The Multiwavelength Picture of GRB 221009A’s Afterglow

We present counts-level fits to the keV–GeV data of the early afterglow of the brightest gamma-ray burst detected to date, GRB 221009A. We discuss the complexity of the data reduction due to the unprecedented brightness and the location in the Galactic plane. We find the energy spectrum to be well described as a smoothly broken power law with a break around 10 keV and no indications for additional features towards GeV energies. An interpretation as synchrotron emission from forward-shock accelerated and subsequently cooled electrons yields three possible types of solutions: (1) a slow cooling solution with low magnetic fields (few percent of a Gauss) but poorly constrained minimum injected electron energy (<100 GeV), (2) a fast cooling solution with stronger magnetic fields (few percent to few Gauss) and minimum injected electron energy 10-100 GeV or (3) the transition between both regimes with low magnetic fields and minimum injected electron energy around 100 GeV. Limited statistics at GeV energies prevent conclusions extrapolating towards a cut-off or the onset of a new component at higher energies.


INTRODUCTION
The non-thermal afterglow emission of gamma-ray bursts (GRBs) constitutes a two-dimensional flux surface as a function of energy and time.In the energy dimension the cleanest observational window ranges from hard X-ray (keV) up to very-high-energy (VHE; >100 GeV) gamma-ray energies.In the VHE band and above, the absorption due to the extragalactic background light (EBL) limits spectral inference.From the soft X-ray down to infra-red bands, both photoelectric absorption and dust scattering also prohibit decisive conclusions, such that optical and UV data serve only as lower limits to the intrinsic source flux.We emphasise that the systematic uncertainty introduced by correcting for these exponential absorption effects is difficult to constrain.At even lower energies, i.e. from infra-red down to the radio band, the propagation becomes unhindered once again; however, an additional emission component, usually attributed to the reverse shock, appears to begin to dominate within this range, limiting the insight on the forward shock component.In the dimension of time, the afterglow's most informative data window lies at early times, starting with the clear onset of the afterglow.Towards later times the significance of the GRB signal over the background quickly drops due to the decaying light curves in combination with the limited sensitivity of GRB detection instruments.
GRB 221009A is the brightest gamma-ray burst detected to date.Its extensive multi-wavelength coverage promises a correspondingly large amount of new insights.Contrary to these expectations, the extraordinarily high flux and its location in the Galactic plane (latitude b = 4.3 degrees) led to additional systematic errors in several instruments, hindering the measurement of the GRB's flux.This is not only limited to the prompt emission phase (≲  0,GBM + 700 s, Lesage et al. 2023); for example its complex dust echos significantly ★ E-mail: marc.klinger@desy.dechallenge the determination of the afterglow X-ray spectrum up to more than 100 ks (e.g.Williams et al. 2023).
We focus thus on the early afterglow with contemporaneous data from keV up to GeV energies, in particular two time intervals around 4 ks and 22 ks after the trigger time of the Fermi Gamma-Ray Burst Monitor (Fermi-GBM).In both intervals the Swift X-ray Telescope (Swift-XRT; Burrows et al. 2005), Swift Burst Alert Telescope (Swift-BAT; Barthelmy et al. 2005) and Fermi Large Area Telescope (Fermi-LAT; Atwood et al. 2009) observations overlap temporally.
Several earlier works have already inferred spectral information on GRB 221009A in this energy window in temporal proximity.The Fermi-GBM data shows an afterglow component with an observed photon spectral index of   = −d log   /d log   ≈ 2 (40 keV-8 MeV), already shining through during low phases of the flaring prompt phase and turning more clearly into the afterglow after ∼ 700 s (Lesage et al. 2023;Zhang et al. 2023).At 1.5 ks GRB 221009A gets occulted by the Earth and at 4 ks only an energy flux level of    ≈ 10 −8 erg/(cm 2 s) at 10 keV is estimated via the Earth occultation technique (Lesage et al. 2023).Williams et al. (2023) find preference for a break around 7 keV with photon spectral indices   of 1.7 (before the break) and 2.2 (after the break) from a combined fit of Swift-XRT, Swift-BAT and the heavily absorbed Swift-UVOT data around 4.2 ks, when linking the spectral indices of a broken power law by 0.5.The residuals show a significant offset between Swift-XRT and Swift-BAT fluxes, highlighting the challenges of the Swift-XRT data in windowed timing (WT) mode (see Section S1 of the supplementary materials for details).The photon spectral index   above the break seems to be in agreement with the rough value of 2 determined from 3 energy bins (20-1220 keV, 5.1-25.7 ks) by Frederiks et al. (2023).Earlier observations (1.35-1.86ks) by GECAM-C (20 keV-6 MeV) show a photon spectral index of   ≈ 2.1, in agreement with their Earth occultation analysis (20-200 keV), although suggesting a harder value (1.6) above 200 keV (An et al. 2023).The combined analysis of Swift- XRT and Fermi-LAT in Laskar et al. (2023) suggests a break between the two instruments based on the time averaged photon spectral indices (  ≈ 1.6 − 1.9 for Swift-XRT,   ≈ 2.1 for Fermi-LAT), without specific information on the time interval or the data reduction in WT mode.Other works like Liu et al. (2023) and Stern & Tkachev (2023) also report photon spectral indices for Fermi-LAT of approximately   ≈ 2.1.GRB 221009A gained particular attention due to its detection by LHAASO at VHE energies (LHAASO Collaboration et al. 2023).Significant detection by the Water Cherenkov Detector Array (WCDA) is however limited to less than 3 ks and upper limits are not significantly constraining for the time windows we consider here.A power-law extrapolation of the light curve to 4 ks indicates a flux at the level of a few 10 −9 erg/(cm 2 s) with big uncertainties of an order of magnitude arising from low statistics and EBL absorption.Due to poor observational conditions, in particular bright moonlight, no other VHE telescopes detected GRB 221009A.
Commonly, these observations are interpreted in a one-zone radiation model coupled to fireball blast wave dynamics (for a review see e.g.Zhang 2018, and references therein).Applying this to GRB 221009A required departures from this simple picture, in various directions (Ren et al. 2023;Sato et al. 2023;Laskar et al. 2023;Gill & Granot 2023;O'Connor et al. 2023;Kann et al. 2023).
In order to clarify this emerging early afterglow spectrumnamely, a hard spectrum (1.6) up to a break at a few keV followed by a consistent softer spectral index (≳2) up to 10 GeV -and its compatibility with this one-zone standard model, we provide in this article a more comprehensive combined fit on the counts-level, using data from 0.6 keV up to 100 GeV.In particular, we give a short summary of our reduced afterglow model, the data reduction and the joint-fit spectral analysis procedure in section 2, present and discuss our results in sections 3 and 4 and conclude in section 5.

