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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 $\alpha$ 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., Comment: Proceedings of HEPRO VIII (Paris 2023)

The physical processes of the gamma-ray emission and particle acceleration during the prompt phase in GRBs are still unsettled. In order to perform an unambiguous physical modelling of observations, a clear identification of the emission mechanism is needed. An instance of a clear identification is the synchrotron emission during the very strong flare in GRB160821A, that occurs during the prompt phase at 135 s. Here we show that the distribution of the radiating electrons in this flare is initially very narrow, but later develops a power-law tail of accelerated electrons. We thus identify for the first time the onset of particle acceleration in a GRB jet. The flare is consistent with a late energy release from the central engine causing an external-shock as it encounters a preexisting ring nebula of a progenitor Wolf-Rayet star. Relativistic forward and reverse shocks develop, leading to two distinct emission zones with similar properties. The particle acceleration only occurs in the forward shock, moving into the dense nebula matter. Here, the magnetisation also decreases below the critical value, which allows for Fermi acceleration to operate. Using this fact, we find a bulk Lorentz factor of $420 \simleq \Gamma \simleq 770$, and an emission radius of $R \sim 10^{18}$ cm, indicating a tenuous gas of the immediate circumburst surrounding. The observation of the onset of particle acceleration thus gives new and independent constraints on the properties of the flow as well as on theories of particle acceleration in collisionless astrophysical shocks., Comment: 16 pages, 6 Figures and 4 Tables. Accepted for publication in The Astrophysical Journal Letters (ApJL)

Using the resultant profiles from 3D hydrodynamic simulations of relativistic jets interacting with neutron star merger wind ejecta, we show how the inhomogeneity of energy and velocity {across the jet surface profile} can alter the observed afterglow lightcurve. We find that the peak afterglow flux depends sensitively on the observer's line-of-sight, not only via the jet inclination but also through the jet rotation: for an observer viewing the afterglow within the GRB-bright jet core, we find a peak flux variability on the order $<0.5$ dex through rotational orientation and $<1.3$ dex for the polar inclination. An observed afterglow's peak flux can be used to infer the jet kinetic energy, and where a top-hat jet is assumed, we find the range of inferred jet kinetic energies for our various model afterglow lightcurves (with fixed model parameters), covers $\sim 1/3$ of the observed short GRB population. Additionally, we present an analytic jet structure function that includes physically motivated parameter uncertainties due to variability through the rotation of the source. % An approximation for the change in collimation due to the merger ejecta mass is included and we show that by considering the observed range of merger ejecta masses from short GRB kilonova candidates, a population of merger jets with a fixed intrinsic jet energy is capable of explaining the observed broad diversity seen in short GRB afterglows., Comment: 21 pages, 8 figures

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 due 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 non-thermal 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., Comment: 17 pages, 6 figures. Manuscript accepted by ApJ

Jets can become collimated as they propagate through dense environments and understanding such interactions is crucial for linking physical models of the environments to observations. In this work, we use 3D special-relativistic simulations to study how jets propagate through the environment created around a neutron star merger remnant by neutrino-driven winds. We simulate four jets with two different initial structures, top-hat and Gaussian, and two luminosities. After jet breakout, we study the angular jet structures and the resulting afterglow light curves. We find that the initial angular structures are efficiently washed out during the propagation, despite the small wind mass of only $\sim 10^{-3}$ M$_\odot$. The final structure depends on the jet luminosity as less energetic jets are more strongly collimated, and entrainment of baryons leads to a moderate outflow Lorentz factor ($\approx 40$). Although our jets are not specifically intended to model the outflows of the GW170817 event, we show that they can be used to produce light curves consistent with the afterglow observed in the aftermath of GW170817. Using this procedure we show how the inferred physical parameters e.g., inclination angle, ambient particle number density, can vary substantially between independent fits of the same dataset and appear to be sensitive to smaller details of the angular jet shape, indicating that observationally inferred parameters may depend sensitively on the employed jet models., Comment: 12 pages, 5 figures, 1 table

