Radially inhomogeneous gamma-ray burst (GRB) jets release variable photospheric emission and can have internal shocks occurring above the photosphere. We generically formulate a photospheric emission model of GRBs including Compton up-scattered photospheric (UP) emission off the electrons (and positrons) in the internal shocks, and find that the photospheric emission may correspond to the traditional (Band) component at <~1 MeV and the UP emission to the high-energy emission observed by Fermi/LAT for some GRBs at >~ 10 MeV. The two components can be separate in the spectrum in some cases or can mimic a smooth broad Band spectrum in other cases. We apply our formulation to the well-studied long and short LAT GRBs, GRB 080916C, GRB 090902B, and GRB 090510, and typically find reasonable parameters for fitting the time-binned spectra, although fine tuning of several parameters is required. The observed delays of the high-energy emission with respect to the MeV emission which are large compared to the variability times are unlikely to be due to simple kinematic effects of a non-evolving jet. These delays may be attributed to the temporal evolution of the physical parameters of the jet, and thus the delay timescales could provide a potential tool for investigating the structures of GRB jets themselves and their progenitors. The difference of the delay timescales of long and short GRBs inferred from the Fermi data might be due to the differences in the progenitors of long and short GRBs. Some other properties and consequences of this model are discussed, including temporal correlations among the prompt optical, the soft X-ray, and the distinct high-energy component as well as the Band component.
We study the spectrum of high frequency radiation emerging from mildly dissipative photospheres of long-duration gamma-ray burst outflows. Building on the results of recent numerical investigations, we assume that electrons are heated impulsively to mildly relativistic energies by either shocks or magnetic dissipation at Thomson optical depths of several and subsequently cool by inverse Compton, scattering off the thermal photons of the photosphere. We show that even in the absence of magnetic field and non-thermal leptons, inverse Compton scattering produces power-law tails that extend from t…
We present a model for gamma-ray bursts where a dissipative photosphere provides the usual spectral peak around MeV energies accompanied by a subdominant thermal component. We treat the initial acceleration of the jet in a general way, allowing for magnetic field- and baryon dominated outflows. In this model, the GeV emission associated with GRBs observed by Fermi LAT, arises as the interaction of photospheric radiation and the shocked electrons at the deceleration radius. Through recently discovered correlations between the thermal and non-thermal peaks within individual bursts, we are able t…
Many different physical processes have been suggested to explain the prompt gamma-ray emission in gamma-ray bursts (GRBs). Although there are examples of both bursts with photospheric and synchrotron emission origins, these distinct spectral appearances have not been generalized to large samples of GRBs. Here, we search for signatures of the different emission mechanisms in the full Fermi Gamma-ray Space Telescope GBM catalogue. We use Gaussian Mixture Models to cluster bursts according to their parameters from the Band function ($α$, $β$, and $E_{pk}$) as well as their fluence and $T_{90}$. W…
Photospheric emission may originate from relativistic outflows in two qualitatively different regimes:\ last scattering of photons inside the outflow at the photospheric radius, or radiative diffusion to the boundary of the outflow. In this work the measurement of temperature and flux of the thermal component in the early afterglows of several gamma-ray bursts (GRBs) along with the total flux in the prompt phase are used to determine initial radii of the outflow as well as its Lorentz factors. Results indicate that in some cases the outflow has relatively low Lorentz factors $Γ<10$, favouring …
We present the results of a set of numerical simulations of long-duration gamma-ray burst jets associated with massive, compact stellar progenitors. The simulations extend to large radii and allow us to locate the region in which the peak frequency of the advected radiation is set before the radiation is released at the photosphere. Light curves and spectra are calculated for different viewing angles as well as different progenitor structures and jet properties. We find that the radiation released at the photosphere of matter-dominated jets is able to reproduce the observed Amati and energy-Lo…
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 p…
