Connection between Energy-dependent Lags and Peak Luminosity in Gamma-Ray Bursts

We suggest a connection between the pulse paradigm at gamma-ray energies and the recently demonstrated luminosity distribution in gamma-ray bursts: The spectral evolution timescale of pulse structures is anticorrelated with peak luminosity and with quantities that might be expected to reflect the bulk relativistic Lorentz factor, such as spectral hardness ratio. We establish this relationship in two important burst samples using the cross-correlation lags between low (25-50 keV) and high (100-300 keV and >300 keV) energy bands. For a set of seven bursts (six with redshifts) observed by CGRO/BATSE and BeppoSAX that also have optical or radio counterparts, the γ/X peak flux ratios and peak luminosities are anticorrelated with spectral lag. For the 174 brightest BATSE bursts with durations longer than 2 s and significant emission above 300 keV, a similar anticorrelation is evident between gamma-ray hardness ratio or peak flux and spectral lag. For the six bursts with redshifts, the connection between peak luminosity and spectral lag is well fitted by a power law, L₅₃ ≈ 1.3 × (τ/0.01 s)^-1.15. While GRB 980425 (if associated with SN 1998bw) would appear to extend this trend qualitatively, with a lag of ~4-5 s and luminosity of ~1.3 × 10⁴⁷ ergs s^-1 , it falls below the power-law relationship by a factor of several hundred. As noted previously by Band, most lags are concentrated on the short end of the lag distribution, near 100 ms, suggesting that the gamma-ray burst luminosity distribution is peaked on its high end.