2022

[1]Benjamin P. Gompertz

1]Institute of Gravitational Wave Astronomy and School of Physics and
Astronomy, University of Birmingham, B15 2TT, UK

2]Department of Astrophysics/IMAPP, Radboud University, 6525 AJ Nijmegen, The
Netherlands

3]INAF, Astronomical Observatory of Brera, via E. Bianchi 46, 23807, Merate
(LC), Italy

4]Center for Computational Astrophysics, Flatiron Institute, 162 W. 5th
Avenue, New York, 10011, NY, USA

5]Department of Physics and Columbia Astrophysics Laboratory, Columbia
University, New York, 10027, NY, USA

6]School of Physics and Astronomy, University of Leicester, University Road,
Leicester, LE1 7RH, UK

7]Center for Interdisciplinary Exploration and Research in Astrophysics and
Department of Physics and Astronomy, Northwestern University, 2145 Sheridan
Road, Evanston, 60208-3112, IL, USA

8]Niels Bohr Institute, University of Copenhagen, Jagtvej 128, 2200,
Copenhagen N, Denmark

9]SRON, Netherlands Institute for Space Research, Niels Bohrweg 4, NL-2333 CA,
Leiden, the Netherlands

10]Bar Ilan University, Ramat Gan, Israel

# A minute-long merger-driven gamma-ray burst from fast-cooling synchrotron
emission

<EMAIL_ADDRESS>Maria Edvige Ravasio  Matt Nicholl  Andrew J. Levan
Brian D. Metzger  Samantha R. Oates  Gavin P. Lamb  Wen-fai Fong  Daniele B.
Malesani  Jillian C. Rastinejad  Nial R. Tanvir  Philip A. Evans  Peter G.
Jonker  Kim L. Page  Asaf Pe’er  [  [  [  [  [  [  [  [  [  [

###### Abstract

Gamma-ray bursts (GRBs) are intense episodes of high-energy emission seen
isotropically across the sky and all through cosmic time. For decades, they
have been broadly divided into ‘long’- and ‘short’-duration bursts, lasting
more or less than 2 s, respectively Kouveliotou93 , but it has been apparent
for several years that this dichotomy is imperfect. The split does not map
directly to the two progenitor channels that are known to produce GRBs – the
merger of compact objects (merger-GRBs) or the collapse of massive stars
(collapsar-GRBs). In particular, the merger population (typically short-
duration) also includes bursts with a short, hard $<$ 2 s spike and subsequent
longer, softer extended emission (EE) (Norris02, ; Norris06, ; Norris10, ;
Gompertz13, ). There have also been examples of apparent short bursts in which
supernova detections indicate a collapsar origin Ahumada21 . The recent
discovery of a kilonova – the radioactive glow of heavy elements made in
neutron star mergers – in the 50 s-duration GRB 211211A Rastinejad22  further
complicates this picture, demonstrating that mergers can drive GRBs with
complex and long-lived light curves whose broad spectral and temporal
properties are consistent with the collapsar population. Here we present
detailed analysis of the high energy emission associated with GRB 211211A. We
demonstrate that the rapidly-evolving spectrum can be fit by purely
synchrotron emission with both the peak and cooling frequencies moving through
the $\gamma$-ray band, down to the X-rays. This is the first time that such
spectral evolution has been demonstrated in a merger-GRB, and we show that it
drives the extended emission signature at late times. The remarkable
consistency of these signatures across the population suggests that GRB
211211A may provide a unifying blueprint for identifying long-duration GRBs
from mergers, potentially paving the way for strong diagnostics of the
progenitor type.

Figure 1: Spectral fits with the 2SBPL model from six representative epochs in
the GBM and BAT light curves. The epochs bracketed by dotted lines in the
light curve correspond to the spectra with frames of the same colour. In the
spectral panels, the peak energy is shown by the dashed red line and the low
energy break (where included in the fit) by the dashed blue line. The top row
shows the highly variable nature of the IPC, while the EE phase along the
bottom row exhibits a more gradual and coherent evolution.

GRB 211211A was detected by _Fermi_ -GBM and _Swift_ -BAT at $t_{0}=13$:09:59
UT on 2021 December 11. It was initially classified as long due to its
$\approx 34.3$ s duration from _Fermi_ Mangan21  and $51.4\pm 0.8$ s from
_Swift_ Stamatikos21 . _Swift_ promptly slewed to point its X-ray Telescope
(XRT; Burrows05 ), which began settled observations of the field $79.2$ s
after the BAT trigger D'ai21 . X-ray observations showed bright emission
($0.3$ – $10$ keV flux $\approx 3\times 10^{-8}$ erg s-1 cm-2) with an
exponential decay lasting until $\sim 300$ s after trigger, consistent with
previous examples of EE (e.g. Gompertz13 ). The Ultra-Violet/Optical Telescope
(UVOT; Roming05 ) began pointed observations of GRB 211211A 92 s after the BAT
trigger Belles21 , and detected the optical counterpart. Late monitoring
Rastinejad22  identified a significant near-IR excess which cannot be
explained by radioactive Nickel decay but is remarkably similar to AT2017gfo,
the kilonova discovered alongside GRB 170817, confirmed to be a binary neutron
star (BNS) merger by gravitational-wave (GW) observations Abbott17_BNS . The
detection of a kilonova conclusively establishes that GRB 211211A originated
from a compact merger. Its association with a host galaxy at $z=0.076$
(Malesani21, ; Rastinejad22, ) makes it the closest confirmed compact object
merger discovered without GWs, at a luminosity distance of just 350 Mpc. Due
to its proximity, GRB 211211A has the best-sampled high energy emission of any
merger-driven GRB, and its surprisingly long duration affords us a remarkable
opportunity to investigate the underpinning processes that enable compact
object mergers to create long-duration GRBs.

We extract time-resolved spectra in narrow windows of 2–20 s from the _Swift_
and _Fermi_ data and initially fit these with a range of spectral models using
xspec v12.11.1 (Arnaud96, ) (see Methods). Spectra from six representative
epochs are shown in Figure 1, covering the spectrally hard Initial Pulse
Complex (IPC) and softer EE. We find that the data are well described by a
double smoothly broken power-law model (2SBPL; Ravasio18 , shown in Figure 1).
A standard Band function (Band93, ) with a single break is strongly
disfavoured by Akaike’s Information Criterion Akaike74 ; Burnham04  (Extended
Data Figure 4). A Band model with an additional thermal component is also
disfavoured with respect to 2SBPL, especially in the brightest pulses, and
further requires a high intrinsic hydrogen column density, inconsistent with
the burst’s afterglow Rastinejad22  (see Methods). The model parameters
derived from our full suite of fits are given in Supplementary Table 1. We
focus the rest of our discussion on the 2SBPL model (though for epochs where
one of the breaks lies outside the observed frequency range, this reduces to
the Band model; see Methods).

Figure 2: The evolution of the synchrotron spectrum from our time-resolved
spectral fits. 2SBPL is fitted to the early data, but simpler models are used
at late times where necessary. Shaded regions indicate the detectors available
for fitting. Top: _Swift_ -BAT and XRT 10 keV flux density light curves of the
prompt + EE phases. Middle: The evolution of Ep and Eb. The BAT bandpass is
marked by two horizontal black dotted lines. The horizontal red dotted line
shows the lower limit of fitted GBM energies and the XRT upper bandpass limit.
Bottom: Evolution of the photon indices derived from fitting. The expectation
values of $\alpha_{1}$ and $\alpha_{2}$ in the fast-cooling regime and the
nominal upper limit of $\beta$ are indicated by the dashed lines.

The 2SBPL model parameterises a synchrotron spectrum, where relativistic
charged particles radiate due to acceleration in magnetic fields. The spectrum
is described by power-law segments connecting characteristic break frequencies
(see e.g. Rybicki1979, ; Sari1998, ; Piran1999, ). The three power-law
segments have photon indices $\alpha_{1}$, $\alpha_{2}$ and $\beta$ (following
the convention $\nu F_{\nu}\propto E^{2-\gamma}$, for a photon index
$\gamma$), smoothly connected at two breaks, $E_{b}$ and $E_{p}$. These breaks
map to the characteristic synchrotron frequency $\nu_{m}$, where most of the
electrons radiate, or the cooling frequency $\nu_{c}$, above which electrons
rapidly lose their energy. If $\nu_{c}<\nu_{m}$, all electrons cool down
rapidly and the system is in the so-called ‘fast cooling’ regime, while
$\nu_{m}<\nu_{c}$ represents a ‘slow cooling’ state (see Methods for more
details).

Figure 3: Top: The evolution of the spectral breaks $E_{p}$ and $E_{b}$ is
well described by an exponential profile. Exponentials are fitted to the
filled symbols of their respective colours. Open symbols are obtained by
fixing the spectral slopes to their theoretical expectations, and are not fit.
The affinity of the blue curve for the late red data therefore provides
further support for the transition of the two breaks. Bottom: BAT and XRT
light curves. The rapid turnover in the light curves corresponds to the breaks
exiting the bandpasses, implying that the duration of EE is sensitive to their
evolution.

