Afterglows of gamma-ray bursts are observed to produce light curveswith the flux following power law evolution in time. However, recent observations reveal bright flares at times on the order of minutes to days.One proposed explanation for these flares is the interaction of a relativisticblast wave with a circumburst density transition. In this paper, we modelthis type of interaction computationally in one and two dimensions, usinga relativistic hydrodynamics code with adaptive mesh refinement calledram, and analytically in one dimension. We simulate a blast wave travelingin a stellar wind environment that encounters a sudden change indensity, followed by a homogeneous medium, and compute the observedradiation using a synchrotron model. We show that flares are not observablefor an encounter with a sudden density increase, such as a windtermination shock, nor for an encounter with a sudden density decrease.Furthermore, by extending our analysis to two dimensions, we are able toresolve the spreading, collimation, and edge effects of the blast wave as itencounters the change in circumburst medium. In all cases considered inthis paper, we find that a flare will not be observed for any of the densitychanges studied

Gat, I.

MacFadyen, A.

van Eerten, H.

English

OPUS

        Citation for published version:Gat, I, van Eerten, H & MacFadyen, A 2013, 'GRB afterglow blast wave encountering sudden circumburstdensity change produces no flares', Paper presented at 7th Huntsville Gamma-Ray Burst Symposium, GRB2013, Tennessee, USA United States, 14/04/13 - 18/04/13.Publication date:2013Document VersionPeer reviewed versionLink to publicationUniversity of BathAlternative formatsIf you require this document in an alternative format, please contact:openaccess@bath.ac.ukGeneral rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Download date: 05. Jul. 2024arXiv:1308.4885v1  [astro-ph.HE]  22 Aug 2013Article 26 in eConf C1304143August 23, 2013GRB Afterglow Blast Wave Encountering SuddenCircumburst Density Change Produces No FlaresIlana Gat, Hendrik van Eerten, Andrew MacFadyenCenter for Cosmology and Particle Physics, Physics DepartmentNew York University, New York, NY 10003Afterglows of gamma-ray bursts are observed to produce light curveswith the flux following power law evolution in time. However, recent ob-servations reveal bright flares at times on the order of minutes to days.One proposed explanation for these flares is the interaction of a relativisticblast wave with a circumburst density transition. In this paper, we modelthis type of interaction computationally in one and two dimensions, usinga relativistic hydrodynamics code with adaptive mesh refinement calledram, and analytically in one dimension. We simulate a blast wave trav-eling in a stellar wind environment that encounters a sudden change indensity, followed by a homogeneous medium, and compute the observedradiation using a synchrotron model. We show that flares are not ob-servable for an encounter with a sudden density increase, such as a windtermination shock, nor for an encounter with a sudden density decrease.Furthermore, by extending our analysis to two dimensions, we are able toresolve the spreading, collimation, and edge effects of the blast wave as itencounters the change in circumburst medium. In all cases considered inthis paper, we find that a flare will not be observed for any of the densitychanges studied.PRESENTED ATHuntsville Gamma Ray Burst SymposiumNashville, Tn, USA, April 14–18, 20131 IntroductionGamma-ray burst (GRB) afterglows are generally modeled as smooth curves withthe slope being a function of the density of the surrounding medium as well as thepower-law slope of the distribution of the accelerated electron population at the shockfront. Recent observations, though, have shown flares in X-ray afterglows. To explainthe causes of these flares, researchers have began to study the interaction of a blastwave with complex structures such as a wind termination shock (e.g., [1, 2, 3]). Inthis paper, we revisit this interaction by modeling the circumburst density structureas a stellar wind with a sudden density increase followed by a homogeneous medium(e.g., an interstellar medium (ISM)). We also extend this analysis to density drops aswell.We use a numerical relativistic hydrodynamics (RHD) code with adaptive meshrefinement called ram [4] to numerically simulate these interactions in one and twodimensions. Our simulations are set up to address a number of interaction scenariosnot previously explored as well as the two dimensional effects of spreading of a colli-mated flow at the shock front. Specifically, we address the following questions in ouranalysis:• When a collimated blast wave traveling in a stellar wind environment encountersa wind termination shock, how does the size of the density jump affect thedynamics and resulting light curve?• What happens when there is a density drop instead of a jump? Does the blastwave speed up, and in turn, recollimate? Will this cause a rebrightening or flarein the light curve?