arXiv subjects

Ehud Nakar

Publications and source records attributed to Ehud Nakar.

At least 55 records · Page 3Linked to original sources

arXiv2020

Physics of radiation mediated shocks and its applications to GRBs, supernovae, and neutron star mergers

The first electromagnetic signal observed in different types of cosmic explosions is released upon emergence of a shock created in the explosion from the opaque envelope enshrouding the central source. Notable examples are the early emission from various types of supernovae and low luminosity GRBs, the prompt photospheric emission in long GRBs, and the gamma-ray emission that accompanied the gravitational wave signal in neutron star mergers. In all of these examples, the shock driven by the explosion is mediated by the radiation trapped inside it, and its velocity and structure, that depend on environmental conditions, dictate the characteristics of the observed electromagnetic emission at early times, and potentially also their neutrino emission. Much efforts have been devoted in recent years to develop a detailed theory of radiation mediated shocks in an attempt to predict the properties of the early emission in the aforementioned systems. These efforts are timely in view of the anticipated detection rate of shock breakout candidates by upcoming transient factories, and the potential detection of a gamma-ray flash from shock breakout in neutron star mergers like GW170817. This review aims at providing a comprehensive overview of the theory and applications of radiation mediated shocks, starting from basic principles. The classification of shock solutions, which are governed by the conditions prevailing in each class of objects, and the methods used to solve the shock equations in different regimes will be described, with particular emphasis on the observational diagnostics. The applications to supernovae, low-luminosity GRBs, long GRBs, neutron star mergers, and neutrino emission will be highlighted.

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arXiv2020

Generalized compactness limit from an arbitrary viewing angle

A $γ$-ray source must have a limited optical depth to pair production. This simple condition, called compactness, implies that gamma-ray bursts (GRBs) must involve a highly relativistic motion ($Γ\gtrsim 100$) giving the first and most important clue on their nature. So far, this condition has been discussed under the assumption that the $γ$-ray sources are viewed on-axis, that is, by an observer within the beaming cone of the relativistic source. Recently, following the detection of the weak short GRB 170817A, an extensive interest arose in the possibility that some $γ$-ray sources are viewed off-axis. We generalize here the compactness formalism for an arbitrary viewing angle taking several possible opacity processes and $γ$-ray spectra into account. We find that for a given observables (peak luminosity, temporal variability, and spectra) the minimal Lorentz factor, $Γ_{\rm min}$, is obtained, as expected, for an on-axis observer. More remarkably we find that compactness dictates also a maximal viewing angle, $θ_{\rm max} \simeq 1/2Γ_{\rm min}$. Our limit implies for regular GRBs a very small allowed viewing angle ($\lesssim10^{-2}\,\rm rad$), making it extremely unlikely that they are viewed off-axis. For GRB 170817A we confirm earlier results that rule out the possibility that the observed $γ$-rays were seen by an on-axis observer as a regular short GRB. The short GRB 150101B was also suggested to be an off-axis event. We show that its maximal viewing angle $\lesssim0.05\,\rm rad$, which is inconsistent with the off-axis model. Finally we show that for low luminosity GRBs, compactness does not exclude by itself an off-axis model, but when combined with other consideration this option is strongly disfavored.

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arXiv2019

GROWTH on S190814bv: Deep Synoptic Limits on the Optical/Near-Infrared Counterpart to a Neutron Star-Black Hole Merger

On 2019 August 14, the Advanced LIGO and Virgo interferometers detected the high-significance gravitational wave (GW) signal S190814bv. The GW data indicated that the event resulted from a neutron star--black hole (NSBH) merger, or potentially a low-mass binary black hole merger. Due to the low false alarm rate and the precise localization (23 deg$^2$ at 90\%), S190814bv presented the community with the best opportunity yet to directly observe an optical/near-infrared counterpart to a NSBH merger. To search for potential counterparts, the GROWTH collaboration performed real-time image subtraction on 6 nights of public Dark Energy Camera (DECam) images acquired in the three weeks following the merger, covering $>$98\% of the localization probability. Using a worldwide network of follow-up facilities, we systematically undertook spectroscopy and imaging of optical counterpart candidates. Combining these data with a photometric redshift catalog, we ruled out each candidate as the counterpart to S190814bv and we placed deep, uniform limits on the optical emission associated with S190814bv. For the nearest consistent GW distance, radiative transfer simulations of NSBH mergers constrain the ejecta mass of S190814bv to be $M_\mathrm{ej} < 0.04$~$M_{\odot}$ at polar viewing angles, or $M_\mathrm{ej} < 0.03$~$M_{\odot}$ if the opacity is $κ< 2$~cm$^2$g$^{-1}$. Assuming a tidal deformability for the neutron star at the high end of the range compatible with GW170817 results, our limits would constrain the BH spin component aligned with the orbital momentum to be $ χ< 0.7$ for mass ratios $Q < 6$, with weaker constraints for more compact neutron stars. We publicly release the photometry from this campaign at http://www.astro.caltech.edu/~danny/static/s190814bv.