The $\gamma$-ray and X-ray light curves of GRB 211211A and the evolution of
the best-fit 2SPBL parameters are shown in Figure 2. During the first 42 s of
evolution, we see a rapid decrease in $E_{p}$ from an initial $2411.3\pm
602.0$ keV to $76.3\pm 15.9$ keV. $E_{b}$ also shows a smooth but much slower
decline from a maximum of $64.3\pm 4.9$ keV to $17.6\pm 4.2$ keV. We find mean
indices of $\alpha_{1}=0.52\pm 0.24$ and $\alpha_{2}=1.61\pm 0.25$. These
values are in excellent agreement with the expected values of 2/3 and 3/2 for
synchrotron emission in the fast-cooling regime. While compelling evidence for
the presence of two breaks has been found in bright long GRBs detected by both
_Fermi_ Ravasio18 ; Ravasio19 ; Ronchi2020 ; Burgess2020 ; Toffano2021  and
_Swift_ Oganesyan17 ; Oganesyan2018 ; Oganesyan2019 , this is the first time
that evidence of synchrotron cooling has been found in the prompt emission
spectrum of a merger-driven GRB.

After 42 s, $E_{b}$ is unresolved and we fit a single photon index, $\alpha$,
below $E_{p}$. Initially, the fitted values of $\alpha$ are in excellent
agreement with the expected value of $\alpha_{1}$ (Figure 2, lower panel,
green points), indicating that $E_{b}$ and $E_{p}$ are unresolved because they
are too close together, rather than $E_{b}$ having left the bandpass. From
$\sim$120 s, the measured value of $\alpha$ begins to rise. We interpret the
change as being due to the synchrotron breaks now moving away from one another
(Methods), resulting in $\alpha_{2}$ dominating the measurement as $E_{b}$
approaches the lower limit of the observed bandpass and pushes $\alpha_{1}$
out of the spectrum.

Indeed, by fixing the photon indices to their expected values, we can once
again resolve $E_{b}$ in our fits starting from 120s (Figure 3, open symbols).
The increasing separation between $E_{b}$ and $E_{p}$ and the coincident
evolution of $\alpha$ from 2/3 towards 3/2 indicates that the more rapidly-
evolving spectral break is now the lower energy of the two, in contrast with
the first 42 s of evolution. This apparent crossing of the two spectral breaks
is consistent with the source having transitioned from a fast-cooling regime
to slow cooling (Rybicki1979, ; Sari1998, ), and would be the first time such
a transition has been measured in any GRB.

We further test this scenario by fitting an exponential profile of the form
$E=Ne^{(-t/\tau)}$ to the evolution of both breaks (Figure 3). The two
profiles cross at $t_{c}=68$ s, and their crossing is further supported by the
affinity of the $E_{b}$ fit to the $E_{p}$ measurements post-$t_{c}$. The
evolution of the breaks has a marked effect on the EE light curve. The
characteristic timescale for the evolution of $\nu_{c}$ ($\tau_{E_{b}}=63.3\pm
20.2$ s) and the turnover of the X-rays ($\tau_{X}=66.9\pm 1.0$ s) are close
to the fast-to-slow cooling transition time ($t_{c}\approx 68$ s) suggesting a
connection between the cooling transition and the EE duration. Moreover, they
are clearly driving the morphology of the late X-ray decline, which steepens
when $\nu_{m}$ evolves below the band and ceases when $\nu_{c}$ follows
(Figure 3). The consistency of this X-ray feature across the EE class (e.g.
Gompertz13 , Extended Data Figure 5) hints that the shock physics may be
remarkably uniform across the population of long-duration merger-GRBs.

At higher energies, the characteristic timescale of $\nu_{m}$
($\tau_{E_{p}}=14.4\pm 1.14$ s) is well matched to the duration of the IPC
($\sim 12$ s). This likely relates to the duration of the jet, which energises
the shock during the IPC, keeping $\nu_{m}$ consistently high. Although the
duration of $\gamma$-ray EE is highly variable across the known sample (e.g.
Supplementary Table 2), the evolution of $E_{p}$ through the BAT bandpass can
explain the relative spectral softness of EE compared to the IPC (e.g.
Norris10 ). This framework also naturally leads to the population of GRBs that
display the same exponential X-ray light curve as GRB 211211A and other EE
GRBs (e.g. Extended Data Figure 5), but lack EE in $\gamma$-rays Lu15 ;
Gompertz20 . This can be achieved with a common evolution in $\nu_{c}$, while
$\nu_{m}$ is found at lower energies below the BAT bandpass (after the IPC).
Further, if $\nu_{c}$ is in fact _below_ the XRT bandpass in the majority of
cases, one might recover a ‘canonical’ short GRB lasting less than $2$ s.
However, this would imply a significant duration of ‘unseen’ jet activity in
these events.

Our analysis shows that the prompt emission spectrum of GRB 211211A is
consistent with the so-called ‘marginally fast-cooling regime’, with
$\nu_{c}\lesssim\nu_{m}$ (KumarMcMahon2008, ; Daigne11, ; Beniamini2013, ).
Detecting the cooling frequency $\nu_{c}$ at $\sim$ tens of keV implies that
accelerated particles do not cool completely via synchrotron processes within
a dynamical timescale (Ghisellini2000, ). By assuming that the electrons cool
on a timescale of the order of the adiabatic one, we can derive self-
consistent constraints on the magnetic field $B$ in the emitting region. For a
typical emitting region radius $R$ and a bulk Lorentz factor of $\Gamma=100$
(consistent with the afterglow; Rastinejad22 ), our findings imply a magnetic
field of the order of $B\sim
90\,\nu_{c,60\rm\,keV}^{-1/3}\,R_{13.5}^{-2/3}\,\Gamma_{2}$ G, where
$Q=Q_{n}\times 10^{n}$ (the magnetic field falls in the range $B\sim 30-200$ G
for a range of $R\sim 10^{13}-10^{14}$ cm). These values are consistent with
those derived for marginally fast-cooling collapsar-GRBs Oganesyan2019 ;
Oganesyan17 ; Oganesyan2018 ; Ravasio18 ; Ronchi2020 , but at odd with the
expectations for a typical GRB emitting region ($B\sim 10^{4}-10^{6}$ G, e.g.
Piran2005 ).

Interestingly, we find that the UVOT data at $\sim$163 s lie significantly
below the extrapolation of the fitted synchrotron spectrum (see Methods,
Extended Data Figure 6). An additional spectral break is required to self-
consistently model the spectral energy distribution (SED) from UV to X-rays.
In the context of synchrotron emission, this can be interpreted as the
synchrotron self-absorption frequency $\nu_{\rm ssa}$, below which the optical
depth to synchrotron self-absorption is larger than unity. Following Shen2009
(but see also Sari1999 ; Granot2000 ; Granot2002 ; Beniamini2013 ), we find
that this implies a low $B$-field ($\sim 100$ G) and/or compact emitting
region ($R<10^{13}$ cm). However, a self-consistent solution that incorporates
incomplete electron cooling and synchrotron self-absorption at UV frequencies
is challenging, and may require alternative sources of absorption or modified
synchrotron models (e.g. Ghisellini2020 ) - particularly to avoid the bright
synchrotron self-Compton emission predicted for such a system (see e.g.
Ghisellini2020 ; KumarMcMahon2008 ; Beniamini2013 ).

The kilonova associated with GRB 211211A is consistent with being a BNS merger
Rastinejad22 , though a neutron star - black hole (NS-BH) cannot be completely
ruled out. The jet responsible for the prompt emission is believed to be
powered by accretion onto a newly-formed black hole remnant (e.g. Narayan92 ).
However, the presence of central engine activity lasting $\sim 100$ s after
the merger is challenging to reconcile with the expected $\lesssim 1$ s disk
lifetime (e.g. Lee09 ; Fernandez&Metzger13 ). Longer accretion activity can be
powered by late-time fallback onto the central remnant, in which case the EE
might be related to the quantity and duration of the fall-back mass (e.g.
Rosswog07 ; Desai19 ). This explanation is more consistent with NS-BH systems
producing larger tidal ejecta (e.g. Foucart18 ). On the other hand, the
characteristic $\sim 100$ s duration of the EE has no obvious explanation in
the fall-back accretion scenario (however, see Kisaka15 ).

An alternative possibility in the BNS scenario is that the EE is powered by a
temporarily or indefinitely stable magnetar remnant (e.g. Metzger08 ;
Giacomazzo13 ; Gompertz14 ), which powers the EE via a relativistic magnetized
wind, potentially shaped by interaction with the merger ejecta into a
collimated jet (e.g. Bucciantini12 ). The mapping between the magnetar outflow
and the prompt emission depends sensitively on the emission model (e.g.
Metzger11 ; Gompertz14 ), but an abrupt change in jet properties is predicted
to occur once the magnetar becomes optically-thin to neutrinos, on a timescale
of $\sim 10-100$ s Pons99 . This transforms the composition of the magnetar
outflow from an electron-ion plasma to an electron-positron outflow similar to
that of a pulsar wind Metzger11 . Depending on how the change in composition
and magnetization maps into the evolution of $\nu_{\rm c}$ and $\nu_{\rm m}$,
this could help explain the ubiquity of the $\sim 100$ s characteristic
timescale across the merger-GRB + EE population.

The brightness of GRB 211211A enables us to deconstruct both the initial
prompt emission complex and the subsequent, softer extended emission. Our
results suggest that the characteristics of EE in a merger-GRB with a long-
lived engine depend mainly on where the synchrotron spectral breaks reside
relative to the observational bandpasses. For the first ten seconds of the
burst, $E_{p}$ and $E_{b}$ show little evolution. Therefore this period shows
no spectral evolution and no spectral lag, a critical distinguishing feature
of EE-GRBs (Gehrels04, ). After this time, $E_{p}$ softens rapidly, creating
the observed softer EE component. Therefore, this evolution naturally explains
both the lack of spectral lag in the early emission and the later softening
seen in EE bursts. While only GRB 211211A has observations of the requisite
quality to measure the motion of the spectral breaks directly, there is
substantial similarity in spectral evolution and X-ray light curves in all EE
bursts (see Methods). This implies that the same physical processes likely
shape the entire class of events. In this case, extended emission can be a
smoking gun for the origin of a given GRB, potentially distinguishing between
merger-GRBs and collapsar-GRBs even in bursts at much larger distances or with
much poorer localisations. Applying this technique to large GRB samples can
significantly improve our ability to reconstruct the merger rate density with
redshift and to perform joint searches for GRBs coincident with gravitational
wave emission.

