Bayesian Time-Resolved Spectroscopy of GRB Pulses
Authors
Yu Hoi-Fung, Ryde Fyde, & Dereli-Bégué Hüsne
Year
2019
Journal
The Astrophysical Journal, 866, 20, 14 pp.
Abstract
We performed time-resolved spectroscopy on a sample of 38 single pulses from 37 gamma-ray bursts detected by the Fermi/Gamma-ray Burst Monitor during the first 9 yr of its mission. For the first time a fully Bayesian approach is applied. A total of 577 spectra are obtained and their properties studied using two empirical photon models, namely the cutoff power law (CPL) and Band model. We present the obtained parameter distributions, spectral evolution properties, and parameter relations. We also provide the result files containing this information for usage in further studies. It is found that the CPL model is the preferred model, based on the deviance information criterion and the fact that it consistently provides constrained posterior density maps. In contrast to previous works, the high-energy power-law index of the Band model, β, has in general a lower value for the single pulses in this work. In particular, we investigate the individual spectrum in each pulse, that has the largest value of the low-energy spectral indexes, α. For these 38 spectra, we find that 60% of the α values are larger than −2/3, and thus incompatible with synchrotron emission. Finally, we find that the parameter relations show a variety of behaviors. Most noteworthy is the fact that the relation between α and the energy flux is similar for most of the pulses, independent of any evolution of the other parameters.
Non-Dissipative Photospheres in GRBs: Spectral Appearance in the Fermi/GBM Catalogue
Authors
Acuner Zeynep, Ryde Fyde, & Yu Hoi-Fung
Year
2019
Journal
Monthly Notices of the Royal Astronomical Society, 487, pp. 5508-5519
Abstract
A large fraction of gamma-ray burst (GRB) spectra are very hard below the peak. Indeed, the observed distribution of sub-peak power-law indices, α, has been used as an argument for a photospheric origin of GRB spectra. Here, we investigate what fraction of GRBs have spectra that are consistent with emission from a photopshere in a non-dissipative outflow. This is the simplest possible photospheric emission scenario. We create synthetic spectra, with a range of peak energies, by folding the theoretical predictions through the detector response of the FERMI/GBM detector. These simulated spectral data are fitted with typically employed empirical models. We find that the low-energy photon indices obtain values ranging −0.4 < α < 0.0, peaking at around −0.1, thus covering a non-negligible fraction of observed values. These values are significantly softer than the asymptotic value of the theoretical spectrum of α ∼ 0.4. The reason for the α values to be much softer than expected, is the limitation of the empirical functions to capture the true curvature of the theoretical spectrum. We conclude that more than a quarter of the bursts in the GBM catalogue have at least one time-resolved spectrum, whose α values are consistent with spectra from a non-dissipative outflow, releasing its thermal energy at the photosphere. The fraction of spectra consistent with emission from the photosphere will increase even more if dissipation of kinetic energy in the flow occurs below the photosphere.
On the α-Intensity Correlation in Gamma-Ray Bursts: Subphotospheric Heating with Varying Entropy
Authors
Ryde Fyde, Yu Hoi-Fung, Dereli-Bégué Hüsne et al.
Year
2019
Journal
Monthly Notices of the Royal Astronomical Society, 484, pp. 1912-1925
Abstract
The emission mechanism during the prompt phase in gamma-ray bursts (GRBs) can be investigated through correlations between spectral properties. Here, we revisit the correlation relating the instantaneous flux, F, and the photon index below the spectral break, α, in individual emission pulses, by studying the 38 most prominent pulses in the Fermi/Gamma-ray Burst Monitor GRB catalogue. First, we search for signatures of the bias in the determination of α due to the limited spectral coverage (window effect) expected in the synchrotron case. The absence of such a characteristic signature argues against the simplest synchrotron models. We instead find that the observed correlation between F and α can, in general, be described by the relation F(t)∝ekα(t), for which the median k = 3. We suggest that this correlation is a manifestation of subphotospheric heating in a flow with a varying entropy. Around the peak of the light curve, a large entropy causes the photosphere to approach the saturation radius, leading to an intense emission with a narrow spectrum. As the entropy decreases the photosphere secedes from the saturation radius, and weaker emission with a broader spectrum is expected. This simple scenario naturally leads to a correlated variation of the intensity and spectral shape, covering the observed range.
