arXiv subjects

Xiao-Fei Dong

Publications and source records attributed to Xiao-Fei Dong.

At least 19 recordsLinked to original sources

arXiv2026

A Missing Tool for Calculating Auto/Cross-correlation Function under Nonuniform Sampling Observations

Nonuniform sampling presents a long-standing challenge in astrophysical time-domain analysis, invalidating the standard autocorrelation and cross-correlation functions and forcing researchers to adopt ad-hoc methods like interpolation or binning, which introduce unquantified biases and lack rigorous error estimation. Here we introduce a new method for calculating the nonuniform autocorrelation function (NUACF) and nonuniform cross-correlation function (NUCCF) for irregularly sampled time series. Instead of relying on interpolation, it naturally evaluates the correlation function by incorporating time-interval weights and misalignment penalties. Monte Carlo simulations provide confidence bands for significance assessment and a complete error budget for the time delays that accounts for both flux uncertainties and sampling irregularity (essential but generally absent from existing methods). Through extensive simulations, we demonstrate our method outperforms traditional methods across various conditions, from strictly periodic to complex repeating variability patterns (e.g., intermittent but aperiodic). Its effectiveness is demonstrated via various real astrophysical data sets, revealing repetitive variability in stellar light curves, measuring time delays for multi-band disc reverberation in the AGN Fairall 9, and providing model-independent validation of time delays for the gravitationally lensed quasar HE 0435-1223. The method provides a rigorous and general solution to the ubiquitous problem of nonuniform sampling, positioning it as a useful tool for large-scale time-domain survey data analysis. The framework is also directly applicable to emerging time-domain phenomena such as fast radio bursts (FRBs), enabling, e.g., the study of correlations between persistent radio source luminosity and repeating FRB activity, or among the multi-parameter variability curves of FRB emission itself.

astro-ph.IM↗

arXiv2026

Constraints on the Low-frequency Radio Emission of the Galactic FRB Source SGR 1935+2154

We present a search for radio pulses from the Galactic magnetar SGR 1935+2154, a well-known source of fast radio bursts (FRBs), at $\sim$110 MHz using the Large Phased Array (LPA) of the Pushchino Radio Astronomy Observatory. Data from two active periods in 2020 (March -- May and September -- November, with $\sim 3.5$ minutes of daily coverage) were analyzed with new methods tailored to both FRB-like single pulses and pulsar-like periodic signals. No significant FRB-like pulses were found. Using Monte Carlo simulations, $3σ$ upper limits were derived for the burst rate: for a log-normal energy distribution the limit is $\sim$${10}^{1.5}~{\rm{d}}^{-1}$ for a mean of average monochromatic isotropic luminosity $L_{ν{\rm ,mean}}\sim1.3\times{10}^{29}~{\rm{erg~s^{-1}~ {Hz}^{-1}}}$ and a natural log-space scatter of $σ\sim0.85$; while for a power-law distribution it is $\sim$${10}^{1.8}~{\rm{d}}^{-1}$ for an index $β\lesssim3.0$ and a minimum average monochromatic isotropic luminosity $L_{ν{\rm{,min}}}\lesssim0.7\times{10}^{25}~{\rm{erg~s^{-1}~{Hz}^{-1}}}$. When folded at the known 3.24781628 s period of SGR 1935+2154, a weak pulse was noted (S/N $<$ 3.16), but the significance is insufficient for a secure detection of the pulsar-like emission signal. A conservative upper limit on the average monochromatic isotropic luminosity of any possible periodic emission is $2.08\times{10}^{19}~{\rm{erg~s^{-1}~{Hz}^{-1}}}$. Our results offer meaningful low-frequency upper limits on the burst rate of SGR 1935+2154, and hint for very faint pulsar-like radiation at meter wavelengths.

astro-ph.HE↗

arXiv2026

Decoding FRB Energetics and Frequency Features Hidden by Observational Incompleteness