## Methods

Data products

We retrieved GBM spectral data and their corresponding response matrix files
(rsp2) from the online HEASARC
archive111https://heasarc.gsfc.nasa.gov/W3Browse/fermi/fermigbrst.html
Gruber14 ; vonKienlin14 ; vonKienlin20 ; Bhat16 . GBM count rate light curves
are created using time-tagged event (TTE) data binned to a time resolution of
64 ms (Figure 1). No signal was detected by the Large Area Telescope (LAT) on
board _Fermi_ during the prompt emission phase. The source incident angle was
greater than 65∘ from the LAT boresight until $\sim$800 s after the GBM
trigger time.

We downloaded _Swift_ data from the UK _Swift_ Science Data Centre (UKSSDC;
Evans07 ; Evans09 ). Data from BAT are processed using the batgrbproduct
pipeline v2.48 from NASA’s High Energy Astrophysics Software (HEAsoft v6.28;
HEAsoft )222http://heasarc.gsfc.nasa.gov/ftools. 15–150 keV count-rate light
curves are extracted using batbinevt with 64 ms time resolution (Figure 1).
Flux density light curves are taken directly from the UKSSDC Burst Analyser.
We use the non-evolving data products binned to a signal-to-noise ratio of 4.

To assess spectral evolution, we extract time-resolved spectra in as narrow an
interval as possible while retaining sufficient counts for the models to
converge. We find that between 0 and 26 s after the BAT trigger, binning the
BAT and GBM data into 2 s slices provides the best balance between cadence and
signal-to-noise, except for a quiescent period at 12–16 s, which sits between
the prompt and EE phases (see Figure 1). This is combined into a 4 s bin. Data
between 26 and 50 s are also grouped in 4 s bins. Beyond 50 s we use 10 s
bins. At 80 s the GBM data end and the XRT data begin. We continue using 10 s
bins of BAT + XRT data up until the end of the BAT data at $\sim$120 s after
trigger. We then extract 10 s bins of XRT data until 140 s, where we widen our
bins to 20 s until the end of the EE phase at 300 s.

_Fermi_ -GBM spectra were extracted using the public software
gtburst333https://fermi.gsfc.nasa.gov/ssc/data/analysis/scitools/gtburst.html.
We analysed the data of the two NaI detectors with the highest count rates and
with the smallest viewing angle (n2, n10) and the most illuminated BGO
detector (b0). We selected the energy channels in the range 10–900 keV for NaI
detectors, excluding the channels in the range 30–40 keV (due to the iodine
K–edge at 33.17 keV), and 0.3–40 MeV for the BGO detector. We modelled the
background by manually selecting time intervals before and after the burst and
fitting them with a polynomial function whose order is automatically found by
gtburst.

After processing with batgrbproduct, time-resolved BAT spectra are extracted
using batbinevt. These spectra have a systematic error vector applied via
batphasyserr, and batupdatephakw is run to update the ray tracing keywords. We
build a detector response matrix for each spectrum using batdrmgen. XRT
spectra are extracted using the UKSSDC webtool (Evans07, ; Evans09, ).

Fitting was performed using xspec v12.11.1 (Arnaud96, ). We include a free
constant representing an effective area correction (EAC) to account for flux
offsets due to the uncertain effective areas of the GBM detectors in flight.
This is found to be a few per cent for intra-GBM calibration and up to $\sim
15$ per cent for GBM-BAT calibration.

Model comparison

We fit our data with three models. The first and simplest is the Band function
(Band93, ), which is the standard GRB continuum model and takes the form of
two power-laws, with low-energy photon index $\alpha$ and a high-energy photon
index $\beta$, smoothly connected at a $\nu F_{\nu}$ peak energy $E_{p}$. When
there are no spectral breaks in the fitted bandpass, we simplify the Band
function to a power-law fit corresponding to either $\alpha$ or $\beta$.

We also test the addition of a blackbody (BB) component, dividing the spectrum
into thermal and non-thermal emission. The thermal component represents the
emission from the photosphere of the GRB at typical radii of a few times
$10^{11}$ cm from the central engine (Pe'er15, ). Non-thermal emission is
produced further out ($\sim 10^{13}$ cm) either via interactions between
expanding shells of material or through magnetic processes.

Finally, we fit a double smoothly broken power-law model (2SBPL; Ravasio18, ).
This model allows us to fit the spectra with three power-law segments (with
photon indices $\alpha_{1}$, $\alpha_{2}$ and $\beta$) smoothly connected at
two breaks (hereafter $E_{b}$ and $E_{p}$). This function represents the
synchrotron spectral shape derived from a population of electrons assumed to
be accelerated into a power-law distribution of energies, i.e.
$N(\gamma_{e})\propto\gamma^{-p}$ for $\gamma_{m}<\gamma_{e}<\gamma_{\rm
max}$. The lower-energy $E_{b}$ and higher-energy $E_{p}$ represent either the
cooling frequency ($\nu_{c}$, mostly emitted by electrons with Lorentz factor
$\gamma_{c}$), or the characteristic synchrotron frequency ($\nu_{m}$, emitted
by electrons at $\gamma_{m}$). The order of these breaks dictates the cooling
regime: ‘slow cooling’ ($\nu_{m}<\nu_{c}$), wherein only electrons with
$\gamma_{e}>\gamma_{c}$ cool efficiently within a dynamical timescale, or
‘fast cooling’ ($\nu_{c}<\nu_{m}$), in which all the electrons cool down
rapidly to $\gamma_{c}<\gamma_{m}$. The two regimes have specific expectation
values for the photon indices between the power-law segments. For fast cooling
($\nu_{c}<\nu_{m}$), we expect $\alpha_{1}=2/3$ (for $\nu<\nu_{c}$),
$\alpha_{2}=3/2$ (for $\nu_{c}<\nu<\nu_{m}$) and $\beta=p/2+1$ (for
$\nu>\nu_{m}$), while for slow cooling ($\nu_{m}<\nu_{c}$) we expect
$\alpha_{1}=2/3$ (for $\nu<\nu_{m}$), $\alpha_{2}=(p+1)/2$ (for
$\nu_{m}<\nu<\nu_{c}$), and $\beta=p/2+1$ (for $\nu>\nu_{c}$). For the typical
parameters of the emitting region ($B\sim 10^{4}-10^{6}$ G, $\Gamma=100$), the
particles are expected to efficiently radiate most of their energy on a
timescale much smaller than the dynamical one and therefore the spectra are
expected to be in fast-cooling regime (Ghisellini2000, ).

The 2SBPL function has been found to fit the spectra of the brightest _Fermi_
long GRBs significantly better than the standard Band-like single-break
function Ravasio19 . The inclusion of the low-energy break (e.g. Oganesyan17 ;
Oganesyan2018 ) helps to solve the tension between the typically measured
values of $\langle\alpha\rangle\approx 1$ in GRB spectra fitted with the Band
function (e.g. Preece98 ) and the expected values of $\alpha_{1}=2/3$ and
$\alpha_{2}=3/2$ from synchrotron theory (e.g. Ghisellini2000 ). This tension
may also be lessened by considering inverse Compton effects in Klein-Nishina
regime (e.g. (Daigne11, )). Recent simulations suggest that
$\langle\alpha\rangle\approx 1$ may actually represent the mean value of these
two unresolved spectral slopes Toffano2021 . Motivated by these results, we
employ the 2SBPL function to test the consistency of GRB 211211A with a
synchrotron-dominated spectrum.

Due to their different treatment of incident photons, the data from the three
instruments used in our study must be fit with different fit statistics. For
GBM, the background is modelled prior to extracting a spectrum, hence the
resultant spectra are fit with PGSTAT, representing a Poissonian source over a
Gaussian background. The mask weighting used in BAT means that its data must
be fit with $\chi^{2}$ statistics. Finally, XRT employs straightforward photon
counting, and hence is fit with Cash statistics (Cash79, ). As a result,
different model fits cannot be reliably compared with $\chi^{2}$ statistic
tools like the F-test. We therefore employ Akaike’s Information Criterion
(AIC; Akaike74 ; Burnham04 ) to compare models. We find that both the 2SBPL
and Band+BB models provide a statistical improvement over the simpler Band
function during the first $\sim 30$ s of data (Extended Data Figure 4), with
$\Delta_{\rm AIC}\gg 10$ indicating no support for the Band function
(Burnham04, ). The 2SBPL model also provides a consistent improvement over
Band+BB fits during the prompt emission phase (see Supplementary Table 1).

In epochs that feature data taken with XRT, we include the effects of
absorption from the neutral hydrogen column along the line-of-sight in our
models. This is split into contributions from the Milky Way and the GRB host
galaxy in the form [model]*tbabs*ztbabs (Wilms00, ). Milky Way absorption is
fixed to N${}_{\rm H}=1.76\times 10^{20}$ cm-2 (Willingale13, ), with the
contribution from the host galaxy at $z=0.076$ left free to vary. We find that
the Band+BB model requires the host NH to be at least an order of magnitude
higher than for fits with the 2SBPL model to achieve similar fit statistics.