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arXiv2019

The electromagnetic counterparts of compact binary mergers

Mergers of binaries consisting of two neutron stars, or a black hole and a neutron star, offer a unique opportunity to study a range of physical and astrophysical processes using two different and almost orthogonal probes - gravitational waves (GW) and electromagnetic (EM) emission. The GW signal probes the binary and the physical processes that take place during the last stages of the merger, while the EM emission provides clues to the material that is thrown out following the merger. The accurate localization, which only the EM emission can provide, also indicates the astrophysical setting in which the merger took place. In addition, the combination of the two signals provides constraints on the nature of gravity and on the expansion rate of the Universe. The first detection of a binary neutron star merger by the LIGO-Virgo collaboration, GW170817, initiated the era of multi-messenger GW-EM astrophysics and demonstrated the great promise it holds. The event produced an unprecedented data set, and although it was only a single event, it provided remarkable results that revolutionized our knowledge of neutron star mergers. GW170817 is especially exciting since we know that it is not one of a kind and that many more events will be detected during the next decade. In this review, I summarize, first, the theory of EM emission from compact binary mergers, highlighting the unique information that the combined GW-EM detection provides. I then describe the entire set of GW and EM observations of GW170817, and summarize the range of insights that it offers. This includes clues about the role that similar events play in the r-process elements budget of the Universe, the neutron star equation of state, the properties of the relativistic outflow that followed the merger, and the connection between neutron star binary mergers and short gamma-ray bursts.

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arXiv2019

Radioactive heating rate of r-process elements and macronova light curve

We study the heating rate of r-process nuclei and thermalization of decay products in neutron star merger ejecta and macronova (kilonova) light curves. Thermalization of charged decay products, i.e., electrons, $α$-particles, and fission fragments is calculated according to their injection energy. The $γ$-ray thermalization processes are also properly calculated by taking the $γ$-ray spectrum of each decay into account. We show that the $β$-decay heating rate at later times approaches a power-law decline as $\propto t^{-2.8}$, which agrees with the result of Waxman et al. (2019). We present a new analytic model to calculate macronova light curves, in which the density structure of the ejecta is accounted for. We demonstrate that the observed bolometric light curve and temperature evolution of the macronova associated with GW170817 are reproduced well by the $β$-decay heating rate with the solar r-process abundance pattern. We interpret the break in the observed bolometric light curve around a week as a result of the diffusion wave crossing a significant part of the ejecta rather than a thermalization break. We also show that the time-weighted integral of the bolometric light curve (Katz integral) is useful to provide an estimate of the total r-process mass from the observed data, which is independent of the highly uncertain radiative transfer. For the macronova in GW170817, the ejecta mass is robustly estimated as $\approx 0.05M_{\odot}$ for $A_{\rm min}\leq 72$ and $85\leq A_{\rm min}\leq 130$ with the solar r-process abundance pattern. The code for computation of the heating rate and light curve for given initial nuclear abundances is publicly available.