Fast radio bursts (FRBs) are millisecond-duration extragalactic radio flashes likely powered by magnetars, yet their radiation mechanism remains unknown. Limited sensitivity and finite observing bandwidth inevitably lead to observational truncation, biasing our understanding of intrinsic burst properties. Assuming Gaussian-like spectra, we present a general inverse-modeling framework that reconstructs the intrinsic frequency and energy characteristics of repeating FRBs directly from truncated data, without spectral profile fitting. In our approach, detected bursts are classified as in-band (affected only by the sensitivity cutoff) or band-chipped (affected by both sensitivity and operating-band cutoffs) events. For in-band events, observed and intrinsic quantities are linked through a set of equations. For band-chipped bursts, with spectral peaks possibly outside the telescope's operating band, a population-based method is used to infer individual burst properties from the statistical properties of the entire sample. Applied to 2,223 bursts from FRB 20121102A, it is found that intrinsically energetic bursts tend to have narrower spectra than weak ones. We further quantify, for the first time, the number of out-of-band bursts, and reveal distinct frequency-evolution behaviors across active periods and frequency bands. Comparisons between reconstructed and original samples show that the sensitivity cutoff barely affects burst energy but biases the observed bandwidth, whereas the operating-band cutoff may cause severe energy leakage and bandwidth underestimation, suggesting that the energy release of some repeaters may be underestimated, with potential implications for the energy supply beyond the magnetar magnetosphere. Our methodology transforms incomplete archival observations into physically meaningful probes, bridging instrumental readouts and intrinsic FRB physics.

astro-ph.HE↗

arXiv2026

Diverse Morphologies of GRB X-Ray Plateaus within a Common Magnetar Framework

The origin of the X-ray plateau phase in gamma-ray bursts (GRBs) remains an open problem. In particular, it is unclear whether GRBs with different temporal morphologies (i.e., with a rising, flat, or decaying plateau) arise from a common underlying mechanism. Although magnetar energy injection is a leading explanation, previous studies have primarily inferred magnetar properties on a burst-by-burst basis and have not tested the model at the population level. Here we perform the first hierarchical population inference of magnetar parameters for a uniform sample of 185 long GRBs with X-ray plateaus within a conditional Poisson point-process framework. It is found that the observed plateau population is well reproduced by physically plausible magnetar populations. The inferred parameter distributions show no strong statistical separation among subclasses with different plateau morphologies. Nevertheless, all subclasses show a substantial intrinsic luminosity scatter, $σ_{L,\rm int}\sim0.5$--1.0 dex, whereas the intrinsic duration scatter remains considerably smaller. The results provide a population-level test of the magnetar interpretation of GRB X-ray plateaus, showing that the observed diversity of plateau morphologies does not require distinct magnetar populations.

astro-ph.HE↗

arXiv2026

Are Repeaters Prevalent Among the Known Fast Radio Burst Sources?

Fast radio bursts (FRBs) are millisecond radio pulses of unknown origin. Despite extensive follow-up observations, only $\sim3\%$ of FRBs have been confirmed as repeaters. It remains unclear whether the rest are truly one-off bursts, or essentially repeating sources that have only been detected once due to limited monitoring time. Using the second CHIME/FRB catalog, we test this debate by comparing non-repeaters with two repeater-based subsamples: the first-detected bursts of repeaters and their highest-fluence bursts. A non-parametric method that accounts for selection effects is employed to derive the energy functions and event rates of these samples. All samples are well described by broken power-law energy distributions with comparable break energies ($\sim 5\times10^{38}$ erg), but with significantly different slopes between repeating and non-repeating populations. Their event-rate evolution also differs significantly. Assuming $ρ(z) \propto (1+z)^B$, we have $B = -5.57^{+0.15}_{-0.15}$ for non-repeaters and $B = -8.63^{+0.46}_{-0.41}$ and $-9.10^{+0.55}_{-0.56}$ for the two repeater samples. Size-matched resampling shows that the repeater event-rate indices lie far outside the 5$σ$ range expected from non-repeater subsamples, ruling out sample size as the reason for the observed difference. These results indicate that at least a subset of one-off FRBs are intrinsically non-repeating, implying that repeating sources may represent a distinct and possibly less common population.

astro-ph.HE↗

arXiv2026

Probabilistic kilonova prediction from gravitational wave inferred binary neutron star parameters