To obtain the best measurement of the intrinsic NH, we perform fits to the
time-integrated X-ray afterglow for the full set of XRT photon counting (PC)
mode data (starting $\sim 4000$ s after trigger). The afterglow spectrum is
well described (C-stat/dof = $337/422$) by a power-law model with a photon
index of $\Gamma=1.56\pm 0.07$. It therefore provides a more reliable
measurement of the absorption column than the rapidly evolving time-resolved
spectra during EE. We find that N${}_{\rm H}=(1.19\pm 1.61)\times 10^{20}$
cm-2, consistent with zero and with a $3\sigma$ upper limit of N${}_{\rm
H}<6.02\times 10^{20}$ cm-2. By contrast, the brightest and best-sampled
BAT+XRT bin at 80 – 90 s requires N${}_{\rm H}=(2.55\pm 0.40)\times 10^{21}$
cm-2 to achieve a good fit with the Band+BB model (Supplementary Table 3).

In short GRBs, the absorption column is expected to be constant over the
lifetime of the source (e.g. Asquini19, ). In rare cases, variations in NH
have been suggested for bright lGRBs (e.g. Campana21, ), but the magnitude of
the effect is at most a factor of two, and is sensitive to the choice of
spectral model. In addition, an anomalously high neutral hydrogen column was
also used to disfavour the thermal model in time-resolved spectral fitting of
the EE GRB 060614 (Mangano07, ). We therefore rule out the Band+BB model
firstly because our AIC test supports the 2SBPL model during the prompt phase,
and secondly because it requires an anomalously high absorption column at
X-ray frequencies. We focus the rest of our discussion on the 2SBPL model.

2SBPL fits

We identify a general trend of variable spectral behaviour during the first
$\sim 12$ s (the IPC), which then gives way to a more coherent smooth
evolution from the onset of EE ($\sim 20$ s) onwards. We describe the
evolution of the model parameters in various time windows here.

0 – 80 s: BAT + GBM.

Between 0 and 80 s our spectral coverage ranges from 10 keV to 10 MeV. We fit
the full 2SBPL model for the first 42 s of evolution. During this time, we see
a rapid decrease in $E_{p}$ from an initial $2411.3\pm 602.0$ keV at 0–2 s to
$76.3\pm 15.9$ keV by 38–42 s. $E_{b}$ also shows a smooth but much slower
decline from an initial $21.0\pm 8.8$ keV to $17.6\pm 4.2$ keV over the same
time range, though is first seen to rise to a peak energy of $64.3\pm 4.9$ keV
at 6–8 s after trigger.

In the same epoch, early values of $\alpha_{1}$ show excellent agreement with
the expectation value of 2/3 before drifting downwards. The mean value of the
low-energy photon index is $\overline{\alpha}_{1}=0.52\pm 0.24$. The later
discrepancy is still consistent with synchrotron expectations within
$3\sigma$, and can be explained by $E_{b}$ falling close to the lower GBM
bandpass, resulting in a poorly-sampled low-energy power-law segment. A
similar issue has been found previously by Ravasio19  (see their figure B.1),
who showed that all spectra with notably hard values of the low-energy photon
index $\alpha_{1}$ also had a break energy of $E_{b}<20$ keV, suggesting an
instrumental effect (the GBM threshold energy is $\sim$ 10 keV). In addition,
the smoothness parameter of the fitting function could influence the value of
$\alpha_{1}$, especially at the edge of the detector bandpass where few energy
channels are available to constrain it. We find that a sharper break results
in $\alpha_{1}$ approaching the synchrotron-predicted value of 2/3. However,
we retain a consistent smoothness across all of our fits to avoid biasing our
results.

The slope $\alpha_{2}$ of the power-law between $E_{b}$ and $E_{p}$ is
initially in excellent agreement with the expected value of $\alpha_{2}=3/2$
for fast cooling, but later evolves upwards towards a photon index of 2. This
trend may be explained by uncertainties in distinguishing $\alpha_{2}$,
$\beta$ and $E_{p}$ as the latter moves downwards though the band. In
particular, as the source fades and the signal-to-noise ratio in the high
energy GBM BGO detectors decreases, $\beta$ becomes poorly constrained. Our
mean values are $\overline{\alpha}_{2}=1.61\pm 0.25$ and
$\overline{\beta}=2.80\pm 0.54$.

After 42 s, the 2SBPL model is no longer statistically preferred over the Band
function. For consistent fitting, we approximate the Band function by freezing
$E_{b}$ below the bandpass, removing $\alpha_{1}$ and $E_{b}$ from the model.
The fitted values of $\alpha$ are in excellent agreement with the expected
value of $\alpha_{1}$ (Figure 2, lower panel, green points), indicating that
$E_{b}$ and $E_{p}$ are unresolved because they are too close together rather
than $E_{b}$ having evolved out of the bandpass. We widen our time bins to 10
s after 50 s to improve the signal-to-noise of our spectra. Fitting the
simpler Band model between 42 and 80 s results in a much tighter constraint on
the post-peak photon index, which now dominates the majority of the bandpass:
$\overline{\beta}=2.19\pm 0.04$. This includes a single power-law fit in the
70–80 s bin, indicating that both $E_{p}$ and $E_{b}$ are either below or very
close to the 10 keV lower bandpass limit of GBM.

We note that, assuming an isotropic-equivalent kinetic energy of the jet
$E_{\rm k,iso}\sim 4\times 10^{52}$ erg derived from the afterglow modelling
reported in Rastinejad22  and the $\gamma$-ray isotropic-equivalent energy
$E_{\rm iso}\sim 7.4\times 10^{51}$ erg we observe in the energy range 10–1000
keV during the first 50 s of emission, the implied prompt $\gamma$-ray
efficiency is $\eta=E_{\rm iso}/(E_{\rm iso}+E_{\rm k,iso})\sim 16\%$. This
value is consistent with estimates for other GRBs in the literature (e.g.
Beniamini2016 ), but requires a large contrast in the jet bulk Lorentz factor
(e.g. Beloborodov2000 ). We note however that recent works in the literature
found a much smaller efficiency ($\eta\sim 10^{-3}$) when the fraction of
electrons accelerated at the shock is included as a free parameter in the
afterglow model (instead of the typical assumption that all electrons
participate – see e.g. Cunningham2020 ; Salafia2021 ). These efficiencies are
more compatible with the expectations of an internal shocks model with a mild
contrast of bulk Lorentz factors (Rees1994, ; Kumar1999, ; Spada2000, ).

The magnetic field value implied by our findings ($B\sim 30$–200 G for a range
of $R\sim 10^{13}-10^{14}$ cm) is consistent with the values derived in the
cases of collapsar-GRBs showing marginally fast-cooling synchrotron spectra
(Oganesyan2019, ; Oganesyan17, ; Oganesyan2018, ; Ravasio18, ; Ronchi2020, ;
Burgess2020, ), but low compared to expectations for a typical GRB emitting
region ($B\sim 10^{4}-10^{6}$ G, e.g. Piran2005 ). For such a low magnetic
field in a small emitting region, synchrotron self-Compton (SSC) is expected
to dominate the cooling rate (see e.g. Ghisellini2020, ; KumarMcMahon2008, ;
Beniamini2013, ). A larger emitting region ($R\sim 10^{15}-10^{16}$ cm) would
reduce the SSC luminosity, but is more commonly associated with afterglow
radiation and would be inconsistent with the rapid variability of the prompt
light curve, unless the Lorentz factor is very high ($\Gamma\gtrsim 10^{3}$).
One interesting solution to this problem has been recently proposed by
Ghisellini2020 , ascribing the emission to proton-synchrotron in dominant
adiabatic cooling. While this model offers an interesting alternative, it
operates in a relatively small parameter space and its ability to explain all
the observations is still under investigation (see e.g. Florou2021, ;
Begue2021, ).

80 – 120 s: BAT + XRT.

After 80 s there are too few GBM counts in 10 s bins to obtain sufficient
signal-to-noise. However, _Swift_ -XRT began pointed observations of GRB
211211A at $79.2$ s after trigger (D'ai21, ), and we are able to fit combined
BAT+XRT spectra between 0.3 and 150 keV (excepting a 5 keV inter-detector gap
between 10 and 15 keV). The extension of our spectral coverage down to $0.3$
keV means that the Band function (approximated by 2SBPL with $E_{b}$ held
below the XRT bandpass) is preferred over the single power-law model once
more. The low energy index continues to be consistent with the expectations
for $\alpha_{1}$, indicating that $E_{b}$ and $E_{p}$ remain unresolved from
one another. $E_{p}$ continues to evolve smoothly downwards, from $E_{p}\sim
8$ keV to $\sim 5$ keV (see Figure 2, Supplementary Table 1). The BAT data
formally end at $t_{0}+122$ s.

120 – 300 s: XRT and a possible transition to slow cooling.

From $\sim$120 s, the measured value of $\alpha$ begins to rise. We continue
to measure a declining $E_{p}$ that has evolved to just a few keV and a
consistent (but poorly constrained) $\beta$. We therefore interpret the change
in $\alpha$ as being due to the synchrotron breaks now moving away from one
another, resulting in an elongation of the 2SBPL $\alpha_{2}$ segment between
them. Our measured $\alpha$ therefore evolves from being dominated by
$\alpha_{1}$ to being a blend of $\alpha_{1}$ and $\alpha_{2}$ around the
unresolved $E_{b}$. The power-law with index $\alpha_{2}$ then begins to
dominate the measurement as it elongates, while $E_{b}$ approaches the lower
bandpass limit and pushes $\alpha_{1}$ out of the spectrum.

