A Cosmological Fireball with Thirty-Percent Gamma-Ray Radiative Efﬁciency


 Gamma-ray bursts (GRBs) are the most powerful explosions in the universe. The composition of the jets is, however, subject to debate\cite{Peer2015,Zhang2018}. Whereas the traditional model invokes a relativistic matter-dominated fireball with a bright photosphere emission component\cite{Meszaros2000}, the lack of the detection of such a component in some GRBs\cite{Abdo2009} has led to the conclusion that GRB jets may be Poynting-flux-dominated\cite{Zhang2009}. Furthermore, how efficiently the jet converts its energy to radiation is poorly constrained. A definitive diagnosis of the GRB jet composition and measurement of GRB radiative efficiency requires high-quality prompt emission and afterglow data, which has not been possible with the sparse observations in the past. Here we report a comprehensive temporal and spectral analysis of the TeV-emitting bright GRB 190114C. Its fluence is one of the highest of all GRBs detected so far, which allows us to perform a high-significance study on the prompt emission spectral properties and their variations down to a very short timescale of about 0.1 s. We identify a clear thermal component during the first two prompt emission episodes, which is fully consistent with the prediction of the fireball photosphere model. The third episode of the prompt emission is consistent with synchrotron radiation from the deceleration of the fireball. This allows us to directly dissect the fireball energy budget in a parameter-independent manner\cite{Zhang2021} and robustly measure a nearly $30\%$ radiative efficiency for this GRB. The afterglow microphysics parameters can be also well constrained from the data. GRB 190114C, therefore, exhibits the evolution of a textbook-version relativistic fireball, suggesting that fireballs can indeed power at least some GRBs with high efficiency.

Gamma-ray bursts (GRBs) are the most powerful explosions in the universe. The composition of the jets is, however, subject to debate 1,2 . Whereas the traditional model invokes a relativistic matter-dominated fireball with a bright photosphere emission component 3 , the lack of the detection of such a component in some GRBs 4 has led to the conclusion that GRB jets may be Poynting-flux-dominated 5 . Furthermore, how efficiently the jet converts its energy to radiation is poorly constrained. A definitive diagnosis of the GRB jet composition and measurement of GRB radiative efficiency requires high-quality prompt emission and afterglow data, which has not been possible with the sparse observations in the past. Here we report a comprehensive temporal and spectral analysis of the TeV-emitting bright GRB 190114C. Its fluence is one of the highest of all GRBs detected so far, which allows us to perform a high-significance study on the prompt emission spectral properties and their variations down to a very short timescale of about 0.1 s. We identify a clear thermal component during the first two prompt emission episodes, which is fully consistent with the prediction of the fireball photosphere model. The third episode of the prompt emission is consistent with synchrotron radiation from the deceleration of the fireball. This allows us to directly dis-sect the fireball energy budget in a parameter-independent manner 6 and robustly measure a nearly 30% radiative efficiency for this GRB. The afterglow microphysics parameters can be also well constrained from the data. GRB 190114C, therefore, exhibits the evolution of a textbook-version relativistic fireball, suggesting that fireballs can indeed power at least some GRBs with high efficiency.
On 14 January 2019 at 20:57:02. 63 Universal Time (UT) (hereafter T 0 ), an ultra-bright burst, GRB 190114C, was first triggered on by the Gamma-ray Burst Monitor (GBM) onboard the Fermi Gamma-ray Space Telescope 7 and the Neil Gehrels Swift Observatory's (Swift hereafter) Burst Alert Telescope (BAT) 8 . Soon after, the Large Area Telescope (LAT) onboard Fermi, Konus-Wind, INTEGRAL/SPI-ACS, AGILE/MCAL, and the Insight-HXMT/HE were also triggered. Long-lasting and multi-wavelength afterglow observations were carried out by Swift in the X-ray and optical bands, and by several ground-based optical and radio telescopes (such as GROND 9 , GTC 10 , VLA 11 , MeerKAT 12 ).