Kilonovae provide a key electromagnetic window into binary neutron star mergers, revealing the properties of the merging system while probing r-process nucleosynthesis of the Universe. However, only a few kilonova candidates have been detected to date, with AT2017gfo being the only one associated with a gravitational wave event, GW170817. In this work, we present \textsc{Genova}, a probabilistic framework for predicting kilonova spectra and light curves directly from gravitational wave posterior samples of binary neutron star mergers. This method uses a conditional normalising flow to learn the distribution of rest-frame spectra conditioned on the source-frame component masses, tidal deformabilities, viewing angle and time since merger. Other kilonova model parameters, such as ejecta opacities, are marginalised over during training, so that their effects are propagated into the predicted spectra as predictive uncertainty. In the self-consistency test, the flow model reproduces the median light curves with residuals typically below $\sim 0.1$ mag, and the ratio of the predicted central 68\% interval widths remains predominantly between $0.8$ and $1.4$ over $\sim 0.4$--$8.0$ days. Comparisons with a physically distinct kilonova model show that the probabilistic prediction can remain informative beyond the model used for training. We apply \textsc{Genova} to GW170817/AT2017gfo using multi-band observations, including newly re-reduced $Y$-, $J$-, $K_s$-band photometry from the Visible and Infrared Survey Telescope for Astronomy, which we present in this work. The resulting predictive intervals broadly encompass the observations while capturing both gravitational wave posterior uncertainty and the variation induced by marginalised kilonova model parameters.

astro-ph.HE↗

arXiv2026

Probing strange quark matter objects with future space-based gravitational wave detectors DECIGO and BBO

The Strange Quark Matter (SQM) hypothesis posits that objects composed of SQM could exist across a wide mass range, from strange planets (SPs) to strange stars (SSs). It has been proposed that gravitational waves (GWs) emitted by inspiraling SS-SP systems may be detectable by ground-based GW observatories such as advanced LIGO and the Einstein Telescope. Nevertheless, such a system may undergo an extended period of orbital evolution in a close configuration before entering the inspiraling phase. During this time, it can generate continuous GW signals at frequencies ranging from milli-hertz (mHz) to deci-hertz (dHz). The detailed characteristics of these GWs have not yet been thoroughly explored. In this study, we delve into the continuous GW features of SS-SP systems, with a focus on exploring the physically viable parameter space. We compared the GW signals emitted by these systems to the sensitivity curves of next-generation space-based GW detectors like the Deci-hertz Interferometer Gravitational wave Observatory (DECIGO) and the Big Bang Observer (BBO). Our analyses demonstrate that both the DECIGO and BBO detectors are capable of detecting continuous GWs from SS-SP systems across a broad parameter space. These GWs carry important information for testing the SQM hypothesis, as well as for advancing our understanding of supernovae and compact star merger processes.

astro-ph.HE↗

arXiv2026

A second-scale periodicity in an active repeating fast radio burst source

Fast radio bursts (FRBs) are fierce radio flashes from the deep sky. Abundant observations have indicated that highly magnetized neutron stars might be involved in these energetic bursts, but the underlying trigger mechanism is still enigmatic. Especially, the widely expected periodicity connected to the spin of the central engine has never been discovered, which leads to further debates on the nature of FRBs. Here we report the first discovery of a $\sim$ 1.7 s period in the repeating source of FRB 20201124A. This is an active repeater, from which more than 2800 bursts have been detected over a total of 49 days. The phase-folding method is adopted to analyze the bursts on each day separately. While no significant periodic signal is found in most days, a clear periodicity does appear on two specific days: a period of 1.706024(13) s on MJD 59310, and a slightly larger period of 1.707968(9) s on MJD 59347. A global Monte Carlo analysis based on all single-day datasets yields a significance level of $5.5 σ$ for the periodicity. A period derivative of $6.11(5)\times10^{-10}$ s s$^{-1}$ can be derived from these two periods, which further implies a surface magnetic field strength of $1.03\times10^{15}$ G and a spin-down age of $44$ years for the central engine. It is concluded that FRB 20201124A should be associated with a young magnetar.

astro-ph.HE↗

arXiv2026

Gamma-Ray Bursts: Evidence for a Common Origin of X-ray Plateaus with Diverse Temporal Decay Index

A significant fraction of gamma-ray bursts (GRBs) exhibit a plateau in the early X-ray afterglow light curve, whose mechanism remains uncertain. While the post-plateau normal decay index ($α_2$) is commonly used to constrain the afterglow dynamics, the shallow-decay slope of the plateau itself ($α_1$) has received comparatively little attention. Recent observations, however, reveal substantial dispersion in $α_1$, raising the question of whether GRBs with rising, flat and mildly decaying plateaus represent intrinsically distinct populations. To address this question, we collect a uniform sample of 185 $\textit{Swift}$ GRBs with a well-defined plateau and divide them into three groups based on $α_1$. Using a non-parametric approach, we reconstruct their X-ray luminosity functions, redshift distributions and event rates. It is found that the three groups exhibit statistically consistent properties across all diagnostics, with no evidence for group-specific features. Monte Carlo perturbation tests further show that these results are insensitive to the adopted classification boundaries of $α_1$. Our results indicate that variations in the plateau slope $α_1$ do not define distinct GRB subclasses, but instead the sample constitutes a statistically uniform population governed by a common framework.