Afterglow model
The ultra-relativistic outflow of a GRB jet decelerates as it sweeps up material from the surrounding environment.A fraction of this swept up material is shock-accelerated to non-thermal energies and subsequently radiates away a part of its energy into the X-ray to gamma-ray energy bands.Our model is described in detail in Klinger et al. (2023) and we give a short summary of the relevant parts here.
Following simple energy conservation arguments (Blandford & McKee 1976), we estimate the self-similarly decelerating bulk Lorentz factor Γ of the outflow to be 34 (18) around 4 ks (22 ks), assuming an isotropic energy of  iso = 10 55 erg (Lesage et al. 2023) converted completely into radiation and a constant circum-burst density  up = 1/cm 3 .We emphasise the weak dependence on these parameters Γ ∝ ( iso / up ) 1/8 , which does not change dramatically for a wind-like density profile.We also assume that a fraction of the upstream ram pressure is converted to turbulent magnetic fields downstream (parameterised by   , see Klinger et al. (2023)).
During the particle acceleration process, the two competing energy loss processes for the electrons, namely adiabatic and radiative energy losses, collectively dictate the shape of the produced electron spectrum.We parameterise the latter as a smoothly broken power law with smoothness parameter   , and spectral indices based on the injected electron spectral index   corresponding to the slow/fast cooling regime (see Klinger et al. (2023) for the definitions of  min  , cb  ,  max  ).We note that we use the injection energy scale,  min  , as a free parameter, rather than the often adopted constant fraction parameters (e.g.Sari et al. 1996): the non-thermal particle number (  ) and energy injection (  ) rates (Although see van der Horst et al. 2014;Misra et al. 2021;Warren et al. 2015Warren et al. , 2018;;Ressler & Laskar 2017;Asano et al. 2020).In the results section, however, the corresponding constraint on   and   are provided.Furthermore, the parameter  controls the electron acceleration time -in units of the Bohm acceleration time -which, in turn, dictates the maximum electron and thereby eventually also synchrotron and inverse Compton photon energy.
The quasi-steady-state energy distribution of these electrons subsequently dictates the spectral energy distribution (SED) of the nonthermal emission from the GRB.For the treatment of the radiative emission, we use the reduced synchrotron-self-Compton (SSC) model of Klinger et al. (2023), within which both a single-component synchrotron model (reduced syn) as well as a two-component SSC model (reduced SSC) can be treated as subclasses.It reduces all the degenerate complexity of the normalisation of the two components of the photon spectrum to two parameters: 1) the normalisation of the synchrotron component  syn at an observed energy of 100 keV and 2) the relative factor of the inverse Compton component  IC , phenomenologically defined as the ratio of the maximum value of the energy flux spectra of both components.This source spectrum is then transformed to the observer's frame by assuming a point-like emission zone, an observation angle of 0 • and a redshift of  = 0.15.
In summary, we explore with our reduced syn model the parameters   ,   ,   ,  min  , ,  syn and in case of the reduced SSC model the additional parameter  IC (for priors see Section S4 of the supplementary materials).We fix  iso = 10 55 erg,  up = 1 cm −3 and  obs ≈ 4.8 (21.8) ks.

