---
abstract: 'Based on the experience gained during the four and a half years of the mission, the [*Fermi*]{}-LAT collaboration has undertaken a comprehensive revision of the event-level analysis going under the name of [[[`P`ass 8]{}]{}]{}. Although it is not yet finalized, we can test the improvements in the new event reconstruction with the special case of the prompt phase of bright Gamma-Ray Bursts (GRBs), where the signal to noise ratio is large enough that loose selection cuts are sufficient to identify gamma-rays associated with the source. Using the new event reconstruction, we have re-analyzed ten GRBs previously detected by the LAT for which an x-ray/optical follow-up was possible and found four new gamma rays with energies greater than 10 GeV in addition to the seven previously known. Among these four is a 27.4 GeV gamma-ray from GRB 080916C, which has a redshift of 4.35, thus making it the gamma ray with the highest intrinsic energy ($\sim$147 GeV) detected from a GRB. We present here the salient aspects of the new event reconstruction and discuss the scientific implications of these new high-energy gamma rays, such as constraining extragalactic background light models, Lorentz invariance violation (LIV) tests, the prompt emission mechanism and the bulk Lorentz factor of the emitting region.'
author:
- 'W. B. Atwood, L. Baldini, J. Bregeon, P. Bruel, A. Chekhtman, J. Cohen-Tanugi, A. Drlica-Wagner, J. Granot, F. Longo, N. Omodei, M. Pesce-Rollins, S. Razzaque, L. S. Rochester, C. Sgrò, M. Tinivella, T. L. Usher, S. Zimmer'
bibliography:
- 'pesc0504.bib'
title: 'New Fermi-LAT event reconstruction reveals more high-energy gamma rays from Gamma-ray bursts'
---

Introduction {#sec:intro}
============

The Large Area Telescope (LAT) on-board the [*Fermi*]{} Gamma-Ray Space Telescope is a pair-conversion telescope designed to detect gamma rays above $\sim$20 MeV. The instrument is comprised of three subsystems acting in synergy to identify and characterize gamma-ray interactions: a silicon tracker-converter (TKR), a hodoscopic electromagnetic calorimeter (CAL) and a segmented anti-coincidence detector (ACD). By design, the TKR subsystem divides into two distinct sections: *front* and *back*—the latter featuring six times thicker conversion foils. Since these two sections are notably different from the standpoint of the angular resolution and the contamination from misclassified cosmic rays, in the following we shall analyze separately front- and back- converting candidate gamma rays. We refer the reader to @LATPaper for further details on the LAT.

Defining the event classes used for high-level scientific analysis is a complex process involving many different steps: the event reconstruction, the adjudication of the event energy and direction and the final event classification. In the following we shall refer to this process as the *event-level analysis*. The pre-launch event-level analysis was solely based on Monte Carlo simulations of the instrument performance and its particle environment—though it is worth emphasizing that a significant effort was put into validating such simulations [see, e.g.: @baldini:190]. The event selection has been periodically updated to reflect the constantly improving knowledge of the detector and the environment in which it operates. [[[`P`ass 7]{}]{}]{} [@P7Paper], released in August 2011, represents the latest major iteration of this incremental process.

In parallel with the development of [[[`P`ass 7]{}]{}]{}, the LAT collaboration has undertaken a coherent long-term effort to develop [[[`P`ass 8]{}]{}]{}, aimed at an extensive revision of the entire event-level analysis [@p8proceedings]. Recovering the effective area lost due to residual signals from out-of-time cosmic-ray events (*ghosts* hereafter), was the original and main motivation for this effort. As we shall see in the following, the scope of this development has substantially expanded along the way.

The full event-level analysis for [[[`P`ass 8]{}]{}]{} is currently under development. Therefore we cannot yet characterize its improvements in terms of instrument response functions. We can, however, test the improvements in the new event reconstruction by systematically searching for events not previously recognized as gamma rays during the prompt phases of bright Gamma-Ray Bursts (GRBs) for which the signal to noise is large enough that loose selection cuts on quantities measured to classify events are sufficient to identify gamma rays associated with the source.

In Section \[sec:recon\] we briefly review some aspects of the LAT event reconstruction, with emphasis on the modifications being introduced in [[[`P`ass 8]{}]{}]{}. In Sections \[sec:selection\] and \[sec:results\] we discuss the analysis underlying the search for new high-energy gamma rays and the results of this search. Finally, in Section \[sec:discussion\] we discuss the implications of these newly-found high-energy gamma rays.

