Correlations Between Lag, Luminosity, and Duration in Gamma-ray Burst Pulses

We derive a new peak lag vs. peak luminosity relation in gamma-ray burst (GRB) pulses. We demonstrate conclusively that GRB spectral lags are pulse rather than burst properties and show how the lag vs. luminosity relation determined from CCF measurements of burst properties is essentially just a rough measure of this newly derived relation for individual pulses. We further show that most GRB pulses have correlated properties: short-lag pulses have shorter durations, are more luminous, and are harder within a burst than long-lag pulses. We also uncover a new pulse duration vs. pulse peak luminosity relation, and indicate that long-lag pulses often precede short-lag pulses. Although most pulse behaviors are supportive of internal shocks (including long-lag pulses), we identify some pulse shapes that could result from external shocks.