We calibrate a neutrino transport approximation, called Advanced Spectral Leakage (ASL), with the purpose of modeling neutrino-driven winds in neutron star mergers. Based on a number of snapshots we gauge the ASL parameters by comparing against both the two-moment (M1) scheme implemented in the FLASH code and the Monte Carlo neutrino code Sedonu. The ASL scheme contains three parameters, the least robust of which results to be a blocking parameter for electron neutrinos and anti-neutrinos. The parameter steering the angular distribution of neutrino heating is re-calibrated compared to the earlier work. We also present a new, fast and mesh-free algorithm for calculating spectral optical depths, which, when using Smoothed Particle Hydrodynamics (SPH), makes the neutrino transport completely particle-based. We estimate a speed-up of a factor of 100 in the optical depth calculation when comparing to a grid-based approach. In the suggested calibration we recover luminosities and mean energies within 25%. A comparison of the rates of change of internal energy and electron fraction in the neutrino-driven wind suggests comparable accuracies of ASL and M1, but a higher computational efficiency of the ASL scheme. We estimate that the ratio between the CPU hours spent on the ASL neutrino scheme and those spent on the hydrodynamics is 0.8 per timestep when considering the SPH code MAGMA2 as source code for the Lagrangian hydrodynamics, to be compared with a factor of 10 from the M1 in FLASH., Comment: Minor revision, accepted for publication in MNRAS. 20 pages, 11 figures

We present the first ab initio simulation of a radiation-mediated shock emerging at the photosphere of a relativistic outflow. The simulation is performed using our code radshock that follows fluid dynamics coupled to time-dependent radiative transfer, calculated with the Monte-Carlo method. We use the code to examine the radiative blast wave emerging from neutron star merger GW~170817. It was previously proposed that the merger ejected a dark, relativistically expanding, homologous envelope, and then an explosion inside the envelope produced the observed gamma-ray burst GRB~170817A. Our simulation demonstrates how the shock wave generates radiation as it propagates through the envelope, approaches its photosphere, releases the radiation, and collapses, splitting into two collisionless shocks of a microscopic thickness. We find the light curve and the spectral evolution of the produced gamma-ray burst; both are similar to the observed GRB~170817A., Comment: 5 pages, submitted to ApJL

Neutron star mergers eject neutron-rich matter in which heavy elements are synthesised. The decay of these freshly synthesised elements powers electromagnetic transients ("macronovae" or "kilonovae") whose luminosity and colour strongly depend on their nuclear composition. If the ejecta are very neutron-rich (electron fraction $Y_\mathrm{e} < 0.25$), they contain fair amounts of lanthanides and actinides which have large opacities and therefore efficiently trap the radiation inside the ejecta so that the emission peaks in the red part of the spectrum. Even small amounts of this high-opacity material can obscure emission from lower lying material and therefore act as a "lanthanide curtain". Here, we investigate how a relativistic jet that punches through the ejecta can potentially push away a significant fraction of the high opacity material before the macronova begins to shine. We use the results of detailed neutrino-driven wind studies as initial conditions and explore with 3D special relativistic hydrodynamic simulations how jets are propagating through these winds. Subsequently, we perform Monte Carlo radiative transfer calculations to explore the resulting macronova emission. We find that the hole punched by the jet makes the macronova brighter and bluer for on-axis observers during the first few days of emission, and that more powerful jets have larger impacts on the macronova., Comment: 13 pages, 6 figures, 1 table, accepted by MNRAS

It has been suggested that the prompt emission in gamma-ray bursts (GRBs) could be described by radiation from the photosphere in a hot fireball. Such models must be tested by directly fitting them to data. In this work we use data from the Fermi Gamma-ray Space Telescope and consider a specific photospheric model, in which kinetic energy of a low-magnetisation outflow is dissipated locally by internal shocks below the photosphere. We construct a table model with a physically motivated parameter space and fit it to time-resolved spectra of the 36 brightest Fermi GRBs with known redshift. We find that about two thirds of the examined spectra cannot be described by the model, as it typically under-predicts the observed flux. However, since the sample is strongly biased towards bright GRBs, we argue that this fraction will be significantly lowered when considering the full population. From the successful fits we find that the model can reproduce the full range of spectral slopes present in the sample. For these cases we also find that the dissipation consistently occurs at a radius of $\sim 10^{12}$ cm and that only a few percent efficiency is required. Furthermore, we find a positive correlation between the fireball luminosity and the Lorentz factor. Such a correlation has been previously reported by independent methods. We conclude that if GRB spectra are due to photospheric emission, the dissipation cannot only be the specific scenario we consider here., Comment: 25 pages, 21 figures, 1 supplementary table

