ray burst jets can be substantially affected by subphotospheric energy dissipation, which is typically caused by radiation-mediated shocks. We study the observational characteristics of such emission, in particular the spectral signatures. Relevant shock initial conditions are estimated using a simple internal collision framework, which then serve as inputs for a radiation-mediated shock model that generates synthetic photospheric spectra. Within this framework, we find that if the free fireball acceleration starts at r 0 similar to 1010 cm, in agreement with hydrodynamical simulations, then the typical spectrum consists of a broad, soft power-law segment with a cutoff at high energies and a hardening in X-rays. The synthetic spectra are generally well fitted with a standard cutoff power-law (CPL) function, as the hardening in X-rays is commonly outside the observable energy range of current detectors. The CPL-fits yield values for the low-energy index, alpha, and the peak energy, E peak, that are centered around similar to -0.8 and similar to 220 keV, respectively, similar to typical observed values. We also identify a nonnegligible parameter region for what we call optically shallow shocks: shocks that do not accumulate enough scatterings to reach a steady-state spectrum before decoupling and thereby produce more complex spectra. These occur for optical depths tau less than or similar to 55uu-2 , where u u = gamma u beta u is the dimensionless specific momentum of the upstream as measured in the shock rest frame.

Shocks that occur below a gamma-ray burst (GRB) jet photosphere are mediated by radiation. Such radiation-mediated shocks (RMSs) could be responsible for shaping the prompt GRB emission. Although well studied theoretically, RMS models have not yet been fitted to data owing to the computational cost of simulating RMSs from first principles. Here we bridge the gap between theory and observations by developing an approximate method capable of accurately reproducing radiation spectra from mildly relativistic (in the shock frame) or slower RMSs, called the Kompaneets RMS approximation (KRA). The approximation is based on the similarities between thermal Comptonization of radiation and the bulk Comptonization that occurs inside an RMS. We validate the method by comparing simulated KRA radiation spectra to first-principle radiation hydrodynamics simulations, finding excellent agreement both inside the RMS and in the RMS downstream. The KRA is then applied to a shock scenario inside a GRB jet, allowing for fast and efficient fitting to GRB data. We illustrate the capabilities of the developed method by performing a fit to a nonthermal spectrum in GRB 150314A. The fit allows us to uncover the physical properties of the RMS responsible for the prompt emission, such as the shock speed and the upstream plasma temperature.

We study the effect of Bethe-Heitler (BeHe) pair production on a proton synchrotron model for the prompt emission in gamma-ray bursts (GRBs). The possible parameter space of the model is constrained by consideration of the synchrotron radiation from the secondary BeHe pairs. We find two regimes of interest. (1) At high bulk Lorentz factor, large radius, and low luminosity, proton synchrotron emission dominates and produces a spectrum in agreement with observations. For part of this parameter space, a subdominant (in the MeV band) power law is created by the synchrotron emission of the BeHe pairs. This power law extends up to few tens or hundreds of MeV. Such a signature is a natural expectation in a proton synchrotron model, and it is seen in some GRBs, including GRB 190114C recently observed by the MAGIC observatory. (2) At low bulk Lorentz factor, small radius, and high luminosity, BeHe cooling dominates. The spectrum achieves the shape of a single power law with spectral index alpha = -3/2 extending across the entire Gamma-ray Burst Monitor/Swift energy window, incompatible with observations. Our theoretical results can be used to further constrain the spectral analysis of GRBs in the guise of proton synchrotron models.

The origin of ultra-high-energy cosmic rays (UHECRs) remains debated. The prompt and afterglow phases of low-luminosity gamma-ray bursts (LLGRBs) are seen as promising candidates for this acceleration. Here, we investigate this connection by looking at the unavoidable emission from the electrons that are co-accelerated together with UHECRs. Specifically, we use the data from the archetypical low-luminosity GRB 060218. We find that if acceleration of UHECRs occurred during the prompt phase, the emission from the electrons would be orders of magnitude brighter than the observations in the optical band. For the afterglow phase, we limit the total available kinetic energy by comparing the emission from the thermal electrons to the radio data at three days. We find that the total energy in the afterglow is not sufficient to supply the UHECR flux observed at Earth. These results challenge the mildly relativistic outflows of LLGRBs as the main sources of UHECRs.