The History of GRB Outflows: Ejection Lorentz Factor and Radiation Location of X-Ray Flares

Abstract

We present time-resolved spectral analysis of the steep decay segments of 29 bright X-ray flares of gamma-ray bursts (GRBs) observed with the Swift/X-ray telescope, and model their lightcurves and spectral index evolution behaviors with the curvature effect model. Our results show that the observed rapid flux decay and strong spectral index evolution with time can be well fit with this model, and the derived characteristic timescales ($t_c$) are in the range of $33\sim 264$ seconds. Using an empirical relation between the peak luminosity and the Lorentz factor derived from the prompt gamma-rays, we estimate the Lorentz factors of the flares (${\Gamma }_{\mathrm{X}}$). We obtain ${\Gamma }_{\mathrm{X}}=17\sim 87$ with a median value of $52$, which is smaller than the initial Lorentz factors of prompt gamma-ray fireballs. With the derived $t_c$ and ${\Gamma }_{\mathrm{X}}$, we constrain the radiating regions of 13 X-ray flares, yielding $R_{\mathrm{X}}=(0.2\sim 1.1)\times 10^{16}$ cm, which are smaller than the radii of the afterglow fireballs at the peak times of the flares. A long evolution feature from prompt gamma-ray phase to the X-ray epoch is found by incorporating our results with a sample of GRBs whose initial Lorentz factors are available in literatures, i.e., $\Gamma \propto [t_p/(1+z){]}^{-0.69\pm 0.06}$. These results may shed lights on the long term evolution of GRB central engines.

arXiv comment28 pages, 33 figures, accepted for publication in ApJ

References in corpus (68)

