Filgas, R.

Greiner, J.

Knust, F.

Van Eerten, H. J.

Van Eerten, H.

MPG.PuRe

Fitting GRB afterglow broadband data to hydrodynamical simulations

Fabian Knust

H.J. Van Eerten

Jochen Greiner

Robert Filgas

Crossref

OPUS

        Citation for published version:Knust, F, Greiner, J, Filgas, R & Van Eerten, HJ 2014, Fitting GRB afterglow broadband data to hydrodynamicalsimulations. in Proceedings of Swift: 10 Years of Discovery (SWIFT 10), held 2-5 December 2014 at LaSapienza University, Rome, Italy . pp. 83.Publication date:2014Document VersionPublisher's PDF, also known as Version of recordLink to publicationUniversity of BathGeneral 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: 13. May. 2019PoS(SWIFT 10)083Fitting hydrodynamical simulations to broad-bandGRB afterglow dataF. Knust∗Max Planck Institute for extraterrestrial physics, 85748 Garching, GermanyE-mail: fknust@mpe.mpg.deH.J. Van EertenMax Planck Institute for extraterrestrial physics, 85748 Garching, GermanyE-mail: hveerten@mpe.mpg.deJ. GreinerMax Planck Institute for extraterrestrial physics, 85748 Garching, GermanyE-mail: jcg@mpe.mpg.deR. FilgasIEAP, Czech Technical University in Prague, 128 00 Praha 2, Czech RepublicE-mail: robert.filgas@utef.cvut.czThe Gamma-Ray burst Optical Near-infrared Detector (GROND) offers early time data of GammaRay Burst (GRB) afterglows in 4 optical and 3 near-infrared (NIR) bands simultaneously. Weextended the SCALEFIT package to allow for joint fits of GROND and Swift/XRT data. UsingGRB 140512A, we demonstrate the improvements over fitting X-ray data only. We are able toconstrain some of the parameters of the fireball model, for others we derive limits.Swift: 10 Years of Discovery,2-5 December 2014La Sapienza University, Rome, Italy∗Speaker.c© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/PoS(SWIFT 10)083Fitting hydrodynamical simulations to broad-band GRB afterglow data F. Knust1. Fitting based on hydrodynamical simulationsWe report on our project to extended the SCALEFIT package (Ryan et al. 2015, van Eerten etal. in preparation) to allow for joint fits of GRB afterglow data from GROND [6] and Swift/XRT[1]. For the first time we apply it to broad-band data, using GRB 140512A as an example. We coverdifferent spectral regimes and thus are able to break some degeneracies, that occur when applyingSCALEFIT to Swift/XRT data only [9].The fireball model describes GRB afterglows as synchrotron emission. We model the wholetime evolution of the Spectral Energy Distribution (SED) of the afterglow, which has the advantagethat we can use data from every spectral regime at every point in time. There is no need for syn-chronous data gathering from different instruments (or interpolations or extrapolations), as wouldbe the case for single SED fitting. The afterglow model is based directly on hydrodynamical sim-ulations [13, 14] that cover the jet dynamics in more detail than the standard asymptotic analyticalapproaches [10], opening the new possibility to constrain the jet opening angle θ0 and the observerangle θobs.Full details of SCALEFIT can be found in [9]. In short: These simulations cover a rangeof opening angles θ0 and can be re-scaled between isotropic equivalent explosion energy E0 andcircumburst medium density n0 [15]. A simulation run takes days to weeks and the results ofthose simulations are stored in templates. Based on these, a radiative transfer code calculates theemission characteristics under an observer angle θobs with luminosity-distance dL (derived fromredshift z) for a given set of micro-physical parameters (electron power law distribution slope p,fraction of energy in the magnetic field εB and fraction of energy in electrons εe). The crucialpart for simulation based fitting is to pre-calculate the whole process for a given set of parametersΘ = {E0,n0,θ0,θobs, p,εe,εB,dL,z} and compress the data in a way that the results are accessiblefrom every iteration step of the fitting process. The results are stored in tables of the time evolutionfor characteristic quantities for the afterglow SED: cooling frequency νc, peak frequency νm andpeak flux fp. Since the model assumes synchrotron radiation as the emission process, the SED isjust a series of connected power-laws, separated by the characteristic frequencies νm and νc, withslopes following the relations from [10].The SCALEFIT package uses parallel tempered Markov Chains to minimize the χ2 [5]. ThisMarkov Chain Monte Carlo (MCMC) method is capable of completely exploring a high dimen-sional parameter space on a justifiable time scale, making the fitting process very robust towardsdegeneracies between parameters and multi-modal behavior of the Posterior Distribution Function(PDF).2. GRB 140512A, an exampleOn 12.05.2014 at 