arXiv subjects

Bin-Bin Zhang

Publications and source records attributed to Bin-Bin Zhang.

At least 37 records · Page 2Linked to original sources

arXiv2025

Spectroscopic evidence of symmetry breaking in the superconducting vortices of UTe2

The recently discovered heavy-fermion superconductor, UTe2, is an excellent candidate for spin-triplet superconductors where electrons form spin-triplet Cooper pairs with spin S = 1 and odd parity. Unconventional superconductivity often hosts unconventional vortices. Yet, the vortex core and lattice in UTe2 have not been directly visualized and characterized. Here, by using ultralow-temperature scanning tunneling microscopy and spectroscopy, we study the superconducting vortices on the (0-11) surface termination of UTe2 with an out-of-plane external magnetic field. At the center of the vortex core, we observe a robust zero-energy vortex-core state which exhibits a cigar-shaped spatial distribution and extends to ~30 nm along the [100] direction (crystallographic a axis) of UTe2. Along the direction perpendicular to [100], the superconducting gap is deeper and the coherence peak on one side of the vortex core is stronger than on the opposite side, and they are even enhanced in comparison with those under zero field. Due to the anisotropy of magnetic susceptibility in UTe2, the asymmetric dI/dV spectra on the two sides of the vortex core result from the interplay between the magnetization-induced bound current and supercurrent around the vortex core. Our work reveals the important role of magnetization in the vortex behaviors of UTe2 and provides essential microscopic information for understanding its superconducting properties in magnetic field.

cond-mat.supr-con↗

arXiv2025

EP240801a/XRF 240801B: An X-ray Flash Detected by the Einstein Probe and Implications of its Multiband Afterglow

We present multiband observations and analysis of EP240801a, a low-energy, extremely soft gamma-ray burst (GRB) discovered on August 1, 2024 by the Einstein Probe (EP) satellite, with a weak contemporaneous signal also detected by Fermi/GBM. Optical spectroscopy of the afterglow, obtained by GTC and Keck, identified the redshift of $z = 1.6734$. EP240801a exhibits a burst duration of 148 s in X-rays and 22.3 s in gamma-rays, with X-rays leading by 80.61 s. Spectral lag analysis indicates the gamma-ray signal arrived 8.3 s earlier than the X-rays. Joint spectral fitting of EP/WXT and Fermi/GBM data yields an isotropic energy $E_{γ,\rm{iso}} = (5.57^{+0.54}_{-0.50})\times 10^{51}\,\rm{erg}$, a peak energy $E_{\rm{peak}} = 14.90^{+7.08}_{-4.71}\,\rm{keV}$, a fluence ratio $\rm S(25-50\,\rm{keV})/S(50-100\,\rm{keV}) = 1.67^{+0.74}_{-0.46}$, classifying EP240801a as an X-ray flash (XRF). The host-galaxy continuum spectrum, inferred using Prospector, was used to correct its contribution for the observed outburst optical data. Unusual early $R$-band behavior and EP/FXT observations suggest multiple components in the afterglow. Three models are considered: two-component jet model, forward-reverse shock model and forward-shock model with energy injection. Both three provide reasonable explanations. The two-component jet model and the energy injection model imply a relatively small initial energy and velocity of the jet in the line of sight, while the forward-reverse shock model remains typical. Under the two-component jet model, EP240801a may resemble GRB 221009A (BOAT) if the bright narrow beam is viewed on-axis. Therefore, EP240801a can be interpreted as an off-beam (narrow) jet or an intrinsically weak GRB jet. Our findings provide crucial clues for uncovering the origin of XRFs.

astro-ph.HE↗

arXiv2024

Unsupervised Domain Adaptation for RF-based Gesture Recognition

Human gesture recognition with Radio Frequency (RF) signals has attained acclaim due to the omnipresence, privacy protection, and broad coverage nature of RF signals. These gesture recognition systems rely on neural networks trained with a large number of labeled data. However, the recognition model trained with data under certain conditions would suffer from significant performance degradation when applied in practical deployment, which limits the application of gesture recognition systems. In this paper, we propose an unsupervised domain adaptation framework for RF-based gesture recognition aiming to enhance the performance of the recognition model in new conditions by making effective use of the unlabeled data from new conditions. We first propose pseudo-labeling and consistency regularization to utilize unlabeled data for model training and eliminate the feature discrepancies in different domains. Then we propose a confidence constraint loss to enhance the effectiveness of pseudo-labeling, and design two corresponding data augmentation methods based on the characteristic of the RF signals to strengthen the performance of the consistency regularization, which can make the framework more effective and robust. Furthermore, we propose a cross-match loss to integrate the pseudo-labeling and consistency regularization, which makes the whole framework simple yet effective. Extensive experiments demonstrate that the proposed framework could achieve 4.35% and 2.25% accuracy improvement comparing with the state-of-the-art methods on public WiFi dataset and millimeter wave (mmWave) radar dataset, respectively.