The photospheric emission in the prompt phase is the natural prediction of the original fireball model for gamma-ray burst (GRB) due to the large optical depth ($τ>1$) at the base of the outflow, which is supported by the quasi-thermal components detected in several Fermi GRBs. However, which radiation mechanism (photosphere or synchrotron) dominates in most GRB spectra is still under hot debate. The shape of the observed photosphere spectrum from a pure hot fireball or a pure Poynting-flux-dominated outflow has been investigated before. In this work, we further study the photosphere spectrum …
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 mo…
Recent observations by the Fermi satellite suggest that a photosphere emission component is contributing to the observed spectrum of many GRBs. One important question is whether the photosphere component can interpret the typical ``Band'' function of GRBs with a typical low energy photon spectral index $α\sim -1$. We perform a detailed study of the photosphere emission spectrum by progressively introducing several physical ingredients previously not fully incorporated, including the probability distribution of the location of a dynamically evolving photosphere, superposition of emission from a…
The emission from a gamma-ray burst (GRB) photosphere can give rise to a variety of spectral shapes. The spectrum can retain the shape of a Planck function or it can be broadened and have the shape of a Band function. This fact is best illustrated by studying GRB090902B: The main gamma-ray spectral component is initially close to a Planck function, which can only be explained by emission from the jet photosphere. Later, the same component evolves into a broader Band function. This burst thus provides observational evidence that the photosphere can give rise to a non-thermal spectrum. We show t…
The physical origin of gamma-ray burst (GRB) prompt emission (photosphere or synchrotron) is still subject to debate after five decades. Here, firstly we find that many observed characteristics of 15 long GRBs, which have the highest prompt emission efficiency $ε_γ$ ($ε_{γ}\gtrsim 80\%$), strongly support the photosphere (thermal) emission origin: (1) the relation between $E_{\text{p}}$ and $E_{\text{iso}}$ is almost $E_{\text{p}}\propto (E_{\text{iso}})^{1/4}$ , and the dispersion is quite small; (2) the simple power-law shape of the X-ray afterglow light curves and the significant reverse sh…
We present a time-resolved spectral analysis of the bright, long GRB 061007 (z=1.261) using Swift BAT and Suzaku WAM data. We find that the prompt emission of GRB 061007 can be equally well explained by a photospheric component together with a power law as by a Band function, and we explore the implications of the former model. The photospheric component, which we model with a multicolour blackbody, dominates the emission and has a very stable shape throughout the burst. This component provides a natural explanation for the hardness-intensity correlation seen within the burst and also allows u…
We present the results of a numerical investigation of the spectra and light curves of the emission from the photospheres of long-duration gamma-ray burst jets. We confirm that the photospheric emission has high efficiency and we show that the efficiency increases slightly with the off-axis angle. We show that the peak frequency of the observed spectrum is proportional to the square root of the photosphere's luminosity, in agreement with the Amati relation. However, a quantitative comparison reveals that the thermal peak frequency is too small for the corresponding total luminosity. As a conse…
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 simul…
We propose a direct and model-independent method to constrain the Lorentz factor of a relativistically expanding object, like gamma-ray bursts. Only the measurements, such as thermal component of the emission, the distance and the variable time scale of the light curve, are used. If the uncertainties are considered, we will obtain lower limits of the Lorentz factor instead. We apply this method to GRB 090618 and get a lower limit of the Lorentz factor to be 22. The method can be used to any relativistically moving object, such as gamma-ray bursts, blazars, and soft gamma-ray repeaters, providi…
It has been suggested that the prompt emission in gamma-ray bursts consists of several components giving rise to the observed spectral shape. Here we examine a sample of the 8 brightest, single pulsed {\it Fermi} bursts whose spectra are modelled by using synchrotron emission as one of the components. Five of these bursts require an additional photospheric component (blackbody). In particular, we investigate the inferred properties of the jet and the physical requirements set by the observed components for these five bursts, in the context of a baryonic dominated outflow, motivated by the stro…