The prompt emission lightcurve ( Figure 1) consists of three distinct emission episodes. The first emission episode (i.e., P 1 ) starts at ∼ T 0 and lasts for ∼ 2.35 s, the second emission episode (i.e., P 2 ) exhibits multiple peaks and lasts from ∼ T 0 +2.35 s to ∼ T 0 +15 s, and the significantly fainter third emission episode (i.e., P 3 ) extends from ∼ T 0 +15 s to ∼ T 0 +25 s. First, P 1 and P 2 exhibit a non-thermal and a sub-dominant thermal component as first discovered in Ref. 13 . The thermal components in P 1 and P 2 evolve independently (Figure 2). Such a feature provides a unique opportunity to study the jet composition and photosphere properties at distinctly different epochs of central engine activities. Second, the non-thermal spectral shape in P 3 is consistent with a synchrotron-radiation origin from afterglow emission 14,15 . The afterglow phase of this GRB has the most complete observations in terms of spectral coverage, from radio all the way to TeV gamma-rays. This provides another unique opportunity to study the GRB afterglow properties within the framework of synchrotron and synchrotron self-Compton model.
We perform a time-resolved spectral analysis for the Fermi-GBM observations. Thanks to its high fluence of (4.436±0.005)×10 −4 erg cm −2 as the fifth highest fluence GRB ever observed with Fermi-GBM, we were able to divide its T 90 (measured as the time interval between when 5% and 95% of the total flux was recorded) duration (116 s) into 48 slices, with each time bin containing enough photons to conduct a high-significance spectral analysis (see Methods). The CPL+BB (CPL: Cutoff powerlaw, BB: Blackbody) model 13, 16 gives a better fit in comparison with the CPL model and other models (see Methods) from T 0 +0.55 s to T 0 +1.93 s in P 1 (includes 8 slices, hereafter P th 1 ) and from T 0 +2.45 s to T 0 +5.69 s in P 2 (includes 16 slices, hereafter P th 2 ) based on the deviance information criterion (DIC). P th 1 and P th 2 correspond to the peak flux of the P 1 and P 2 , respectively, which precisely correspond to the epochs when the power-law index α of the single CPL fits (see Methods) are beyond the limits of the synchrotron line of death 17 , i.e. α > −2/3. This is an indication of the existence of a thermal component as also reported in Ref. 16 . An example of an νF ν spectrum for one time slice (4.95 s-5.45 s) with the CPL+BB model giving the best fit is displayed in Figure 3. In this example, a thermal component is superimposed on the CPL component that is presumably of a synchrotron origin.
We compared the properties of the thermal components identified in P 1 and P 2 . The evolutions of the characteristic temperatures (kT ) in P 1 and P 2 follow distinct broken power-law decays: a smooth decay of the temperature followed by a fast drop (see the left panel in Figure 2). The temporal feature in each individual pulse is consistent with the typical observations that showed a temperature evolution with a broken power law in time 18, 19 , but such a feature in two independent pulses in one burst has never been identified in previous observations. The temporal behaviours showing different decay indices between two different pulses within a single GRB suggests that the GRB central engine ejects distinct independent jet components during its active phase. We note that several GRBs with statistically significant thermal components have been observed by BATSE, Konus, Swift, and Fermi before 13, 16, 20, 21 . However, they are either single-pulse bursts (e.g. GRB 110721A 21 ), or highly overlapping multi-pulse bursts (e.g. GRB 090902B 20 ), or their thermal emission component is not strong enough (e.g. GRB 100724B 13 ), so that the photosphere properties could not be studied in detail among distinct pulses. The unique advantages of GRB 190114C, i.e. its low redshift, high fluence, several well-separated pulses in one single GRB, and a strong thermal component, make such a study possible.
Within the framework of the standard fireball photosphere model 22 , we can infer the photosphere characteristics and the ratio of thermal to non-thermal emission to obtain information on the jet properties, such as the bulk Lorentz factor Γ and the initial size of the jet r 0 . Figures 2 and Extended Data 2 show the evolution of the bulk Lorentz factor Γ and the parameter (the effective transverse size of the emitting region 19 ), respectively; they exhibit similar temporal behaviors in P 1 and P 2 , i.e., a broken power-law evolution behavior, with increasing with time and Γ decreasing over time. The comparison of the properties with a global view is summarised in Table 1. The best-fitting results of the relevant parameters with a power-law model are listed in Table 2.