• When the blast wave encounters an extreme density increase, does it immedi-ately spread outwards from this high energy collision and cause flares in thelight curve? Does this sideways spreading depend on the size of the densityjump?We answer these questions through our numerical and analytical simulations.These results are explained in detail in [5], which can also be referenced for a morecomplete list of relevant citations.2 Dynamics of Blast Wave EncountersOur numerical simulations of the adiabatic blast wave (“jet”) formed by a GRB areset up in spherical coordinates following the Blanford & Mckee solution [6]. Theyhave a jet half opening angle of θ0 = 0.1 and a starting fluid Lorentz factor, γ = 15.Figure 1 shows two snapshots: one from a simulation of a blast wave encountering a1density jump (left panel) and the other from a simulation of a blast wave encounteringa density drop (right panel). The left panel in Figure 1 shows the recollimation of theblast wave as it enters the higher density region as well as the strong reverse shockcaused from the encounter. Conversely, the right panel in Figure 1 illustrates thespreading of the blast wave as it encounters the much lower density region. Theseresults, at first, seem counter-intuitive as a blast wave traveling with low Lorentzfactors usually spreads and a blast wave with high Lorentz factors is more collimated.Here, the blast wave that is slowed by the higher density region recollimates, and theblast wave that speeds up spreads out. This is explained by the fact that the blastwave traveling into a higher density medium has more pressure pushing back at it,forcing it to recollimate as it pushes into the new region. The blast wave travelinginto the lower density region has much less pressure against it, allowing the blastwave to spread as it travels into the ISM.Figure 1: Figures of the two dimensional numerical simulations showing specific en-ergy. Left: simulation of a blast wave encountering a density jump of factor 100at a radius corresponding to the fluid shock Lorentz factor, γ = 10 at a time,T = 2.97 × 108s. Right: simulation of a blast wave encountering a density dropof factor 100 at a radius corresponding to the fluid shock Lorentz factor, γ = 5 at atime, T = 1.15× 109s.In addition to the recollimation of the blast wave encountering a large densityjump (left panel in Figure 1), the reverse shock created from the encounter shocksand spreads the fluid still in the stellar wind environment. This causes vortices toform that get trapped within the stellar wind environment and never pass throughto the ISM. There is also a small amount of sideways spreading from the actual en-counter itself, however this is a very small amount. The most energetic fluid puncturesthrough to the higher density medium at the time of the encounter instead of spread-ing outwards. Yet, sideways spreading is still observed as the reverse shock spreads2the fluid remaining in the stellar wind environment. The blast wave encountering adensity drop (right panel in Figure 1) does not create a strong reverse shock or spreadsideways in the stellar wind, and thus the fluid behind the drop is still able to travelthrough to the new medium.With the understanding of the dynamics of the blast wave encountering a suddenchange in circumburst medium, the next section discusses the resulting light curves.3 Light CurvesWe calculate the GRB afterglow light curves using the radiation calculation method-ology from [7] at an X-ray frequency of 5×1017 Hz, similar to the frequency detectedby Swift. We studied light curves at other frequencies, however the results were qual-itatively the same. We use values of ǫB = 0.01, ǫe = 0.1, and p = 2.5, where ǫBand ǫe are the fractions of internal energy that contribute to the magnetic field atthe shock front and to accelerating electrons respectively, and p expresses the energydistribution index of the shock-accelerated particles. We also do not consider electroncooling in our light curves shown here, but have found that this does not qualitativelychange our results.Figure 2 depicts that there are no observable flares in the flux emitted from ablast wave encountering a jump or a drop. The time labeled “Tobs,enc” in the plots ofFigure 2 is the first time the encounter should be observable. The two dimensionalsimulations of a density jump (top left panel in Figure 2) show that there will beno flare at the time of the encounter for an observer on or off axis. However, themagnitude of the light curve will drop and the slope of the light curve will change.For the case of the density drop, the light curve also smoothly transitions to a newslope after the encounter, which can be seen in the top right panel of Figure 2.When a blast wave traveling in a stellar wind encounters a change in densityfollowed by an ISM, the slope of the flux observed will change after the encounterto match the slope of the flux observed if the blast wave was solely traveling in theISM. This is depicted in the bottom left panel in Figure 2. This smooth transitionto the new slope results in no sudden increase in flux. For the case of a densityjump, the flux does not immediately jump up to the new magnitude because theblast wave has been slowed by the encounter and is not energetic enough to causea rebrightening. For the case of a drop, the flux observed from a blast wave inthe new ISM environment is at a lower magnitude than the flux observed from ablast wave in the wind environment. This results in the flux observed from the blastwave encountering the new environment to decrease, instead of increase, after theencounter to evolve in the new environment. For both cases, though, of a drop or ajump, the magnitude of the flux observed after the encounter is lower than the fluxwould have been if the blast wave was traveling solely in the ISM. This is due to the3different regions of the post-encounter blast wave. The fluid swept up prior to theencounter is held behind the contact discontinuity and all the fluid swept up after theencounter is contained in front of the contact discontinuity. Thus, there is much lessfluid radiating at the post encounter Lorentz factor than there would be if the blastwave was traveling solely in the ISM, resulting in the magnitude of the flux observedto be lowered.The bottom light panel in Figure 2 shows the light curves from a blast wavetraveling in a stellar wind environment that