Gamma-ray burst afterglow light curves from a Lorentz-boosted simulation frame and the shape of the jet break
Hendrik van Eerten, Andrew MacFadyen
备注：
17 pages, 12 figures. ApJaccepted. Arxiv update contains some minor corrections, plus correction of absolute flux levels in tables and Figs 3ab,5, 9, 11. Also added a discussion of transition duration of jet breaks
GRB afterglow jets have been notoriously difficult to resolve numerically using 2D hydrodynamical simulations due to high outflow Lorentz factors. By performing simulations in a boosted frame, it is possible to calculate light curves from numerically computed flows in sufficient detail to accurately quantify the shape of the jet break and the post-break steepening of the light curve. We study jet breaks for jets with opening angles of theta_0 = 0.05, 0.1 and 0.2 radians decelerating in a constant density medium, observed at angles (theta_obs) ranging from on-axis to the jet edge. We present a single set of scale-invariant functions describing the time evolution of synchrotron spectral break frequencies and peak flux, depending only on theta_0 and theta_obs, sufficient to reconstruct light curves for arbitrary explosion energy, circumburst density and synchrotron slope p. We compare our light curves to fit functions using sharp breaks and smooth transitions and confirm that the measured jet break time can be delayed due to theta_obs. We find that the difference in temporal indices across the jet break is larger than theoretically anticipated leading to post-break slopes of roughly 0.25 - 1.3 p, sufficiently steep to not easily reconcile with post-break slopes measured for the Swift sample, suggesting that most Swift GRBs do not explode in homogeneous media or that jet breaks are hidden by additional physics such as prolonged energy injection or viewing angle effects. Light curves and spectral break and peak flux evolution functions will be made publicly available on-line at http://cosmo.nyu.edu/afterglowlibrary .
We develop two methods to estimate the bulk Lorentz factor of X-ray flare outflow. In the first method the outflow is assumed to be baryonic and is accelerated by the thermal pressure, for which the final bulk Lorentz factor is limited by the outflow luminosity as well as the initial radius of the outflow getting accelerated. Such a method may be applied to a considerable fraction of flares. The second method, based on the curvature effect interpretation of the quick decline of the flare, can give a tightly constrained estimate of the bulk Lorentz factor but can only be applied to a few giant …
We develop a numerical formalism for calculating the distribution with energy of the (internal) pairs formed in a relativistic source from unscattered MeV--TeV photons. For GRB afterglows, this formalism is more suitable if the relativistic reverse-shock that energizes the ejecta is the source of the GeV photons. The number of pairs formed is set by the source GeV output (calculated from the Fermi-LAT fluence), the unknown source Lorentz factor, and the unmeasured peak energy of the LAT spectral component. We show synchrotron and inverse-Compton light-curves expected from pairs formed in the s…
In the fireball model, it is more physically realistic that gamma-ray burst (GRB) ejecta have a range of bulk Lorentz factors (assuming $M\propto Γ^{-s}$). The low Lorentz factor part of the ejecta will catch up with the high Lorentz factor part when the latter is decelerated by the surrounding medium to a comparable Lorentz factor. Such a process will develop a long-lasting weak reverse shock until the whole ejecta are shocked. Meanwhile, the forward shocked materials are gradually supplied with energy from the ejecta that are catching-up, and thus the temporal decay of the forward shock emis…
The peak time of optical afterglow may be used as a proxy to constrain the Lorentz factor Gamma of the gamma-ray burst (GRB) ejecta. We revisit this method by including bursts with optical observations that started when the afterglow flux was already decaying; these bursts can provide useful lower limits on Gamma. Combining all analyzed bursts in our sample, we find that the previously reported correlation between Gamma and the burst luminosity L_gamma does not hold. However, the data clearly shows a lower bound Gamma_min which increases with L_gamma. We suggest an explanation for this feature…
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Recent analytical and numerical work argue that successful relativistic Fermi acceleration requires a weak magnetization of the unshocked plasma, all the more so at high Lorentz factors. The present paper tests this conclusion by computing the afterglow of a gamma-ray burst outflow propagating in a magnetized stellar wind using "ab initio" principles regarding the microphysics of relativistic Fermi acceleration. It is shown that in magnetized environments, one expects a drop-out in the X-ray band on sub-day scales as the synchrotron emission of the shock heated electrons exits the frequency ba…
