Steep Decay Phase Shaped by the Curvature Effect. II. Spectral Evolution

Abstract

We derive a simple analytical formula to describe the evolution of spectral index $\beta$ in the steep decay phase shaped by the curvature effect with assumption that the spectral parameters and Lorentz factor of jet shell is the same for different latitude. Here, the value of $\beta$ is estimated in 0.3$-$10keV energy band. For a spherical thin shell with a cutoff power law (CPL) intrinsic radiation spectrum, the spectral evolution can be read as a linear function of observer time. For the situation with Band function intrinsic radiation spectrum, the spectral evolution may be complex. If the observed break energy of radiation spectrum is larger than 10keV, the spectral evolution is the same as that shaped by jet shells with a CPL spectrum. If the observed break energy is less than 0.3keV, the value of $\beta$ would be a constant. Others, the spectral evolution can be approximated as a logarithmal function of the observer time in generally.

24 pages, 13 figures, accepted for publication in ApJ

References in corpus (10)

• A comprehensive analysis of Swift/XRT data: I. Apparent spectral evolution of GRB X-ray tails
• Gamma-ray Burst 080319B: Evidence for Relativistic Turbulence, Not Internal Shocks
• Gamma Ray Bursts as Electromagnetic Outflows
• A Turbulent Model of Gamma-Ray Burst Variability
• Curvature Effect of a Non-Power-Law Spectrum and Spectral Evolution of GRB X-Ray Tails
• X-ray Hardness Variations as an Internal/External Shock Diagnostic
• Swift captures the spectrally evolving prompt emission of GRB 070616
• The History of GRB Outflows: Ejection Lorentz Factor and Radiation Location of X-Ray Flares
• Variabilities of Gamma-ray Bursts from Black Hole Hyper-accretion Disks
• Central Engine Memory of Gamma-Ray Bursts and Soft Gamma-Ray Repeaters

Cited by in corpus (4)

• Spectral index-flux relation for investigating the origins of steep decay in $\gamma$-ray bursts
• First Electromagnetic Pulse Associated with a Gravitational-Wave Event: Profile, Duration, and Delay
• A lower occurrence rate of bright X-ray flares in SN-GRBs than $z<1$ GRBs: evidence of energy partitions?
• Late Afterglow Bump/Plateau around the Jet Break: Signature of a free-to-shocked wind Environment in Gamma-ray Burst