The time-resolved analysis shows that almost all the low-energy photon index α values of the CPL-only fits in P 3 are much softer than those in P 1 and P 2 (Figure 1), suggesting that the emission has a different origin. α gradually decreases toward −2 (similar to the results reported in Ref. 16 ), a typical value for synchrotron radiation, which indicates that the fireball is entering the afterglow phase. Assuming that the peak time of P 3 is the deceleration time when the mass of the ambient medium collected by the forward shock is comparable to 1/Γ of the mass entrained in the fireball 23, 24 , one can also estimate the Lorentz factor of the fireball at the deceleration radius, Γ 0 , using an independent method (see Methods). We find that the average bulk Lorentz factors measured during the prompt emission phase (Γ = 741 ± 18 for P 1 , Γ = 571 ± 12 for P 2 ) are slightly higher than the bulk Lorentz factor measured at the deceleration radius (Γ 0 = 507 ± 5 for P 3 ). This is fully consistent with the prediction of the GRB fireball model, which predicts that a fraction of the kinetic energy is dissipated during the prompt emission phase.
The derived Lorentz factors and the photosphere radii exhibit systematic variations, with the Lorentz factor decreasing from ∼ 1000 to ∼ 200 (Figure 2), and the photosphere radius varying on the order of 10 12 cm (Extended Data Figure 3). This is likely related to the behavior of the GRB central engine. The decay of Γ in P 1 and P 2 is consistent with the expectation that faster ejecta from the engine tends to reach the photosphere earlier than slower ejecta, and the rapid decline at the end of each episode may be related to the high-latitude emission of the fireball as the engine activity abruptly ceases 25, 26 . Since the Lorentz factor range is not very wide, it is expected that the deceleration of the fireball is essentially prompt without a significant energy injection phase due to the pile up of the slow materials. This is consistent with the power-law decay with time of multi-wavelength afterglow emission from the source 27-29 .
The above-mentioned two methods of measuring Lorentz factors both rely on some unknown parameters. By combining the photosphere data in P 1 and P 2 and the afterglow data in P 3 , one can dissect various energy components in the fireball in a parameter-independent way 6 . A systematic search for previously detected GRBs did not reveal a single case showing both a significant photosphere signature and an afterglow deceleration signature 6 . GRB 190114C therefore provides the first case with which a parameter-independent diagnosis of fireball parameters can be carried out. We perform a time-integrated spectral fit to the prompt emission spectrum of P 1 and P 2 (0.55 -1.93 s and 2.45-5.69 s) with the CPL+BB model and derived the observed properties (including both the thermal and non-thermal components) of the fireball as shown in Table 3. Following Ref. 6 (Methods), we can for the first time robustly derive the following physical parameters of a GRB fireball (Table 3): initial dimensionless specific enthalpy density η = 708±8, bulk Lorentz factor at the photosphere Γ ph = 666 ± 6, bulk Lorentz factor before deceleration Γ 0 = 507 ± 5, and fireball isotropic-equivalent mass loading M iso = (8.6 ± 0.6) × 10 −4 M . This gives a direct measurement of the fireball radiative efficiency η γ = (28.3 ± 1.4)%. This measured efficiency has much smaller uncertainties than the values derived for previous GRBs using afterglow modeling 30, 31 . A high fireball radiative efficiency has been theorized in the past but with a large uncertainty 3, 32 . Our measured η γ ∼ 30% suggests that a GRB fireball can indeed emit both thermal and non-thermal gamma-rays efficiently.
