The softening phenomenon due to the curvature effect: in the case of extremely short intrinsic emission

Abstract

The curvature effect is explored in the case of extremely short intrinsic emission. Assuming a $\delta$ function emission we get formulas that get rid of the impacts from the intrinsic emission duration, which are applicable to any forms of continuum. The formulas predict that the same form of spectrum could be observed at different times, with the peak energy of the spectrum shifting from higher energy bands to lower bands following $E_{peak}\propto t^{-1}$. When the emission is early enough the light curve in the form $f_{\nu }(t)t^2$ will possess exactly the intrinsic spectral form, for which the temporal power law index and the spectral power law index will be related by $\alpha =2+\beta$. The analysis shows that there do exist a temporal steep decay phase and a spectral softening which occur simultaneously, and both are caused by the shifting of the Band function spectrum. According to the analysis, we predict that the softening due to the curvature effect will appear at different frequencies; it occurs earlier for higher frequencies and later for lower frequencies; the maximum spectral index time follows the $t_{b,max}\propto {\nu }^{-1}$ law. We also find: the softening duration would be linearly correlated with the maximum spectral index time; the observed ${\beta }_{min}$ and ${\beta }_{max}$ are determined by the low and high energy indexes of the observed Band function spectrum. We propose to check the curvature effect with the $\log f_{\nu }(t)t^3$ vs. $logt$ curve which would be in agreement with the $\log \nu f_{\nu }$ vs. $log\nu$ curve. Applying this to GRB 060614 shows that the peak energy of its observed spectrum is expected to pass through the observation band at $\sim$175 s.

33 pages, 11 figures, accepted by ApJ

References in corpus (17)

• The shock break-out of GRB 060218/SN 2006aj
• Swift detects a remarkable gamma-ray burst, GRB 060614, that introduces a new classification scheme
• Gamma-Ray Bursts in the Swift Era
• Making a Short Gamma-Ray Burst from a Long one: Implications for the Nature of GRB 060614
• Testing the Curvature Effect and Internal Origin of Gamma-Ray Burst Prompt Emissions and X-ray Flares with Swift Data
• A comprehensive analysis of Swift/XRT data: I. Apparent spectral evolution of GRB X-ray tails
• Swift observations of GRB 060614: an anomalous burst with a well behaved afterglow
• X-ray Hardness Evolution in GRB Afterglows and Flares: Late Time GRB Activity Without N_H Variations
• Are GRB 980425 and GRB 031203 real outliers or twins of GRB 060218?
• Evidence of Exponential Decay Emission in the Swift Gamma-ray Bursts
• The Interpretation and Implication of the Afterglow of GRB 060218
• A test of the power law relationship between gamma-ray burst pulse width ratio and energy expected in fireballs or uniform jets
• Swift captures the spectrally evolving prompt emission of GRB 070616
• The full curvature effect expected in early X-ray afterglow emission of gamma-ray bursts
• The rapid decline of the prompt emission in Gamma-Ray Bursts
• Spectral evolution of GRB 060904A observed with Swift and Suzaku -- Possibility of Inefficient Electron Acceleration
• Hardness ratio evolutionary curves of gamma-ray bursts expected by the curvature effect

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