When neutron stars (NS) accrete gas from low-mass binary companions, explosive nuclear burning reactions in the NS envelope fuse hydrogen and helium into heavier elements. The resulting thermonuclear (type-I) X-ray bursts produce energy spectra that are fit well with black bodies, but a significant number of burst observations show deviations from Planck spectra. Here we present our analysis of RXTE/PCA observations of X-ray bursts from the NS low-mass X-ray binary HETE J1900.1-2455. We have discovered that the non-Planckian spectra are caused by photo-ionization edges. The anti-correlation be…
GRB110721A was observed by the Fermi Gamma-ray Space Telescope using its two instruments the Large Area Telescope (LAT) and the Gamma-ray Burst Monitor (GBM). The burst consisted of one major emission episode which lasted for ~24.5 seconds (in the GBM) and had a peak flux of 5.7\pm0.2 x 10^{-5} erg/s/cm^2. The time-resolved emission spectrum is best modeled with a combination of a Band function and a blackbody spectrum. The peak energy of the Band component was initially 15\pm2 MeV, which is the highest value ever detected in a GRB. This measurement was made possible by combining GBM/BGO data …
We show that the photospheres of "failed" Gamma-Ray Bursts (GRBs), whose bulk Lorentz factors are much lower than 100, can be outside of internal shocks. The resulting radiation from the photospheres is thermal and bright in UV/Soft X-ray band. The photospheric emission lasts for about one thousand seconds with luminosity about several times 10^46 erg/s. These events can be observed by current and future satellites. It is also shown that the afterglows of failed GRBs are peculiar at the early stage, which makes it possible to distinguish failed GRBs from ordinary GRBs and beaming-induced orpha…
X-ray flares of gamma-ray bursts (GRBs) are usually observed in the soft X-ray range and the spectral coverage is limited. In this paper, we present an analysis of 32 GRB X-ray flares that are simultaneously observed by both BAT and XRT on board the Swift mission, so a joint spectral analysis with a wider spectral coverage is possible. Our results show that the joint spectra of 19 flares are fitted with the absorbed single power-law or the Band function models. More interestingly, the joint spectra of the other 13 X-ray flares are fitted with the absorbed single power-law model plus a black bo…
The quasi-thermal components found in many Fermi gamma-ray bursts (GRBs) imply that the photosphere emission indeed contributes to the prompt emission of many GRBs. But whether the observed spectra empirically fitted by the Band function or cutoff power law, especially the spectral and peak energy ($E_{p}$) evolutions can be explained by the photosphere emission model alone needs further discussion. In this work, we investigate in detail the time-resolved spectra and $E_{p}$ evolutions of photospheric emission from a structured jet, with an inner-constant and outer-decreasing angular Lorentz f…
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 {\em Fermi} GBM and LAT, an…
The radiation released at the transparency radius of an ultrarelativistic flow can account for the observed properties of gamma-ray bursts (GRBs) provided that sufficient energy is dissipated in the sub-photospheric region. Here, I investigate how the peak energy of the E*f(E) spectrum and its overall shape depend on the properties of the jet for various "dissipative photospheres". I find that continuous energy release which results in electron heating over a wide range of distances may be the key to explain the GRB emission. In this picture, the peak of the spectrum forms at a Thomson optical…
We present calculations of the time evolution of the prompt spectra of gamma-ray burst models involving generic internal dissipation regions, including internal shocks, either by itself or in the presence of an external photon source such as a photosphere. The method uses a newly developed time-dependent code involving synchrotron emission and absorption, inverse Compton scattering and pair formation. The models reproduce the typical observed Band spectra and their generic time evolution, including the appearance of an extra keV-GeV component, whose delay in simple SSC models, however, is only…
The jet composition and radiative efficiency of GRBs are poorly constrained from the data. If the jet composition is matter-dominated (i.e. a fireball), the GRB prompt emission spectra would include a dominant thermal component originating from the fireball photosphere, and a non-thermal component presumably originating from internal shocks whose radii are greater than the photosphere radius. We propose a method to directly dissect the GRB fireball energy budget into three components and measure their values by combining the prompt emission and early afterglow data. The measured parameters inc…
We present a dissipative photospheric model for gamma-ray bursts where the usual Band peak around MeV energies arises as synchrotron emission from around the photosphere. We treat the initial acceleration in a general way and the GeV emission arises as the interaction of photospheric radiation and the shocked electrons at the deceleration radius. We show some applications of this model.