With the solved fireball parameters, the isotropic kinetic energy of the fireball at the afterglow phase is measured as E k,iso 7.8 × 10 53 erg. This allows us to make use of this prompt-emissionmeasured E k,iso in the afterglow model to constrain shock microphysics parameters (Methods). Using broad-band afterglow data, we can derive an electron injection power law index p 2.85 and the inverse Compton parameter Y ∼ 0.75. This leads to the solution to the two equipartition parameters of electrons and magnetic fields: e 0.14 and B ∼ 9 × 10 −4 (Methods). These parameters are usually poorly constraints in other GRBs and are often assumed to perform modeling. We are able to measure these values precisely, which are also broadly consistent with the more detailed afterglow modeling on the event 29

Author contributions
LL led the data analysis (the spectral fittings, the tables, and the plots), and contributed to part of the physical explanations of this particular event. YW assisted the data analysis and inspired the discovery of dual thermal evaluations, and contributed to the theoretical explanation. BZ was in charge of the framework of this article, and proposed the method of deriving fireball parameters from data. FR and AP participated in the physical explanations. DAK analysed and constructed the optical lightcurve. KP analysed the Swift-XRT data. FR, SG and AJC-T helped with the data analysis. LL, YW, BZ, DAK and KP wrote the article. All co-authors contributed to the article.
Correspondence and requests for materials should be addressed to LL (liang.li@icranet.org), YW (yu.wang@uniroma1.it), and BZ (zhang@physics.unlv.edu). (pink) and P th 2 (blue). Two horizontal dashed lines represent the limiting values of α=-2/3 and α=-3/2 for electrons in the synchrotron slow-and fast-cooling regimes, respectively. The data points connected by solid lines (orange) represent the temporal evolution of the low-energy photon index α of the CPL-only model.      Table 1: Comparison of properties between the two independent thermal emission episodes in GRB 190114C, which includes the observed and photospheric properties. For each thermal pulse, the table lists the durations; the best-fit parameters for the cut-off energy (E c ) and the temperature (kT ), which are based on the CPL+BB model considering the time-integrated spectral analysis; the derived parameters, thermal F BB and total F tot energy flux; the averaged thermal flux ratio (F BB /F tot ); the thermal (S BB ) and total (S) fluence, the averaged thermal (L BB,γ,iso ) and total (L γ,iso ) luminosities; and the isotropic thermal (E BB,γ,iso ) and total (E γ,iso ) energies, the bulk Lorentz factor Γ, the photospheric radius r ph , saturation radius r s , and nozzle radius r 0 .   The measured quantities from observations and the derived fireball parameters using our new methods (see Methods) with assuming Y = 1 and n = 1 cm −3 . The measured quantities include the isotropic equivalent thermal energy E th,iso and the non-thermal energy E nth,iso , the total F obs γ and the thermal F obs BB flux, the deceleration time t dec , the average temperature kT obs of the thermal component, and the redshift; the derived fireball parameters consist of the dimensionless specific enthalpy density at the engine η, the bulk Lorentz factor at the site of the photopshere Γ ph , the initial afterglow Lorentz factor before the deceleration phase Γ 0 , the isotropic equivalent total mass M iso , the kinetic energy in the fireball E k,iso , and the γ-ray radiative efficiency η γ , as well as the energy fractions assigned to electrons ( e ) and magnetic ( B ) fields, the characteristic synchrotron frequency (ν m ) and the cooling frequency (ν c ) of minimum-energy injected electrons, and the Klein-Nishina frequency (ν KN )

Methods
Uniqueness of Thermal Pulses of GRB 190114C GRB 190114C is unique in terms of the following aspects. (1) It has three well-separated emission episodes, which can be defined as the first, second, and third pulses. (2) The emission of the first two main pulses consists of two strong thermally-dominated episodes, which independently exhibit similar temporal properties. (3) The first two pulses (thermal) and the third pulse (non-thermal) have distinct spectral properties. (4) The thermal component has a thermal to total flux ratio of around 30%, which is the second highest among the GRBs observed with Fermi-GBM so far (the highest one is observed in GRB 090902B, with thermal flux ratio ∼ 70%). (5) Strong TeV emission was observed, setting the record of the highest photon energy in any GRB 27 . The two well-separated pulses with independent and analogous thermal component evolution pattern make this extraordinarily bright GRB a unique event to study the jet composition and photospheric properties evolution in a single GRB. We note that in the cases of a hot fireball jet characterised by a quasi-thermal Planck-like spectrum (e.g. GRB 090902B 4 ), a Poynting-flux-dominated outflow characterised by a Band (or cutoff power-law)-only function (e.g., GRB 080916C 33 and GRB 130427A 34 ), a hybrid jet characterised by either a twocomponent spectral scenario (composed of a non-thermal component and a thermal component simultaneously, e.g., GRB 110721A 21, 35 ), or a transition from fireball to Poynting-flux-dominated outflow within a single GRB (e.g., GRB 160625B [36][37][38], have been observed in the past. However, GRB 190114C presented unique information not available before.