We investigate this possibility by re-fitting the 2SBPL model with
$\alpha_{1}$ and $\alpha_{2}$ fixed to their expected values (2/3 and 3/2,
respectively), leaving the break energies and $\beta$ free. We find that
between 50 – 120 s after trigger, the two breaks cannot be resolved from one
another even with fixed photon indices. However, after 120 s we measure a
clear division again (Figure 3, open symbols). The fixed indices mean that the
spectral shape observed at this time is still consistent with the fast-cooling
regime ($\nu_{c}<\nu_{m}$), but it is worth noting that the increasing
separation between $E_{b}$ and $E_{p}$ and the coincident evolution of
$\alpha$ from 2/3 towards 3/2 indicates that the more rapidly-evolving
spectral break is now the lower energy of the two, in contrast with the first
42 s of evolution. This apparent crossing of the two spectral breaks is
consistent with the source having transitioned from a fast-cooling regime to
slow cooling (Rybicki1979, ; Sari1998, ). This would be the first time that
such a transition has been observed in a GRB (see however Burgess2020  for a
possible slow-to-fast cooling transition).

If the spectrum is now slow cooling, $\alpha_{2}$ is no longer expected to
have a value of 3/2, and instead should be $\alpha_{2}=(p+1)/2$. We caution
that slow cooling requires $p<3$. Given that $\beta=p/2+1$, this is in
contrast with the steep values of $\beta\gtrsim 2.5$ measured in the early
spikes of emission, but is consistent with the values of $\beta$ measured at
the implied time of transition ($\beta<2.5$, Figure 2). The transition from
fast to slow cooling would therefore also require a change in the electron
energy distribution power-law index $p$ over time.

For the epochs in which $E_{b}$ and $E_{p}$ are unresolved (which are covered
by the Band fits in Supplementary Table 1) we find a mean
$\overline{\beta}=2.42\pm 0.19$, which points to $p=2.84\pm 0.38$ and thus an
expectation value of $\alpha_{2}=1.92\pm 0.19$ in the slow-cooling regime.
Unfortunately, beyond 180 s our best fitting model reduces to a power-law
while $\alpha_{2}$ is still evolving, meaning that we are unable to determine
whether it supports fast or slow cooling. Our best-fitting 2SBPL model (which
is not supported over the power-law fit by AIC) indicates $\alpha_{2}=1.68\pm
0.12$, broadly consistent with either scenario. We note that at very late
times $\beta$ evolves to extremely soft values ($\sim 3.5$). This is likely
driven by an increase in free NH (see Supplementary Table 1) and the
decreasing signal-to-noise at higher energies in the bandpass.

UVOT: evidence for additional absorption?

Regardless of the cooling regime, the spectral index below the break energy
$E_{b}$ should be $\alpha_{1}=2/3$. A recent analysis of optical detections
obtained during the prompt emission of 21 long GRBs revealed the spectrum
between optical and $\gamma$-rays is well-modelled with synchrotron emission,
i.e. optical data are consistent with the extrapolation of the expected 2/3
power-law index Oganesyan2019 .

The UVOT detection at $162.9\pm 74.9$ s allows us to investigate this
possibility in GRB 211211A. We extract a 10 s wide XRT spectrum centred at
$162.9$ s and perform a combined fit of the UVOT and XRT data. The UVOT data
require the further addition of two zdust components to the model to account
for extinction in the GRB host galaxy and the Milky Way. The Milky Way
extinction is fixed to $E(B-V)=0.015$ (Schlafly11, ). Host extinction is fixed
to $E(B-V)=0.18$, representing the $3\sigma$ upper limit that we derive from
modelling the afterglow SED (see Methods: Afterglow SED).

To perform a joint fit of XRT and UVOT data, we use the 2SBPL model and fix
$\alpha_{1}=2/3$, $\alpha_{2}=3/2$ and $E_{b}=0.3$ keV based on the results
from our coincident spectral fit in Supplementary Table 1. $E_{p}$ was allowed
to vary to obtain the best match to the X-ray data, since the fitted epoch is
offset in time with respect to the template at $170\pm 10$ s. We find
$E_{p}=6.63\pm 1.60$ keV.

The extrapolation of $\alpha_{1}=2/3$ between the XRT and UVOT data over-
predicts the UVOT flux by an order of magnitude (Extended Data Figure 6).
Larger values of extinction would be inconsistent with the afterglow SED
observations; a free fit finds $E(B-V)=0.60\pm 0.06$, which is $\sim
7.5\sigma$ inconsistent with our model fit with the highest $E(B-V)$ (see
Supplementary Table 4). An additional spectral break may therefore be required
between the UVOT white filter and the XRT bandpass. One possibility for this
break is the synchrotron self-absorption frequency ($\nu_{\rm ssa}$), below
which photons are absorbed by the emitting electrons (Rybicki1979, ). This
region of the spectrum has an expected photon index of $\alpha=-1$ (or
$\nu^{-3/8}$ for an inhomogeneous distribution of electrons; Granot2000 ), and
hence can resolve the tension if it lies close to but above the UV.

The co-moving frame synchrotron self-absorption frequency can be computed by
equating the co-moving synchrotron flux at $\nu_{ssa}^{\prime}$ to the flux
from a blackbody in the Rayleigh–Jeans part of the spectrum. Following
Shen2009 , we derived the distance $R$ of the emitting region from the central
engine that is required to match the observations (i.e. that produce $6\times
10^{-3}$ keV $<\nu_{\rm ssa}<$ 0.3 keV). The synchrotron self-absorption
frequency $\nu_{\rm ssa}$ depends on the magnetic field of the emitting region
$B$ and on the bulk Lorentz factor $\Gamma$ of the jet. In our computations,
we required the magnetic field $B$ to be consistent with the one derived from
the observed $\nu_{c}\sim 20-60$ keV during the early prompt emission (see
Supplementary Table 1 and Figure 2) and assumed the same bulk Lorentz factor
as before: $\Gamma=100$.

We find that a compact emitting segion at $R\sim 10^{11-12}$ cm is required to
place $\nu_{\rm ssa}$ between UV and X-rays. We note that the variability
timescale implied by such a compact source is in contrast with the smooth
emission $\sim 160$ s after trigger. Moreover, such a small region would imply
a high radiation density $U_{\rm rad}$, increasing the expected SSC luminosity
and making it difficult to be optically thin to Thomson scattering and pair
production. A larger radius ($R\sim$ a few $10^{12-13}$ cm) can be
accommodated while still having UVOT $<\nu_{ssa}<$ XRT by assuming $B\sim
10^{4}-10^{6}$ G, but this is inconsistent with the observation of incomplete
cooling of the electrons. We therefore conclude it is unlikely that the UVOT
flux is suppressed due to synchrotron self-absorption. Other causes of
absorption (e.g. synchrotron photons absorbed by a cloud of not completely
cooled electrons in the same line of sight, or pair-production with higher-
energy photons) have to play a role in shaping the spectrum at low
frequencies, but further, more quantitative investigations are needed to
assess the feasibility of this process.

Afterglow SED We construct an optical-X-ray SED centred at $5.5{\rm ks}$. The
SED was constructed using the methodology of sch10 , using data within a time
range of 3 – 10 ks. To construct the pha files for the different optical
filters at $5.5$ ks, we first construct a single filter light curve by
normalising the individual filter light curves together. Then using this
single filter light curve we determine the temporal slope within the 3 – 10 ks
interval. We then fit a power-law to the individual filter light curves within
this same time interval, fixing the slope to the value determined from the
single filter light curve. We use the derived normalisations to compute the
count rate and count rate error at $5.5$ ks, which was then applied to the
relevant spectral file. For the XRT data, we take PC mode time-slice spectral
files built using the UKSSDC webtool Evans09  within the 3 – 10 ks interval.
The spectral files were normalised to correspond to the 3 – 10 ks flux of the
afterglow at $5.5$ ks. The flux, used to normalise a given spectrum, was
determined by fitting a power-law to the temporal data within the SED selected
time range. The best-fit decay index was used to compute the flux at $5.5$ ks,
in the same way as was done for the optical data.

The SED was fit using xspec v12.11.1, following the procedure outlined in
schady07 ; sch10 . We tested two different models for the continuum: a power-
law and a broken power-law, with the lower energy photon index fixed to be
$\alpha=2/3$, which corresponds to the expected spectral slope below the
synchrotron peak frequency (Sari1998, ). In each of these models, we also
included two dust and gas components to account for the Galaxy and host galaxy
dust extinction and photoelectric absorption (phabs, zphabs, zdust; we used
zdust for both the Galaxy and host galaxy dust components, but with the
redshift set to zero for the Galaxy dust component and set to $z=0.076$ for
the host components). The Galactic components were frozen to the reddening and
column density values from schlegel  and kalberla , respectively. For the host
galaxy dust extinction, we tested the dependence of dust extinction on
wavelength for three different scenarios: the Small and Large Magellanic
clouds (SMC and LMC, respectively) and on the Milky Way (MW), finding no
strong preference for any of these scenarios. In addition, we also account for
the absorption due to the Lyman series in the $912-1215$Å restframe wavelength
range, with the XSPEC zigm component. We set this component to use the
prescription of mad95  to estimate the effective optical depth from the Lyman
series as a function of wavelength and redshift and we set this component to
also include attenuation due to photoelectric absorption. The results are
provide in Supplementary Table 4.