We numerically analyze the evolution of a long-duration gamma-ray burst jet as it leaves the progenitor star and propagates to the photospheric radius, where radiation can be released. We find that the interaction of the relativistic material with the progenitor star has influences well beyond the stellar surface. Tangential collimation shocks are observed throughout the jet evolution, out to about 100 stellar radii, which is the whole range of our simulation. We find that the jet is internally hot at the photospheric radius and we compute the photospheric emission. The photosphere is a very e…
A large fraction of gamma-ray burst (GRB) spectra are very hard below the peak. Indeed, the observed distribution of sub-peak power-law indices, $α$, has been used as an argument for a photospheric origin of GRB spectra. Here, we investigate what fraction of GRBs have spectra that are consistent with emission from a photopshere in a non-dissipative outflow. This is the simplest possible photospheric emission scenario. We create synthetic spectra, with a range of peak energies, by folding the theoretical predictions through the detector response of the FERMI/GBM detector. These simulated spectr…
Collisionless entrainment of the surrounding matter imports the relativistic baryon component in the Gamma-Ray Burst (GRB) fireball frame. We show that half the fireball energy can be transferred from radiation to the comoving hot motions of baryons under the photosphere. The yet baryon-poor fireball can reexpand to a very high Lorentz factor (VHLF) Γ~ 10^3-10^6 by its own relativistic collisionless pressure beyond the photosphere (so-called collisionless bulk acceleration), leading to internal and external shocks. A simple synchrotron emission from the VHLF internal shocks produces (i) the ex…
It is proposed that the prompt emission observed in bursts that exhibit a thermal component originates from relativistic radiation mediated shocks that form below the photosphere of the GRB outflow. It is argue that such shocks are expected to form in luminous bursts via collisions of shells that propagate with moderate Lorentz factors $Γ\lesssim 500$. Faster shells will collide above the photosphere to form collisionless shocks. We demonstrate that in events like GRB 090902B a substantial fraction of the explosion energy is dissipated below the photosphere, in a region of moderate optical dep…
{\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 $Γ\sim 1000$ to $\sim 150$ (assuming a redshift $z=2$; the values are only weakly dependent on unknown efficiency parameters). Such a decrease is co…
On August 24th 2008 the new magnetar SGR 0501+4516 (discovered by SWIFT) emitted a bright burst with a pronounced double-peak structure in hard X-rays, reminiscent of the double-peak temporal structure seen in some bright thermonuclear bursts on accreting neutron stars. In the latter case this is due to Photospheric Radius Expansion (PRE): when the flux reaches the Eddington limit, the photosphere expands and cools so that emission becomes softer and drops temporarily out of the X-ray band, re-appearing as the photosphere settles back down. We consider the factors necessary to generate double-…
For many gamma-ray bursts (GRBs), hardness-intensity correlation (HIC) can be described by a power-law function, $E_{\rm p}\propto F^κ$, where $E_{\rm p}$ is the peak energy of $νF_ν$ spectrum, and $F$ is the instantaneous energy flux. In this paper, HIC of the non-dissipative photospheric emission from a structured jet is studied in different regimes. An intermediate photosphere, which contains both of unsaturated and saturated emissions is introduced, and we find positive $κ<1/4$ in this case. The same conclusion could be generalized to the photospheric emission from a hybrid jet without mag…
Since the launch of the Fermi Gamma-ray Space Telescope on 11 June 2008, significant detections of high energy emission have been reported only in six Gamma-ray Bursts (GRBs) until now. In this work we show that the lack of detection of a GeV spectrum excess in almost all GRBs, though somewhat surprisingly, can be well understood within the standard internal shock model and several alternatives like the photosphere-internal shock (gradual magnetic dissipation) model and the magnetized internal shock model. The delay of the arrival of the >100 MeV photons from some Fermi bursts can be interpret…