The emission mechanism during the prompt phase in gamma-ray bursts (GRBs) can be investigated through correlations between spectral properties. Here, we revisit the correlation relating the instantaneous flux, $F$, and the photon index below the spectral break, $\alpha$, in individual emission pulses, by studying the 38 most prominent pulses in the Fermi/GBM GRB catalogue. First, we search for signatures of the bias in the determination of $\alpha$ due to the limited spectral coverage (window effect) expected in the synchrotron case. The absence of such a characteristic signature argues against the simplest synchrotron models. We instead find that the observed correlation between $F$ and $\alpha$ can, in general, be described by the relation $F(t) \propto {\rm e}^{k\,\alpha(t)}$, for which the median $k = 3$. We suggest that this correlation is a manifestation of subphotospheric heating in a flow with a varying entropy. Around the peak of the light curve, a large entropy causes the photosphere to approach the saturation radius, leading to an intense emission with a narrow spectrum. As the entropy decreases the photosphere secedes from the saturation radius, and weaker emission with a broader spectrum is expected. This simple scenario naturally leads to a correlated variation of the intensity and spectral shape, covering the observed range., Comment: 15 pages, 10 figures, 1 table, accepted for publication in MNRAS

We suggest that neutron star mergers eject an ultra-relativistic envelope of mass $m\sim 10^{-7}M_\odot$, which helps explain the gamma-ray burst from GW170817. One ejection mechanism is the ablation of the neutron star surface by the burst of neutrinos in the first $30\,\mu$s of the merger. Another, more efficient, mechanism for inflating the ultra-relativistic envelope is an internal shock in the massive ejecta from the merger. A strong shock is expected if the merger product is a magnetar, which emits a centrifugally accelerated wind. The shock propagates outward through the ejecta and accelerates in its outer layers at radii $r\sim 10^9-10^{10}$cm, launching an ultra-relativistic opaque envelope filled with $\sim 10^4$ photons per nucleon. The Lorentz factor profile of the envelope rises outward and determines its homologous expansion, which adiabatically cools the trapped photons. Once the magnetar loses its differential rotation and collapses into a black hole, a powerful jet forms. It drives a blast wave into the envelope, chasing its outer layers and eventually catching up with the envelope photosphere at $r\sim 10^{12}$cm. The ultra-relativistic photospheric breakout of the delayed blast wave emits a gamma-ray burst in a broad solid angle around the merger axis. This model explains the gamma-ray pulse from merger GW170817 with luminosity $L_\gamma\sim 10^{47}$erg/s, duration $\Delta t_{\rm obs}\sim 0.5$s, and characteristic photon energy $\sim 100$keV. The blast wave Lorentz factor at the envelope photosphere is consistent with $\Gamma\geq 5$ that we derive from the observed light curve of the burst. We suggest future tests of the model., Comment: 18 pages, 8 figures, published in ApJ 2020

We examine the possible role of turbulence in feeding the emission of gamma-ray bursts (GRBs). Turbulence may develop in a GRB jet as the result of hydrodynamic or current-driven instabilities. The jet carries dense radiation and the turbulence cascade can be damped by Compton drag, passing kinetic fluid energy to photons through scattering. We identify two regimes of turbulence dissipation: (1) "Viscous" - the turbulence cascade is Compton damped on a scale $\ell_{\rm damp}$ greater than the photon mean free path $\ell_\star$. Then turbulence energy is passed to photons via bulk Comptonization by smooth shear flows on scale $\ell_\star<\ell_{\rm damp}$. (2) "Collisionless" - the cascade avoids Compton damping and extends to microscopic plasma scales much smaller than $\ell_\star$. The collisionless dissipation energizes plasma particles, which radiate the received energy; how the dissipated power is partitioned between particles needs further investigation with kinetic simulations. We show that the dissipation regime switches from viscous to collisionless during the jet expansion, at a critical value of the jet optical depth which depends on the amplitude of turbulence. Turbulent GRB jets are expected to emit nonthermal photospheric radiation. Our analysis also suggests revisions of turbulent Comptonization in black hole accretion disks discussed in previous works.

Gamma-ray bursts (GRBs) are exceptionally bright electromagnetic events occurring daily on the sky. The prompt emission is dominated by X-/$\gamma$-rays. Since their discovery over 50 years ago, GRBs are primarily studied through spectral and temporal measurements. The properties of the emission jets and underlying processes are not well understood. A promising way forward is the development of missions capable of characterising the linear polarisation of the high-energy emission. For this reason, the SPHiNX mission has been developed for a small-satellite platform. The polarisation properties of incident high-energy radiation (50-600 keV) are determined by reconstructing Compton scattering interactions in a segmented array of plastic and Gd$_3$Al$_2$Ga$_3$O$_{12}$(Ce) (GAGG(Ce)) scintillators. During a two-year mission, $\sim$200 GRBs will be observed, with $\sim$50 yielding measurements where the polarisation fraction is determined with a relative error $\leq$10%. This is a significant improvement compared to contemporary missions. This performance, combined with the ability to reconstruct GRB localisation and spectral properties, will allow discrimination between leading classes of emission models., Comment: Accepted for publication in Astroparticle Physics