Bayesian Analysis on the X-Ray Spectra of the Binary Neutron Star Merger GW170817
Authors
Lin En-Tzu, Yu Hoi-Fung, & Kong Albert K. H.
Year
2019
Journal
Journal of High Energy Astrophysics, 21, pp. 1-5
Abstract
For the first time, we present a Bayesian time-resolved spectral study of the X-ray afterglow datasets of GW170817/GRB17017A observed by the Chandra X-ray Observatory. These include all 12 public datasets, from the earliest observation taken at t ∼ 9 d to the newest observation at ∼ 359 d post-merger. While our results are consistent with the other works using Cash statistic within uncertainty, the Bayesian analysis we performed in this work have yielded Gaussian-like parameter distributions. We also obtained the parameter uncertainties directly from their posterior probability distributions. We are able to confirm that the power-law photon index has remained constant of Γ ∼ 1.6 throughout the entire year-long observing period, except for the first dataset observed at t = 8.9 d when Γ = 1.04 ± 0.44 is marginally harder. We also found that the unabsorbed X-ray flux peaked at t ∼ 155 d, temporally consistent with the X-ray flare model suggested recently by Piro et al. (2019). The X-ray flux has been fading since ∼ 160 days after the merger and has returned to the level as first discovered after one year. Our result shows that the X-ray spectrum of GW170817/GRB170817A is well-described by a simple power-law originated from non-thermal slow-cooling synchrotron radiation.
Awakening the BALROG: BAyesian Location Reconstruction Of GRBs
Authors
Burgess J. Michael, Yu Hoi-Fung, Greiner Jochen, & Mortlock Daniel J.
Year
2018
Journal
Monthly Notices of the Royal Astronomical Society, 476, 1427-1444
Abstract
The accurate spatial location of gamma-ray bursts (GRBs) is crucial for both accurately characterizing their spectra and follow-up observations by other instruments. The Fermi Gamma-ray Burst Monitor (GBM) has the largest field of view for detecting GRBs as it views the entire unocculted sky, but as a non-imaging instrument it relies on the relative count rates observed in each of its 14 detectors to localize transients. Improving its ability to accurately locate GRBs and other transients is vital to the paradigm of multimessenger astronomy, including the electromagnetic follow-up of gravitational wave signals. Here we present the BAyesian Location Reconstruction Of GRBs (BALROG) method for localizing and characterizing GBM transients. Our approach eliminates the systematics of previous approaches by simultaneously fitting for the location and spectrum of a source. It also correctly incorporates the uncertainties in the location of a transient into the spectral parameters and produces reliable positional uncertainties for both well-localized sources and those for which the GBM data cannot effectively constrain the position. While computationally expensive, BALROG can be implemented to enable quick follow-up of all GBM transient signals. Also, we identify possible response problems that require attention and caution when using standard, public GBM detector response matrices. Finally, we examine the effects of including the uncertainty in location on the spectral parameters of GRB 080916C. We find that spectral parameters change and no extra components are required when these effects are included in contrast to when we use a fixed location. This finding has the potential to alter both the GRB spectral catalogues and the reported spectral composition of some well-known GRBs.
Bayesian Inference on the Radio-quietness of Gamma-ray Pulsars
Authors
Yu Hoi-Fung, Hui Chung Yue, Kong Albert K. H., & Takata Jumpei
Year
2018
Journal
The Astrophysical Journal, 857, 120, 8 pp.
Abstract
For the first time we demonstrate using a robust Bayesian approach to analyze the populations of radio-quiet (RQ) and radio-loud (RL) gamma-ray pulsars. We quantify their differences and obtain their distributions of the radio- cone opening half-angle δ and the magnetic inclination angle α by Bayesian inference. In contrast to the conventional frequentist point estimations that might be non-representative when the distribution is highly skewed or multi-modal, which is often the case when data points are scarce, Bayesian statistics displays the complete posterior distribution that the uncertainties can be readily obtained regardless of the skewness and modality. We found that the spin period, the magnetic field strength at the light cylinder, the spin-down power, the gamma-ray- to-X-ray flux ratio, and the spectral curvature significance of the two groups of pulsars exhibit significant differences at the 99% level. Using Bayesian inference, we are able to infer the values and uncertainties of δ and α from the distribution of RQ and RL pulsars. We found that δ is between 10° and 35° and the distribution of α is skewed toward large values.