19:21UT, the Burst Alert Monitor (BAT) triggered on GRB140512A andthe XRT began observing 98.4 seconds thereafter [8]. GROND began its follow up observationson 13.05.2014 at 03:36UT, around 8 hrs after the trigger, for a total of 58 observations, distributedover 4 nights. To reduce the GROND data we used our IRAF/PyRAF [12] based pipeline [16, 7].GROND magnitudes are corrected for galactic foreground extinction with an AV = 0.4 mag towardsthe direction of the burst [11], and using the CCM law with RV = 3.08. For this individual GRBthe GROND SED does not indicate significant host extinction nor host flux contribution. The XRT2PoS(SWIFT 10)083Fitting hydrodynamical simulations to broad-band GRB afterglow data F. Knustlight curve (integrated over the 0.3-10keV range) is fetched from the Swift online repository [3] andcorrected for absorption. Unlike [9] we use broadband data, covering several orders of magnitudein energy, which raises the issue that a fit always will be biased by the spectral regime with themost data points. To mitigate this effect, we added a weighing scheme which ensures that bothinstruments contribute equally to the fit. We use a redshift of z= 0.725 [2] leading to a luminositydistance dL = 1.37× 1028 cm with standard cosmology (H0 = 71 km/sMpc , Ωm = 0.27, ΩΛ = 0.73).Since the model describes the deceleration phase of the GRB, we omit the data before tobs = 10000s, and run the fitting process.The light curve (data and best fitting model) are shown in Fig. 1, a visualization of the completePDF for our broad band data set is shown in Fig. 2. Compared to a fit with XRT data only (seeFig.3), the distributions are substantially more narrow.10-1410-1310-1210-1110-1010-9Band integrated Flux  [ ergcm2s] g r i z J H K x1×1052×104 3×104 4×104 5×104 2×105Observer Time tobs [s]-8-6-4-20246Residuals [σ]Figure 1: Light curve of GRB140512A. The dots are data points and their 1σ error. The dashed lines arethe best fitting model. (Preliminary)3. DiscussionIn general, the fit captures the optical/NIR temporal curvature. An offset of 1 to 2 σ to themodel can be seen, especially in the optical bands. This may be due to extinction in the host,which we did not account for, or due to small-scale effects not covered in the dust maps for thegalactic extinction. In the X-ray regime, the last 3 data points are not well modelled. While from astatistical point of view 3 out of 146 data points can be off the model for a 68% confidence level,having the 3 data points next to each other indicates that the fitting process missed to model a breakin the light curve.The chromaticity of the break rules out a clean jet break. Additionally, the transition froman X-ray temporal power law slope α of 1.25+0.06−0.06 before the break to 1.94+0.22−0.17 after the breakat t = 5.25+0.86−1.19× 104 s (from the live XRT GRB catalogue 1) does not fulfill the relations from1http://www.swift.ac.uk/xrt_live_cat/5988193PoS(SWIFT 10)083Fitting hydrodynamical simulations to broad-band GRB afterglow data F. Knust4202log 10(n0)0.10.20.30.4θ 00.00.10.20.30.4θ obs2.102.162.222.28p43210log 10(² e)1 0 1 2 3log10(Eiso)543210log 10(² B)4 2 0 2log10(n0 )0.10.20.30.4θ00.00.10.20.30.4θobs2.102.162.222.28p4 3 2 1 0log10(²e )5 4 3 2 1 0log10(²B )Figure 2: PDF of the MCMC sample for GROND and XRT data for GRB 140512A. The contour plotsshow the correlations between all pairs of parameters. The histograms in the diagonal show the marginalizedprobabilities for each parameter. The dotted vertical lines are the median and its 68% confidence range. Theblue dot and lines mark the best-fit. Eiso is given in units of 1053 erg, n0 is given in cm−3, θ0 and θobs aregiven in radians. All other quantities are dimensionless. (Preliminary)[10] for the pre- and post cooling break α for any electron distribution index p, neither for an InterStellar Medium (ISM) type environment nor for a stellar-wind type environment. Since the morecomplex dynamics of the simulations (assuming ISM) also fails to model the break, it becomesdifficult to reconcile the X-ray break with a single transition of a basic forward-shock synchrotronmodel.As an alternative explanation, a temporal variation of εB as suggested by [4] is also unlikely,since with Fν ∝ ε(p−2)/4B (above the cooling break, in the ISM case) the effect would be too smallto explain the steepening of the light curve.We are able to constrain θ0 = 0.42+0.01−0.04 rad = 24.1+0.6−2.3 deg , θobs = 0.25+0.01−0.03 rad = 14.3+0.6−2.3deg and p = 2.18+0.01−0.02. For the other micro-physical parameters we derive limits 10−2 . εe < 1and εB . 