Fermi has shown GRBs to be a source of >10 GeV photons. We present an estimate of the detection rate of GRBs with the future Cherenkov Telescope Array (CTA). Our predictions are based on the observed properties of GRBs detected by Fermi, combined with the spectral properties and redshift determinations for the bursts population by in struments operating at lower energies. We develop two model for high energy prompt and early afterglow emission, and show how the probability of detection is affected by instrument effecti ve area, response time, and energy threshold. While detection of VHE emission from GRBs has eluded ground-based instruments thus far, our results suggest that ground-based detection may be within reach of CTA, though detections would be infrequent even with prompt followup to all valid satellite triggers. We estimate a rate of one GRB every 2 ‐ 3 years based on the trigger rate from the Swift satellite, provided that no spectral softening or cutoff features below 100 GeV exist in a significant number of GRBs. Such a detection would help constrain the emission mechanism of gamma-ray emission from GRBs. Photons at these energies from distant GRBs are affected by the UV-optical background light, and a ground-based detection could also provide a valuable probe of the Extragalactic Background Light (EBL) in place at high redshift

Aurelien Bouvier

Joel R. Primack

Nepomuk Otte

Rudy Gilmore

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Modeling GeV observations of gamma-ray bursts

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PoS(Texas 2010)163Modeling GeV Observations of Gamma-ray BurstsRudy Gilmore∗SISSA - Astrophysics Sector - Via Bonomea 265 - 34136, Trieste - ItalyE-mail: rgilmore@sissa.itAurelien BouvierSanta Cruz Institute for Particle Physics, University of California, Santa Cruz, CA 95064, USANepomuk OtteSanta Cruz Institute for Particle Physics, University of California, Santa Cruz, CA 95064, USAJoel R. PrimackDepartment of Physics, University of California, Santa Cruz, CA 95064, USAFermi has shown GRBs to be a source of>10 GeV photons. We present an estimate of the detec-tion rate of GRBs with the future Cherenkov Telescope Array (CTA). Our predictions are basedon the observed properties of GRBs detected by Fermi, combined with the spectral propertiesand redshift determinations for the bursts population by instruments operating at lower energies.We develop two model for high energy prompt and early afterglow emission, and show how theprobability of detection is affected by instrument effective area, response time, and energy thresh-old. While detection of VHE emission from GRBs has eluded ground-based instruments thus far,our results suggest that ground-based detection may be within reach of CTA, though detectionswould be infrequent even with prompt followup to all valid satellite triggers. We estimate a rateof one GRB every 2 – 3 years based on the trigger rate from the Swift satellite, provided that nospectral softening or cutoff features below 100 GeV exist ina significant number of GRBs. Sucha detection would help constrain the emission mechanism of gamma-ray emission from GRBs.Photons at these energies from distant GRBs are affected by the UV-optical background light, anda ground-based detection could also provide a valuable probe of the Extragalactic BackgroundLight (EBL) in place at high redshift.25th Texas Symposium on Relativistic Astrophysics - TEXAS 2010December 06-10, 2010Heidelberg, Germany∗Speaker.c© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licen. http://pos.sissa.it/PoS(Texas 2010)163Modeling GeV Observations of GRBs Rudy Gilmore1. IntroductionThe observation of gamma-ray bursts (GRBs) with ground-based imaging atmospheric Cherenkovtelescopes (IACTs) has been a tantalizing possibility in recent years. Powerful>10-meter telescopearrays such as H.E.S.S., MAGIC, and VERITAS have come onlinein the last decade, and satellitedetectors such as Swift are capable of providing the necessary localization of events within sec-onds. Despite major campaigns to respond to satellite burstalerts at all three of these instruments(e.g., [1, 2, 3]), no conclusive detection of a GRB with an IACT has yet been made. However,observations of GRBs with the LAT instrument on the Fermi satellite have provided new insightinto the emission of GRBs in the VHE band. Since its launch on June 11, 2008, Fermi LAT hasdetected GRBs at>100 MeV energies at a rate of about 10/yr. The highest energy detected photonshave had rest frame energies exceeding 90 GeV.In a recent paper [4] (GPP10), we addressed the possibility of detecting GeV-scale emissionfrom GRBs with the Fermi LAT and MAGIC telescopes. Using simple assumptions about the GRBrate and spectral extrapolation based on the Swift GRB population, this work predicted the numberof GRBs that could be detected per year, and the likely numberof photons events per backgroundfor each case. GPP10 predicted the Fermi LAT to have a detection rate of 