Swift-XRT
The Swift-XRT started observing GRB 221009A 3.3 ks after the Fermi-GBM trigger.As reported in Williams et al. (2023), the first 12 snapshots of XRT data, out to 89 ks post-trigger, were obtained in Windowed Timing (WT) mode, which is a fast (1.78 ms time resolution), 1D, readout mode, used to minimise the effects of pileup on the detected photons when a source is bright.
1D spatial profiles from the early WT observations indicated the presence of a strong dust scattering component, which was later seen as a set of expanding rings (i.e.dust scattering echos) in the 2D Photon Counting (PC) mode images.Compared to a regular point source, these rings add a significant, but intrinsically inseparable component to the 1D region used to extract the GRB signal for the two time periods covered here (3.9 − 4.5 ks and 21.6 − 22.1 ks; see Figure S1).By modelling the dust echo profile in WT mode, we have attempted to minimise its effect on the GRB spectral extractions and identified an appropriate background region for the later time interval (see Section S1 of the supplementary materials for details).
In addition to the effect of the dust rings, we model the observed GRB flux suppression due to photoelectric absorption, whose exponential nature introduces particularly large uncertainties at lower energies (≲ few keV).We use the conventionally adapted combination of an absorber close to the GRB and a small contribution of the Milky ways absorption ( H = 5.38 × 10 21 cm −2 ), as in Williams et al. (2023).

Swift-BAT
The Swift-BAT produces survey data when it is not triggering on a GRB.As outlined in Williams et al. (2023), we used the BatAnalysis python package1 (Parsotan et al. 2023) to download individual Swift-BAT survey data in the time windows 3907-4534s (4 ks) and 21.6-22.1 ks (22 ks) and process them to produce spectra in 8 energy bins from 14-195 keV (compare Section S2 of the supplementary materials).