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Violations of both the weak equivalence principle (WEP) and Lorentz invariance can produce vacuum birefringence, which leads to an energy-dependent rotation of the polarization vector of linearly polarized emission from a given astrophysical source. However, the search for the birefringent effect has been hindered by our ignorance concerning the intrinsic polarization angle in different energy bands. Considering the contributions to the observed linear polarization angle from both the intrinsic polarization angle and the rotation angles induced by violations of the WEP and Lorentz invariance, …
It is well known that collisionless shocks are major sites of particle acceleration in the Universe, but the details of the acceleration process are still not well understood. The particle acceleration rate, which can shed light on the acceleration process, is rarely measured in astrophysical environments. Here we use observations of gamma-ray burst afterglows, which are weakly magnetized relativistic collisionless shocks in ion-electron plasma, to constrain the rate of particle acceleration in such shocks. We find, based on X-ray and GeV afterglows, an acceleration rate that is most likely ve…
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We investigate the implications of energy-dependence of the speed of photons, one of the candidate effects of quantum-gravity theories that has been most studied recently, from the perspective of observations in different reference frames. We examine how a simultaneous burst of photons would be measured by two observers with a relative velocity, establishing some associated conditions for the consistency of theories. For scenarios where the Lorentz transformations remain valid these consistency conditions allow us to characterize the violations of Lorentz symmetry through an explicit descripti…
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It is largely recognized that Gamma-Ray Burst (GRB) jets involve ultra-relativistic motion. However, the value of the Lorentz factor Gamma_0 is still not clear and only lower limits are known for most bursts. We suggest here a new method to obtain upper limits on Gamma_0. The early high-energy synchrotron afterglow flux depends strongly on Gamma_0. Upper limits on GeV emission therefore provide uppers limit on Gamma_0. Applying this method to 190 Fermi GRBs that have not been detected by the Fermi-LAT we place upper limits on the high-energy afterglow flux, and in turn on Gamma_0. For bursts a…
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The various stages of baryonic gamma-ray burst afterglow blast waves are reviewed. These are responsible for the afterglow emission from which much of our understanding of gamma-ray bursts derives. Initially, the blast waves are confined to the dense medium surrounding the burster (stellar envelope or dense wind), giving rise to a jet-cocoon structure. A massive ejecta is released and potentially fed by ongoing energy release from the burster and a forward-reverse shock system is set up between ejecta and ambient density. Ultimately the blast wave spreads sideways and slows down, and the domin…
Energy injection into the external shock system that generates the afterglow to a gamma-ray burst (GRB) can result in a re-brightening of the emission. Here we investigate the off-axis view of a re-brightened refreshed shock afterglow. We find that the afterglow light-curve, when viewed from outside of the jet opening angle, could be characterised by a slow rise, or long-plateau, with a maximum flux determined by the total system energy. Using the broadband afterglow data for GRB170817A, associated with the gravitational wave detected binary neutron star merger GW170817, we show that a refresh…
We present a model for relativistic jets which generates a particular angular distribution of Lorentz factor and energy per solid angle. We consider a fireball with specific internal energy E/M launched with bulk Lorentz factor γ_B. This "boosted fireball" model is motivated by the phenomenology of collapsar jets, but is applicable to a wide variety of relativistic flows. In its center-of-momentum frame the fireball expands isotropically, converting its internal energy into radially expanding flow with asymptotic Lorentz factor η_0 ~ E/M. In the lab frame the flow is beamed, expanding with Lor…
We present multi-wavelength observations and modeling of Gamma-ray Bursts (GRBs) that exhibit a simultaneous re-brightening in their X-ray and optical light curves, and are also detected at radio wavelengths. We show that the re-brightening episodes can be modeled by injection of energy into the blastwave and that in all cases the energy injection rate falls within the theoretical bounds expected for a distribution of energy with ejecta Lorentz factor. Our measured values of the circumburst density, jet opening angle, and beaming corrected kinetic energy are consistent with the distribution of…
For a sample of Swift and Fermi GRBs, we show that the minimum variability timescale and the spectral lag of the prompt emission is related to the bulk Lorentz factor in a complex manner: For small $Γ$'s, the variability timescale exhibits a shallow (plateau) region. For large $Γ$'s, the variability timescale declines steeply as a function of $Γ$ ($δT\proptoΓ^{-4.05\pm0.64}$). Evidence is also presented for an intriguing correlation between the peak times, t$_p$, of the afterglow emission and the prompt emission variability timescale.