cs.CV↗

arXiv2024

Triggering the Untriggered: The First Einstein Probe-Detected Gamma-Ray Burst 240219A and Its Implications

The Einstein Probe (EP) achieved its first detection and localization of a bright X-ray flare, EP240219a, on 2024 February 19, during its commissioning phase. Subsequent targeted searches triggered by the EP240219a alert identified a faint, untriggered gamma-ray burst (GRB) in the archived data of Fermi Gamma-ray Burst Monitor (GBM), Swift Burst Alert Telescope (BAT), and Insight-HXMT/HE. The EP Wide-field X-ray Telescope (WXT) light curve reveals a long duration of approximately 160 s with a slow decay, whereas the Fermi/GBM light curve shows a total duration of approximately 70 s. The peak in the Fermi/GBM light curve occurs slightly later with respect to the peak seen in the EP/WXT light curve. Our spectral analysis shows that a single cutoff power-law (PL) model effectively describes the joint EP/WXT--Fermi/GBM spectra in general, indicating coherent broad emission typical of GRBs. The model yielded a photon index of $\sim -1.70 \pm 0.05$ and a peak energy of $\sim 257 \pm 134$ keV. After detection of GRB 240219A, long-term observations identified several candidates in optical and radio wavelengths, none of which was confirmed as the afterglow counterpart during subsequent optical and near-infrared follow-ups. The analysis of GRB 240219A classifies it as an X-ray rich GRB (XRR) with a high peak energy, presenting both challenges and opportunities for studying the physical origins of X-ray flashes, XRRs, and classical GRBs. Furthermore, linking the cutoff PL component to nonthermal synchrotron radiation suggests that the burst is driven by a Poynting flux-dominated outflow.

astro-ph.HE↗

arXiv2024

GTC optical/NIR upper limits and NICER X-ray analysis of SGR J1935+2154 for the outburst in 2022

The Galactic magnetar SGR J1935+2154 has undergone another outburst since 2022 October 10. We present the results of searching for an optical/NIR counterpart of SGR J1935+2154 before and during this outburst. No counterpart was detected at the magnetar's position in ${r'}$ and ${z'}$ bands, providing stringent upper limits of $r'\gtrsim 28.65$ and $z'\gtrsim 26.27$. Using archival X-ray data from NICER, we investigated the properties of the bursts and the spectral evolution of persistent emission. The burst flux $F$ showed a power-law distribution of $N\propto F^{-0.76\pm0.10}$ for flux $\gtrsim 2.6\times 10^{-9}\rm{\ erg\ cm^{-2}\ s^{-1}}$, while the temperature and radius followed a lognormal distribution with $kT=1.63^{+0.73}_{-0.50}\ \rm{keV}$ and $R_{\rm bb}=4.35_{-1.35}^{+1.95}\ \rm{km}$, respectively. The persistent flux evolution experienced a quick decay and an enhancement $\sim 27$ days after the BAT trigger. Using the near-infrared (NIR) and X-ray emission, together with the GTC optical/NIR upper limits, we discussed the origin of the NIR emission from the magnetar based on the fallback disk model and magnetosphere model. We found that either model cannot be ruled out with currently available data. Further mid-infrared observations are needed to find out the mechanism for producing the NIR emission from SGR J1935+2154.