Among the more than 1000 gamma-ray bursts observed by the Fermi Gamma-ray Space Telescope, a large fraction show narrow and hard spectra inconsistent with non-thermal emission, signifying optically thick emission from the photosphere. However, only a few of these bursts have spectra consistent with a pure Planck function. We will discuss the observational features of photospheric emission in these GRBs as well as in the ones showing multi-component spectra. We interpret the observations in light of models of subphotospheric dissipation, geometrical broadening and multi-zone emission, and show …
A correlation between the peak luminosity and the peak energy has been found by Yonetoku et al. as $L_{p}\propto E_{p,i}^{2.0}$ for 11 pre-Swift long gamma-ray bursts. In this study, for a greatly expanded sample of 148 long gamma-ray bursts in the Swift era, we find that the correlation still exists, but most likely with a slightly different power-law index, i.e., $L_{p}\propto E_{p,i} ^{1.7}$. In addition, we have collected 17 short gamma-ray bursts with necessary data. It is found that the correlation of $L_{p}\propto E_{p,i} ^{1.7}$ also exists for this sample of short events. It is argued…
There is no complete description of the emission physics during the prompt phase in gamma-ray bursts. Spectral analyses, however, indicate that many spectra are narrower than what is expected for non-thermal emission models. Here, we reanalyse the sample of 37 bursts in \citet{Yu2019}, by fitting the narrowest time-resolved spectrum in each burst. We perform model comparison between a photospheric and a synchrotron emission model based on Bayesian evidence. We choose to compare the shape of the narrowest expected spectra: emission from the photosphere in a non-dissipative flow and slow-cooled …
We review the physics of GRB production by relativistic jets that start highly opaque near the central source and then expand to transparency. We discuss dissipative and radiative processes in the jet and how radiative transfer shapes the observed nonthermal spectrum released at the photosphere. A comparison of recent detailed models with observations gives estimates for important parameters of GRB jets, such as the Lorentz factor and magnetization. We also discuss predictions for GRB polarization and neutrino emission.
We present global radiative transfer models for heated relativistic jets. The simulations include all relevant radiative processes, starting deep in the opaque zone and following the evolution of radiation to and beyond the photosphere of the jet. The transfer models are compared with three gamma-ray bursts GRB 990123, GRB 090902B, and GRB 130427A, which have well-measured and different spectra. The models provide good fits to the observed spectra in all three cases, and we obtain estimates for the jet magnetization parameter $\varepsilon_{\rm B}$ and the Lorentz factor $Γ$. In the small sampl…
The Neutron Star Interior Composition Explorer (NICER) on the International Space Station (ISS) observed strong photospheric expansion of the neutron star in 4U 1820-30 during a Type I X-ray burst. A thermonuclear helium flash in the star's envelope powered a burst that reached the Eddington limit. Radiation pressure pushed the photosphere out to ~200 km, while the blackbody temperature dropped to 0.45 keV. Previous observations of similar bursts were performed with instruments that are sensitive only above 3 keV, and the burst signal was weak at low temperatures. NICER's 0.2-12 keV passband e…
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, $α$, 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 $α$ due to the limited spectral coverage (window effect) expected in the synchrotron case. The absence of such a characteristic signature argues against the simp…
We consider a model in which the ultra-relativistic jet in a gamma-ray burst (GRB) is cold and magnetically accelerated. We assume that the energy flux in the outflowing material is partially thermalized via internal shocks or a reverse shock, and we estimate the maximum amount of radiation that could be produced in such magnetized shocks. We compare this estimate with the available observational data on prompt gamma-ray emission in GRBs. We find that, even with highly optimistic assumptions, the magnetized jet model is radiatively too inefficient to be consistent with observations. One way ou…