[lcc]{} GRB 080916C & 4.35 & $48{\fdg}8$\
GRB 090323 & 3.57 & $57{\fdg}2$\
GRB 090328 & 0.74 & $64{\fdg}6$\
GRB 090510 & 0.90 & $13{\fdg}6$\
GRB 090902B & 1.82 & $50{\fdg}8$\
GRB 090926 & 2.11 & $48{\fdg}1$\
GRB 091003 & 0.90 & $12{\fdg}3$\
GRB 091208B & 1.06 & $55{\fdg}6$\
GRB 100414A & 1.37 & $69{\fdg}0$\
GRB 110731A & 2.83 & $3{\fdg}4$\
\[tab:grbs\]

Event reconstruction {#sec:recon}
====================

A detailed description of the LAT event reconstruction is beyond the scope of this paper. In the following we shall only give a brief description of the development being implemented in the context of [[[`P`ass 8]{}]{}]{} that is relevant for the analysis presented here. We refer the reader to @p8proceedings for more details.

Tracker reconstruction {#subsec:tkr_recon}
----------------------

High-energy gamma-ray interactions in the CAL tend to generate *backsplash* in the lower portion of the TKR, i.e, randomly hit strips due to secondary particles that have no relation to the trajectory of the original gamma ray. For back-converting events, and especially at large incidence angle, it is not uncommon for this backsplash to represent the vast majority of the TKR hits.

The [[[`P`ass 6]{}]{}]{}/[[[`P`ass 7]{}]{}]{} TKR reconstruction is based on a track-by-track *combinatoric* pattern recognition—seeded by the CAL information when available. As such, it is subject to confusion in backsplash-dominated events, particularly if the initial position and direction estimates from the CAL are not accurate. These features combine to produce two main effects: (i) the loss of events where the TKR reconstruction fails to find any tracks, and (ii) the migration of events from the core of the point-spread function (PSF) to the tails because of poorly reconstructed tracks.

In [[[`P`ass 8]{}]{}]{} we introduced a *global* approach, largely decoupled from the CAL reconstruction, which looks at the gamma-ray conversion as a pre-shower process and attempts to model this process by linking hits together into one or more tree-like structures. The individual tracks are then extracted from these structures and fitted. This new pattern recognition proved to be significantly more efficient at finding tracks and more robust in terms of pointing accuracy. Tests with Monte Carlo simulations and flight data show that the new TKR pattern recognition has the potential to provide a 15–20% increase of the high-energy acceptance, with even larger improvement in the off-axis effective area, especially for photons converting in the lower part of the TKR.

Calorimeter reconstruction {#subsec:cal_recon}
--------------------------

The [[[`P`ass 6]{}]{}]{}/[[[`P`ass 7]{}]{}]{} CAL reconstruction treats the energy deposit in the CAL as a monolithic entity, grouping all the crystals with greater than 4 MeV energy deposited together. Residual ghost signals in the CAL away from the gamma-ray shower can result in such a large lever arm in the moments analysis used to derive the shower direction that they can introduce substantial errors in the measurement of the centroid and direction of the shower itself. Since the matching in event position and direction between the TKR and the CAL constitutes an important input to the background rejection, this is actually one of the main mechanisms for the ghost-induced loss of effective area at high energy.

In [[[`P`ass 8]{}]{}]{} we introduced a clustering stage, based on a Minimum Spanning Tree algorithm, which proved to be effective in separating the genuine gamma-ray signal from the ghost one. In addition, the 3D shower profile fit, which is our primary energy reconstruction method at high energy, was substantially improved. While the objective of this part of the work was to extend the energy reach of the LAT above 1 TeV the new method proved to provide an approximately 10% improvement in the energy resolution over the entire energy and inclination angle range.

ACD reconstruction {#subsec:acd_recon}
------------------

The basic purpose of the ACD reconstruction is to match tracks in the TKR and hits in the ACD to find reasons to classify an event as a charged particle. The most significant improvement in the ACD reconstruction we introduced in [[[`P`ass 8]{}]{}]{} was to propagate the full covariance matrices associated to the TKR tracks to the ACD surfaces—i.e., effectively we now measure the distances between tracks and ACD hits in terms of measurement uncertainties rather than absolute lengths.