Fermi-LAT
GRB 221009A became visible to Fermi-LAT during orbital windows of around 2 ks, being occulted by the Earth for a bit more than 3 ks in-between.The exact overlapping windows with Swift-XRT and Swift-BAT result in very low statistic for Fermi-LAT, such that we extend the temporal selection range for Fermi-LAT to the maximal visible windows, 4-6 ks and 21.2-22.5 ks.
Due to the systematic effects from energy dispersion, we select only photons with energies above 200 MeV (Fermi-LAT Collaboration 2018a).We limit our energy range to 100 GeV, whereas the highest detected photon energies are 7.8 GeV (3 GeV) for 4 ks (22 ks).
Motivated by the large point spread function at low energies, we include photons within a cone of 10°around GRB 221009A.We highlight its distance of less than 5°from the Galactic plane means that the Galactic diffuse background emission is non-negligible on these timescales.This limits our ability to reliably infer the spectral index in the Fermi-LAT energy range.We find that other background sources play no significant role (see Section S3 of the supplementary materials for details).

Joint-fit spectral analysis procedure
The joint-fit spectral analysis is based on the method described in Klinger et al. (2023).We define the likelihood L for each instrument on the counts level based on the corresponding suitable statistic: Poisson (4 ks) and C-stat2 (22 ks) for Swift-XRT,  2 for Swift-BAT, and PG-stat3 for Fermi-LAT.The instrument response function is incorporated via forward folding.To account for inter-instrumental cross-calibration uncertainties we add a constant floating norm of up to ±15% to each instrument (Madsen et al. 2017;Krimm et al. 2013;Fermi-LAT Collaboration 2018b).To account for the expected large background contribution of the dust features of 10-20% at 4 ks, we increase the range in this time window to a factor between 0.95 and 1.3 (see Section S1 of the supplementary materials).
Following a Bayesian approach, we furthermore assume flat priors (see Section S4 of the supplementary materials) to sample the parameters' posterior distributions and integrate the total evidence for model comparison via the Bayes factor.

RESULTS
We expect from single-instrument and combined-subset fits (see Section S5 of the supplementary materials for details) that the SED should roughly resemble a broken power law.This is based on a statistical preference for a break around 10 keV at 4 ks, while this is less clear for the 22 ks interval with lower statistics.At higher energies Swift-BAT and Fermi-LAT can be fitted together by a power law without statistical preference for a break, with photon spectral indices of ≈ 2.2 (4 ks) and ≈ 2.1 (22 ks).We note that the large uncovered MeV gap from 0.2-200 MeV and the large uncertainties of Fermi-LAT's spectral index complicate the exclusion of additional features in-between.
We proceed with the results obtained from a combined fit including all three instruments, in order to extract the spectral properties of this rough broken-power-law behaviour in the framework of our reduced syn model: The break energy, the indices below and above the break and a potential additional spectral feature in between Swift-BAT and Fermi-LAT.
We start by performing a combined fit using our reduced syn model with a single component ( IC = 0), our syn-only case.Motivated by the non-standard Swift-XRT background treatment, we perturb synonly case by releasing our assumption on the Swift-XRT effective area correction (more than 30%), the XRT-floating case (subsection 3.1).Finally, we allow for an additional SSC component ( IC > 0 in the reduced SSC) in the SSC case (subsection 3.2).
Figure 1 shows for each time bin (4 ks in blue and 22 ks in green) the 3 best-fit models with a 1-envelope and for the synonly case the corresponding residuals at the counts-level for all three detectors.The syn-only case's posterior distributions are given in supplementary materials (Section S6).The single instrument power law fits are added to the SED plot in grey to guide the eye.
The best fit shape of the syn-only case resembles the broken power law expectation with a break energy of a few keV and a photon spectral index of ≈ 2.2.