astro-ph.HE↗

arXiv2024

GRB 240529A: A Tale of Two Shocks

Thanks to the rapidly increasing time-domain facilities, we are entering a golden era of research on gamma-ray bursts (GRBs). In this Letter, we report our observations of GRB 240529A with the Burst Optical Observer and Transient Exploring System, the 1.5-meter telescope at Observatorio Sierra Nevada, the 2.5-meter Wide Field Survey Telescope of China, the Large Binocular Telescope, and the Telescopio Nazionale Galileo. The prompt emission of GRB 240529A shows two comparable energetic episodes separated by a quiescence time of roughly 400 s. Combining all available data on the GRB Coordinates Network, we reveal the simultaneous apparent X-ray plateau and optical re-brightening around $10^3-10^4$ s after the burst. Rather than the energy injection from the magnetar as widely invoked for similar GRBs, the multi-wavelength emissions could be better explained as two shocks launched from the central engine separately. The optical peak time and our numerical modeling suggest that the initial bulk Lorentz factor of the later shock is roughly 50, which indicates that the later jet should be accretion-driven and have a higher mass loading than a typical one. The quiescence time between the two prompt emission episodes may be caused by the transition between different accretion states of a central magnetar or black hole, or the fall-back accretion process. A sample of similar bursts with multiple emission episodes in the prompt phase and sufficient follow-up could help to probe the underlying physics of GRB central engines.

astro-ph.HE↗

arXiv2024

Bridging the Gap: GRB 230812B -- A Three-Second Supernova-Associated Burst Detected by the GRID Mission

GRB 230812B, detected by the Gamma-Ray Integrated Detectors (GRID) constellation mission, is an exceptionally bright gamma-ray burst (GRB) with a duration of only 3 seconds. Sitting near the traditional boundary ($\sim$ 2 s) between long and short GRBs, GRB 230812B is notably associated with a supernova (SN), indicating a massive star progenitor. This makes it a rare example of a short-duration GRB resulting from stellar collapse. Our analysis, using a time-evolving synchrotron model, suggests that the burst has an emission radius of approximately $10^{14.5}$~cm. We propose that the short duration of GRB 230812B is due to the combined effects of the central engine's activity time and the time required for the jet to break through the stellar envelope. Our findings provide another case that challenges the conventional view that short-duration GRBs originate exclusively from compact object mergers, demonstrating that a broader range of durations exists for GRBs arising from the collapse of massive stars.

astro-ph.HE↗

arXiv2024

Repeated partial disruptions in a WD-NS or WD-BH merger modulate the prompt emission of long-duration merger-type GRBs

The progenitors of gamma-ray bursts (GRBs) have long been an unresolved issue. GRB 230307A stands out as an exceptionally bright event, belonging to the long-duration GRBs but also exhibiting a late emission component reminiscent of a kilonova. Together with the similar events GRBs 060614 and 211211A, they make up a new sub-group of GRBs with intriguing progenitors. If such long-duration merger-type GRBs originated from the coalescence of a white dwarf (WD) with a neutron star (NS) or a black hole (BH), as proposed in the recent literature, then the larger tidal disruption radius of the WD, together with a non-negligible residual orbital eccentricity, would make repeated partial tidal disruptions inevitable. This may modulate the mass accretion and jet launching process at the NS or BH, resulting in a quasi-periodic modulation (QPM) in the light curve of the GRB, on the orbital period. The detection of potential QPMs during the early episode of prompt emission of these three GRBs supports this scenario, and the relatively slow QPM ($>$ 1 s) suggests that the lighter object can not be a NS. We propose that the progenitor system of GRBs 230307A, 060614, and 211211A consist of a WD of mass 1.3 $M_\odot$, 0.9 $M_\odot$ and 1.4 $M_\odot$, respectively, and a NS (or BH). After several cycles of modulations, the WD is completely destructed, and the accretion of the remaining debris dominates the extended emission episode.

astro-ph.HE↗

arXiv2024

Unconventional superconductivity emerging along with the strange-metal behavior in UAs2 under pressure

The recently discovered spin-triplet superconductor candidate UTe2 with Tc = 2 K has attracted enormous attention because it possesses many interesting properties, such as the extremely high upper critical field Hc2(0), chiral superconductivity and spontaneous time-reversal symmetry breaking, etc., all these suggest that it may be the long-sought spin-triplet superconductor. Here we report the discovery of superconductivity up to Tc = 4K in one of its siblings, i.e., UAs2 under high pressures. Interestingly, the UAs2 shows metallic behavior with an antiferromagnetic (AFM) transition at about 274 K under ambient pressure. Upon applying pressure, this transition is pushed down to lower temperatures with improved electric conductivity. When the pressure rises to about 20-22 GPa, superconductivity occurs together with the emergence of a linear temperature dependence of normal state resistance, the latter is a hallmark of the strange-metal state. The superconductivity with the highest Tc = 4 K is reached under a pressure of about 26.8 GPa, and it is robust against magnetic field with the upper critical field μ0Hc2(0) ~ 12 T, far beyond the Pauli limit. Higher pressures will suppress the superconductivity and bring back the Fermi liquid behavior, showing a clear signature of quantum criticality. Our results open a new avenue for investigating the unconventional superconductivity concerning the mysterious 5f-band electrons in this uranium-based system.

