Correlation studies of prompt and afterglow emissions from gamma-ray bursts (GRBs) between different spectral bands has been difficult to do in the past because few bursts had comprehensive and intercomparable afterglow measurements. In this paper we present a large and uniform data set for correlation analysis based on bursts detected by the Swift mission. For the first time, short and long bursts can be analyzed and compared. It is found for both classes that the optical, X-ray and gamma-ray emissions are linearly correlated, but with a large spread about the correlation line; stronger bursts tend to have brighter afterglows, and bursts with brighter X-ray afterglow tend to have brighter optical afterglow. Short bursts are, on average, weaker in both prompt and afterglow emissions. No short bursts are seen with extremely low optical to X-ray ratio as occurs for dark long bursts. Although statistics are still poor for short bursts, there is no evidence yet for a subgroup of short bursts with high extinction as there is for long bursts. Long bursts are detected in the dark category at the same fraction as for pre-Swift bursts. Interesting cases are discovered of long bursts that are detected in the optical, and yet have low enough optical to X-ray ratio to be classified as dark. For the prompt emission, short and long bursts have different average tracks on flux vs fluence plots. In Swift, GRB detections tend to be fluence limited for short bursts and flux limited for long events.
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