Perturbation 1: XRT-floating case (𝑁
Inspecting the residuals of Swift-XRT and Swift-BAT (Figure 1) as well as the posterior distributions of their cross-correlation uncertainty factors (Figure S2) indicates an increased effective area correction between them.The non-standard background treatment due to the dust ring pollution motivates us to explore in our XRT-floating case the effect on our results when we extend the Swift-XRT floating norm prior distribution to a shift of more than 30% downwards.Such a preference for large effective area corrections of up to a factor of 2 is not uncommon for bright GRB afterglows (see e.g.Klinger et al. (2023) for GRB 190114C).
We observe for 4 ks that the Swift-XRT data gets shifted down by a factor of 2 ± 0.3, while the correction factors for Swift-BAT and Fermi-LAT remain negligible (≈ 1).This results in a change of the spectral index above the break from   ≈ 2.3 − 2.2, corresponding to a change of the electron injection index from   ≈ 2.6 − 2.5.We emphasise that the uncertainty to this values is likely underestimated due to the systematic effects in the Swift-XRT analysis as well as the absorption model.For 22 ks, Swift-XRT requires a shift down by a factor of 2.2 ± 0.5 and the evidence for a break is less clear than at 4 ks.Additionally, the posterior distributions become multimodal and very broad, such that the systematic uncertainties from the Swift-XRT analysis are limiting the conclusions drawn from the syn-only case at 22 ks.
We conclude that an extended Swift-XRT floating norm enlarges mainly the uncertainty on the inferred spectral index of the electrons.

Perturbation 2: SSC case (𝑁 IC > 0)
An additional spectral component is expected for the case  IC > 0, becoming relevant at the highest energies.The ad-hoc assumption of Figure 1.Top: 1 envelope of intrinsic SED at 4 ks (blue) and 22 ks (green) for the cases: syn-only (  = 0, darkest), XRT-floating (  = 0 with extended floating norm factor for Swift-XRT, lowest at 10 keV) and SSC (  > 0, resulting in large uncertainties above 10 GeV).Grey butterflies correspond to single-instrument power law fits (compare Table S5).The blue line corresponds to the best fit SED and the blue dashed one shows the observed, absorbed best fit spectrum (dotted line) for 4 ks interval.Bottom: Counts-level comparison for the syn-only-case (blue dashed line from top panel) for each detector (Swift-XRT, Swift-BAT and Fermi-LAT) with corresponding residuals below.Floating norm factors for detectors ("const") and Fermi-LAT's galactic diffuse background template ("galdiff") correspond to default priors from syn-only-case.
acceleration at the Bohm rate ( = 1) results for both time intervals in a cut-off (the observed synchrotron burn-off) around a few GeV, where the Fermi-LAT counts become sparse.We investigate with this SSC perturbation the possibility that an IC component from an additional free parameter ( IC > 0) might dominate the Fermi-LAT observation by displacing the synchrotron cut-off to lower energies.
We find no preference for this behaviour.Instead, the only difference to the syn-only case's fit result is the additional uncertainty above a few GeV, see Figure 1.This visualises the limited power of the Fermi-LAT data to constrain an IC component.
We conclude that our combined fit is not sensitive to the onset of an additional IC component.