3-4 GRBs/yr above10 GeV per year, a rate that was matched well in the first year oftelescope operations, but mayhave since proven to be an overestimate. The detection rate for MAGIC, ignoring instrumentalbackground, was calculated to be 0.2-0.3 events per year, afte somewhat optimistic assumptionswere made about the telescope response time to satellite burst triggers. While the rate predicted forMAGIC was low, and may explain the lack of detections by the current generation of ground-basedinstruments, the predicted gamma-ray rates for a GRB detection near zenith were found to be upto thousands of counts in the lower energy range of the experiment within the prompt and earlyafterglow phases of the GRB, a large potential scientific payoff.Here, we describe a new calculation with a more sophisticated treatment of the spectral ex-trapolation to high energies and the telescope detection capabilities. We have also implemented thet−1.5 afterglow feature that has been seen in several GRBs by LAT [5], and may more realisticallyrepresent the signal visible at GeV energies. In the next section, we describe the ingredients andmotivation of our model for high energy emission.2. MethodsTo a large extent, the challenge of modeling GRBs arises out of the large variance in propertiesseen between bursts, and the lack of a simple model describing the radiative mechanism. In GPP10,our extrapolation of GRB emission to high energies was basedon the assumption that flux at VHEenergies could be described as a fixed fraction of the flux at lower energies. In that work, a fluxratio ofF(100 MeV−5 GeV)F(20 keV− 2 MeV)= 0.1was assumed, reflecting the typical ratio inferred from coinident BATSE/EGRET observations.While photon statistics for EGRET-observed GRBs were severely limited, LAT observations havenow given us an opportunity to reexamine our assumptions about these flux correlations.2PoS(Texas 2010)163Modeling GeV Observations of GRBs Rudy Gilmore-8 -7 -6 -5 -4 -3Log Fluence [20 keV - 2 MeV] (erg/cm^2)050100150200250NFigure 1: Left: Histogram of total fluence in the BATSE energy range for our sample of GRBs.Right: Theredshifts determined for Swift GRBs. The dashed line shows the fi used in this work.In this work, we have turned to the large sample of GRBs available from the BATSE catalog,providing the GRB fluence distribution and Band [6] spectralfits used in our analysis which webriefly describe in this section. The redshift distributionf GRBs is assumed to follow that of theSwift GRB population. Figure 1 shows input distributions for fluence and redshift used in our work.Attempting to build a sample of GRBs for analysis from populations of two different instrumentswill necessarily introduce biases. These biases will be studied in a upcoming publication andincluded amongst a comparison of different populations. Our calculation includes the impact ofattenuation by UV-optical background photons on GRB emission using the fiducial model of [7].2.1 Spectral extrapolationEach of the 4 bright GRBs seen by LAT above 10 GeV shows differing behavior. GRB080916C, the first such detection by LAT (seen about 3 months after l unch), was found to bewell-described in all time bins by a continuation of the Bandfunction determined at GBM en-ergies [8]. Separate spectral components from the Band function were found to be required tomatch the GeV-scale emission of the 3 other brightest GRBs inthe LAT catalog, long-durationGRBs 090902B and 090926, and short burst 090510. We have therefor considered two methodsof extrapolating the lower energy emission to higher energies in this work.As a minimal model, we consider the visibility predicted forGRBs at high energy withoutany significant deviation from the Band fit. In this model, labeled ‘bandex’ below, the high-energyspectrum is simply a continuation of the Band spectra determined at lower energy. The high energynormalization is therefore determined by the Band functionpeak energy, normalization, and theupper energy indexβ , which continues to GeV energies. We have enforced the requirement thatβnot be harder than -2, and the bursts in the sample with harderspectra are reset to this value.In the fixed-parameter (“fixed”) model, we make the assumption hat the fluence betweenBATSE (20 keV to 2 MeV) energies and GeV-scale (100 MeV to 10 GeV) nergies can be de-scribed by a single ratio. We use here a flux ratio of 0.1, whichis well supported by observationsof GBM-LAT observations of long-duration GRBs [11]. The spectral index at high energies is setto -2, consistent with the mean value for EGRET GRBs of -1.95 [12, 13], and near the center ofthe distribution for LAT-detected events [5]. Both of thesevalues are quite similar to the prompt3PoS(Texas 2010)163Modeling GeV Observations of GRBs Rudy GilmoreFigure 2: The effective area functions used in this work. Solid green is the MAGIC effective area withstandard cuts [9], and the dashed green line is the sum trigger implementation [10]. The two dotted blackcurves are the