cond-mat.supr-con↗

arXiv2024

GRBs from Collapse of Thorne-Żytkow-like Objects as the Aftermath of WD-NS Coalescence

The Type II gamma-ray burst (GRB) 200826A challenges collapsar models by questioning how they can generate a genuinely short-duration event. The other Type I GRB 211211A confused us with a kilonova signature observed in the afterglow of a \textit{long} burst. Here, we propose a comprehensive model in which both bursts are the results of the collapse of Thorne-Żytkow-like Objects (TZlOs). The TZlO consists of a central neutron star (NS), with a dense white dwarf (WD) material envelope, which is formed as the aftermath of a WD-NS coalescence. We find that the characteristics of the resultant GRBs depend on whether the TZlO collapses immediately following the WD-NS merger or not. Additionally, the observational properties of the consequent GRBs manifest variations contingent upon whether the collapse of the TZlO results in a magnetar or a black hole. We also show that our model is consistent with the observations of GRB 211211A and GRB 200826A. Specifically, the optical excess in GRB 211211A can be attributed to an engine-fed kilonova, while the \textit{supernova bump} in GRB 200826A is likely due to the collision between the ejecta and the disk wind shell.

astro-ph.HE↗

arXiv2024

A Comptonized Fireball Bubble Fits the Second Extragalactic Magnetar Giant Flare GRB 231115A

Magnetar giant flares (MGFs), originating from noncatastrophic magnetars, share noteworthy similarities with some short gamma-ray bursts (GRBs). However, understanding their detailed origin and radiation mechanisms remains challenging due to limited observations. The discovery of MGF GRB 231115A, the second extragalactic MGF located in the Cigar galaxy at a luminosity distance of $\sim 3.5$ Mpc, offers yet another significant opportunity for gaining insights into the aforementioned topics. This Letter explores its temporal properties and conducts a comprehensive analysis of both the time-integrated and time-resolved spectra through empirical and physical model fitting. Our results reveal certain properties of GRB 231115A that bear resemblances to GRB 200415A. We employ a Comptonized fireball bubble model, in which the Compton cloud, formed by the magnetar wind with high density $e^{\pm}$, undergoes Compton scattering and inverse Compton scattering, resulting in reshaped thermal spectra from the expanding fireball at the photosphere radius. This leads to dynamic shifts in dominant emission features over time. Our model successfully fits the observed data, providing a constrained physical picture, such as a trapped fireball with a radius of $\sim 1.95 \times 10^{5}$ cm and a high local magnetic field of $2.5\times 10^{16}$ G. The derived peak energy and isotropic energy of the event further confirm the burst's MGF origin and its contribution to the MGF-GRB sample. We also discuss prospects for further gravitational wave detection associated with MGFs, given their high-event-rate density ($\sim 8\times 10^5\ \rm Gpc^{-3}\ yr^{-1}$) and ultrahigh local magnetic field.

astro-ph.HE↗

arXiv2024

The Very Early Soft X-ray Plateau of GRB 230307A: Signature of an Evolving Radiative Efficiency in Magnetar Wind Dissipation?

Very recently, a particularly long gamma-ray burst (GRB) 230307A was reported and proposed to originate from a compact binary merger based on its host galaxy property, kilonova, and heavy elements. More intriguingly, a very early plateau followed by a rapid decline in soft X-ray band was detected in its light curve by the Lobster Eye Imager for Astronomy, indicating strong evidence of the existence of a magnetar as the merger product. This work explores that the Magnetar Wind Internal Gradual MAgnetic Dissipation (MIGMAD) model, in which the radiative efficiency evolves over time, successfully fits it to the observed data. Our results reinforce the notion that the X-ray plateau serves as a powerful indicator of a magnetar and imply that an evolving efficiency is likely to be a common feature in X-ray plateaus of GRB afterglows. In addition, we also discuss the explanations for the prompt emission, GRB afterglows, as well as kilonova, and predict possible kilonova afterglows in a magnetar central engine.

