GCN Circular 7682

Many long GRBs have optical light-curves which are initially slowly 
rising. The optical light curve of the short hard burst (SHB) 080503 (Mao 
et al. GCN 7665
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; Ukwatta et al. GCN 7673
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; Guidorzi et al. GCN 7674
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) 
discovered by Perley et al. (GCNs 7678
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, 7680
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) may be their analog 
slow-rise optical afterglow (AG) changing to a plateau phase and entering 
the gradual transition to an asymptotic decline, which, in the CB model, 
has roughly the form,

            Fnu ~ [1/(t+t_b}^{\beta_O+1/2}] * nu^{-beta_O}

for a constant low-density SHB environment, or

            Fnu  ~ [1/ (t+t_b)^{beta_O+1}] * nu^{-beta_O}

for an isothermal sphere environment with a density propto 1/r^2.
t_b is the bending time of its canonical AG, and beta_O = Gamma - 1 ~ 1.1 is 
the spectral index above the bend frequency. In the CB model, the initial 
increase of the CB's radius, R^2 ~ t^2/(t^2+t_exp^2), where t_exp is the time 
beyond which the CB's radius settles to its approximate constant value, 
produces the initial rise of the synchrotron AG.  The low density environments 
of SHBs yields typically, t_b~ 10^5 s, and a long expansion time, t_exp, of the 
CB's radius relative to its values in slow-rise optical AGs of long GRB such as 
071010A (Covino et el. arXiv:0804.4367).