On the Fermi GBM Event 0.4 sec after GW 150914
Authors
Greiner Jochen, Burgess Michael J., Savchenko Volodymyr, & Yu Hoi-Fung
Year
2016
Journal
The Astrophysical Journal Letters, 827, L38, 9 pp.
Abstract
In view of the recent report by Connaughton et al., we analyze continuous time-tagged event (TTE) data of Fermi-gamma-ray burst monitor (GBM) around the time of the gravitational-wave event GW 150914. We find that after proper accounting for low-count statistics, the GBM transient event at 0.4 s after GW 150914 is likely not due to an astrophysical source, but consistent with a background fluctuation, removing the tension between the INTEGRAL/ACS non-detection and GBM. Additionally, reanalysis of other short GRBs shows that without proper statistical modeling the fluence of faint events is over-predicted, as verified for some joint GBM–ACS detections of short GRBs. We detail the statistical procedure to correct these biases. As a result, faint short GRBs, verified by ACS detections, with significances in the broadband light curve even smaller than that of the GBM–GW150914 event are recovered as proper non-zero source, while the GBM–GW150914 event is consistent with zero fluence.
The Fermi GBM Gamma-Ray Burst Time-resolved Spectral Catalog: Brightest Bursts in the First Four Years
Authors
Yu Hoi-Fung, Preece Robert D., Greiner Jochen et al.
Year
2016
Journal
Astronomy and Astrophysics, 588, A135, 19 pp.
Abstract
Aims. We aim to obtain high-quality time-resolved spectral fits of gamma-ray bursts observed by the Gamma-ray Burst Monitor (GBM) on board the Fermi Gamma-ray Space Telescope.
Methods. We performed time-resolved spectral analysis with high temporal and spectral resolution of the brightest bursts observed by Fermi GBM in its first four years of mission.
Results. We present the complete catalog containing 1491 spectra from 81 bursts with high spectral and temporal resolution. Distributions of parameters, statistics of the parameter populations, parameter-parameter and parameter-uncertainty correlations, and their exact values are obtained and presented as main results in this catalog. We report a criterion that is robust enough to automatically distinguish between different spectral evolutionary trends between bursts. We also search for plausible blackbody emission components and find that only three bursts (36 spectra in total) show evidence of a pure Planck function. It is observed that peak energy and the averaged, time-resolved power-law index at low energy are slightly harder than the time-integrated values. Time-resolved spectroscopic results should be used instead of time-integrated results when interpreting physics from the observed spectra.
The Sharpness of Gamma-Ray Burst Prompt Emission Spectra
Authors
Yu Hoi-Fung, van Eerten Hendrik J., Greiner Jochen et al.
Year
2015
Journal
Astronomy and Astrophysics, 583, A129, 16 pp.
Abstract
Context. We study the sharpness of the time-resolved prompt emission spectra of gamma-ray bursts (GRBs) observed by the Gamma-ray Burst Monitor (GBM) on board the Fermi Gamma-ray Space Telescope.
Aims. We aim to obtain a measure of the curvature of time-resolved spectra that can be compared directly to theory. This tests the ability of models such as synchrotron emission to explain the peaks or breaks of GBM prompt emission spectra.
Methods. We take the burst sample from the official Fermi GBM GRB time-resolved spectral catalog. We re-fit all spectra with a measured peak or break energy in the catalog best-fit models in various energy ranges, which cover the curvature around the spectral peak or break, resulting in a total of 1113 spectra being analyzed. We compute the sharpness angles under the peak or break of the triangle constructed under the model fit curves and compare them to the values obtained from various representative emission models: blackbody, single-electron synchrotron, synchrotron emission from a Maxwellian or power-law electron distribution.
Results. We find that 35% of the time-resolved spectra are inconsistent with the single-electron synchrotron function, and 91% are inconsistent with the Maxwellian synchrotron function. The single temperature, single emission time, and location blackbody function is found to be sharper than all the spectra. No general evolutionary trend of the sharpness angle is observed, neither per burst nor for the whole population. It is found that the limiting case, a single temperature Maxwellian synchrotron function, can only contribute up to 58-18+23% of the peak flux.