Data Reduction
We reduced the GBM data using a Python package, namely, The Multi-Mission Maximum Likelihood Framework (3ML 39 ). The data we used for our spectral analysis includes the two most strongly illuminated sodium iodide (NaI) scintillation detectors (n3, n4) and the mostilluminated bismuth germanium oxide (BGO) scintillation detector (b0) on board Fermi-GBM, as well as the corresponding response files (.rsp2 files are adopted). The detector selections were made considering to obtain an angle of incidence less than 40, 41 60 • for NaI and the lowest angle of incidence for BGO. The Time-Tagged Event (TTE) data type is used for the NaI data (8 keV-1 MeV) and BGO data (200 keV-40 MeV). In order to aviod the K-edge at 33.17 keV, the spectral energy range was also considered to cut from 30 to 40 keV. The background fitting is chosen using two off-source intervals, including the pre-burst (-20∼-10 s) and post-burst (180∼200 s) epochs, and with the determined polynomial order (0-4) by applying a likelihood ratio test. The source interval is selected over the duration (-1∼116 s) reported by the Fermi-GBM team. The maximum likelihood-based statistics, the so-called Pgstat, are used, given by a Poisson (observation)-Gaussian (background) profile likelihood 42 .
Bayesian Spectral Analysis The spectral parameters are obtained by adopting a fully Bayesian analysis approach. The main idea is that after the experimental data are obtained, Bayes's theorem is applied to infer and update the probability distribution of a specific set of model parameters. Building up a Bayesian profile model (M ), and given an observed data set (D), the posterior probability distribution p(M | D), according to the Bayes's theorem, is given by where, p(D | M ) is the likelihood that combines the model and the observed data, and expresses the probability to observe (or generate) the dataset D from a given a model M with its parameters; p(M ) is the prior on the model parameters; and p(D) is called the evidence, which is a constant with the purpose of normalisation. We utilise the typical spectral parameters from the F ermi-GBM catalogue as the prior distributions: We employ a Markov Chain Monte Carlo (MCMC) sampling method (emcee 43 ) to sample the posterior. The parameter estimation is obtained at a maximum a posteriori probability from the Bayesian posterior density distribution, and its uncertainty (or the credible level) is evaluated from the Bayesian highest posterior density interval at 1σ (68%) Bayesian credible level.

Time-integrated and time-resolved Spectral Analysis
We first perform the time-integrated spectral analysis (treating the entire T 90 as one time bin, i.e., from T 0 to T 0 + 116 s) by using various GRB spectral models, including power-law (PL), cutoff power law (CPL), Band function 44 , PL+blackbody (BB), CPL+BB, and Band+BB, respectively. The time-integrated spectral analysis suggests that the CPL+BB model can best characterise the spectral shape of the burst (see Sec. Model Comparison). The corresponding corner plot is shown in Figure 1 of the Extended Data.
GRB spectra are known to evolve over different pulses, or even within a pulse. The timeintegrated spectral analysis, therefore, must be replaced by the time-resolved spectral analysis in order to study the GRB radiation mechanism in great detail. We first use the typical GRB spectral model, the Band model 44 , to fit the time-resolved spectra in each slice (see Sec. BBlocks Methods). We found that the low-energy photon index α exhibits a wide-spread temporal variability (-0.14 to -1.99), and the majority of α values in the first two pulses are harder than the typical value of α defined by the synchrotron line of death (α=-2/3) 17 , suggesting a significant contribution from thermal emission from the fireball photosphere 3, 20 . The majority of the high energy photon index β values are not well-constrained, indicating that the CPL model is preferred in comparison with the Band model. The violation of the synchrotron limit encourages us to search for an additional thermal component. In order to search for the best model to characterise the spectral shape of the burst, we attempt to fit the time-resolved spectra in each slice with both the CPL and the CPL+BB models. The DIC of the CPL+BB model is at least by 10 and can be hundreds less than the CPL model, indicating that adding a thermal component improves the spectral fitting greatly (∆DIC > 10, Ref. 45 ).