Comparison to other GRBs

The identification of a kilonova by Rastinejad22  means that despite its
duration, GRB 211211A is a high-confidence merger event. While this discovery
appears to answer the almost 20-year old question posed by the lack of
supernovae in the nearby merger candidates GRBs 050724 and 060614
(Barthelmy05b, ; Gehrels06, ), 211211A is also not a typical EE GRB. In
particular, the IPC is at least a factor of two longer than any previously
identified example, which are generally consistent with the $t_{90}<2$ s hard
spikes of the broader short GRB class (e.g. Perley09 ; Lien16 ). We note that
in this case both BAT and GBM triggered on an extremely faint spike almost 2 s
before the ‘main’ episode of prompt emission (e.g. Figure 1). Such a weak
pulse would likely not be detectable from much further away than GRB 211211A,
and may represent a ‘precursor’ event that artificially extended the IPC
duration compared to other EE GRBs. Precursors like this have been suggested
to arise from flares due to the resonant shattering of the crusts of pre-
merger neutron stars (Tsang12, ; Tsang13, ; Neill21, ). Quasi-periodic
oscillations have also been claimed in this feature (Xiao22, ).

We compare the broad properties of GRB 211211A with the sample of EE GRBs with
redshifts from Gompertz20 , which we update to include EE GRB 211227A (Lu22,
). We note that Yang22  found GRB 211211A to be spectrally harder than
previous EE GRBs during both the IPC and EE phases, though their Band function
and cutoff power-law model fits do not capture all of the complex evolution
presented here. GRB 211211A has both the shortest $t_{90}$ and highest $E_{\rm
iso}$ of the known EE sample (Supplementary Table 2). 070714B has a shorter
$t_{90}$ in the rest-frame and a comparable $E_{\rm iso}$, though accounting
for redshift in the durations of GRBs has been shown to not be straightforward
Littlejohns13 . Despite the diversity in $\gamma$-rays, the X-ray profile of
EE is highly similar across all known events (Extended Data Figure 5).

The sample of merger-driven GRBs investigated by Ravasio19  present a single
power-law below the $\nu F_{\nu}$ peak, characterized by a hard photon index
that is consistent with the expected 2/3 power-law below $\nu_{c}$ (if in fast
cooling) or $\nu_{m}$ (if in slow cooling). GRB 211211A is the first merger-
driven GRB in which _both_ synchrotron breaks have been distinctively
identified and tracked in detail, demonstrating that the cooling of electrons
via synchrotron processes occurs in merger-driven GRBs. Conversely, the
discovery of a power-law segment with photon index 3/2 between $\nu_{c}$ and
$\nu_{m}$ in GRB 211211A is consistent with previous findings for collapsar
GRBs, in addition to its long duration.

The $E_{p}$ measured in GRB 211211A is towards the higher end of the
distribution found for the merger-driven GRBs in Ravasio19 , where the value
of $E_{p}=2411.3\pm 602.0$ measured between 0 – 2 s would rank 2/11 (between
$E_{p}=2892.0^{+299.0}_{-205.0}$ keV for GRB 120624A and
$E_{p}=1576.0^{+67.3}_{-67.1}$ keV for GRB 090227B). This is also higher than
the collapsar-driven sample. However, collapsar GRBs display a higher $E_{b}$
on average by a factor of several. In the extremely bright collapsar GRB
160625B, $E_{p}$ reached as high as $E_{p}=6596.0^{+1220.0}_{-1400.0}$ keV and
$E_{b}=196.7^{+31.2}_{-26.3}$ keV at the peak of the main emission episode
(Ravasio19, ). There is therefore no particular trend between our 2SBPL fit
results for GRB 211211A and those given in the literature for collapsar- and
merger-driven GRBs (Ravasio18, ; Ravasio19, ).

Evolution of the breaks

The evolution of the spectral breaks is well-described by an exponential
profile of the form $E=Ne^{(-t/\tau)}$ in both cases (Figure 3). $E_{p}$ is
best fit with $N_{E_{p}}=1344\pm 214$ keV and $\tau_{E_{p}}=14.4\pm 1.14$ s,
while for $E_{b}$ we find $N_{E_{b}}=36.2\pm 4.39$ keV and
$\tau_{E_{b}}=63.3\pm 20.2$ s. The two profiles cross at $t_{c}=68$ s,
suggesting a transition from fast to slow cooling. Indeed, from $\sim$ 50 s
onwards (after the IPC and the peak of the EE luminosity), the spectral shape
is consistent with a slow-cooling regime with $p\approx 2.2$ (Figure 2).
Measurements of $\beta>2.5$ at early times ($\lesssim 50$ s) are not
consistent with this interpretation, and require that the index of the
particles’ energy distribution injected by the acceleration mechanism changes
before the transition to slow cooling. Notably, $\beta$ is only seen to exceed
$2.5$ during spikes in emission, suggesting that this may indeed be the case.

A change in cooling regimes has been claimed recently in Burgess2020 , where
the authors found that single-pulse GRB spectra detected by _Fermi_ -GBM are
well modelled with idealized synchrotron emission. The majority of the spectra
are found to be in the slow-cooling regime, while a transition from slow to
fast cooling has been found in some of them during the decay of the
luminosity. The associated _increase_ in radiative efficiency of such a
transition even as luminosity is seen to decrease further challenges the
energetics in the jet. Conversely, the implied fast-to-slow cooling transition
in GRB 211211A (the first observed in any GRB) happens at late times, during
the decaying phase of the luminosity. It is therefore more easily reconciled
with the expected evolution of the jet.

Once the jet has ceased, the fading luminosity and downwards evolution of
$E_{p}$ may be explained by a combination of adiabatic cooling (cf.
Ronchini2021, ) and high-latitude effects. Within a structured jet, the energy
dissipation that gives rise to the prompt emission may, in the wider regions
where the bulk Lorentz factor is $\lesssim 30$, occur below the photospheric
radius, $R_{p}$. If this dissipation radius, $R_{d}$, is below the
photosphere, photons will be coupled to the plasma until the optical depth
reaches unity. Unless the condition for efficient thermalisation is met the
resultant emission will have a lower luminosity and a spectral peak energy
$\propto(R_{p}/R_{d})^{-2/3}$ (Lamb16, ).

It is not clear how the exponential profile relates to EE in the BAT bandpass,
though we note that Figure 3 suggests that $\tau_{E_{p}}$ may be under-
estimated and perhaps includes the EE phase before the turnover. Indeed, the
turnover of the BAT light curve coincides with the faster-evolving break
(identified here as $\nu_{m}$) exiting the BAT bandpass. $t_{90}$, which
measures the $\gamma$-ray duration exclusively, is highly variable across the
EE sample (e.g. Table 2), and this may point towards less uniform behaviour
from $\nu_{m}$, corresponding to a greater diversity in IPC durations, which
is indeed observed. However, $t_{90}$ is also subject to other effects like
redshift or viewing angle, which would serve to obfuscate the implied
correlation between the durations of the IPC and of EE at X-ray frequencies.

## Declarations

Acknowledgments

We thank Adam Goldstein for his insights into fitting GBM data. We thank Scott
Barthelmy, David Palmer, Amy Lien and Donggeun Tak for discussions on the
performance of BAT. We would like to thank Gabriele Ghisellini for fruitful
discussions on emission physics.

The work makes use of data supplied by the UK _Swift_ Science Data Centre at
the University of Leicester and the _Neil Gehrels Swift Observatory_.

This research has made use of data obtained through the High Energy
Astrophysics Science Archive Research Center Online Service provided by the
NASA/Goddard Space Flight Center, and specifically this work has made use of
public _Fermi_ -GBM data.

B. Gompertz and M. Nicholl are supported by the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation
programme (grant agreement No. 948381). M. Nicholl acknowledges a Turing
Fellowship. A.J. Levan and D.B. Malesani are supported by the European
Research Council (ERC) under the European Union’s Horizon 2020 research and
innovation programme (grant agreement No. 725246). The Cosmic Dawn Center is
funded by the Danish National Research Foundation under grant No. 140. G. Lamb
is supported by the UK Science Technology and Facilities Council grant,
ST/S000453/1. The Fong Group at Northwestern acknowledges support by the
National Science Foundation under grant Nos. AST-1814782, AST-1909358 and
CAREER grant No. AST-2047919. W.F. gratefully acknowledges support by the
David and Lucile Packard Foundation. P.A. Evans and K.L. Page acknowledge
funding from the UK Space Agency.

Data Availability

The majority of data generated or analysed during this study are included in
this published article (and its supplementary information files). _Swift_ and
_Fermi_ data may be downloaded from the UK _Swift_ Science Data Centre
(https://www.swift.ac.uk/) and the online HEARSAC archive at
https://heasarc.gsfc.nasa.gov/W3Browse/fermi/fermigbrst.html. Additional data
is available upon reasonable request.

Code Availability

The codes used in this publication are all publicly available. Fitting was
performed in xspec Arnaud96 , available from
https://heasarc.gsfc.nasa.gov/xanadu/xspec/. _Swift_ tools are available from
https://heasarc.gsfc.nasa.gov/lheasoft/, and _Fermi_ tools from
https://fermi.gsfc.nasa.gov/ssc/data/analysis/scitools/gtburst.html. The 2SBPL
model is published in Ravasio18 . Plots were created using matplotlib Hunter07
in Python v3.9.7.

Conflict of interest

We declare no conflicts of interests.