[lccccccccc]{}\
\
243215785–2033380 & 16.545 & back & 13.2 & 12.4 & 0.09 & 0.11 & 1.000 & Diffuse\
243215785–2075096$^\star$ & 40.509 & back & - & 27.4 & - & 0.07 & 1.000 & -\
\
263605997–3472705 & 0.828 & front & 31.3 & 29.9 & 0.09 & 0.08 & 0.999 & Transient\
\
273579835–4719473 & 11.671 & front & 11.2 & 11.9 & 0.21 & 0.07 & 0.999 & Transient\
273579835–4724519$^\star$ & 14.166 & back & 14.2 & 14.2 & 2.61 & 0.11 & 0.980 & -\
273579835–4748164$^\star$ & 26.168 & back & - & 18.1 & - & 0.11 & 0.999 & -\
273579835–4778868 & 42.374 & front & 8.9 & 12.7 & 0.03 & 0.04 & 0.999 & Diffuse\
273579835–4784978 & 45.608 & front & 12.5 & 15.4 & 0.07 & 0.10 & 0.995 & Diffuse\
273579835–4852498 & 81.746 & back & 33.4 & 39.9 & 0.78 & 1.77 & 0.998 & Transient\
\
275631595–173595 & 24.835 & front & 19.6 & 19.5 & 0.05 & 0.09 & 0.999 & Diffuse\
\
292903615–2268542$^\star$ & 33.365 & front & 29.8 & 29.7 & 7.64 & 0.16 & 0.999 & -\
\[tab:events\_table\]

Data selection {#sec:selection}
==============

Among the bursts in the First LAT GRB catalog [@GRBCatalog], we concentrate on the ten GRBs for which an x-ray/optical follow-up (and therefore a measurement of the redshift) was obtained (see Table \[tab:grbs\] for a listing of the GRBs used). The typical localization error for these bursts is negligible compared with the event-by-event direction accuracy of the LAT and, for all practical purposes, we can consider the localizations measured in the optical or X-ray afterglows as the true source positions when defining the region of interest (ROI). We further refine our sample by considering only energies greater than 10 GeV, where the width of the core of the LAT PSF is close to its asymptotic high-energy limit. It is important to stress here that analysis described in @GRBCatalog was done using the [[[`P`ass 6]{}]{}]{} version of the gamma-ray data (and the associated `P6_V3_TRANSIENT` IRFs), rather than the reprocessed [[[`P`ass 7]{}]{}]{} data made available in August 2011. However, the event reconstruction between [[[`P`ass 6]{}]{}]{} and [[[`P`ass 7]{}]{}]{} remained essentially unchanged and therefore this is largely irrelevant for the purpose of this paper.

For each GRB we reprocessed all the available data within 90 s from the trigger time using the [[[`P`ass 8]{}]{}]{} event reconstruction available at the time of writing. We select gamma-ray candidates by requiring that the reconstruction find at least one track and that this track extrapolates to more than 4 radiation lengths of active material in the CAL (this helps avoiding poorly reconstructed events). In addition, we use the ACD to remove *likely* charged-particle events by requiring that the track-tile association most likely to veto the event is incompatible with being generated by a minimum ionizing particle. Note that the event selection used here does not include any requirement on the quality of the direction/energy reconstruction.

The choice of the ROI is dictated by the need to minimize the amount of solid angle over which we integrate the background of residual (mis-classified) cosmic rays while at the same time retaining a reasonable efficiency for well-reconstructed gamma rays. For each GRB we used a circular ROI around the nominal source position with a radius of $0\fdg6$ for front-converting and $1\fdg2$ for back-converting events. It is worth noting that, while these are comparable with the PSF 95% contaiment radii for the cleanest [[[`P`ass 6]{}]{}]{}/[[[`P`ass 7]{}]{}]{} event classes, based on Monte Carlo simulations we estimate that the actual containment level for the back-converting events passing our loose selection cuts is only about 80%, so that the ROI cut has a significant impact on the event topology of our sample (i.e., it plays a role in selecting well-reconstructed events).

The expected rate of background events passing these basic selection criteria can be estimated from the flight data by sideband subtraction[@P7Paper] using an annulus around the source position and rescaling the number of counts to the solid angle subtended by the original ROI. As the level of charged-particle background varies across the [*Fermi*]{} orbit, the results are slightly different for each individual GRB, but on average we expect $\sim 0.1$ cosmic-ray events passing our basic selection cuts within each of the 90 s time windows.