astro-ph.HE↗

arXiv2024

Prospects for detecting neutron star-white dwarf mergers with decihertz gravitational-wave observatories

Based on different neutron star-white dwarf (NS-WD) population models, we investigate the prospects of gravitational-wave (GW) detections for NS-WD mergers, with the help of early warnings from two space-borne decihertz GW observatories, DO-Optimal and DECIGO. We not only give quick assessments of the GW detection rates for NS-WD mergers with the two decihertz GW detectors, but also report systematic analyses on the characteristics of GW-detectable merger events using the method of Fisher matrix. With a sufficient one-day early-warning time, the yearly GW detection number for DO-Optimal is in the range of $ (1.5$-$1.9) \times 10^{3}$, while it is $ (3.3$-$4.6) \times 10^{4}$ for DECIGO. More importantly, our results show that most NS-WD mergers can be localized with an uncertainty of $O(10^{-2})\,\mathrm{deg}^2$. Given the NS-WD merger as a possible origin for a peculiar long-duration gamma-ray burst, GRB 211211A, followed with kilonova-like emissions, we further suggest that the GW early-warning detection would allow future electromagnetic telescopes to get prepared to follow-up transients after some special NS-WD mergers. Based on our analyses, we emphasize that such a feasible "wait-for" pattern can help to firmly identify the origin of GRB 211211A-like events in the future and bring excellent opportunities for the multimessenger astronomy.

astro-ph.HE↗

arXiv2024

One Fits All: A Unified Synchrotron Model Explains GRBs with FRED-Shaped Pulses

The analysis of gamma-ray burst (GRB) spectra often relies on empirical models lacking a distinct physical explanation. Previous attempts to couple physical models with observed data focus on individual burst studies, fitting models to segmented spectra with independent physical parameters. However, these approaches typically neglect to explain the time evolution of observed spectra. In this study, we propose a novel approach by incorporating the synchrotron radiation model to provide a self-consistent explanation for a selection of single-pulse GRBs. Our study comprehensively tests the synchrotron model under a unified physical condition, such as a single injection event of electrons. By tracing the evolution of cooling electrons in a decaying magnetic field, our model predicts time-dependent observed spectra that align well with the data. Using a single set of physical parameters, our model successfully fits all time-resolved spectra within each burst. Our model suggests that the rising phase of the GRB light curve results from the increasing number of radiating electrons, while the declining phase is attributed to the curvature effect, electron cooling, and the decaying magnetic field. Our model provides a straightforward interpretation of the peak energy's evolution, linked to the decline of the magnetic field and electron cooling due to the expansion of the GRB emission region. Our findings strongly support the notion that spectral and temporal evolution in GRB pulses originates from the expansion of the GRB emission region, with an initial radius of approximately $10^{15}$ cm, and synchrotron radiation as the underlying emission mechanism.

astro-ph.HE↗

arXiv2023

GRB 211211A-like Events and How Gravitational Waves May Tell Their Origins

GRB 211211A is a rare burst with a genuinely long duration, yet its prominent kilonova association provides compelling evidence that this peculiar burst was the result of a compact binary merger. However, the exact nature of the merging objects, whether they were neutron star pairs, neutron star--black hole systems, or neutron star--white dwarf systems, remains unsettled. This {\it Letter} delves into the rarity of this event and the possibility of using current and next-generation gravitational wave detectors to distinguish between the various types of binary systems. Our research reveals an event rate density of $\gtrsim 5.67^{+13.04}_{-4.69} \times 10^{-3}\ \rm Gpc^{-3}\ yr^{-1}$ for GRB 211211A-like gamma-ray bursts (GRBs), which, assuming GRB 211211A is the only example of such a burst, is significantly smaller than that of typical long- and short-GRB populations. We further calculated that if the origin of GRB 211211A is a result of a neutron star--black hole merger, it would be detectable with a significant signal-to-noise ratio (S/N), given the LIGO-Virgo-KAGRA designed sensitivity. On the other hand, a neutron star--white dwarf binary would also produce a considerable S/N during the inspiral phase at decihertz and is detectable by next-generation spaceborne detectors DECIGO and the Big Bang Observer. However, to detect this type of system with millihertz spaceborne detectors like LISA, Taiji, and TianQin, the event must be very close, approximately 3 Mpc in distance or smaller.