DISCUSSION
We discuss now the posterior distribution of the best fit scenarios, resulting at 4 ks in an apparent small uncertainty on the best fit values of   ,   and  min  .We examine the validity of these uncertainties in the following.In the reduced syn model, both, the break energy and the spectral index below (  < 10 keV) are driven by the combination of (i) the photoelectric absorption factor ( H in proximity to the GRB) and (ii) the intrinsic break determined by the interplay between magnetic field (  → cooling break energy) and minimum injected electron energy ( min  ).Note that we directly treat  min  as a fit parameter.
Focusing on the intrinsic break energy within the reduced syn model, the observed energy  b,obs  ≈ few keV can be matched by a break in the synchrotron component in three conceptually different solutions.They correspond to three different features in the electron spectrum: 1) slow cooling ( min  ≪  cb  ), i.e., a cooling break from the change from the dominance of adiabatic to synchrotron cooling; 2) fast cooling ( min  ≫  cb  ), i.e., a cooling tail in the electron spectrum or 3) their transition ( min  ≈  cb  ), i.e., a cut-off in the electron spectrum resulting in the low energy tail of the synchrotron spectrum of the lowest energy electrons transitioning to the synchrotron spectrum of the cooled electrons.
Figure 2 illustrates three representative cases for each regime, in terms of their electron (bottom) and photon (top) SEDs and shows the syn-only-case's posterior distribution of the corresponding parameters ( min  vs.   , on the left).Placing  b,obs  ∼ few keV restricts the parameter space to the two arms (boomerang), as is found for both time intervals (blue/green for 4 ks/22 ks).Note that we also provide a second x-axis and y-axis, to indicate the corresponding magnetic field strength and ratio between number and energy of upstream electrons converted into non-thermal particles, respectively 4 .We note that in particular the later mapping is based on multiple uncertain assumptions.
For all three solutions the photon spectrum above the break energy corresponds to the cooled electrons and is the same (  = −d log   /d log   = (   + 1)/2), whereas the spectral indices below differ: 4/3 for the transition solution, 1.5 for the fast cooling solution or (   + 1)/2 ≈ 1.7 (using an injected electron spectral index of   = 2.4).Despite the power-law spectral index of   ≈ 1.6 for Swift-XRT alone, we find from our combined fits a strong preference in the data for a very hard spectrum below a few keV (  ≈ 0 from a broken-power law fit), which limits the best fit parameters on the boomerang further into the lower-right corner, corresponding to the transition regime.
It is important to note in this context the strong effect (one order of magnitude at 1 keV) of the exponential absorption factor in this spectral regime below the break energy, as visible in the dotted line in Figure 1 showing the observed absorbed spectrum.
The interpretation of this hardening to discriminate between the three solutions is thus limited by the uncertainties of the absorption model, introduced by e.g. the chemical composition of the photoelectric model (see e.g.Dalton & Morris 2020;Valan et al. 2023).For heavily absorbed sources with large statistics like GRB 221009A, it becomes relevant to propagate this uncertainty into the likelihood evaluation.A quantitative evaluation of these uncertainties is additionally complicated by the non-standard background estimation as well as uncertainties in the instrument response from e.g.instrumental edges and aging effects and goes beyond the scope of this paper.
We thus conclude that an inferred limitation of the solution type to the transition regime in the 4 ks interval is not robust due to the underestimation of the above systematic uncertainties.
The inference of physical properties of the radiation zone from the observed break energy  b,obs  , however, depends strongly on the solution type (qualitatively similar for wind-like density profiles): Within the slow cooling solution, fixing the observed break position to the keV regime would effectively fix the comoving magnetic field to  ≈ 0.03 G,   → 10 −5 (for  up ≈ 1 cm −3 ).It is important to note that the steady state approximation is only accurate to a factor of order unity in this case.
On the other hand, the fast cooling solution is compatible with a large range of magnetic field values, up to a few Gauss.Here the dependence on the minimum injected electron energy  min  becomes dominant, placing it from 10 to 100 GeV.It is important to notice that in the fast cooling solution, in particular when approaching the transition solution,  b,obs  relates directly to the electron spectrum at the minimum injection scale, where the spectral shape is poorly understood.In particular the nature of the typically assumed steplike cut-on of the non-thermal electron spectrum is expected to be affected by the thermal population (see e.g. Warren et al. 2022), but commonly neglected.
In terms of the micro-physical parameters, the left side of the slow cooling arm with   ≪   requires the injection scale of the nonthermal electrons to be lower than the average proton energy (i.e. min  < (  − 2)/(  − 1)Γ   2 ≈ 10 GeV).This is in contrast to the typical values obtained from particle-in-cell simulations,   ≈ 3  (Marcowith et al. 2016, ch. 4), a result which better aligns with the fast cooling solution we find (  /  ≈ 3 − 10).It is also worth mentioning that for the right side of the figure ( min  ∼ 100 GeV), typical values of   ∼ 0.1 would require a value of  ∼ 0.01 (a percent of the electrons).However, effects like pair-loading of the upstream medium can significantly influence this ratio, preventing us from drawing strong conclusions on the microphysics (Grošelj et al. 2022).
Comparing our finding of   ≈ 2.2 − 2.3 to Williams et al. ( 2023) and the observational picture sketched in section 1, we find consistency.Modeling results in other works find consistent values of the spectral index of the electrons, spanning   ≈ 2.2 − 2.8, whereas the estimates for   ≈ 10 −1 − 10 −7 vary greatly (Ren et al. 2023;Sato et al. 2023;Laskar et al. 2023;Kann et al. 2023;Gill & Granot 2023;LHAASO Collaboration et al. 2023).In particular our results for the electron spectral index   help to constrain its value to 2.4-2.5.
Additionally, one could constrain a possible inverse Compton component using the LHAASO non-observation at 4 ks to  IC < 1.We highlight, that our findings for GRB 221009A are thus also consistent with, but not more conclusive than the picture emerging from GRB 190114C (Klinger et al. 2023) andGRB 190829A (H.E.S.S. Collaboration et al. 2021), such that the physical origin of the VHE afterglow observations can not be determined more clearly from this brightest GRB detected so far.