effective area functions used in this work, denoted CTA realistic (lower) and CTA optimistic(upper).emission assumptions used in GPP10. In general, this model requires a significant departure fromthe extrapolated Band function, and implies the appearanceof a separate high-energy spectral com-ponent.2.2 Telescope PropertiesAs many of the properties of the CTA are indeterminate at the tim of writing, we have reliedon the design concept for the array described in [14], as wellas reasonable extrapolations fromthe current generation of IACTs, particularly the MAGIC telescope. Our assumptions for realisticand optimistic effective area functions of CTA, shown in Figure 2, are based on configuration E,which assumes a central cluster of four 24-meter class telescop that determine the low-energysensitivity of the instrument. Sensitivity at energies above a few hundred GeV, which is providedby more dispersed arrays of 12- and 7-meter class instruments, is not crucial to our results here, asmost GRBs will occur at redshifts for which emission at thesen rgies is strong attenuated by theEBL.The transient and random nature of GRB emission represent thmain difficulty in detectingemission from these sources. The satellite localization time of the event, transmission of the data tothe ground, and slew time for the IACT all contribute to a total delay time for the commencementof observation. The localization time is dependent on the instrument and brightness of the GRB,but times of< 15 sec are typical, and the transmission time is expected to be nearly instantaneous[15]. The largest class of telescopes in CTA, which provide coverage at the crucial low energies,are expected to have a slew time of 20 to 30 seconds. As a baseline assumption, we assume a totalresponse time of 60 seconds in this work.3. Results and DiscussionThe GRB detection capabilities of the CTA can be described asthe product of two independentfactors: the detection efficiency, or probability that a randomly-selected GRB from our populationoccurring within the field-of-view of the telescope produces a detectable signal, and the rate atwhich the telescope is able to respond to triggers from satellite instruments within that field of4PoS(Texas 2010)163Modeling GeV Observations of GRBs Rudy GilmoreFigure 3: Left: The integral distribution of sigma values (significance of detection) for GRBs in our popula-tion. The solid line is for the direct extrapolation of Band functions (‘bandex’ model), from the distributionseen in BATSE GRBs, and the broken line is for the ‘fixed model’, using parameters described in the lastsection.Right: The integral distribution of counts above background, in the timescale bin with maximumsigma for each GRB that is detected using the criteria discussed in the text.view. Our modeling of the former is done by simulating observations from the population of GRBsdescribed in the previous section. For each GRB, we determinthe integrated photon counts andexpected background counts on timescales varying from 1 to 104 sec. The significance of thedetection is then calculated using the procedure describedin [16]. The GRB is then assumed to bedetected if the significance (σ ) is higher than 5 and at least 10 photons were seen above backgroundin at least one timescale bin.In Figure 3, we show results for an analysis done for a field of view θzenith < 60 deg, i.e.,assuming the GRB occurs randomly on the sky within 60 deg of zenith. The curves in each plotare the integral probability distribution for the significance of the recorded gamma-ray signal, andthe number of photons above background.This baseline model predicts a detection efficiency of GRBs of 11% and 18% in the ‘bandex’and ‘fixed’ models, respectively, for the realistic effective area function ( Figure 2) and 14% and26% for the optimistic case. Corresponding numbers for the MAGIC standard cuts effective areaare found to be 4.8% and 6.8%. While these two models do predict somewhat different distribu-tions in terms of significances for recorded signal and absolute photon counts, the predictions fordetection efficiency using our above criterion (Nγ ≥ 10;σ ≥ 5) differ by less than a factor of 2.In the first panel of Figure 4, we show the overall impact of parameterTdelay on detectionefficiency, for the two effective area curves shown in Figure2. The impact of VHE observationdelay time due to GRB localization and telescope slew time isdependent on the assumed modelfor the GRB lightcurve at these energies, which we have modeled here as at−1.5 decay. In theright-hand side of Figure 4, we show how a higher value of the tel scope energy threshold thanthe 20 GeV assumed above would influence the detection efficiency. Effective area functions areassumed here to have the same shape as presented in Figure 2, bt with a shift to higher energy by aconstant factor, and the delay time set to 60 s. As discussed in the introduction, GRB observationsare strongly affected by spectral cutoffs due to extragalactic background