astro-ph.HE↗

arXiv2026

Short-duration GRB 250221A Afterglow Driven by Two-Component Jets from the merger of a compact star

GRB 250221A is a short gamma-ray burst (GRB) at redshift $z=0.768$, with a duration of 1.8 s and no extended emission in either Swift/Burst Alert Telescope or Konus-Wind bands. A remarkable rebrightening feature in both optical and X-ray bands was observed at $\sim$0.6 days after the burst trigger, but no supernova or kilonova signature was detected. The burst properties and empirical correlations or distributions (e.g., duration, spectral hardness, location in the Amati correlation, $\varepsilon-$value, $f_{\rm eff}$ parameter, and physical offset) favor a compact binary merger origin. However, a dense circumburst medium with $n\sim 80\rm~cm^{-3}$, obtained by adopting the energy injection into a jet to interpret the late-time rebrightening is inconsistent with the compact binary merger origin. In this paper, we propose a two-component jet model to explain the multiwavelength afterglow observations of GRB 250221A, in which the relativistic narrow jet ($\rm θ_{c} \sim 3.8^\circ$) produces the prompt and the early decay afterglow emission, while the mildly relativistic wide jet ($\rm θ_{w} \sim 4.4^\circ$) dominates at later times, resulting in the observed rebrightening feature. If this is the case, one can obtain a lower medium density with $n\sim 0.72\rm~cm^{-3}$ which is a little bit higher than that of short GRBs in merger environments, but falls into the reasonable and acceptable range. Finally, a possible kilonova emission is also discussed within the scenario of compact star merger origin of GRB 250221A.

astro-ph.HE↗

arXiv2026

Modeling the Multi-Wavelength Afterglow of Short Gamma-Ray Bursts with a Plateau Phase

Short gamma-ray bursts (GRBs) exhibiting a plateau phase provide valuable insights into the post-merger activity of their central engines. Although the physical origin of the plateau remains uncertain, the magnetar energy injection model offers a compelling explanation that reproduces the observed temporal and luminosity features. However, previous studies relying solely on X-ray data have suffered from strong parameter degeneracies when constraining the magnetar parameters. Here we perform broadband afterglow modeling on seven short GRBs with plateau features by combining X-ray, optical, and radio observations within the framework of the magnetar energy injection model. Key model parameters are derived by using the Markov Chain Monte Carlo method. It is found that the energy injection substantially modifies the afterglow dynamics in most events. Compared with X-ray-only analyses, our broadband modeling yields systematically a lower magnetic field strength and a shorter spin period for the central magnetar, corresponding to a higher injection luminosity. The study clearly shows that incorporating multi-wavelength data effectively alleviates the degeneracy between the magnetar parameters and X-ray radiative efficiency. In addition, the distribution of our short GRBs differs markedly from long GRBs when they are plotted on the initial Lorentz factor versus gamma-ray energy plane. This offset, consistent with the observed harder spectrum of short GRBs, may serve as a useful diagnostic for investigating the progenitor as larger samples are available.

astro-ph.HE↗

arXiv2025

A Statistical Analysis of Fluence and Energy Distributions of Non-repeating Fast Radio Bursts Detected by CHIME

Fast Radio Bursts (FRBs) are energetic radio bursts that typically last for milliseconds. They are mostly of extragalactic origin, but the progenitors, trigger mechanisms and radiation processes are still largely unknown. Here we present a comprehensive analysis on 415 non-repeating FRBs detected by CHIME, applying manual filtering to ensure sample completeness. It is found that the distribution of fluence can be approximated by a three-segment power-law function, with the power-law indices being $-3.76 \pm 1.61$, $0.20 \pm 0.68$ and $2.06 \pm 0.90$ in the low, middle, and high fluence segments, respectively. Both the total dispersion measure (\text{DM}) and the extragalactic \text{DM} follow a smoothly broken power-law distribution, with characteristic break DM values of $\sim 703$ pc $\rm cm^{-3}$ and $\sim 639$ pc $\rm cm^{-3}$, respectively. The redshifts are estimated from the extragalactic \text{DM} by using the Macquart relation, which are found to peak at $ z \sim 0.6$. The isotropic energy release ($E_{\text{iso}}$) is also derived for each burst. Two-Gaussian components are revealed in the distribution of $E_{\text{iso}}$, with the major population narrowly clustered at $\sim 2.3 \times 10^{40} {\rm erg}$. The minor population have a characteristic energy of $\sim 1.6 \times 10^{39}$ erg and span approximately one order of magnitude. The distribution hints a near-uniform energy release mechanism for the dominant population as expected from some catastrophic channels, whereas the lower-energy component (potentially including repeat-capable sources) may reflect a broader diversity in FRB origins, emission mechanisms and evolutionary stages.