Results {#sec:results}
=======

The First LAT GRB catalog includes seven candidate gamma rays with energies greater than 10 GeV associated with the ten GRBs considered here; in the reprocessed version of the data we find four additional (previously misreconstructed) events passing our selection criteria. In Table \[tab:events\_table\] we summarize the basic properties of the four new gamma rays together with the seven previously known ones. All of the seven aforementioned gamma-ray candidates pass our loose selection cuts (and their topologies are highly gamma-ray-like). However one of them (a $\sim33$ GeV event from GRB 090902B) is reconstructed as being marginally outside our ROI. While this is not entirely surprising (the quality of the direction reconstruction for this particular event is fairly poor both in the [[[`P`ass 6]{}]{}]{} and in the [[[`P`ass 8]{}]{}]{} versions of the event-level analysis), assessing the actual probability for this event to be associated with the GRB in the context of any of the actual [[[`P`ass 8]{}]{}]{} event classes will only be possible once the definitions of the classes are frozen and the corresponding response functions defined.

It is interesting to note how the mechanisms through which these events are recovered tie to the problematic aspects of the LAT event reconstruction outlined in Section \[sec:recon\]: two of them had no tracks in [[[`P`ass 6]{}]{}]{}, one was significantly mis-tracked (to more than $7^\circ$ off the source) and the last one was compromised by a ghost cluster in the CAL. We would like to stress here that the [[[`P`ass 8]{}]{}]{} event reconstruction is in its final phase; therefore we are confident that the basic topological properties of these four new photons will not vary significantly and that no additional photons will be found in the same 90 s interval explored in this work.

Table \[tab:events\_table\] shows how the preliminary [[[`P`ass 8]{}]{}]{} event selection described in @p8proceedings assigns a fairly high value for the measure of gamma-ray probability $p_{\rm all}$ to all the eleven gamma-ray candidates considered here. While this is an uncalibrated quantity with no *direct* physical meaning (and it might very well change in future iterations of the [[[`P`ass 8]{}]{}]{}event-level analysis) we find that the fraction of background events with such a high value of $p_{\rm all}$ is of the order of $10^{-3}$. This is effectively a multiplicative factor for the $\sim 0.1$ Hz rate of background events quoted in Section \[sec:selection\].

Finally, we note that most of the events in the table have angular distances to the nominal source position much smaller than the radius of our ROI. Under the reasonable assumption that the background is approximately isotropic in our $\sim 1^{\circ}$ circle, we would expect background events to be preferentially near the edge of the ROI (just because it subtends a larger solid angle).

We estimated the increase in effective area over the [[[`P`ass 6]{}]{}]{} `TRANSIENT` class expected for our selection[^1] by means of a gamma-ray Monte Carlo simulation similar to those that we routinely use for generating effective area tables. Between 10 and 30 GeV this improvement is of the order of $\sim 10\%$ at $50^\circ$ off-axis angle and reaches $\sim 50\%$ at $70^\circ$. Note that the choice of off-axis angles corresponds to those of the GRBs from which we recovered the four new gamma rays. Though the small statistics in our GRB event sample does not allow a validation of the increase in effective area, these factors are consistent with our findings. We also stress that the factors refer to the particular selection used in this analysis and do not represent the actual performance of any of the still-forthcoming [[[`P`ass 8]{}]{}]{} event classes.

Spectral analysis
-----------------

[lcccc]{} N$_{obs}$: Number of [[[`P`ass 6]{}]{}]{} events & & &\
with energy $>$ new [[[`P`ass 8]{}]{}]{} event & 0 & & 0\
Best fit value of the gamma ray index & 2.1 $\pm$ 0.09 & & 2.1 $\pm$ 0.4\
Expected number of events (N$_{exp}$) & 0.5 & 3.3 & 2.5 & 0.1\
Probability of observing N$_{obs}$ events & 0.60 & 0.13 & 0.21 & 0.88\
Probability of observing $>$N$_{obs}$ events & 0.40 & 0.63$^{\ast}$ & 0.71 & 0.12\
\[tab:events\]