Internal shocks provide a plausible heating mechanism in the jets of gamma-ray bursts (GRBs). Shocks occurring below the jet photosphere are mediated by radiation. It was previously found that radiation mediated shocks (RMSs) inside GRB jets are inefficient photon producers, and the photons that mediate the RMS must originate from an earlier stage of the explosion. We show that this conclusion is valid only for non-magnetized jets. RMSs that propagate in moderately magnetized plasma develop a collisionless subshock which locally heats the plasma to a relativistic temperature, and the hot electrons emit copious synchrotron photons inside the RMS. We find that this mechanism is generally effective for mildly relativistic shocks and may be the main source of photons observed in GRBs. We derive a simple analytical formula for the generated photon number per proton, $Z$, which gives $Z=10^5$-$10^6$, consistent with observations. The photons are initially injected with low energies, well below the observed GRB peak. Their number is controlled by two main factors: (1) the abundance of electron-positron pairs created in the shock, which is self-consistently calculated, and (2) the upper limit on the brightness temperature of soft radiation set by induced downscattering. The injected soft photons that survive induced downscattering gain energy in the RMS via bulk Comptonization and shape its nonthermal spectrum., Comment: 10 pages, submitted to ApJ

Sub-photospheric shock dissipation is one of the main proposed mechanisms for producing the prompt gamma-ray burst (GRB) emission. Such shocks are mediated by scattering of radiation. We introduce a time dependent, special relativistic code which dynamically couples Monte Carlo radiative transfer to the flow hydrodynamics. The code also self-consistently implements electron-positron pair production and annihilation. We simulate shocks with properties relevant for GRBs and study the steady-state solutions, which are accurate deep below the jet photosphere. The shock generates a power-law photon spectrum through the first-order Fermi mechanism, extending upwards from the typical upstream photon energy. Strong shocks (for which the downstream pressure is much larger than the upstream pressure) have rising $\nu F_\nu$ shock spectra. The spectrum extends up to $\epsilon_{max} \equiv E_{max}/m_e c^2 \sim v^2$ for non-relativistic shocks, where $m_e$ is the electron rest mass and $v$ is the relative speed between the upstream and downstream in units of the speed of light $c$. For mildly relativistic shocks the power law softens at $\epsilon \gtrsim 10^{-1}$ due to Klein-Nishina effects, and shocks with $v\gamma \gtrsim 1$, where $\gamma \equiv (1-v^2)^{-1/2}$, produce electron-positron pairs. As an example, a strong shock with $v\gamma = 3$ and a photon-to-proton ratio of $n_\gamma/n_p = 2 \times 10^5$ has a peak pair-to-proton ratio of $Z_\pm \approx 225$. The main effect of pairs in a steady-state shock is to decrease its spatial width by a factor of $\sim Z_\pm$. The post-shock spectrum thermalizes in the downstream. In absence of emission and absorption processes, kinetic equilibrium at temperature $\theta_d \equiv kT_d/m_e c^2 \approx \epsilon_d/3$ is reached at an optical depth of $\tau \gg \theta_d^{-1}$ behind the shock, where $\epsilon_d$ is the average downstream photon energy., Comment: 14 pages, 8 figures, submitted to ApJ

We study the narrowest spectra expected from gamma-ray bursts. We present an analytical function for the spectrum that is emitted from the photosphere of a radiation-dominated flow that is under acceleration. This is the narrowest possible spectrum and it differs from a Planck function. We also present numerical spectra from photospheres occurring during the transition into the coasting phase of the flow. Using these spectral models, we reanalyse Fermi observations of GRB100507 and GRB101219, which both have been reported to have very narrow spectra. The bursts can be fitted by the spectral models: For GRB101219 the spectrum is consistent with the photosphere occurring below or close to the saturation radius, while for GRB100507 the photosphere position relative to the saturation radius can be determined as a function of time. In the latter case, we find that the photosphere initially occurs in the acceleration phase and thereafter transitions into the coasting phase. We also find that this transition occurs at the same time as the change in observed cooling behaviour: the temperature is close to constant before the break and decays after. We argue that such a transition can be explained by an increasing mass outflow rate. Both analysed bursts thus give strong evidence that the jets are (initially) radiation dominated., Comment: Accepted by MNRAS