Gamma-ray bursts (GRBs) are fascinating extragalactic objects. They represent a fantastic opportunity to investigate unique properties not exhibited in other sources. Multi-wavelength afterglow observations from some short- and long-duration GRBs reveal an atypical long-lasting emission that evolves differently from the canonical afterglow light curves favoring the off-axis emission. We present an analytical synchrotron afterglow scenario, and the hydrodynamical evolution of an off-axis top-hat jet decelerated in a stratified surrounding environment. The analytical synchrotron afterglow model …
The conventional derivation of the gamma-ray burst afterglow jet break time uses only the blast wave fluid Lorentz factor and therefore leads to an achromatic break. We show that in general gamma-ray burst afterglow jet breaks are chromatic across the self-absorption break. Depending on circumstances, the radio jet break may be postponed significantly. Using high-accuracy adaptive mesh fluid simulations in one dimension, coupled to a detailed synchrotron radiation code, we demonstrate that this is true even for the standard fireball model and hard-edged jets. We confirm these effects with a si…
We work on a GRB sample whose initial Lorentz factors ($Γ_0$) are constrained with the afterglow onset method and the jet opening angles ($θ_{\rm j}$) are determined by the jet break time. We confirm the $Γ_0$ - $E_{γ,\rm iso}$ correlation by Liang et al. (2010), and the $Γ_0$ - $L_{γ,\rm iso}$ correlation by L{ü} et al. (2012). Furthermore, we find correlations between $Γ_0$ and the beaming corrected $γ$-ray energy ($E_γ$) and mean $γ$-ray luminosity ($L_γ$). By also including the kinetic energy of the afterglow, we find rough correlations (with larger scatter) between $Γ_0$ and the total ($γ…
Orphan afterglows from short $γ$-ray bursts (GRB) are potential candidates for electromagnetic (EM) counterpart searches to gravitational wave (GW) detected neutron star or neutron star black hole mergers. Various jet dynamical and structure models have been proposed that can be tested by the detection of a large sample of GW-EM counterparts. We make predictions for the expected rate of optical transients from these jet models for future survey telescopes, without a GW or GRB trigger. A sample of merger jets is generated in the redshift limits $0\leq z\leq 3.0$, and the expected peak $r$-band …
We systematically investigate the outflow structure of GW170817 in comparison with a sample of 27 cosmological short GRBs by modelling their afterglow light curves. We find that cosmological short GRBs share the same outflow structures with GW170817, relativistic structured jets. The jet opening angle of GW170817 is $6.3^{+1.1}_{-0.6}{}^{\circ}$, which is consistent with that of cosmological short GRBs ($θ_0 = 6.9^\circ \pm 2.3^{\circ}$). Our analysis indicates that GW170817 is viewed off-axis ($θ_{\rm obs} = 30^{+7}_{-4}{}^{\circ}$), while cosmological short GRBs are viewed on-axis ($θ_{\rm o…
The Fermi Gamma-ray Burst Monitor reported the possible detection of the gamma-ray counterpart of a binary black hole merger event, GW150914. We show that the gamma-ray emission is caused by a relativistic outflow with Lorentz factor larger than 10. Subsequently, debris outflow pushes the ambient gas to form a shock, which is responsible for the afterglow synchrotron emission. We find that the 1.4 GHz radio flux peaks at $\sim10^5$ sec after the burst trigger. If the ambient matter is dense enough with density larger than $\sim10^{-2}$ cm$^{-3}$, then the peak radio flux is $\sim0.1$ mJy, whic…
Jet breaks in gamma ray burst (GRB) afterglows provide a direct probe of their collimation angle. Modeling a jet break requires an understanding of the "jet spreading" process, whereby the jet transitions from a collimated outflow into the spherical Sedov-Taylor solution at late times. Currently, direct numerical calculations are the most accurate way to capture the deceleration and spreading process, as analytical models have previously given inaccurate descriptions of the dynamics. Here (in paper I) we present a new, semi-analytical model built empirically by performing relativistic numerica…