Conclusions. Our results show that even the sharpest but non-realistic case, the single-electron synchrotron function, cannot explain a large fraction of the observed GRB prompt spectra. Because any combination of physically possible synchrotron spectra added together will always further broaden the spectrum, emission mechanisms other than optically thin synchrotron radiation are likely required in a full explanation of the spectral peaks or breaks of the GRB prompt emission phase.
Taking the Band Function Too Far: A Tale of Two α’s
Authors
Burgess J. Michael, Ryde Felix, Yu Hoi-Fung
Year
2015
Journal
Monthly Notices of the Royal Astronomical Society, 451, pp. 1511-1521
Abstract
The long standing problem of identifying the emission mechanism operating in gamma-ray bursts (GRBs) has produced a myriad of possible models that have the potential of explaining the observations. Generally, the empirical Band function is fit to the observed gamma-ray data and the fit parameters that are used to infer which radiative mechanisms are at work in GRB outflows. In particular, the distribution of the Band function’s low-energy power-law index, α, has led to the so-called synchrotron ‘line-of-death’ (LOD) which is a statement that the distribution cannot be explained by the simplest of synchrotron models alone. As an alternatively fitting model, a combination of a blackbody in addition to the Band function is used, which in many cases provide a better or equally good fit. It has been suggested that such fits would be able to alleviate the LOD problem for synchrotron emission in GRBs. However, these conclusions rely on the Band function’s ability to fit a synchrotron spectrum within the observed energy band. In order to investigate if this is the case, we simulate synchrotron and synchrotron+blackbody spectra and fold them through the instrumental response of the Fermi Gamma-ray Burst Monitor (GBM). We then perform a standard data analysis by fitting the simulated data with both Band and Band+blackbody models. We find two important results: the synchrotron LOD is actually more severe than the original predictions: αLOD ∼ −0.8. Moreover, we find that intrinsic synchrotron+blackbody emission is insufficient to account for the entire observed α distribution. This implies that some other emission mechanism(s) are required to explain a large fraction of observed GRBs.
Synchrotron Cooling in Energetic Gamma-Ray Bursts Observed by the Fermi Gamma-Ray Burst Monitor
Authors
Yu Hoi-Fung, Greiner Jochen, Eerten Hendrik J., Burgess J. Michael et al.
Year
2015
Journal
Astronomy and Astrophysics, 573, A81, 20 pp.
Abstract
Context. We study the time-resolved spectral properties of energetic gamma-ray bursts (GRBs) with good high-energy photon statistics observed by the Gamma-Ray Burst Monitor (GBM) onboard the Fermi Gamma-Ray Space Telescope.
Aims. We aim to constrain in detail the spectral properties of GRB prompt emission on a time-resolved basis and to discuss the theoretical implications of the fitting results in the context of various prompt emission models.
Methods. Our sample comprises eight GRBs observed by the Fermi GBM in its first five years of mission, with 1 keV–1 MeV fluence f> 1.0 × 10-4 erg cm-2 and a signal-to-noise ratio level of S/N ≥ 10.0above 900 keV. We performed a time-resolved spectral analysis using a variable temporal binning technique according to optimal S/N criteria, resulting in a total of 299 time-resolved spectra. We performed Band function fits to all spectra and obtained the distributions for the low-energy power-law index α, the high-energy power-law index β, the peak energy in the observed νFν spectrum Ep, and the difference between the low- and high-energy power-law indices Δs = α − β. We also applied a physically motivated synchrotron model, which is a triple power-law with constrained power-law indices and a blackbody component, to test the prompt emission for consistency with a synchrotron origin and obtain the distributions for the two break energies Eb,1 and Eb,2, the middle segment power-law index β, and the Planck function temperature kT.