Model Comparison
The best-fit model is reached by comparing the DIC values of different models and picking the one with the lowest value. The DIC is defined as DIC=-2log[p(data|θ)]+2p DIC , whereθ is the posterior mean of the parameters, and p DIC is the effective number of parameters. The preferred model is the one that provides the lowest DIC score. We report the ∆DIC values by comparing the best model with other models in Table 1 in the Extended Data. Log(posterior) is adopted by the method of the maximum likelihood ratio test, which is treated as a reference of the model comparison 46 .
BBlocks Methods We use a method called Bayesian blocks (BBlocks) 47 to rebin the Time Tagged Event (TTE) lightcurve. Time bins are selected in such a way as to capture the true variability of the data. Such a calculation requires each bin to be consistent with a constant Possion rate. In each bin, it allows for a variable time width and signal-to-noise (S/N) ratio. We therefore apply the BBlocks method with the false alarm probability p 0 = 0.01 and the consideration of adequate significance to repartition the TTE lightcurve of the most strongly illuminated GBM detector (n4), other used detectors are binned in matching slices. We notice that the BBlocks analysis generates two slices (0.70 ∼ 1.58 s and 1.58 ∼ 1.71 s) from 0.70 s to 1.71 s. On the other hand, the two slices have a very high significance (263.97 and 115.59). In order to study the parameter evolution in great detail, we therefore rebin the time intervals with five narrower slices > 80 instead. We also did the same analysis on the last slice of P 2 (5.51 ∼ 5.69 s), generating two narrower slices (5.51 ∼ 5.65 s and 5.65 ∼ 5.69 s), with the significance > 70 each, to study the temperature evolution in more detail. We therefore obtain 8 slices for P th 1 and 16 slices for P th 2 to study the photosphere properties.

Multi-wavelength Observations TeV (MAGIC) Observations:
The Major Atmospheric Gamma Imaging Cherenkov (MAGIC) telescopes observed for the first time very-high-energy gamma-ray (> 1 TeV) emission from T 0 +57 s until T 0 +15912 s 27 , setting the record of the highest energy photon detected from any GRB. Both the TeV lightcurve and spectrum can be well-described by a power-law model 1 , with the temporal decay indexα MAGIC =1.40±0.04 and the spectral decay indexβ MAGIC =2.16±0.30 ( Figure 5 in the Extended Data). The total TeVband (0.3-1 TeV) energy integrated between T 0 +6 s and T 0 +2454 s is E MAGIC iso ∼ 2.0×10 52 erg (Ref. 27 ).
keV (Swift-XRT) Observations: Following the trigger by Swift-BAT, the spacecraft slewed immediately to the location of the burst. The X-ray Telescope (XRT) began observing the afterglow at T 0 +64 s. Pointed Windowed Timing mode data were collected from T 0 +68 s to T 0 +626 s, after which the count rate was low enough for Photon Counting mode to be utilised. The burst was followed for more than 28 days, although the last detection occurred on T 0 +20 day. The XRT lightcurve showed a typical power-law behaviour with a power-law indexα XRT =1.39+0.01 ( Figure  5 in the Extended Data). The isotropic X-ray energy release E XRT,iso measured by Swift-XRT (0.3-10 keV) from T 0 +68 s to T 0 +13.86 days is 2.11×10 52 erg.