The Chinese CubeSat Mission, Gamma Ray Integrated Detectors (GRID), recently detected its first gamma-ray burst, GRB 210121A, which was jointly observed by the Gravitational wave high-energy Electromagnetic Counterpart All-sky Monitor (GECAM). This burst is confirmed by several other missions, including \fermi and \textit{Insight}-HXMT. We combined multi-mission observational data and performed a comprehensive analysis of the burst's temporal and spectral properties. Our results show that the burst is relatively special in its high peak energy, thermal-like low energy indices, and large fluenc…
In explaining the physical origin of the jet composition of gamma-ray bursts (GRBs), a more general picture, i.e. the hybrid jet model (which introduced another magnetization parameter $σ_{0}$ on the basis of the traditional fireball model), has been well studied in Gao \& Zhang. However, it still has not yet been applied to a large GRB sample. Here, we first employ the "top-down" approach of Gao \& Zhang to diagnose the photosphere properties at the central engine to see how the hybrid model can account for the observed data as well, through applying a {\it Fermi} GRB sample (eight bursts) wi…
We discuss a very peculiar subgroup of gamma-ray bursts among the BATSE sources. These bursts are very short ($T_{90} \le $0.1 s), hard, and came predominantly from a restricted direction of the sky (close to the Galactic anti-center). We analyze their arrival times and possible correlations, as well as the profiles of individual bursts. We find no peculiarities in the arrival times of Very Short Bursts (VSBs) despite their highly non-uniform spatial distribution. There is no dependence in the burst shapes on location. Bursts coming both from the burst-enhancement Galactic Anticenter region an…
The low energy spectral slopes of the prompt emission of most gamma-ray bursts (GRBs) are difficult to reconcile with radiatively efficient optically thin emission models irrespective of the radiation mechanism. An alternative is to ascribe the radiation around the spectral peak to a thermalization process occurring well inside the Thomson photosphere. This quasi-thermal spectrum can evolve into the observed non-thermal shape by additional energy release at moderate to small Thomson optical depths, which can readily give rise to the hard spectral tail. The position of the spectral peak is dete…
We investigate the constraints on neutron star mass and radius in GS 1826-24 from models of lightcurves and spectral evolution of type I X-ray bursts. This source shows remarkable agreement with theoretical calculations of burst energies, recurrence times, and lightcurves. We first exploit this agreement to set the overall luminosity scale of the observed bursts. When combined with a measured blackbody normalization, this leads to a distance and anisotropy independent measurement of the ratio between the redshift 1+z and color correction factor f_c. We find 1+z=1.19-1.28 for f_c=1.4-1.5. We th…
The IceCube Collaboration recently reported a stringent upper limit on the high energy neutrino flux from GRBs, which provides a meaningful constraint on the standard internal shock model. Recent broad band electromagnetic observations of GRBs also challenge the internal shock paradigm for GRBs, and some competing models for gamma-ray prompt emission have been proposed. We describe a general scheme for calculating the GRB neutrino flux, and compare the predicted neutrino flux levels for different models. We point out that the current neutrino flux upper limit starts to constrain the standard i…
We calculate the high energy neutrino spectrum from gamma-ray bursts where the emission arises in a dissipative jet photosphere determined by either baryonically or magnetically dominated dynamics, and compare these neutrino spectra to those obtained in conventional internal shock models. We also calculate the diffuse neutrino spectra based on these models, which appear compatible with the current IceCube 40+59 constraints. While a re-analysis based on the models discussed here and the data from the full array would be needed, it appears that only those models with the most extreme parameters …