Recently, ground-based Imaging Atmospheric Cherenkov Telescopes have reported the detection of very-high-energy (VHE) gamma-rays from some gamma-ray bursts (GRBs). One of them, GRB~190829A, was triggered by the Swift satellite, and about 20000 s after the burst onset the VHE gamma-ray emission was detected by H.E.S.S. with ~ 5 sigma significance. This event had unusual features of having much smaller isotropic equivalent gamma-ray energy than typical long GRBs and achromatic peaks in X-ray and optical afterglow at about 1400 s. Here we propose an off-axis jet scenario that explains these obser…
The shallow decay phase and flares in the afterglows of gamma-ray bursts (GRBs) is widely believed to be associated with the later activation of central engine. Some models of energy injection involve with a continuous energy flow since the GRB trigger time, such as the magnetic dipole radiation from a magnetar. However, in the scenario involving with a black hole accretion system, the energy flow from the fall-back accretion may be delayed for a fall-back time $\sim t_{\rm fb}$. Thus we propose a delayed energy injection model, the delayed energy would cause a notable rise to the Lorentz fact…
Studies of gamma-ray bursts (GRBs) and their multi-wavelength afterglows have led to insights in electron acceleration and emission properties from relativistic, high-energy astrophysical sources. Broadband modeling across the electromagnetic spectrum has been the primary means of investigating the physics behind these sources, although independent diagnostic tools have been developed to inform and corroborate assumptions made in particle acceleration simulations and broadband studies. We present a methodology to constrain three physical parameters related to electron acceleration in GRB blast…
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 $(F_ν \propto T^{0.8})$. Here we reconsider the model of stratified ejecta with energy profile of $E(>Γβ)=E_0(Γβ)^{-k}$ as the origin of the afterglow light curves of the burst, where $Γ$ and $β$ are the Lorentz factor and speed of the ejecta, respectively. $k$ is the power-law slope of the energy profile. We consider t…
The detection of GRB 180722B and GRB 190114C in sub-TeV gamma-rays has opened up a new window to study gamma-ray bursts in high energy gamma-rays. Recently it is shown that the synchrotron and inverse Compton processes are responsible for the production of these high energy gamma-rays during the afterglow. Here, for the first time we demonstrate that, the photohadronic scenario which is successful in explaining the multi-TeV flaring in high energy blazars is also applicable for gamma-ray bursts. We show that the sub-TeV spectra of GRB 190114C and GRB 180720B are due to the interaction of high …
We demonstrate that the steep decay and long plateau in the early phases of gamma ray burst (GRB) X-ray afterglows are naturally produced in the collapsar model, by a means ultimately related to the dynamics of relativistic jet propagation through a massive star. We present two-dimensional axisymmetric hydrodynamical simulations which start from a collapsar engine and evolve all the way through the late afterglow phase. The resultant outflow includes a jet core which is highly relativistic after breaking out of the star, but becomes baryon-loaded after colliding with a massive outer shell, cor…
Gravitational-wave detected neutron star mergers provide an opportunity to investigate short gamma-ray burst (GRB) jet afterglows without the GRB trigger. Here we show that the post-peak afterglow decline can distinguish between an initially ultra-relativistic jet viewed off-axis and a mildly relativistic wide-angle outflow. Post-peak the afterglow flux will decline as $F_ν\propto t^{-α}$. The steepest decline for a jet afterglow is $α>3p/4$ or $> (3p+1)/4$, for an observation frequency below and above the cooling frequency, respectively, where $p$ is the power-law index of the electron energy…
We use published data in radio, optical and X-ray bands to analyze and model afterglows of GW/GRB 170817A. Our analysis is based on a phenomenological gamma-ray burst generator model which we previously used to study the prompt gamma-ray emission of this important transient. We find a multi-component model and a few of its variants that are consistent with broad band $\sim 1$ year observations of afterglows, once the contribution of kilonova in optical/IR band is taken into account. Considering beaming and off-axis view, we interpret the components of the model as approximately presenting the …