Optical Observations: Optical data have been gathered from refs. 27, 50, 51 as well as GCN data from refs. 52-59 . The automatically processed UVOT data are also used. All afterglow data have been host-subtracted using the host-galaxy values taken from ref. 60 . Note that ref. 50 found chromatic evolution in their early RINGO3 data. However, this effect is small, which leads to some additional scatter around the first steep-to-shallow decay transition. After the respective host galaxy magnitude has been subtracted for each band, all the bands are shifted to the R c band to produce a composite lightcurve stretching from 33 s to 14.2 days after the GRB trigger. The lightcurve can be described by multiple power-law decay segments in a steep-shallow-steep arrangement. The first two segments have slopesα opt,1 = 2.076 ± 0.023 andα opt,2 = 0.544 ± 0.011, with a break time at t b,1 = 0.00508 ± 0.0003 d and a smooth transition index with n = −0.5 ( Figure 5 in the Extended Data). After a second, sharp break at t b,2 = 0.576 ± 0.028 d, the lightcurve decays witĥ α opt,3 = 1.067 ± 0.011. We find no evidence for a further break, in agreement with X-ray data, implying that the final slope seen in the data is either an unprecedentedly shallow post-jet-break decay slope (see the sample of 61 for comparison) or there is no jet break up to ≈ 10 d after the GRB trigger.
Deriving the Photosphere Properties Using the Traditional Method The thermal emission of GRB 190114C is extremely strong, ranking second in thermal-to-total flux ratio (30%) among the over 2700 GRBs observed by Fermi-GBM up to date (Figure 4 and Table 4 in the Extended Data). The identification of the strong thermal component in GRB 190114C allows us to determine the physical properties of the relativistic outflow within the framework of the non-dissipative photosphere theory 22, 62 . The photosphere photons observed at a given time, corresponding to one time bin in our time-resolved analysis, are assumed to be emitted from an independent thin shell. Therefore, the observed BB temperature kT obs , the BB flux F BB , and the total flux F tot (thermal+non-thermal) of a given time bin determine the photosphere properties of the corresponding shell. The entire duration of photosphere emission is conjugated by the emissions from a sequence of such shells. One can infer the bulk Lorenz factor Γ, and the initial size of the flow R 0 in each time bin and their temporal evolutions (Table 3 in the Extended Data).
The photosphere properties can be derived by considering the framework within the standard fireball model 22 . For a given shell, it is generated at an initial radius and self-accelerates to reach a saturated Lorentz factor in the coasting phase. If the photosphere radius is greater than the saturation radius, it reads where the dimensionless parameter presents the effective transverse size of the photosphere. The burst luminosity L 0 = 4πd 2 L Y F tot is given by the observation, Y is the ratio between the total fireball energy and the energy emitted in gamma-rays. The numerical factor ξ is of the order of unity that can be obtained from angular integration. The luminosity distance d L of redshift z is integrated by assuming the standard Friedmann-Lemaître-Robertson-Walker (FLRW) metric. Other physical constants are the Thomson cross section σ T , the proton rest mass m p , the speed of light c, and the Stefan-Boltzmann constant σ B .
Directly Deriving the Fireball Properties from Observations GRB 190114C has a redshift measurement. Its prompt emission is thermally dominated and its lightcurve has a clear early pulse indicating the afterglow initiation. These three properties make it the first case where one can use observational properties to directly determine the fireball characteristics including the dimensionless specific enthalpy density at the engine η, isotropic equivalent total mass M , bulk Lorentz factor at the site of the photopshere Γ ph , initial afterglow Lorentz factor before the deceleration phase Γ 0 , the kinetic energy in the fireball E k , and γ-ray radiative efficiency η γ . The method described below follows Ref. 6 .
The initial, total energy of a fireball is The fireball undergoes rapid acceleration and reaches a Lorentz factor Γ ph at the photosphere. The internal energy released as thermal emission can be estimated as Afterwards, the fireball moves at an almost constant speed until internal dissipation at internal shocks occurs at a larger distance. The emitted non-thermal emission can be estimated as where Γ 0 is the Lorentz factor after the dissipation and also the initial Lorentz factor in the afterglow phase.
The Lorentz factor at photosphere radius Γ ph can be estimated as (modified from Ref. 22, 63 , see Ref. 6 for details) which involves several direct observables including redshift z, total flux F obs γ , thermal flux F obs BB and the observed temperature T . Other parameters are the pair multiplicity parameter Y which is commonly taken as 1, the luminosity distance D L computed from the redshift adopting the FLRW cosmology, and fundamental constants such as speed of light c, proton mass m p , Thomson cross section σ T , and Stefan-Boltzmann constant σ B .
