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Register a new userHydrodynamics and Radiation from a Relativistic Expanding Jet with Applications to GRB Afterglow
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Authors
Jonathan Granot
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We describe fully relativistic three dimensional calculations of the slowing down and spreading of a relativistic jet by an external medium like the ISM. We calculate the synchrotron spectra and light curves using the conditions determined by the hydrodynamic calculations. Preliminary results with a moderate resolution are presented here. Higher resolution calculations are in progress.
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We perform fully relativistic hydrodynamic simulations of the deceleration and lateral expansion of a relativistic jet as it expands into an ambient medium. The hydrodynamic calculations use a 2D adaptive mesh refinement (AMR) code, which provides adequate resolution of the thin shell of matter behind the shock. We find that the sideways propagation is different than predicted by simple analytic models. The physical conditions at the sides of the jet are found to be significantly different than at the front of the jet, and most of the emission occurs within the initial opening angle of the jet. The light curves, as seen by observers at different viewing angles with respect to the jet axis, are then calculated assuming synchrotron emission. For an observer along the jet axis, we find a sharp achromatic `jet break in the light curve at frequencies above the typical synchrotron frequency, at $t_{jet}approx 5.8(E_{52}/n_1)^{1/3}(theta_0/0.2)^{8/3}$ days, while the temporal decay index $alpha$ ($F_{ u}propto t^{alpha}$) after the break is steeper than $-p$ ($alpha=-2.85$ for $p=2.5$). At larger viewing angles $t_{jet}$ increases and the jet break becomes smoother.
The afterglow of GRB 170817A has been detected for more than three years, but the origin of the multi-band afterglow light curves remains under debate. A classical top-hat jet model is faced with difficulties in producing a shallow rise of the afterglow light curves as observed $(F_{ u} propto T^{0.8})$. Here we reconsider the model of stratified ejecta with energy profile of $E(>Gamma beta)=E_0(Gamma beta)^{-k}$ as the origin of the afterglow light curves of the burst, where $Gamma$ and $beta$ are the Lorentz factor and speed of the ejecta, respectively. $k$ is the power-law slope of the energy profile. We consider the ejecta are collimated into jets. Two kinds of jet evolutions are investigated, including a lateral-spreading jet and a non-lateral-spreading jet. We fit the multi-band afterglow light curves, including the X-ray data at one thousand days post-burst, and find that both the models of the spreading and non-spreading jets can fit the light curves well, but the observed angular size of the source and the apparent velocity of the flux centroid for the spreading jet model are beyond the observation limits, while the non-spreading jet model meets the observation limits. Some of the best-fit parameters for the non-spreading jet model, such as the number density of the circumburst medium $sim10^{-2}$ cm$^{-3}$ and the total jet kinetic energy $E sim 4.8times 10^{51}$ erg, also appear plausible. The best-fit slope of the jet energy profile is $k sim 7.1$. Our results suggest that the afterglow of GRB 170817A may arise from the stratified jet and that the lateral spreading of the jet is not significant.
Relativistic hydrodynamics is a powerful tool to simulate the evolution of the quark gluon plasma (QGP) in relativistic heavy ion collisions. Using 10000 initial and final profiles generated from 2+1-d relativistic hydrodynamics VISH2+1 with MC-Glauber initial conditions, we train a deep neural network based on stacked U-net, and use it to predict the final profiles associated with various initial conditions, including MC-Glauber, MC-KLN and AMPT and TRENTo. A comparison with the VISH2+1 results shows that the network predictions can nicely capture the magnitude and inhomogeneous structures of the final profiles, and nicely describe the related eccentricity distributions $P(varepsilon_n)$ (n=2, 3, 4). These results indicate that deep learning technique can capture the main features of the non-linear evolution of hydrodynamics, showing its potential to largely accelerate the event-by-event simulations of relativistic hydrodynamics.
In this proceeding, we will briefly review our recent progress on implementing deep learning to relativistic hydrodynamics. We will demonstrate that a successfully designed and trained deep neural network, called {tt stacked U-net}, can capture the main features of the non-linear evolution of hydrodynamics, which could also rapidly predict the final profiles for various testing initial conditions.
GRB 190114C is the first gamma-ray burst detected at Very High Energies (VHE, i.e. >300 GeV) by the MAGIC Cherenkov telescope. The analysis of the emission detected by the Fermi satellite at lower energies, in the 10 keV -- 100 GeV energy range, up to ~ 50 seconds (i.e. before the MAGIC detection) can hold valuable information. We analyze the spectral evolution of the emission of GRB 190114C as detected by the Fermi Gamma-Ray Burst Monitor (GBM) in the 10 keV -- 40 MeV energy range up to ~60 sec. The first 4 s of the burst feature a typical prompt emission spectrum, which can be fit by a smoothly broken power-law function with typical parameters. Starting on ~4 s post-trigger, we find an additional nonthermal component, which can be fit by a power law. This component rises and decays quickly. The 10 keV -- 40 MeV flux of the power-law component peaks at ~ 6 s; it reaches a value of 1.7e-5 erg cm-2 s-1. The time of the peak coincides with the emission peak detected by the Large Area Telescope (LAT) on board Fermi. The power-law spectral slope that we find in the GBM data is remarkably similar to that of the LAT spectrum, and the GBM+LAT spectral energy distribution seems to be consistent with a single component. This suggests that the LAT emission and the power-law component that we find in the GBM data belong to the same emission component, which we interpret as due to the afterglow of the burst. The onset time allows us to estimate the initial jet bulk Lorentz factor Gamma_0 is about 500, depending on the assumed circum-burst density.
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