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arXiv2019

Jet-driven bubbles in Fanaroff-Riley type I sources

Observations of several Fanaroff-Riley (FR) type I sources reveal outflowing bipolar bubbles of hot gas surrounded by a weak forward shock. We consider the possibility that these bubbles were driven by choked relativistic jets which failed to penetrate the ambient intracluster medium (ICM). Using new results on choked jets linking the geometry of the forward shock to the jet properties, we infer robust limits on the radius $R_{ch}$ at which the jet was quenched in 5 well-studied FRI sources, finding typically $R_{ch}\sim 10$ kpc. We further show that, in order to reach this radius in less than the current age of the system, the jet must have been tightly collimated, with the jet head subtending an angle of $θ_h < 2^\circ$. The ambient pressure is not high enough to explain this collimation, suggesting that the jet was collimated by interaction with its own cocoon. Although the choking radius is well-constrained, we find a degeneracy between the initial jet opening angle before collimation, $θ_0$, and the duration of jet activity, $t_b$, with $(t_b/1\rm{Myr})(θ_0/5^\circ)^{-2} \sim 0.1$. We speculate that the working time and/or opening angle of the jet may be important factors contributing to the FR type I/type II morphology in galaxy clusters, with short-lived or wide jets being choked to form bipolar bubbles filled with diffuse radio emission, and longer-lived or narrow jets successfully escaping the cluster core to produce cocoons with radio hotspots.

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arXiv2019

The propagation of choked jet outflows in power-law external media

Observations of both gamma-ray bursts (GRBs) and active galactic nuclei (AGNs) point to the idea that some relativistic jets are suffocated by their environment before we observe them. In these "choked" jets, all the jet's kinetic energy is transferred into a hot and narrow cocoon of near-uniform pressure. We consider the evolution of an elongated, axisymmetric cocoon formed by a choked jet as it expands into a cold power-law ambient medium $ρ\propto R^{-α}$, in the case where the shock is decelerating ($α<3$). The evolution proceeds in three stages, with two breaks in behaviour: the first occurs once the outflow has doubled its initial width, and the second once it has doubled its initial height. Using the Kompaneets approximation, we derive analytical formulae for the shape of the cocoon shock, and obtain approximate expressions for the height and width of the outflow versus time in each of the three dynamical regimes. The asymptotic behaviour is different for flat ($α\le 2$) and steep ($2 < α< 3$) density profiles. Comparing the analytical model to numerical simulations, we find agreement to within $\sim15$ per cent out to 45 degrees from the axis, but discrepancies of a factor of 2-3 near the equator. The shape of the cocoon shock can be measured directly in AGNs, and is also expected to affect the early light from failed GRB jets. Observational constraints on the shock geometry provide a useful diagnostic of the jet properties, even long after jet activity ceases.

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arXiv2019

Detectability of neutron star merger afterglows

VLBI and JVLA observations revealed that GW170817 involved a narrow jet ($ θ_j \approx 4^\circ $) that dominated the afterglow peak at our viewing angle, $ θ_{\rm obs} \approx 20^\circ $. This implies that at the time of the afterglow peak, the observed signal behaved like an afterglow of a top-hat jet seen at $ θ_{\rm obs} \gg θ_j $, and it can be modeled by analytic expressions that describe such jets. We use a set of numerical simulations to calibrate these analytic relations and obtain generic equations for the peak time and flux of such an afterglow as seen from various observing angles. Using the calibrated equations and the estimated parameters of GW170817, we estimate the detectability of afterglows from future double neutron star mergers during the Advanced LIGO/Virgo observation run O3. GW170817 took place at a relatively low-density environment. Afterglows of similar events will be detectable only at small viewing angles, $ θ_{\rm obs} \lesssim 20^\circ $, and only $\sim 20\% $ of the GW detections of these events will be accompanied by a detectable afterglow. At higher densities, more typical to sGRB sites, up to $ 70\% $ of the GW detections are expected to be followed by a detectable afterglow, typically at $ θ_{\rm obs} \sim 30^\circ $. We also provide the latest time one should expect an afterglow detection. We find that for typical parameters, if the jet emission had not been detected within about a year after the merger, it is unlikely to be ever detected.

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arXiv2019

High efficiency photospheric emission entailed by formation of a collimation shock in gamma-ray bursts

The primary dissipation mechanism in jets of gamma-ray bursts (GRBs), and the high efficiency of the prompt emission are long standing issues. One possibility is strong collimation of a weakly magnetized relativistic jet by the surrounding medium, which can considerably enhance the efficiency of the photospheric emission. We derive a simple analytic criterion for the radiative efficiency of a collimated jet showing that it depends most strongly on the baryon loading. We confirm this analytic result by 3D numerical simulations, and further find that mixing of jet and cocoon material at the collimation throat leads to a substantial stratification of the outflow as well as sporadic loading, even if the injected jet is uniform and continuous. One consequence of this mixing is a strong angular dependence of the radiative efficiency. Another is large differences in the Lorentz factor of different fluid elements that lead to formation of internal shocks. Our analysis indicates that in both long and short GRBs a prominent photospheric component cannot be avoided when observed within an angle of a few degrees to the axis, unless the asymptotic Lorentz factor is limited by baryon loading at the jet base to $Γ_\infty <100$ (with a weak dependence on outflow power). Photon generation by newly created pairs behind the collimation shock regulates the observed temperature at $\sim 50~θ_0^{-1}$ keV, where $θ_0$ is the initial jet opening angle, in remarkable agreement with the observed peak energies of prompt emission spectra. Further consequences for the properties of the prompt emission are discussed at the end.