CONCLUSION
GRB 221009A was extraordinarily bright, which led to complications in the analysis of the data in several energy bands.Furthermore, its position close to the Galactic plane led to increased background levels which further broadened the systematic uncertainties.
Its SED from keV to GeV energies is in both time intervals (4 ks and 22 ks after  0,GBM ) well described by a smoothly broken powerlaw, with break energy  b,obs  ≈ few keV.The photon spectral index above the break is (  = −d log   /d log   = 2.2 − 2.3) with dominant systematic uncertainties driven by the Swift-XRT background estimation.For the same reasons the photon spectral index below the break is less clear (  ≈ 1.5 − 2).
Within our GRB spectral model, the inferred break energy  b,obs  ≈ few keV can have three possible interpretations.Either (1) as a slow cooling break, resulting in a weak magnetic field with only an upper limit on the minimum electron energy.Or (2) a fast cooling break, requiring a stronger magnetic field and a higher minimum Table 1.A summary of the constraints on key parameters for each of the three solutions of the energy break origin.
electron energy.Or (3) the transition between (1) and ( 2), requiring a weak magnetic field and a large minimum electron energy.We summarise these results in Table 5.We note that the preference at 4 ks for the transition regime is not robust, and that both time intervals only limit  and  min  to the boomerang shape region shown in Figure 2. low counts (≤ 3) introduce large uncertainties.This prevents robust inference of the spectral index and limits the Fermi-LAT data alone to information on the energy flux level.Combined power-law vs. smoothly-broken-power-law fits of Swift-XRT and Swift-BAT require at 4 ks a break at an energy between 5 and 10 keV, depending on the prior width of the floating norms (Δ log 10  ≈ 50).At 22 ks, either a break or an extended floating norm of around a factor 2.4 ± 0.5 statistically only indicate a minor improvement at a similar level (Δ log 10  ≈ 3).
Swift-BAT and Fermi-LAT data combined can be fit well by a single power law for both time intervals, see also Table S5.
A combined fit to all three data sets with a smoothly broken power law confirms this picture of a break in the keV regime and a single power law component extending up to the GeV energies.

Figure 2 .
Figure 2. Left: posterior distributions in  min  −   plane for the 4 ks (small blue region) and 22 ks (large green boomerang) with the two arms fixing the observed break energy  b,obs  ∼ 10 keV, corresponding to the slow (red) and fast (purple) cooling solution, meeting in the transition region (grey).Note that we treat  min  directly as a parameter instead of fixing it via   and our prior is  min  > 10 8 eV.For three representative solutions S (slow), F (fast) and T (transition) the differences in electron and observed photon spectral energy distributions are visualised.