astro-ph.HE↗

arXiv2023

Quasi-periodic oscillation in short gamma-ray bursts from black hole-neutron star mergers

Short-duration gamma-ray bursts (sGRBs) are commonly attributed to the mergers of double neutron stars (NSs) or the mergers of a neutron star with a black hole (BH). While the former scenario was confirmed by the event GW170817, the latter remains elusive. Here, we consider the latter scenario in which, a NS is tidally disrupted by a fast spinning low-mass BH and the accretion onto the BH launches a relativistic jet and hence produces a sGRB. The merging binary's orbit is likely misaligned with the BH's spin. Hence, the Lense-Thirring precession around the BH may cause a hyper-accreting thick disk to precess in a solid-body manner. We propose that a jet, initially aligned with the BH spin, is deflected and collimated by the wind from the disk, therefore being forced to precess along with the disk. This would result in a quasi-periodic oscillation or modulation in the gamma-ray light curve of the sGRB, with a quasi-period of $\sim 0.01-0.1$ s. The appearance of the modulation may be delayed respective to the triggering of the light curve. This feature, unique to the BH-NS merger, may have already revealed itself in a few observed sGRBs (such as GRB 130310A), and it carries the spin-obit orientation information of the merging system. Identification of this feature would be a new approach to reveal spin-orbit-misaligned merging BH-NS systems, which are likely missed by the current gravitational-wave searching strategy principally targeting aligned systems.

astro-ph.HE↗

arXiv2023

Synchrotron Radiation Dominates the Extremely Bright GRB 221009A

The brightest Gamma-ray burst, GRB 221009A, has spurred numerous theoretical investigations, with particular attention paid to the origins of ultra-high energy TeV photons during the prompt phase. However, analyzing the mechanism of radiation of photons in the $\sim$MeV range has been difficult because the high flux causes pile-up and saturation effects in most GRB detectors. In this letter, we present systematic modeling of the time-resolved spectra of the GRB using unsaturated data obtained from Fermi/GBM (precursor) and SATech-01/GECAM-C (main emission and flare). Our approach incorporates the synchrotron radiation model, which assumes an expanding emission region with relativistic speed and a global magnetic field that decays with radius, and successfully fits such a model to the observational data. Our results indicate that the spectra of the burst are fully in accordance with a synchrotron origin from relativistic electrons accelerated at a large emission radius. The lack of thermal emission in the prompt emission spectra supports a Poynting-flux-dominated jet composition.

astro-ph.HE↗

arXiv2023

Temporal and Spectral Evolution of Gamma-ray Burst Broad Pulses: Identification of High Latitude Emission in the Prompt Emission

We perform a detailed analysis on broad pulses in bright Gamma-ray bursts (GRBs) to understand the evolution of GRB broad pulses. Using the temporal and spectral properties, we test the high latitude emission (HLE) scenario in the decaying phase of broad pulses. The HLE originates from the curvature effect of a relativistic spherical jet, where higher latitude photons are delayed and softer than the observer's line-of-sight emission. The signature of HLE has not yet been identified undisputedly during the prompt emission of GRBs. The HLE theory predicts a specific relation, F$_{ν, E_{p}}$ $\propto$ E$_{p}\!^{2}$, between the peak energy $E_{p}$ in $ν$F$_ν$ spectra and the spectral flux F$_ν$ measured at $E_{p}$, F$_{ν, E_{p}}$. We search for evidence of this relation in 2157 GRBs detected by the Gamma-ray Burst Monitor (GBM) on board the Fermi Gamma-ray Space Telescope (Fermi) from the years 2008 to 2017. After imposing unbiased selection criteria in order to minimize contamination in a signal by background and overlaps of pulses, we build a sample of 32 broad pulses in 32 GRBs. We perform a time-resolved spectral analysis on each of these 32 broad pulses and find that the evolution of 18 pulses (56%) is clearly consistent with the HLE relation. For the 18 broad pulses, the exponent $δ$ in the relation of F$_{ν, E_{p}}$ $\propto$ E$_{p}\!^δ$ is distributed as a Gaussian function with median and width of 1.99 and 0.34, respectively. This result provides constraint on the emission radius of GRBs with the HLE signature.

astro-ph.HE↗