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arXiv2019

Recombination Effects on Supernova Light Curves

The light curves of type-II supernovae (SNe) are believed to be highly affected by recombination of hydrogen that takes place in their envelopes. In this work, we analytically investigate the transition from a fully ionized envelope to a partially recombined one and its effects on the SN light curve. The motivation is to establish the underlying processes that dominate the evolution at late times when recombination takes place in the envelope, yet early enough so that $^{56}$Ni decay is a negligible source of energy. We consider the diffusion of photons through the envelope while analyzing the ionization fraction and the coupling between radiation and gas, and find that the main effect of recombination is on the evolution of the observed temperature. Before recombination the temperature decreases relatively fast, while after recombination starts it significantly reduces the rate at which the observed temperature drops with time. This behaviour is the main cause for the observed flattening in the optical bands, where for a typical red supergiant explosion, the recombination wave affects the bolometric luminosity only mildly during most of the photospheric phase. Moreover, the plateau phase observed in some type-II SNe is not a generic result of recombination, and it also depends on the density structure of the progenitor. This is one possible explanation to the different light curve decay rates observed in type II (P and L) SNe.

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arXiv2019

The Spectrum of a Fast Shock Breakout from a Stellar Wind

The breakout of a fast ($>0.1 c$), yet sub-relativistic shock from a thick stellar wind is expected to produce a pulse of X-rays with a rise time of seconds to hours. Here, we construct a semi-analytic model for the breakout of a sub-relativistic, radiation-mediated shock from a thick stellar wind, and use it to compute the spectrum of the breakout emission. The model incorporates photon escape through the finite optical depth wind, assuming a diffusion approximation and a quasi-steady evolution of the shock structure during the breakout phase. We find that in sufficiently fast shocks, for which the breakout velocity exceeds about $0.1c$, the time-integrated spectrum of the breakout pulse is non-thermal, and the time-resolved temperature is expected to exhibit substantial decrease (roughly by one order of magnitude) during breakout, when the flux is still rising, because of the photon generation by the shock compression associated with the photon escape. We also derive a closure relation between the breakout duration, peak luminosity, and characteristic temperature that can be used to test whether an observed X-ray flare is consistent with being associated with a sub-relativistic shock breakout from a thick stellar wind or not. We also discuss implications of the spectral softening for a possible breakout event XRT 080109/SN 2008D.

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arXiv2018

Observational constraints on the structure of gamma-ray burst jets

Motivated by GW170817 we examine constraints that observations put on the angular structure of long gamma-ray burst (GRB) jets. First, the relatively narrow observed distribution of $E_{X}/E_γ$ (the isotropic equivalent early X-ray afterglow to prompt $γ$-ray energy ratio) implies that at any angle that $γ$-rays are emitted the Lorentz factor must be high. Specifically, the Lorentz factor of $γ$-ray emitting material cannot drop rapidly with angle, and must be $Γ(θ)\gtrsim 50$ even if there are angles for which the gamma-ray received energy is lower by three orders of magnitude compared to the jet core. Second, jets with an angular structure of the $γ$-ray emission that over-produce events with a $γ$-ray luminosity below the peak of the observed luminosity function are ruled-out. This eliminates models in which the $γ$-ray energy angular distribution isn't sufficiently steep and the Lorentz factor distribution isn't sufficiently shallow. Finally, models with a steep structure (e.g. Gaussian) which are detected away from the jet core generate afterglow light-curves that were never observed. We conclude that even if the jet kinetic energy distribution drops continuously with latitude, efficient $γ$-ray emission seems to be restricted to material with $Γ\gtrsim 50$ and is most likely confined to a narrow region around the core. While our study is confined to long GRBs, where the observed sample is larger and more complete, there are indications that similar conclusions may be applicable also to short GRBs. We discuss the possible implications to the $γ$-rays observed in GRB 170817A.