10−3 (all numbers are still under consideration). Pairwise degeneracies between e.g. Eisoand n0 can only be reduced by including radio or sub-mm data, which would constrain the peak4PoS(SWIFT 10)083Fitting hydrodynamical simulations to broad-band GRB afterglow data F. Knust5.02.50.02.55.0log 10(n0)0.10.20.30.40.5θ 00.00.10.20.30.40.5θ obs2.02.22.42.62.83.0p3.22.41.60.80.0log 10(² e)1 0 1 2 3log10(Eiso)543210log 10(² B)5.02.50.02.55.0log10(n0 )0.10.20.30.40.5θ00.00.10.20.30.40.5θobs2.02.22.42.62.83.0p3.22.41.60.80.0log10(²e )5 4 3 2 1 0log10(²B )Figure 3: PDF for the same burst, but with XRT data only. In comparison to broad band data, the fittingparameters are barely constrained. (Preliminary)frequency νm of the synchrotron spectrum.4. Summary and outlookWe have demonstrated the feasibility of fitting hydrodynamical simulations to non-simultaneousbroad band data with 405 individual data points. These simulations treat the jet dynamics in sub-stantially more detail than asymptotic analytical approaches, opening a new possibility to constrainthe observer angle. With combined optical/NIR and X-ray data, the parameters of interest are muchbetter constrained, in comparison to the fit obtained by using data from a single spectral regime.Since we model the time evolution of the SED, observations in different spectral regimes do notnecessarily have to be time synchronous. The applied statistical method is capable of exploring ahigh dimensional parameter space effectively, and is robust towards multi-modal behavior of theparameter distribution.For the future we will apply this kind of analysis to the full GROND sample. The GRONDinstrument has observed basically every GRB visible from the ESO La Silla observatory for the5PoS(SWIFT 10)083Fitting hydrodynamical simulations to broad-band GRB afterglow data F. Knustlast 7 years, building up a sample of over 200 afterglow detections, around half of them with adata coverage sufficient for light curve fitting. The implementation of data from additional spectralregimes will be a logical next step.5. AcknowledgmentsWe acknowledge the contributions of all GROND observers, especially K. Varela, C. Delvaux,J. Graham, S.Schmidl, M. Tanga. JG acknowledges support by the DFG cluster of excellence "Ori-gin and Structure of the Universe" (www.universe-cluster.de). HJvE is supported by the Alexandervon Humboldt foundation. RF acknowledges support through the German Academic ExchangeService DAAD PPP-57066218 and through the Czech Ministry of Education, Youth and Sports,Grant 7AMB14DE001. Part of the funding for GROND (both hardware as well as personnel) wasgenerously granted from the Leibniz-Prize to Prof. G. Hasinger (DFG grant HA 1850/28-1). Weacknowledge the support by the DFG Cluster of Excellence "Origin and Structure of the Universe".The simulations have been carried out in part on the computing facilities of the Computational Cen-ter for Particle and Astrophysics (C2PAP). This work made use of data supplied by the UK SwiftScience Data Centre at the University of Leicester.References[1] D. N. Burrows et al., The Swift X-Ray Telescope, Space science reviews 120 (2005) 165–195[2] A. de Ugarte Postigo et al., GRB 140512A: Redshift from NOT, GCN 16310 (2014)[3] P. A. Evans et al., Methods and results of an automatic analysis of a complete sample ofSwift-XRT observations of GRBs, MNRAS 397 (2009) 1177–1201[4] R. Filgas et al., GRB 091127: The cooling break race on magnetic fuel, A&A 535 (2011) A57[5] D. Foreman-Mackey et al., emcee: The MCMC Hammer, ASP 125 (2013) 306–312[6] J. Greiner et al., GROND, a 7-Channel Imager, ASP 120 (2008) 405–424[7] T. Krühler et al., The 2175 Å Dust Feature in a Gamma-Ray Burst Afterglow at Redshift 2.45,ApJ 685 (2008) 376–383[8] C. Pagani et al., GRB 140512A: Swift detection of a burst with an optical counterpart, GCN16249 (2014)[9] G. Ryan et al., Gamma-Ray Bursts are Observed Off-axis, ApJ 799 (2015) 3[10] R. Sari et al., Spectra and Light Curves of GRB Afterglows, ApJ 497 (1998) L17[11] E. F. Schlafly and D. P. Finkbeiner, Measuring Reddening with Sloan Digital Sky SurveyStellar Spectra and Recalibrating SFD, ApJ 737 (2011) 103[12] D. Tody et al., IRAF in the Nineties, Astronomical Data Analysis Software and Systems II,ASP Conference Series 52 (1993) 173[13] H. van Eerten et al., Off-axis Gamma-ray Burst Afterglow Modeling Based on a Two-dimensional Axisymmetric Hydrodynamics Simulation, ApJ 722 (2010) 235–247[14] H. J. van Eerten et al., Gamma-ray burst afterglows from transrelativistic blast wave simula-tions, MNRAS 403 (2010) 300–316[15] H. J. van Eerten and A. I. MacFadyen. Gamma-Ray Burst Afterglow Scaling Relations for theFull Blast Wave Evolution, ApJ 747 (2012) L30[16] A. K. Yoldas¸ et al., First Results of GROND, AIP Conf. Series 1000 (2008) 227–2316

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Fitting GRB afterglow broadband data to hydrodynamical simulations

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