astro-ph.HE↗

arXiv2025

A Statistical Study of the Gamma-Ray Burst and Supernova Association

The association between long gamma-ray bursts (LGRBs) and core-collapse supernovae (SNe) has been well established since the discovery of SN 1998bw, which was linked to the low-luminosity LGRB 980425. However, long-term monitoring of several well-localized, low-redshift LGRBs has yielded compelling evidence for the absence of accompanying SNe. Notably, two long bursts, GRB 211211A and GRB 230307A, show signatures consistent with kilonova emission from compact binary mergers, indicating that at least some long events may originate from progenitors other than core-collapse SNe. In this study, we conduct a comparative analysis of two samples of LGRBs, i.e., LGRBs with and without SN associations, to investigate the differences that may reveal intrinsic distinctions in their progenitors. A detailed examination of their prompt emission properties, host galaxy environments, and event rates is performed. While the two samples exhibit considerable overlap in most observed properties, a significant discrepancy in their event rate is revealed. LGRBs without SN association have an event rate that aligns well with the star formation rate, whereas that of SN-associated LGRBs differs significantly. It indicates that LGRBs without an SN association may constitute a distinct subclass with intrinsically different progenitors.

astro-ph.HE↗

arXiv2025

Axial current as the origin of quantum intrinsic orbital angular momentum

We show that the axial current density is the physical origin (generator) of quantum intrinsic orbital angular momentum (IOAM). Without the axial current, the IOAM of particles vanishes. Broadly speaking, we argue that the spiral or interference characteristics of the axial current density determine the occurrence of nonlinear or tunneling effects in any spacetime-dependent quantum systems. Our findings offer a comprehensive theoretical framework that addresses the limitations of Keldysh's ionization theory and provides new insights into the angular momentum properties of quantum systems, particularly in tunneling-dominated regimes. Using Wigner function methods, fermionic generalized two-level model, and Berry phase simulations, we predict that IOAM effect can persist even in pure quantum tunneling processes. These results open the door for experimental verification of IOAM effects in future high-intensity QED experiments, such as those using X-ray free electron lasers.

hep-ph↗

arXiv2025

Magnetic Reconnection as a Potential Driver of X-ray Variability in Active Galactic Nuclei

We present a systematic analysis on the X-ray variability in 13 bright quasars at z > 4.5, combining recent Swift observations from 2021 to 2023 and archival multi-epoch observations. Upper limits of the luminosity measurements were included in the analysis by using the Kaplan-Meier estimator method. It is found that the high-z quasars exhibit X-ray variability on both short-term (hours-to-days) and intermediate-term (weeks-to-months) timescales, with short-term variability dominating the overall variation. A linear correlation exists between the global mean ($μ_{\mathrm{L_{2-10\,keV}}}$) and standard deviation ($σ_{\mathrm{L_{2-10\,keV}}}$) of X-ray luminosities, which is independent of the X-ray photon index and optical-to-X-ray spectral slope. The localized stochastic magnetic reconnection mechanism is strongly favored, which can naturally lead to a scale-invariant power-law energy distribution and satisfactorily explain the correlation. The $σ$-$μ$ correlation parallels with the well-documented rms-flux relation of low-z active galactic nuclei (AGNs), implying the magnetic reconnection mechanism could drive short-timescale X-ray variability in both high- and low-z AGNs. The highest-z quasar in our sample, J142952+544717 (z = 6.18), shows a luminosity distribution extending to ${10}^{47}\ \rm{erg\ {s}^{-1}}$ with a not conspicuous median luminosity. On the other hand, J143023+420436 (z = 4.7), which hosts the most relativistic jet among known high-z blazars, is dominated in the high-luminosity regime (${10}^{47}\ \rm{erg\ {s}^{-1}}$ ), making it an ideal target for multi-wavelength follow-up observations. J090630+693030 is found to have a rest-frame period of 182.46 days and J143023+420436 has a period of 16.89 days, both could be explained by the global evolution of plasmoid chains, in which magnetic islands formed during reconnection may merge successively.