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arXiv2018

The role of radioactive nickel in shaping the plateau phase of Type II supernovae

In the present study, we systematically explore the effect of the radioactive 56Ni and its mixing properties in the ejecta on the plateau of Type IIP supernovae (SNe). We evaluate the importance of 56Ni in shaping light curves of SNe IIP by simulating light curves for two red supergiant models using different amounts of 56Ni and with different types of mixing: uniform distribution of 56Ni out to different fractions of the envelope and "boxcar" distribution of 56Ni. We find, similarly to previous studies, that 56Ni extends duration of the plateau. We find a formula to estimate the extension based on the observed bolometric light curves and show that for most SNe IIP 56Ni extends the plateau by about 20%. Another effect of 56Ni consists in reduction of the plateau decline rate, i.e. 56Ni presented in the ejecta flattens the plateau. Our simulations suggest that for typical SNe IIP it can reduce the decline rate by about 1 mag/100 day. We find that for the contribution of 56Ni seen in most SNe our simulated bolometric light curves resemble observed ones for various types of 56Ni mixing. We thereby cannot determine the level of 56Ni mixing in these SNe based on the light curve alone. However, for SN2009ib we find that only a model where 56Ni is mixed significantly throughout most of the hydrogen envelope is consistent with the observed light curve. Our light curves are available via link https://wwwmpa.mpa-garching.mpg.de/ccsnarchive/data/Kozyreva2018/.

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arXiv2018

Numerical simulations of AGN wind feedback on black hole accretion: probing down to scales within the sphere of influence

Several processes may limit the accretion rate onto a super-massive black hole (SMBH). Two processes that are commonly considered (e.g., for sub-grid prescriptions) are Bondi-Hoyle-Lyttleton accretion and the Eddington limit. A third one is AGN wind feedback. It has been long suggested that such a wind feedback regulates the final SMBH mass, however, it has been shown recently that AGN winds can also regulate the average accretion rate at a level consistent with observations of high redshift AGNs. In this paper we study the effect of wind feedback on the accretion rate using 2D, high resolution hydrodynamic simulations, that incorporate a self-consistent wind injection scheme and resolves the SMBH sphere of influence. Two different cases are explored and compared: one in which the initial gas density is uniform, and one in which it has an isothermal sphere profile. We also compare simulations with and without cooling. Our main finding is that for reasonable parameters, AGN feedback always limits the accretion rate to be far below the Bondi-Hoyle-Lyttleton limit. For typical wind parameters and a uniform ISM densities of the order $1 {cm}^{-3}$, the accretion rate is found to be several orders of magnitudes smaller than that inferred in large samples of high redshift AGNs. On the other hand, the accretion rate obtained for initially isothermal density profile is found to be consistent with the observations, particularly when cooling is included. Furthermore, it roughly scales as $σ^{5}$ with the velocity dispersion of the bulge, in accord with the $M-σ$ relation.

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arXiv2018

Constraints on the emitting region of the gamma-rays observed in GW170817

The gravitational waves from the neutron star merger event GW170817 were accompanied by an unusually weak short GRB 170817A, by an optical/IR macronova/kilonova and by a long lasting radio to X-rays counterpart. While association of short GRBs with mergers was predicted a long time ago, the luminosity of this prompt γ-ray emission was weaker by a few orders of magnitude than all known previous sGRBs and it was softer than typical sGRBs. This raise the question whether the γ-rays that we have seen were a regular sGRB viewed off-axis. We revisit this question following recent refined analyses of the γ-ray signal and the VLBI observations that revealed the angular structure of the relativistic outflow: observing angle of $\sim\,20^\circ$, a narrow jet with core $\lesssim5^\circ$ and $E_{\rm iso}>10^{52}\,{\rm ergs}$. We show here that: (i) The region emitting the observed $γ$-rays must have been moving with a Lorentz factor $Γ\gtrsim5$; (ii) The observed γ-rays were not "off-axis" emission (viewing angle $>1/Γ$) emerging from the core of the jet, where a regular sGRB was most likely produced; (iii) The $γ$-ray emission region was either "on-axis" (at an angle $<1/Γ$) or if it was "off-axis" then the observing angle must have been small ($<5^\circ$) and the on-axis emission from this region was too faint and too hard to resemble a regular sGRB.