Authors’ Contributions

B.P.G. extracted the _Swift_ data, performed the spectral analysis, provided
the interpretation of the spectral evolution and the EE context, and wrote the
text. M.E.R. extracted the _Fermi_ data, performed the spectral analysis,
provided the interpretation on the emission physics, and co-wrote the text.
M.N. and A.J.L. contributed vital insights into the direction of the study and
co-wrote the text. B.D.M. provided theoretical interpretation, insights into
the progenitor, and contributed to the text. S.R.O. performed the afterglow
SED fits, reduced the UVOT data and contributed to the text. G.P.L. provided
theoretical interpretation, self-consistency checks of the physics, and made
contributions to the text. D.B.M. helped with the interpretation of the
emission physics and in writing the text. W.F., J.C.R., N.R.T., P.G.J. and
A.P. helped in the discussion and writing of the text. P.A.E. and K.L.P.
provided insights into _Swift_ data reduction and handling, and commented on
the text.

Supplementary Information

Supplementary Information is available for this paper.

## Supplementary Tables

2SBPL |  |  |  |  |  |  |  |
---|---|---|---|---|---|---|---|---
Epoch | $\alpha_{1}$ | $E_{b}$ | $\alpha_{2}$ | $E_{p}$ | $\beta$ |  NH | fit | dof
(s) |  | (keV) |  | (keV) |  |  (1020 cm-2) | statistic |
1.0 $\pm$ 1.0 |  0.69 $\pm$ 0.32 |  21.0 $\pm$ 8.8 |  1.50 $\pm$ 0.06 |  2411.3 $\pm$ 602.0 |  4.74 $\pm$ 1.87 | — | 315 | 353
3.0 $\pm$ 1.0 |  0.54 $\pm$ 0.07 |  46.7 $\pm$ 8.2 |  1.40 $\pm$ 0.04 |  951.6 $\pm$ 47.4 |  2.74 $\pm$ 0.08 | — | 480 | 353
5.0 $\pm$ 1.0 |  0.39 $\pm$ 0.10 |  30.7 $\pm$ 3.3 |  1.49 $\pm$ 0.03 |  721.0 $\pm$ 47.5 |  2.89 $\pm$ 0.11 | — | 401 | 353
7.0 $\pm$ 1.0 |  0.48 $\pm$ 0.03 |  64.3 $\pm$ 4.9 |  1.44 $\pm$ 0.02 |  1543.0 $\pm$ 47.5 |  3.09 $\pm$ 0.07 | — | 496 | 353
9.0 $\pm$ 1.0 |  0.33 $\pm$ 0.09 |  30.0 $\pm$ 2.7 |  1.49 $\pm$ 0.02 |  1053.6 $\pm$ 72.0 |  2.90 $\pm$ 0.12 | — | 378 | 353
11.0 $\pm$ 1.0 |  0.31 $\pm$ 0.12 |  28.5 $\pm$ 2.4 |  1.78 $\pm$ 0.04 |  567.1 $\pm$ 135.7 |  2.99 $\pm$ 0.36 | — | 387 | 353
14.0 $\pm$ 2.0 |  0.27 $\pm$ 0.37 |  19.9 $\pm$ 3.6 |  1.84 $\pm$ 0.29 |  257.3 $\pm$ 205.7 |  2.29 $\pm$ 0.52 | — | 378 | 353
17.0 $\pm$ 1.0 |  0.35 $\pm$ 0.25 |  20.6 $\pm$ 4.2 |  1.64 $\pm$ 0.09 |  275.0 $\pm$ 40.9 |  2.74 $\pm$ 0.23 | — | 391 | 353
19.0 $\pm$ 1.0 |  0.39 $\pm$ 0.12 |  27.2 $\pm$ 2.8 |  1.68 $\pm$ 0.04 |  580.0 $\pm$ 86.5 |  3.02 $\pm$ 0.28 | — | 389 | 353
21.0 $\pm$ 1.0 |  0.30 $\pm$ 0.16 |  23.8 $\pm$ 2.9 |  1.69 $\pm$ 0.06 |  319.6 $\pm$ 45.8 |  2.89 $\pm$ 0.25 | — | 366 | 353
23.0 $\pm$ 1.0 |  0.35 $\pm$ 0.14 |  24.2 $\pm$ 2.6 |  1.73 $\pm$ 0.05 |  335.2 $\pm$ 51.5 |  3.04 $\pm$ 0.30 | — | 363 | 353
25.0 $\pm$ 1.0 |  0.34 $\pm$ 0.14 |  24.8 $\pm$ 2.7 |  1.75 $\pm$ 0.05 |  305.5 $\pm$ 47.9 |  3.01 $\pm$ 0.29 | — | 353 | 353
28.0 $\pm$ 2.0 |  0.49 $\pm$ 0.09 |  24.3 $\pm$ 0.9 |  1.98 $\pm$ 0.02 |  83.9 $\pm$ 30.3 |  3.26 $\pm$ 0.67 | — | 393 | 353
32.0 $\pm$ 2.0 |  0.18 $\pm$ 0.46 |  17.2 $\pm$ 3.7 |  1.85 $\pm$ 0.24 |  69.8 $\pm$ 16.9 |  2.61 $\pm$ 0.39 | — | 341 | 353
36.0 $\pm$ 2.0 |  0.19 $\pm$ 0.18 |  20.2 $\pm$ 1.6 |  1.89 $\pm$ 0.04 |  225.6 $\pm$ 50.9 |  3.99 $\pm$ 0.73 | — | 381 | 353
40.0 $\pm$ 2.0 |  0.23 $\pm$ 0.47 |  17.6 $\pm$ 4.2 |  1.85 $\pm$ 0.25 |  76.3 $\pm$ 15.9 |  2.64 $\pm$ 0.42 | — | 331 | 353
Band |  |  |  |  |  |  |  |
Epoch | $\alpha$ |  |  | $E_{p}$ | $\beta$ |  NH | fit | dof
(s) |  |  |  | (keV) |  |  (1020 cm-2) | statistic |
44.0 $\pm$ 2.0 |  0.67 $\pm$ 0.39 | — | — |  37.7 $\pm$ 3.06 |  2.23 $\pm$ 0.05 | — | 334 | 355
48.0 $\pm$ 2.0 |  0.67 $\pm$ 0.47 | — | — |  42.2 $\pm$ 5.61 |  2.14 $\pm$ 0.05 | — | 337 | 355
55.0 $\pm$ 5.0 |  0.85 $\pm$ 0.19 | — | — |  35.5 $\pm$ 2.29 |  2.24 $\pm$ 0.05 | — | 384 | 355
65.0 $\pm$ 5.0 |  0.92 $\pm$ 0.35 | — | — |  36.4 $\pm$ 4.32 |  2.18 $\pm$ 0.08 | — | 317 | 355
85.0 $\pm$ 5.0 |  0.88 $\pm$ 0.13 | — | — |  7.74 $\pm$ 0.81 |  2.58 $\pm$ 0.11 | $4.81\pm 3.99$ | 373 | 453
95.0 $\pm$ 5.0 |  0.92 $\pm$ 0.17 | — | — |  5.81 $\pm$ 0.83 |  2.62 $\pm$ 0.15 | $<13.1$ | 468 | 530
105.0 $\pm$ 5.0 |  0.63 $\pm$ 0.75 | — | — |  4.59 $\pm$ 0.54 |  2.42 $\pm$ 0.10 | $<11.7$ | 442 | 445
115.0 $\pm$ 5.0 |  0.87 $\pm$ 0.30 | — | — |  4.88 $\pm$ 0.89 |  2.28 $\pm$ 0.12 | $<20.0$ | 468 | 616
125.0 $\pm$ 5.0 |  0.71 $\pm$ 0.63 | — | — |  3.30 $\pm$ 0.37 |  2.56 $\pm$ 0.54 | $<14.1$ | 310 | 408
135.0 $\pm$ 5.0 |  1.06 $\pm$ 0.35 | — | — |  4.04 $\pm$ 0.67 |  2.61 $\pm$ 0.74 | $<15.2$ | 375 | 567
150.0 $\pm$ 10.0 |  1.15 $\pm$ 0.15 | — | — |  3.31 $\pm$ 0.49 |  2.47 $\pm$ 0.39 | $0$ | 372 | 427
170.0 $\pm$ 10.0 |  1.37 $\pm$ 0.14 | — | — |  2.51 $\pm$ 0.30 |  2.73 $\pm$ 0.41 | $0$ | 348 | 478
Power-law |  |  |  |  |  |  |  |
Epoch |  |  |  |  | $\beta$ |  NH | fit | dof
(s) |  |  |  |  |  |  (1020 cm-2) | statistic |
75.0 $\pm$ 5.0 | — | — | — | — |  2.18 $\pm$ 0.04 | — | 360 | 357
190.0 $\pm$ 10.0 | — | — | — | — |  2.38 $\pm$ 0.11 | $9.52\pm 2.20$ | 297 | 573
210.0 $\pm$ 10.0 | — | — | — | — |  2.42 $\pm$ 0.08 | $8.33\pm 1.51$ | 345 | 528
230.0 $\pm$ 10.0 | — | — | — | — |  2.86 $\pm$ 0.13 | $8.46\pm 2.03$ | 311 | 630
250.0 $\pm$ 10.0 | — | — | — | — |  3.33 $\pm$ 0.18 | $11.6\pm 2.64$ | 228 | 714
270.0 $\pm$ 10.0 | — | — | — | — |  3.46 $\pm$ 0.20 | $14.0\pm 3.05$ | 181 | 251
290.0 $\pm$ 10.0 | — | — | — | — |  3.55 $\pm$ 0.28 | $13.4\pm 4.08$ | 122 | 523
Afterglow | — | — | — | — |  1.56 $\pm$ 0.07 |  1.19 $\pm$ 1.61 | 337 | 425
Table 1: Fitting results. Fits are grouped by model type and so are not necessarily in chronological order. GRB | $z$ | t90 | Eiso
---|---|---|---
|  | (s) | (erg)
050724 | $0.257$ | $98.7\pm 8.6$ | $1.71^{+0.13}_{-0.12}\times 10^{50}$
060614 | $0.125$ | $109.1\pm 3.4$ | $7.65^{+0.36}_{-0.33}\times 10^{50}$
061006 | $0.438$ | $129.8\pm 30.7$ | $6.74^{+0.41}_{-0.41}\times 10^{50}$
061210 | $0.41$ | $85.2\pm 13.1$ | $4.22^{+0.42}_{-0.41}\times 10^{50}$
070714B | $0.923$ | $65.6\pm 9.5$ | $1.16^{+0.09}_{-0.09}\times 10^{51}$
071227 | $0.381$ | $142.5\pm 48.4$ | $1.96^{+0.30}_{-0.29}\times 10^{50}$
150424A | $0.3$ | $81.1\pm 17.5$ | $6.25^{+0.65}_{-0.57}\times 10^{50}$
211211A | $0.076$ | $51.4\pm 0.8$ | $2.06^{+0.03}_{-0.02}\times 10^{51}$
211227A | $0.228$ | $83.8\pm 8.5$ | $1.14^{+0.03}_{-0.03}\times 10^{51}$
Table 2: Known EE GRBs from Gompertz13 ; Lien16 ; Gompertz20 . Values for $t_{90}$ are taken from Lien16 ; Lien21 . Here, $E_{\rm iso}$ is calculated in the 15 – 150 keV bandpass for consistency across all GRBs in the sample, and assumes a time-averaged spectrum. Epoch | $\alpha$ | $E_{c}$ | $\beta$ | fit statistic | dof | $\Delta_{\rm AIC}$
---|---|---|---|---|---|---
(s) |  | (keV) |  |  |  |
$1.0\pm 1.0$ | $1.41\pm 0.02$ | $3561.9\pm 1034.6$ | $<3.4\times 10^{5}$ | $413$ | $355$ | $94$
$3.0\pm 1.0$ | $0.92\pm 0.01$ | $624.4\pm 25.6$ | $2.35\pm 0.04$ | $642$ | $355$ | $159$
$5.0\pm 1.0$ | $1.02\pm 0.01$ | $453.5\pm 23.2$ | $2.36\pm 0.05$ | $582$ | $355$ | $177$
$7.0\pm 1.0$ | $0.86\pm 0.01$ | $716.9\pm 20.3$ | $2.22\pm 0.02$ | $1286$ | $355$ | $786$
$9.0\pm 1.0$ | $1.02\pm 0.01$ | $471.9\pm 26.8$ | $2.15\pm 0.03$ | $637$ | $355$ | $255$
$11.0\pm 1.0$ | $0.42\pm 0.09$ | $50.0\pm 6.04$ | $1.85\pm 0.02$ | $455$ | $355$ | $63$
$14.0\pm 2.0$ | $0.16\pm 0.23$ | $23.3\pm 4.62$ | $1.92\pm 0.02$ | $386$ | $355$ | $4$
$17.0\pm 1.0$ | $1.14\pm 0.03$ | $210.1\pm 21.7$ | $2.26\pm 0.08$ | $435$ | $355$ | $41$
$19.0\pm 1.0$ | $1.00\pm 0.03$ | $184.7\pm 16.2$ | $2.05\pm 0.04$ | $492$ | $355$ | $99$
$21.0\pm 1.0$ | $1.07\pm 0.03$ | $180.9\pm 15.7$ | $2.18\pm 0.06$ | $466$ | $355$ | $99$
$23.0\pm 1.0$ | $1.00\pm 0.04$ | $133.1\pm 12.7$ | $2.05\pm 0.04$ | $467$ | $355$ | $100$
$25.0\pm 1.0$ | $0.80\pm 0.05$ | $83.7\pm 8.32$ | $1.97\pm 0.03$ | $453$ | $355$ | $96$
$28.0\pm 2.0$ | $0.76\pm 0.09$ | $50.0\pm 5.96$ | $2.09\pm 0.03$ | $442$ | $355$ | $45$
$32.0\pm 2.0$ | $0.72\pm 0.14$ | $37.2\pm 6.17$ | $2.09\pm 0.03$ | $357$ | $355$ | $13$
$36.0\pm 2.0$ | $0.67\pm 0.13$ | $42.0\pm 6.79$ | $1.96\pm 0.02$ | $434$ | $355$ | $54$
$40.0\pm 2.0$ | $0.66\pm 0.14$ | $36.0\pm 5.92$ | $2.07\pm 0.03$ | $351$ | $355$ | $15$
$44.0\pm 2.0$ | $0.58\pm 0.23$ | $25.0\pm 5.58$ | $2.16\pm 0.03$ | $339$ | $355$ | $2$
$48.0\pm 2.0$ | $0.55\pm 0.28$ | $23.8\pm 6.49$ | $2.07\pm 0.03$ | $339$ | $355$ | $0$
Table 3: Best spectral fits obtained with the Band function during the IPC and EE phases. The Band function features a low and high energy photon index $\alpha$ and $\beta$, respectively. $E_{c}$ is the characteristic energy, related to the peak by $E_{c}=E_{p}/(2+\alpha)$. The $\Delta_{\rm AIC}$ column gives the AIC relative to the best fitting model, where $\Delta_{\rm AIC}>4$ is disfavoured and $\Delta_{\rm AIC}>10$ indicates no support for the model. Model | $\beta$ | $N_{\rm H}$ | $E(B-V)$ | $E_{b}$ |  $\chi^{2}$ (dof) | Null Hypothesis
---|---|---|---|---|---|---
|  | ($10^{20}{\rm cm^{-2}}$) | (mag) | (keV) |  | Probability
MW/POW | $1.22^{+0.03}_{-0.03}$ | $<3.45$ | $0.03^{+0.03}_{-0.03}$ | $-$ | 53 (32) | 0.012
LMC/POW | $1.22^{+0.03}_{-0.03}$ | $<3.45$ | $0.03^{+0.03}_{-0.03}$ | $-$ | 53 (32) | 0.011
SMC/POW | $1.21^{+0.02}_{-0.02}$ | $<3.35$ | $0.02^{+0.03}_{-0.02}$ | $-$ | 53 (32) | 0.01
MW/BKP | $1.48^{+0.11}_{-0.07}$ | $0.74^{+4.00}_{-0.74}$ | $0.06^{+0.04}_{-0.04}$ | $0.02^{+0.02}_{-0.01}$ | 34 (31) | 0.341
LMC/BKP | $1.48^{+0.11}_{-0.07}$ | $0.74^{+4.00}_{-0.74}$ | $0.06^{+0.03}_{-0.03}$ | $0.02^{+0.02}_{-0.01}$ | 33 (31) | 0.355
SMC/BKP | $1.48^{+0.11}_{-0.07}$ | $0.74^{+4.00}_{-0.74}$ | $0.05^{+0.03}_{-0.03}$ | $0.03^{+0.02}_{-0.01}$ | 33 (31) | 0.357
Table 4: Results from simultaneous UV/optical and X-ray spectral fits for the
SMC, LMC and MW dust-extinction law models, for both a power-law (POW) and a
broken power-law (BKP) continuum to the $5.5~{}{\rm ks}$ spectral energy
distribution. The lower energy photon index of broken-power-law model is fixed
to be $\alpha=2/3$, the $\beta$ listed below is for the higher energy spectral
index. The columns are: the model, photon index $\beta$, the host galaxy
equivalent column density (upper limits are given at $3\sigma$), host
$E(B-V)$, the break energy for the broken power-law $E_{b}$, the $\chi^{2}$
and degree of freedom (dof) of the fit, and finally the null hypothesis
probability. We take the fit with the highest value of $E(B-V)$ (MW/BKP) for
our $3\sigma$ limit in the main text.

