Early observations of 15 GRB afterglows taken (2008-09) by ROTSE-III along with the published data of 26 others have been used to study the rising temporal nature seen at optical frequencies. A good fraction of early time temporal rising indices found to be flatter than the model predicted values. Under the assumptions of "onset of the afterglow", the peak times of the rising optical light curves have been used to estimate the initial Lorentz factor (GAMMA)_(0) of the fireball, ranging from approx100 to approx1000. The estimated values of (GAMMA)_(0) seems correlated with the isotropic equivalent gamma-ray energies of GRBs i.e. highly energetic GRBs have higher values of (GAMMA)_(0). The analysis also indicates that for a larger sample of GRBs, the peak times of the rising afterglow light curves and the derived values of the initial Lorentz factors along with the respective prompt emission properties like E_(peak) can be used to better constrain possible scenarios like off-axis emission and structured outflow.
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