• The Physics of Gamma-Ray Bursts
• Methods and results of an automatic analysis of a complete sample of Swift-XRT observations of GRBs
• Unsteady Outflow Models for Cosmological Gamma-Ray Bursts
• Optical and Long Wavelength Afterglow from Gamma-Ray Bursts
• Beaming in Gamma-Ray Bursts: Evidence for a Standard Energy Reservoir
• Physical processes shaping GRB X-ray afterglow lightcurves: theoretical implications from the Swift XRT observations
• Evidence for a Canonical GRB Afterglow Light Curve in the Swift/XRT Data
• Gamma-Ray Bursts: Progress, Problems & Prospects
• The shock break-out of GRB 060218/SN 2006aj
• Wind Interaction Models for Gamma-Ray Burst Afterglows: The Case for Two Types of Progenitors
• Bright X-ray Flares in Gamma-Ray Burst Afterglows
• Predictions for The Very Early Afterglow and The Optical Flash
• Lower Limits on Lorentz Factors in Gamma Ray Bursts
• Afterglow Emission from Naked Gamma-Ray Bursts
• The early X-ray emission from GRBs
• X-Ray Flares from Postmerger Millisecond Pulsars
• A new population of ultra-long duration gamma-ray bursts
• A Complete Catalog of Swift GRB Spectra and Durations: Demise of a Physical Origin for Pre-Swift High-Energy Correlations
• Expanding Relativistic Shells and Gamma-Ray Burst Temporal Structure
• Flares in long and short Gamma-Ray Bursts: a common origin in a hyperaccreting accretion disk
• A Comprehensive Analysis of Fermi Gamma-Ray Burst Data. I. Spectral Components and Their Possible Physical Origins of LAT/GBM GRBs
• The First Survey of X-ray Flares from Gamma Ray Bursts Observed by Swift: Temporal Properties and Morphology
• REM observations of GRB 060418 and GRB 060607A: the onset of the afterglow and the initial fireball Lorentz factor determination
• Constraining GRB Initial Lorentz Factor with the Afterglow Onset Feature and Discovery of a Tight Gamma_0-E_iso Correlation
• Testing the Curvature Effect and Internal Origin of Gamma-Ray Burst Prompt Emissions and X-ray Flares with Swift Data
• Late internal shock model for bright X-ray flares in Gamma-ray Burst afterglows and GRB 011121
• The First Survey of X-ray Flares from Gamma Ray Bursts Observed by Swift: Spectral Properties and Energetics
• The late time evolution of Gamma-Ray Bursts: ending hyperaccretion and producing flares
• Unveiling the origin of X-ray flares in Gamma-Ray Bursts
• Gamma Ray Bursts in the comoving frame
• The Giant X-ray Flare of GRB 050502B: Evidence for Late-Time Internal Engine Activity
• A comprehensive analysis of Swift/XRT data: I. Apparent spectral evolution of GRB X-ray tails
• Lag-luminosity relation in gamma-ray burst X-ray flares: a direct link to the prompt emission
• Analysis of the X-ray Emission of Nine Swift Afterglows
• Curvature Effects in Gamma Ray Burst Colliding Shells
• The Escape of High-Energy Photons from Gamma-Ray Bursts
• A Comprehensive Analysis of Fermi Gamma-ray Burst Data: III. Energy-Dependent T90 Distributions of GBM GRBs and Instrumental Selection Effect on Duration Classification
• A Comprehensive Study of Gamma-Ray Burst Optical Emission: II. Afterglow Onset and Late Re-Brightening Components
• The Epeak-Eiso plane of long Gamma Ray Bursts and selection effects
• How Long does a Burst Burst?
• Lorentz Factor-Isotropic Luminosity/Energy Correlations of GRBS and Their Interpretation
• Empirical Constraints on Source Properties and Host Galaxies of Cosmological Gamma-Ray Bursts
• Comprehensive study of the X-ray flares from gamma-ray bursts observed by Swift
• X-ray flare in XRF 050406: evidence for prolonged engine activity
• The Dust Extinction Curves of Gamma-Ray Burst Host Galaxies
• GRB 091024A and the nature of ultra-long gamma-ray bursts
• The Onset of Gamma-Ray Burst Afterglow
• Gamma-Ray Burst afterglows as probes of environment and blastwave physics I: absorption by host galaxy gas and dust
• On the average Gamma-Ray Burst X-ray flaring activity
• Modeling Gamma-Ray Burst X-Ray Flares within the Internal Shock Model
• The Energetics and Environment of the Short-GRB Afterglows 050709 and 050724
• Curvature Effect of a Non-Power-Law Spectrum and Spectral Evolution of GRB X-Ray Tails
• On the Curvature Effect of a Relativistic Spherical Shell
• Thick fireballs and the steep decay in the early X-ray afterglow of gamma-ray bursts
• The Epeak-Eiso relation revisited with Fermi GRBs: Resolving a long-standing debate?
• A Tight $L_{\mathrm{p},\mathrm{iso}}-E_{\mathrm{p}}^{\prime }-{\Gamma }_0$ Correlation of Gamma-Ray Bursts
• Photosphere emission in the X-Ray Flares of Swift Gamma-Ray Bursts and Implications for the Fireball Properties
• X-ray Hardness Variations as an Internal/External Shock Diagnostic
• A common stochastic process rules gamma-ray burst prompt emission and X-ray flares
• Diagnosing GRB Prompt Emission Site with Spectral Cut-Off Energy
• X-ray flares, neutrino cooled disks, and the dynamics of late accretion in GRB engines
• X-ray flares in GRBs: general considerations and photospheric origin
• Swift and Fermi observations of X-ray flares: the case of Late Internal Shock
• A Statistical Study of GRB X-ray Flares: Evidence of Ubiquitous Bulk Acceleration in the Emission Region
• Determining the Dust Extinction of Gamma-ray Burst Host Galaxies: A Direct Method Based on Optical and X-ray Photometry
• The full curvature effect expected in early X-ray afterglow emission of gamma-ray bursts
• The bulk Lorentz factor of outflow powering X-ray flare in GRB afterglow
• Spectral evolution of GRB 060904A observed with Swift and Suzaku -- Possibility of Inefficient Electron Acceleration

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• Constraining Properties of GRB Central Engines with X-ray flares
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• External Shock in a Multi-Bursting Gamma-ray Burst: Energy Injection Phase induced by the Later Launched Ejecta
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• Time Evolution of Optical Darkness in GRB Afterglow: The Case of GRB 240825A
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