As stated in Section \[sec:intro\], a final [[[`P`ass 8]{}]{}]{} event-level analysis is not yet available and therefore we cannot perform a spectral analysis. We can however estimate the probability to detect these high-energy gamma rays, given the spectral properties inferred from [[[`P`ass 6]{}]{}]{} analysis. Using `gtobssim`, we simulated 90 s observations of a very bright source located at the position of each of the three GRBs with new candidate gamma rays, using the best fitted values (from @GRBCatalog) for the index of the power-law spectrum. We normalized the output of the simulation to the observed number of [[[`P`ass 6]{}]{}]{} `TRANSIENT` counts above 100 MeV in a ROI of 5$^{\circ}$ in order to estimate the expected number of events, $N_{exp}$, above the energy of the new [[[`P`ass 8]{}]{}]{} gamma ray. Finally, we use the Poisson distribution to compute the probability of observing exactly $N_{obs}$ events when the number of expected events is $N_{exp}$. In addition, we calculate the probabilities of observing at least one additional gamma ray – or two additional gamma rays for GRB090902B – with an energy equal to or greater than those recovered with [[[`P`ass 8]{}]{}]{}. Results are reported in Table \[tab:events\].

We have studied the potential impacts that a spectral evolution during the considered time interval (90 s) may have on the resulting probabilities, P(N$_{exp}$,N$_{obs}$) by repeating the Monte Carlo simulation with a varying index for the spectral distribution of gamma rays. We find that the associated variation in the probability in the worst case[^2] is of the order of 10%–15%. The calculated probabilities suggest that the additional gamma rays are statistically consistent with the shape and intensity of the spectra derived using [[[`P`ass 6]{}]{}]{} data.

Discussion {#sec:discussion}
==========

Our most interesting finding is the $27.4\;$GeV gamma ray from GRB080916C that was detected $40.5\;$s after the burst onset. At a redshift of $z
\approx 4.35$ the measured energy corresponds to an energy of $\approx
147\;$GeV in the GRB cosmological rest frame. This is the highest intrinsic energy measured so far for a gamma ray from a GRB.

![image](figure1){width="0.5\linewidth"} ![image](figure2){width="0.5\linewidth"}

The high energy of the new gamma ray from GRB 080916C is very constraining for a possible origin from synchrotron radiation. A reasonable assumption for the acceleration time of the radiating electron, that it is at least the time it takes to complete one Larmor gyration[^3], would imply a minimum bulk Lorentz factor of the emitting region larger than $5000$. Similarly, the $29.7\;$GeV gamma ray from GRB 100414A at $z = 1.37$ would require $\Gamma\gtrsim 2300$ for a synchrotron origin. For GRB 090902B [@GRB090902B] at $z =1.822$ the two new gamma rays are less constraining than the $33.4\;$GeV gamma ray detected $82\;$s after the burst onset with [[[`P`ass 6]{}]{}]{}, after the end of the prompt emission, which implies $\Gamma\gtrsim 3200$ (making a synchrotron origin unlikely for the $33.4\;$GeV gamma ray due to its later arrival time).

Given the arrival time of $40.5\;$s after the burst onset of the $27.4\;$GeV gamma ray from GRB080916C, during interval d defined in  [@GRB080916C], the lower limit on $\Gamma$ due to intrinsic opacity to pair production is increased by only $15\%$ compared to the limit from the $13\;$GeV gamma ray observed in the same time interval, of $\Gamma_{\rm min}\approx 600$ for a simple one-zone model, or $\sim 3$ times lower than this for a more realistic self-consistent time-dependent model [@2008ApJ...677...92G; @Hascoet:2011gp].

Due to its later arrival time, the constraints that the new gamma ray from GRB080916C provides on linear ($n=1$) Lorentz invariance violation (LIV) are slightly weaker (by 15%) than the previously highest energy gamma ray from the same GRB (of energy $\approx 13.2\;$GeV detected at $t = 16.5\;$s after the GRB trigger time, which implied[^4] $\xi_1 = M_{\rm
QG,1}/M_{\rm Planck} > 0.11$). For a quadratic leading LIV term ($n=2$) it does slightly better with $M_{\rm QG,2} > 1.13\times 10^{10}\;{\rm
GeV}/c^2$, which is only $\approx 2.6$ times below the best limit from GRB 090510 [@2009Natur.462..331A]. The limits from the other new gamma rays are not as constraining.