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arXiv2018

A Hubble constant measurement from superluminal motion of the jet in GW170817

The Hubble constant ($H_0$) measures the current expansion rate of the Universe, and plays a fundamental role in cosmology. Tremendous effort has been dedicated over the past decades to measure $H_0$. Notably, Planck cosmic microwave background (CMB) and the local Cepheid-supernovae distance ladder measurements determine $H_0$ with a precision of $\sim 1\%$ and $\sim 2\%$ respectively. A $3$-$σ$ level of discrepancy exists between the two measurements, for reasons that have yet to be understood. Gravitational wave (GW) sources accompanied by electromagnetic (EM) counterparts offer a completely independent standard siren (the GW analogue of an astronomical standard candle) measurement of $H_0$, as demonstrated following the discovery of the neutron star merger, GW170817. This measurement does not assume a cosmological model and is independent of a cosmic distance ladder. The first joint analysis of the GW signal from GW170817 and its EM localization led to a measurement of $H_0=74^{+16}_{-8}$ km/s/Mpc (median and symmetric $68\%$ credible interval). In this analysis, the degeneracy in the GW signal between the source distance and the weakly constrained viewing angle dominated the $H_0$ measurement uncertainty. Recently, Mooley et al. (2018) obtained tight constraints on the viewing angle using high angular resolution imaging of the radio counterpart of GW170817. Here we obtain a significantly improved measurement $H_0=68.9^{+4.7}_{-4.6}$ km/s/Mpc by using these new radio observations, combined with the previous GW and EM data. We estimate that 15 more localized GW170817-like events (comparable signal-to-noise ratio, favorable orientation), having radio images and light curve data, will potentially bring resolution to the tension between the Planck and Cepheid-supernova measurements, as compared to 50-100 GW events without such data.

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arXiv2018

A cocoon shock breakout as the origin of the $ γ$-ray emission in GW170817

The short Gamma-Ray Burst, GRB170817A, that followed the binary neutron star merger gravitational waves signal, GW170817, is not a usual sGRB. It is weaker by three orders of magnitude than the weakest sGRB seen before and its spectra, showing a hard early signal followed by a softer thermal spectrum, is unique. We show, first, that the $γ$-rays must have emerged from at least mildly relativistic outflow, implying that a relativistic jet was launched following the merger. We then show that the observations are consistent with the predictions of a mildly relativistic shock breakout: a minute $γ$-ray energy as compared with the total energy and a rather smooth light curve with a hard to soft evolution. We present here a novel analytic study and detailed numerical 2D and 3D relativistic hydrodynamic and radiation simulations that support the picture in which the observed $γ$-rays arose from a shock breakout of a cocoon from the merger's ejecta (Kasliwal 2017). The cocoon can be formed by either a choked jet which does not generate a sGRB (in any direction) or by a successful jet which generates an undetected regular sGRB along the system's axis pointing away from us. Remarkably, for the choked jet model, the macronova signal produced by the ejecta (which is partially boosted to high velocities by the cocoon's shock) and the radio that is produced by the interaction of the shocked cocoon material with the surrounding matter, agree with the observed UV/optical/IR emission and with current radio observations. Finally, we discuss the possibility that the jet propagation within the ejecta may photodissociate some of of the heavy elements and may affect the composition of a fraction of ejecta and, in turn, the opacity and the early macronova light.

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arXiv2018

Is the macronova in GW170817 powered by the central engine?

The gravitational wave event GW170817 from a binary neutron star (NS) merger is accompanied by electromagnetic counterparts, and the optical and near-infared emission is called a macronova (or kilonova). Although the radioactivity of synthesized r-process elements is widely discussed as an energy source, its decisive evidence is not clearly shown yet. We discuss a macronova powered by the central engine activities such as jet activities and X-rays from the matter fallback, and show that the engine model allows much broader parameter spaces, in particular smaller ejecta mass ($\sim10^{-4}-0.01\,\Msun$) than the r-process model. The blue and red macronovae are naturally explained by various combinations of the ejecta such as a cocoon and merger ejecta with the energy sources of jets and X-rays. The required energy injection is very similar to the X-ray excess observed in GRB 130603B with the power-law slope of $\sim-1.3$. The required lanthanoid fraction for the opacity can be also consistent with the Galactic one. Early or late multi-wavelength observations are crucial for revealing the central engine of short gamma-ray bursts and the r-process nucleosynthesis.

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