Results. The Band function parameter distributions are α = -0.73+0.16-0.21, β =ي-2.13+0.28-0.56, Ep = 374.4+307.3-187.7 , , keV (log10Ep = 2.57+0.26-0.30), and Δs = 1.38+0.54-0.31 , with average errors σα ~ 0.1, σβ ~ 0.2, and σEp ~ 0.1Ep. Using the distributions of Δs and β, the electron population index p is found to be consistent with the “moderately fast” scenario, in which fast- and slow-cooling scenarios cannot be distinguished. The physically motivated synchrotron-fitting function parameter distributions are Eb,1 = 129.6+132.2-32.4 keV, Eb,2 = 631.4+582.6-309.6 keV, β = -1.72+0.48-0.25 , and kT = 10.4+4.9-3.7keV, with average errors σβ ~ 0.2, σEb,1 ~ 0.1Eb,1, σEb,2 ~ 0.4Eb,2, and σkT ~ 0.1kT. This synchrotron function requires the synchrotron injection and cooling break (i.e., Emin and Ecool) to be close to each other within a factor of ten, often in addition to a Planck function.
Conclusions. A synchrotron model is found that is consistent with most of the time-resolved spectra for eight energetic Fermi GBM bursts with good high-energy photon statistics as long as both the cooling and injection break are included and the leftmost spectral slope is lifted either by including a thermal component or when an evolving magnetic field is accounted for.
GROND Coverage of the Main Peak of Gamma-Ray Burst 130925A
Authors
Greiner Jochen, Yu Hoi-Fung, Krühler T. et al.
Year
2014
Journal
Astronomy and Astrophysics, 568, A75, 9 pp.
Abstract
Aims. Prompt or early optical emission in gamma-ray bursts (GRBs) is notoriously difficult to measure, and observations of the dozen cases show a large variety of properties. Yet, such early emission promises to help us achieve a better understanding of the GRB emission process(es).
Methods. We performed dedicated observations of the ultra-long duration (T90 about 7000 s) Swift GRB 130925A in the optical/near-infrared with the 7-channel Gamma-Ray burst Optical and Near-infrared Detector (GROND) at the 2.2 m MPG/ESO telescope.
Results. We detect an optical/near-infrared flare with an amplitude of nearly 2 mag which is delayed with respect to the keV−MeV prompt emission by about 300−400 s. The decay time of this flare is shorter than the duration of the flare (500 s) or its delay.
Conclusions. While we cannot offer a straightforward explanation, we discuss the implications of the flare properties and suggest ways toward understanding it.
Prompt Emission of GRB 121217A from Gamma-rays to the Near-infrared
Authors
Greiner Jochen, Yu Hoi-Fung, Krühler T. et al.
Year
2014
Journal
Astronomy and Astrophysics, 562, A100, 12 pp.
Abstract
The mechanism that causes the prompt-emission episode of gamma-ray bursts (GRBs) is still widely debated despite there being thousands of prompt detections. The favoured internal shock model relates this emission to synchrotron radiation. However, it does not always explain the spectral indices of the shape of the spectrum, which is often fit with empirical functions, such as the Band function. Multi-wavelength observations are therefore required to help investigate the possible underlying mechanisms that causes the prompt emission. We present GRB 121217A, for which we were able to observe its near-infrared (NIR) emission during a secondary prompt-emission episode with the Gamma-Ray burst Optical Near-infrared Detector (GROND) in combination with the Swift and Fermi satellites, which cover an energy range of 5 orders of magnitude (10-3 keV to 100 keV). We determine a photometric redshift of z = 3.1±0.1 with a line-of-sight with little or no extinction (AV ~ 0 mag) utilising the optical/NIR SED. From the afterglow, we determine a bulk Lorentz factor of Γ0 ~ 250 and an emission radius of R < 1018 cm. The prompt-emission broadband spectral energy distribution is well fit with a broken power law with β1 = −0.3±0.1 and β2 = 0.6±0.1 that has a break at E = 6.6±0.9 keV, which can be interpreted as the maximum injection frequency. Self-absorption by the electron population below energies of Ea < 6 keV suggest a magnetic field strength of B ~ 105 G. However, all the best fit models underpredict the flux observed in the NIR wavelengths, which also only rebrightens by a factor of ~2 during the second prompt emission episode, in stark contrast to the X-ray emission, which rebrightens by a factor of ~100. This suggests an afterglow component is dominating the emission. We present GRB 121217A, one of the few GRBs that has multi-wavelength observations of the prompt-emission period and shows that it can be understood with a synchrotron radiation model. However, due to the complexity of the GRB’s emission, other mechanisms that result in Band-like spectra cannot be ruled out.
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