The MeV spectral peak of gamma-ray bursts (GRBs) is best explained as photospheric emission from a dissipative relativistic jet. The observed non-blackbody spectrum shows that sub-photospheric dissipation involves both thermal plasma heating and injection of nonthermal particles, which quickly cool through inverse Compton scattering and emission of synchrotron radiation. Synchrotron photons emitted around and above the photosphere are predicted to dominate the low-energy part of the GRB spectrum, starting from roughly a decade in energy below the MeV peak. We show that this leads to a unique polarization signature: a rise in GRB polarization toward lower energies. We compute the polarization degree of GRB radiation as a function of photon energy for a generic jet model, and show the predictions for GRBs 990123, 090902B and 110721A. The expected polarization is significant in the X-ray band, in particular for bursts similar to GRB 090902B. Radiation in the MeV peak (and at higher energies) is unpolarized as long as the jet is approximately uniform on angular scales $\delta\theta \gtrsim \Gamma^{-1}$ where $\Gamma$ is the bulk Lorentz factor of the jet., Comment: 10 pages, 3, figures, submitted to ApJ

We introduce the package LatticePolytopes for Macaulay2. The package provides methods for computations related to Cayley structures, local positivity and smoothness for lattice polytopes., Comment: 5 pages

In this paper we study multidimensional persistence modules [5,13] via what we call tame functors and noise systems. A noise system leads to a pseudo-metric topology on the category of tame functors. We show how this pseudo-metric can be used to identify persistent features of compact multidimensional persistence modules. To count such features we introduce the feature counting invariant and prove that assigning this invariant to compact tame functors is a 1-Lipschitz operation. For 1-dimensional persistence, we explain how, by choosing an appropriate noise system, the feature counting invariant identifies the same persistent features as the classical barcode construction., Comment: Found Comput Math (2016)

Much evidence points towards that the photosphere in the relativistic outflow in GRBs plays an important role in shaping the observed MeV spectrum. However, it is unclear whether the spectrum is fully produced by the photosphere or whether a substantial part of the spectrum is added by processes far above the photosphere. Here we make a detailed study of the $\gamma-$ray emission from single pulse GRB110920A which has a spectrum that becomes extremely narrow towards the end of the burst. We show that the emission can be interpreted as Comptonisation of thermal photons by cold electrons in an unmagnetised outflow at an optical depth of $\tau \sim 20$. The electrons receive their energy by a local dissipation occurring close to the saturation radius. The main spectral component of GRB110920A and its evolution is thus, in this interpretation, fully explained by the emission from the photosphere including localised dissipation at high optical depths., Comment: 14 pages, 11 figures, accepted to MNRAS

We study Gauss maps of order $k$, associated to a projective variety $X$ embedded in projective space via a line bundle $L.$ We show that if $X$ is a smooth, complete complex variety and $L$ is a $k$-jet spanned line bundle on $X$, with $k\geq 1,$ then the Gauss map of order $k$ has finite fibers, unless $X=\mathbb{P}^n$ is embedded by the Veronese embedding of order $k$. In the case where $X$ is a toric variety, we give a combinatorial description of the Gauss maps of order $k$, its image and the generic fibers., Comment: Final version, to appear in Michigan Math J

The Bounded Negativity Conjecture predicts that for any smooth complex surface $X$ there exists a lower bound for the selfintersection of reduced divisors on $X$. This conjecture is open. It is also not known if the existence of such a lower bound is invariant in the birational equivalence class of $X$. In the present note we introduce certain constants $H(X)$ which measure in effect the variance of the lower bounds in the birational equivalence class of $X$. We focus on rational surfaces and relate the value of $H({\mathbb P}^2)$ to certain line arrangements. Our main result is Theorem 3.3 and the main open challenge is Problem 3.10., Comment: v2, rewritten, extra material on arrangements of real lines, to appear in International Mathematics Research Notices

The purpose of this note is to study initial sequences of zero-dimensional subschemes of Hirzebruch surfaces and classify subschemes whose initial sequence has the minimal possible growth., Comment: 9 pages