light, and raising thetelescope threshold energy reduces the redshift range overwhich GRBs are detectable. Detection5PoS(Texas 2010)163Modeling GeV Observations of GRBs Rudy GilmoreFigure 4: The effect on detection efficiency of varying instrument parameters.Left: The detection ratevs. observation delay time (Tdelay). The thick solid black and dashed blue lines are predictions from ourbandex and fixed model, respectively, for the ‘realistic’ effective area function. Thinner grey and cyanlines show the corresponding results using the ‘optimistic’ effective area.Right: The effect on the overalldetection efficiency of raising the energy threshold of eachof our assumed effective area functions (Figure2) from their initial values of 20 GeV.efficiency is seen here vary strongly with energy threshold,f r both spectral extrapolation models.An approximate prediction for the trigger rate can be easilycalculated using the alert ratefrom satellite instruments. The Swift satellite has historically observed GRBs at a rate of about95/yr [17]. With a 10% duty cycle and a correction for the anti-solar bias present in Swift alerts(see discussion in [4]), a rate of∼2 GRBs per year within 60 degrees of zenith can be estimated.Our results for the realistic CTA effective area function suggest that a diligent GRB observationcampaign could detect GRBs at a rate of one every 2–3 years (0.36 and 0.60 yr−1 for the bandexand fixed models), with great scientific impact. We note that te presence of a GeV-scale spectralcutoff, which we have not considered here, could reduce thisrate significantly. Another upcomingexperiment which could provide well-localized alerts in real time is the SVOM satellite [18], whichis expected to detect GRBs at nearly the same rate as Swift, though the detected GRBs could bebiased towards a softer, high redshift population, and may therefore be more difficult to detect athigh energies.In this proceeding we have described a method for determining the detection probability ofGRBs with ground-based IACT instruments. An upcoming publication will include a detailedpresentation of our model and results for the CTA experiment, as well as a careful test of our modelagainst the GRB rate seen by Fermi LAT and upper limits set by current generation IACTs. Alertsfrom other satellite instruments, including Fermi GBM and the upcoming SVOM experiment, couldcontribute to the trigger rate and will be considered as well.6PoS(Texas 2010)163Modeling GeV Observations of GRBs Rudy GilmoreAcknowledgmentsRCG acknowledges a research fellowship from the SISSA Astrophysics Sector. RCG and JRPacknowledge Fermi Gamma Ray Telescope Theory grants.References[1] F. Aharonian et al.,HESS observations ofγ-ray bursts in 2003-2007, A&A 495, 505–512 (2009)[2] J. Albert, et al.,MAGIC Upper Limits on the Very High Energy Emission from Gamma-Ray Bursts,ApJ667, 358–366 (2007)[3] D. Horan,Observations of Gamma-ray Bursts with VERITAS and Whipple, in International CosmicRay Conference3, 1107–1110 (2008)[4] R. C. Gilmore, F. Prada, and J. Primack,Modelling gamma-ray burst observations by Fermi andMAGIC including attenuation due to diffuse background light, MNRAS402, 565–574 (2010)[5] G. Ghisellini, G. Ghirlanda, L. Nava, and A. Celotti,GeV emission from gamma-ray bursts: aradiative fireball?, MNRAS403, 926–937 (2010)[6] D. Band et al.,BATSE observations of gamma-ray burst spectra. I - Spectraldiversity, ApJ413,281–292 (1993)[7] R. C. Gilmore, P. Madau, J. R. Primack, R. S. Somerville, and F. Haardt,GeV gamma-ray attenuationand the high-redshift UV background, MNRAS399, 1694–1708 (2009)[8] J. Greiner et al.,The redshift and afterglow of the extremely energetic gamma-ray burst GRB080916C, A&A 498, 89–94 (2009)[9] J. Albert et al.,VHEγ-Ray Observation of the Crab Nebula and its Pulsar with the MAGIC Telescope,ApJ674, 1037–1055 (2008)[10] M. Rissi et al.,A New Sum Trigger to Provide a Lower Energy Threshold for the MAGIC Telescope, inIEEE Transactions on Nuclear Science56, No. 6, 3840 (2009)[11] C. D. Dermer,First Light on GRBs with Fermi, ArXiv:1008.0854.[12] B. L. Dingus,EGRET Observations of> 30 MeV Emission from the Brightest Bursts Detected byBATSE, Ap&SS231, 187–190 (1995)[13] T. Le, and C. D. Dermer,Gamma-ray Burst Predictions for the Fermi Gamma Ray Space Telescope,ApJ700, 1026–1033 (2009),ArXiv:0807.0355.[14] The CTA Consortium,Design Concepts for the Cherenkov Telescope Array, ArXiv:1008.3703[15] D. Bastieri et al.,The MAGIC Telescope and the observation of Gamma Ray Bursts, Nuovo Cimento CGeophysics Space Physics C28, 711 (2005),[16] T. Li, and Y. Ma,Analysis methods for results in gamma-ray astronomy, ApJ272, 317–324 (1983)[17] N. Gehrels, E. Ramirez-Ruiz, and D. B. Fox,Gamma-Ray Bursts in the Swift Era, ARA&A47,567–617 (2009)[18] D. Götz et al.,SVOM: a new mission for Gamma-Ray Burst Studies, in American Institute of PhysicsConference Series1133, 25–30 (2009)7

Modeling GeV Observations of Gamma-ray Bursts

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