A very interesting implication arises for the extragalactic background light (EBL), from the fact that a 27.4 GeV gamma ray has reached us from a fairly high redshift of $z \approx 4.35$, and was not attenuated (through pair production, $\gamma\gamma \to e^+e^-$) by the EBL. In particular, it is useful to compare the constraints that it provides to those from previously-detected gamma rays from GRBs [@GRBCatalog] and AGN [@2010ApJ...723.1082A], as illustrated in Figure \[fig:ebl\]. It is the most constraining gamma ray so far from a GRB (see Figs. 3 and 5 in @2010ApJ...723.1082A; notice in particular that Fig. 5 also applies to the newly-found $27.4\;$GeV from GRB080916C). Moreover, it is in fact comparable to or even slightly more constraining than the [*Fermi*]{}-LAT gamma rays from AGN (for most EBL models[^5] especially for $\tau = 3$ as shown in Figure \[fig:ebl\]).

In conclusion, the improvements in event reconstruction implemented in [[[`P`ass 8]{}]{}]{} promise to yield scientific gains, as illustrated in this work.

The *Fermi* LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT as well as scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States, the Commissariat à l’Energie Atomique and the Centre National de la Recherche Scientifique / Institut National de Physique Nucléaire et de Physique des Particules in France, the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK) and Japan Aerospace Exploration Agency (JAXA) in Japan, and the K. A. Wallenberg Foundation, the Swedish Research Council and the Swedish National Space Board in Sweden.

Additional support for science analysis during the operations phase is gratefully acknowledged from the Istituto Nazionale di Astrofisica in Italy and the Centre National d’Études Spatiales in France.

[^1]: We included the effect of the ROI in our estimate by requiring, in addition to the preliminary Pass 8 event selection that we applied, that the angle between the true and reconstructed gamma-ray direction is smaller than the radius of the ROI itself.

[^2]: GRB080916C [@GRB080916C] is the GRB in our sample that shows the largest spectral variation, with a gamma ray index varying from 2.3 to 2.1 with an error of 0.09.

[^3]: This assumption implies a maximum electron Lorentz factor of $\gamma_{\rm max} =\sqrt{3e/\sigma_T B'}$ where $B'$ is the comoving (measured in the rest frame of the emitting plasma) magnetic field. The corresponding comoving typical synchrotron gamma ray energy averaged over an isotropic pitch-angle distribution is $E'_{\rm
    syn,max} = 3heB'\gamma_{\rm max}^2/(16 m_ec) = (27/64)m_ec^2/\alpha$, where $\alpha = e^2/\hbar c\approx 1/137$ is the fine structure constant. The corresponding observed energy is $E_{\rm syn,max} =
    E'_{\rm syn,max}\Gamma/(1+z)\approx 29.5(1+z)^{-1}(\Gamma/1000)\;$GeV. Therefore, a synchrotron origin for this gamma ray would imply $E_{\rm
    obs} \lesssim E_{\rm syn,max}$ or $\Gamma \gtrsim 2030 [(1+z)/3] (E_{\rm
    obs}/20\,{\rm GeV})$. The peak of the electron synchrotron spectral emissivity is $0.29$ times the value for $E_{\rm syn,max}$ used above, and using it would increase the limit correspondingly (by a factor of 1/0.29) to $\Gamma
    \gtrsim 7000[(1+z)/3](E_{\rm obs}/20\,{\rm GeV})$. Allowing the acceleration time to be as small as the time it takes to deflect the electron by one radian (which is quite extreme) lowers the limit by a factor of $2\pi$, to $\Gamma \gtrsim 323[(1+z)/3](E_{\rm obs}/20\,{\rm
    GeV})$. Combining such a short acceleration time with the factor of $0.29$ mentioned above leads to $\Gamma \gtrsim 1110[(1+z)/3](E_{\rm
    obs}/20\,{\rm GeV})$. Recently, @2012MNRAS.tmpL.529K have proposed a way to lower this limit by assuming two zones with significantly different magnetic field strength, where in the lower-field region electrons can be accelerated to high Lorentz factors, and then radiate energetic synchrotron gamma rays after crossing to the high-field region. This could in principle accommodate the production of $\gtrsim 100\;$GeV gamma rays with significantly lower bulk Lorentz factors.

[^4]: The limits we quote conservatively use the lowest values within the 1-$\sigma$ confidence intervals for the gamma ray energy (and the GRB redshift when relevant).

[^5]: A description of the different models is beyond the scope of this work; we refer the reader to the original works on the various EBL models