astro-ph.HE↗

arXiv2025

The Event Rate and Luminosity Function of Fermi/GBM Gamma-Ray Bursts

Luminosity function and event rate of Gamma-Ray Bursts (GRBs) are easily biased by the instrument and selection effects. We select 115 Fermi/GBM GRBs with good spectra fitted by a smoothly broken power-law function. The $τ$-statistic method is used to describe how the luminosity evolves with redshift. The non-parametric Lynden-Bell's c$^{-}$ method has been applied to get the cumulative luminosity function and event rate which is compared with the star formation history. How the selection and instrument effects bias the deduced event rate has been carefully studied. We find that the event rate always exceeds the star formation rate (SFR) at lower redshift and matches with each other at higher redshift, which is independent of energy bands and consistent with previous findings of other satellites. Furthermore, it is found that sample completeness does not affect the deduced event rate too much as mentioned for the Swift lGRBs in Dong et al.. A triple power-law function has been used to fit the cumulative flux distribution and categorize the total sample into three subsamples of bright, medium and faint GRBs. We find that the event rates of bright GRBs, unlike medium and faint ones, comply with the SFR ideally, which indicates that these bright GRBs with higher luminosity are possibly produced from the core-collapse of massive stars.

astro-ph.HE↗

arXiv2025

Two Periodic Activity Epochs in FRB 20201124A: Coincident with Critical RM Evolution Epochs and Its Implications

Recent observations of the repeating fast radio burst FRB 20201124A by the Five-hundred-meter Aperture Spherical radio Telescope (FAST) revealed a second-scale periodic modulation ($\sim$1.7\,s) in burst activity during two distinct observational windows. We find that these two periodic activity epochs temporally coincide with the transitional states of the source's Faraday rotation measure (RM), and the chance coincidence is only about 0.07$\%$. This correlation is can be understood within the magnetar/Be-star binary system framework. Considering that only the polar cap region can remain stable for such an extended period, we apply a coherent linear periodic evolution model to jointly constrain the initial burst period $ P_0 $ and the period derivative $ \dot{P} $ across both observation windows (MJD 59310 and MJD 59347). We obtain spin parameters consistent with blind search results: an initial spin period $P_0 = 1.7060155$\,s at the reference time and spin period derivative $\dot{P} = 6.1393 \times 10^{-10}$\,s\,s$^{-1}$. We conclude that during these two observational windows, the magnetar was just crossing the disk of the Be star. The disk-magnetar interaction at these two geometric positions may surpress the multi-polar magnetic fields at low latitudes of the magnetar, which enhances the dominance of the polar cap region emissions and makes the periodic activity detectable.

astro-ph.HE↗

arXiv2025

Softness Ratio of SWIFT Gamma-ray Bursts and Relevant Correlations

The properties of X-ray flashes (XRFs) and X-ray rich gamma-ray bursts (XRRs) as compared with classical gamma-ray bursts (C-GRBs) have been widely discussed during the \emph{Swift} era. It has been proposed that XRFs and XRRs are low-energy extensions of the GRB population so that they should follow similar correlations. To further examine this idea, we collect a sample of $303$ GRBs detected by \emph{Swift} over the past two decades, all of which have reliable redshifts and spectral parameters. The bursts are classified into XRFs, XRRs, and C-GRBs based on their softness ratio (SR), which is calculated by dividing the $25-50$ keV fluence with the $50-100$ keV fluence. A strong correlation is found among the isotropic energy $E_{\mathrm{iso}}$, peak luminosity $L_{\mathrm{p}}$, and rest frame burst duration $T_{90, \mathrm{rest}}$, i.e., $E_{\mathrm{iso}} \propto L_{\mathrm{p}}^{0.88\pm0.02} T_{90, \mathrm{rest}}^{0.58\pm0.02}$. Additionally, two tight three-parameter correlations involving SR and the rest-frame peak energy $E_{\mathrm{p}}$ are also derived, i.e. $E_{\mathrm{p}} \propto E_{\mathrm{iso}}^{0.20\pm0.02} \mathrm{SR}^{-2.27\pm0.15}$ and $E_{\mathrm{p}} \propto L_{\mathrm{p}}^{0.17\pm0.02} \mathrm{SR}^{-2.33\pm0.14}$. It is interesting to note that XRFs, XRRs, and C-GRBs all follow the above correlations. The implications of these correlations and their potential application in cosmology are discussed.

astro-ph.HE↗