We consider the polarization properties of photospheric emission originating in jets consisting of a highly relativistic core of opening angle theta_j and Lorentz factor Gamma_0, and a surrounding shear layer where the Lorentz factor is decreasing as a power law of index p with angle from the jet axis. We find significant degrees of linear polarization for observers located at viewing angles theta_v \gtrsim theta_j. In particular, the polarization degree of emission from narrow jets (theta_j \approx 1/Gamma_0) with steep Lorentz factor gradients (p \gtrsim 4) reaches \sim 40%. The angle of polarization may shift by pi/2 for time-variable jets. The spectrum below the thermal peak of the polarized emission appears non-thermal due to aberration of light, without the need for additional radiative processes or energy dissipation. Furthermore, above the thermal peak a power law of photons forms due to Comptonization of photons that repeatedly scatter between regions of different Lorentz factor before escaping. We show that polarization degrees of a few tens of percent and broken power law spectra are natural in the context of photospheric emission from structured jets. Applying the model to gamma-ray bursts, we discuss expected correlations between the spectral shape and the polarization degree of the prompt emission., Comment: 17 pages, 12 figures, submitted to MNRAS

For any non-negative integer $k$ the $k$-th osculating dimension at a given point $x$ of a variety $X$ embedded in projective space gives a measure of the local positivity of order $k$ at that point. In this paper we show that a smooth toric embedding having maximal $k$-th osculating dimension, but not maximal $(k+1)$-th osculating dimension, at every point is associated to a Cayley polytope of order $k$. This result generalises an earlier characterisation by David Perkinson. In addition we prove that the above assumptions are equivalent to requiring that the Seshadri constant is exactly $k$ at every point of $X$, generalising a result of Atsushi Ito., Comment: 16 pages, 5 figures

{\it Fermi Gamma-ray Space Telescope} observations of GRB110721A have revealed two emission components from the relativistic jet: emission from the photosphere, peaking at $\sim 100$ keV and a non-thermal component, which peaks at $\sim 1000$ keV. We use the photospheric component to calculate the properties of the relativistic outflow. We find a strong evolution in the flow properties: the Lorentz factor decreases with time during the bursts from $\Gamma \sim 1000$ to $\sim 150$ (assuming a redshift $z=2$; the values are only weakly dependent on unknown efficiency parameters). Such a decrease is contrary to the expectations from the internal shocks and the isolated magnetar birth models. Moreover, the position of the flow nozzle measured from the central engine, $r_0$, increases by more than two orders of magnitude. Assuming a moderately magnetised outflow we estimate that $r_0$ varies from $10^6$ cm to $\sim 10^9$ cm during the burst. We suggest that the maximal value reflects the size of the progenitor core. Finally, we show that these jet properties naturally explain the observed broken power-law decay of the temperature which has been reported as a characteristic for GRB pulses., Comment: Contains 11 pages and 9 figures; Accepted for publication in MNRAS

Relativistic outflows in the form of jets are common in many astrophysical objects. By their very nature, jets have angle dependent velocity profiles, Gamma = Gamma(r, theta, phi), where Gamma is the outflow Lorentz factor. In this work we consider photospheric emission from non-dissipative jets with various Lorentz factor profiles, of the approximate form Gamma \approx Gamma_0/[(theta/theta_j)^p + 1], were theta_j is the characteristic jet opening angle. In collimated jets, the observed spectrum depends on the viewing angle, theta_v. We show that for narrow jets (theta_j Gamma_0 \lesssim few), the obtained low energy photon index is alpha \approx -1 (dN/dE \propto E^alpha), independent of viewing angle, and weakly dependent on the Lorentz factor gradient (p). A similar result is obtained for wider jets observed at theta_v \approx theta_j. This result is surprisingly similar to the average low energy photon index seen in gamma-ray bursts. For wide jets (theta_j Gamma_0 \gtrsim few) observed at theta_v \ll theta_j, a multicolor blackbody spectrum is obtained. We discuss the consequences of this theory on our understanding of the prompt emission in gamma-ray bursts., Comment: 15 pages, 11 figures; Minor changes in latest version, accepted for publication in MNRAS

We provide a complete classification up to isomorphism of all smooth convex lattice 3-polytopes with at most 16 lattice points. There exist in total 103 different polytopes meeting these criteria. Of these, 99 are strict Cayley polytopes and the remaining 4 are obtained as inverse stellar subdivisions of such polytopes. We derive a classification, up to isomorphism, of all smooth embeddings of toric threefolds in $\mathbb{P}^N$ where $N\le 15$. Again we have in total 103 such embeddings. Of these, 99 are projective bundles embedded in $\mathbb{P}^N$ and the remaining 4 are blow-ups of such toric threefolds., Comment: 25 pages, 130 figures; Journal of Algebraic Combinatorics Online First, 2012