## Extended Data

Figure 4: Count rate light curves for GBM (top) and BAT (middle) showing the
initial pulse complex ($t\lesssim 12$ s) and EE ($t\gtrsim 16$ s). The first
pulse, on which both detectors triggered, is remarkably weak and is separated
from the main emission episode by almost 2 s. It may represent a ‘precursor’
event before the merger. The lower panel shows the relative AIC ($\Delta_{\rm
AIC}$) for the models described in Methods. The preferred model always has
$\Delta_{\rm AIC}=0$. Spectral slices are indicated by the dotted grey lines.
Figure 5: The X-ray light curves of the sample in Supplementary Table 2 in
luminosity space. They have been all fit with an exponential profile, and show
remarkably consistent behaviour with the exception of the poorly-sampled GRB
061006. Combined with the blueprint of spectral evolution found for GRB
211211A in this work, this implies very uniform emission physics. Figure 6: A
joint fit of XRT and UVOT data centred around 163 s. The red dashed line marks
the position of $E_{p}$ in the fit, while $E_{b}$ is marked by the blue dashed
line. The expected synchrotron photon index of 2/3 over-predicts the UV
detection by an order of magnitude. This requires a spectral break or an
additional source of absorption that cannot be explained by host galaxy
extinction along the line of sight (see Methods).

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