encounters jumps of various sizes at aradius corresponding to the fluid Lorentz factor, γ = 25. This figure illustrates thatthe conclusion that the flux observed will smoothly transition to the slope of the lightcurve in the new medium holds for a wide range of jump factors. At the time of theencounter, the flux observed from the blast wave will not suddenly increase. It willtransition to the new base line in the new medium.4 ConclusionsWe have shown numerically and analytically that a blast wave evolving partially ina stellar wind environment that encounters a sudden change in density, either anincrease or a decrease, followed by a constant density environment for a wide rangeof initial conditions does not cause an observable rebrightening. The size of thedensity jump does affect the dynamics and resulting light curve, but there are stillno observable flares at the time of the encounter.We found that for a blast wave traveling in a stellar wind environment encoun-tering an ISM environment, the resulting flux observed will gradually transition fromone environment to the next. If the flux observed from a blast wave traveling solelyin the ISM is lower than the flux observed with a blast wave traveling solely in thewind environment at the time of the encounter, the flux observed from the blast wavewill simply dim and follow the same light curve slope of the ISM. If the flux observedfrom a blast wave traveling solely in the ISM is higher than the flux observed froma blast wave traveling solely in a wind environment at the time of the encounter,the observed flux from the blast wave will not suddenly increase, but stay relativelysteady as it transitions to the new slope of the ISM.We have studied the two dimensional and one dimensional effects of a density dropand have shown that the blast wave does increase in speed, but does not recollimate.There is also no rebrightening caused by this sudden increase in blast wave speed.Our two dimensional studies of a density jump have yielded the conclusion that thereis some sideways spreading from a high energy collision of the blast wave with a largejump in circumburst density, and the amount by which the blast wave spreads ishighly dependent on the size of the density jump.From our analytical solutions and our numerical simulations, we have answered4Figure 2: Top: light curves from the two dimensional numerical simulations.Top Left:blast wave encountering a density jump of factor 100 at a radius corresponding tothe fluid shock Lorentz factor, γ = 10 for on and off axis observations. Top Right:blast wave encountering a density drop of factor 100 at a radius corresponding tothe fluid shock Lorentz factor, γ = 5 for on and off axis observations. Bottom: lightcurves from the analytical model (described in [5]) assuming spherical outflow for ablast wave encountering a density change at a radius corresponding to the fluid shockLorentz factor, γ = 25. Bottom Left: blue light curves are of blast wave travelingin a stellar wind environment encountering a density jump of factor 100 (solid blueline) and a density drop of factor 10000 (dashed blue line) followed by a homogeneousmedium. These are plotted against the light curve for a blast wave traveling solely ina stellar wind environment (green line) and the light curves for blast waves travelingsolely in the homogeneous medium of the jump (red solid line) and of the drop (dashedsolid line). Bottom Right: light curves for a blast wave encountering encountering adensity change of various magnitudes.the questions listed in the Introduction and have concluded that a blast wave travelingin a stellar wind environment that encounters a change in density followed by an ISM5environment will not cause observable flares. We conclude that a wind terminationshock, or more generally, any sudden transition in circumburst density (even extremechanges), is very unlikely to be the cause of the flares observed. In addition, flaresobserved by Swift return to the same baseline as the light curve prior to the flare [8].If the flare occurred at the time of the encounter, the light curve would transitionto the new slope of the ISM material, not the slope of the stellar wind. This makesit highly unlikely that a flare seen at the encounter with the change in circumburstenvironment could be the explanation for the flares seen by Swift.ACKNOWLEDGEMENTSThis research was supported in part by NASA through grant NNX10AF62G issuedthrough the Astrophysics Theory Program and by the NSF through grant AST-1009863 and by the Chandra grant TM3-14005X. Resources supporting this work wereprovided by the NASA High-End Computing (HEC) Program through the NASA Ad-vanced Supercomputing (NAS) Division at Ames Research Center. The software usedin this work was in part developed by the DOE-supported ASCI/Alliance Center forAstrophysical Thermonuclear Flashes at the University of Chicago.References[1] E. Ramirez-Ruiz et al., Astrophys. J. 631, 435 (2005)[2] A. Pe’er and R. A. M. J. Wijers, Astrophys. J. 643 1036 (2006)[3] E. Nakar and J. Granot, Mon. Not. Roy. Astron. Soc. 380, 1744 (2007)[4] W. Zhang and A. I. MacFadyen, Astrophys. J. Suppl. 164, 255 (2006)[5] I. Gat, H. van Eerten and A. MacFadyen, Astrophys. J. 773 2 (2013)[6] R. D. Blandford and C. F. McKee, Phys. Fluids 19, 1130 (1976).[7] H. van Eerten, W. Zhang and A. MacFadyen, Astrophys. J. 722, 235 (2010)[8] D. N. Burrows et al., Science 309, 1833 (2005)6

GRB afterglow blast wave encountering sudden circumburst density change produces no flares

https://purehost.bath.ac.uk/ws/files/158569586/1308.4885v1_proceedings.pdf

GRB afterglow blast wave encountering sudden circumburst density change produces no flares

Abstract

Similar works

Full text

Available Versions

OPUS