ON THE CURVATURE EFFECT OF A RELATIVISTIC SPHERICAL SHELL

• Published in: The Astrophysical journal Vol. 808; no. 1; pp. 1 - 6
• Main Authors: Uhm, Z. Lucas, Zhang, Bing
• Format: Journal Article
• Language: English
• Published: United Kingdom The American Astronomical Society 20.07.2015
• Subjects: Acceleration; Alpha decay; ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; Beta decay; Constants; COSMIC GAMMA BURSTS; EMISSION; gamma-ray burst: general; Lorentz factor; LORENTZ FORCE; Mathematical analysis; Mathematical models; radiation mechanisms: non-thermal; relativistic processes; RELATIVISTIC RANGE; SPHERICAL CONFIGURATION; Spherical shells
• ISSN: 0004-637X; 1538-4357; 1538-4357
• DOI: 10.1088/0004-637X/808/1/33

ABSTRACT We consider a relativistic spherical shell and calculate its spectral flux as received by a distant observer. Using two different methods, we derive a simple analytical expression of the observed spectral flux and show that the well-known relation (between temporal index and spectral index ) of the high-latitude emission is naturally achieved in our derivation but holds only when the shell moves with a constant Lorentz factor Γ. Presenting numerical models in which the shell is undergoing acceleration or deceleration, we show that the simple relation does indeed deviate as long as Γ is not constant. For the models under acceleration, we find that the light curves produced purely by the high-latitude emission initially exhibit much steeper decay than in the constant Γ case and gradually resume the relation in about one and a half orders of magnitude in observer time. For the models under deceleration, the trend is opposite. The light curves made purely by the high-latitude emission initially exhibit a shallower decay than in the constant Γ case and gradually resume the relation in a similar order of magnitude in observer time. We also show that how fast the Lorentz factor Γ of the shell increases or decreases is the main ingredient determining the initial steepness or shallowness of the light curves.