The initial Lorentz factor of the afterglow phase Γ 0 can be derived by equating the kinetic energy to the swept-up ISM mass at the deceleration time t dec , which is an observable indicated by a light-curve pulse (the third pulse for 190114C). Using Eq.(7.81) of 2 and above arguments, we derive where n is the ISM density assumed as one particle per cubic centimetre as usual. The value of t dec is determined in Figure 6.
Simultaneously solving Eqs. 8 -11, we obtain fireball parameters η, Γ ph , M and Γ 0 , and in turn. Then we can calculate the kinetic energy of the afterglow and the efficiency of the prompt gamma-ray emission Applying this to GRB 190114C, all the measured quantities are presented in the upper panel of Table 3, and all the derived parameters are presented in the lower panel of Table 3.

Further Estimate of the Energy Fractions Assigned to Electrons ( e ) and Magnetic ( B ) fields
Once E k is precisely obtained from the observational data using our new methods discussed above, one can estimate the energy fractions assigned to electrons ( e ) and magnetic ( B ) fields using afterglow models (ref. 30 ).
The isotropic blastwave kinetic energy (E K,iso ) can also be measured from the afterglow emission (normal decay) using the Swift-XRT data. For a constant density interstellar medium (ISM), the characteristic synchrotron frequency and the cooling frequency of minimum-energy injected electrons, and the peak spectral flux, therefore, can be given by 30, 64, 65 ν c = 6.3 × 10 15 Hz(1 where p is the electron spectral distribution index, e and B are the energy fractions assigned to electrons and magnetic fields, t d is the time in the observer frame in units of days, D 28 = D/10 28 , is the luminosity distance in units 2 of 10 28 cm, n is the number density in the constant density ambient medium, and The spectral regime can be determined by using the closure relation in the afterglow emission via the observed temporal (α) and spectral (β) indices. The temporal indexα XRT is measured from the Swift-XRT lightcurve (see Figure 5), and the corresponding spectral indexβ XRT = −(Γ XRT − 1) = −0.93 ± 0.10 (Γ XRT is the photon spectral index) is available from the Swift online server 66,67 . Using the temporal and spectral indices, one can therefore determine that the X-ray emission in GRB 190114C is in the ν m < ν x < ν c regime. With the spectral regime known, the electron index p can be derived using the observed temporal index: p = (3 − 4α XRT )/3 = 2.85 ± 0.01.

21
This gives, E K,iso,52 = νF ν (ν = 10 18 Hz) 6.5 × 10 −13 ergs −1 cm −2 4/(p+3) ×D 8/(p+3) 28 where νF ν (ν = 10 18 ) Hz is the energy flux at frequency 10 18 Hz in units of erg s −1 cm −2 , and is a function of the electron power-law index p. Extended Data Figure 6: The count GBM lightcurve (black) with the best fitting (purple line) to the third pulse using the FRED model. Table 1: Comparison of ∆DIC between the best model to other various models, which is based on the time-integrated spectral analysis. Table 2: Spectral parameters of the slices having a thermal component in GRB 190114C. Table 3: Photosphere properties of the slices having a thermal component in GRB 190114C. Table 4: Time-resolved spectral fit results of GRB 190114C.   1) The LAT data are separated into two part at ∼15 s, and here we only fit the second (afterglow) part (>15s).

Extended Data
(2) The optical Rc-band has been corrected for Galactic and host extinction, and the contribution from the host galaxy has also been subtracted. This lightcurve has been created by shifting data from different bands to the R band (see Methods). Right panel: multi-wavelength spectrum covering the energy in MeV, GeV, and TeV emission, which is simultaneously observed from T 0 +68 s to T 0 +110 s by Fermi-GBM, Fermi-LAT, and MAGIC, respectively    best-fitted model, the ∆DIC between CPL+BB and CPL models, the temperature, the thermal and total flux, and the ratio of thermal flux. Flux is defined in the energy band of 1 keV to 10 MeV. For the slices of ∼ 3 s to ∼ 4 s, Band+BB offers a very close goodness of fitting as CPL+BB, for the global consistency, and considering the time-integrated spectrum is best fitted by CPL+BB, here we perform all the thermal analysis using CPL+BB.