A Possible Cepheid‐like Luminosity Estimator for the Long Gamma‐Ray Bursts

Abstract

We present a possible Cepheid-like luminosity estimator for the long gamma-ray bursts based on the variability of their light curves. To construct the luminosity estimator, we use CGRO/BATSE data for 13 bursts, W ind/Konus data for Ðve bursts, Ulysses/GRB data for one burst, and NEAR/XGRS data for one burst. Spectroscopic redshifts, peak Ñuxes, and high-resolution light curves are available for 11 of these bursts ; partial information is available for the remaining nine bursts. We Ðnd that the isotropic equivalent peak luminosities L of these bursts positively correlate with a rigorously constructed measure V of the variability of their light curves. We Ðt to these data a model that accommodates both intrinsic scatter (statistical variance) and extrinsic scatter (sample variance). We Ðnd that If one L D V 3.3~0 1 . . 9 1 . excludes GRB 980425 from the Ðt, on the grounds that its association with SN 1998bw at a redshift of z \ 0.0085 is not secure, the luminosity estimator spans B2.5 orders of magnitude in L , and the slope of the correlation between L and V is positive with a probability of 1 [ (1.4 ] 10~4) (3.8 p). Although GRB 980425 is excluded from this Ðt, its L and V values are consistent with the Ðtted model, which suggests that GRB 980425 may well be associated with SN 1998bw and that GRB 980425 and the cosmological bursts may share a common physical origin. If one includes GRB 980425 in the Ðt, the luminosity estimator spans B6.3 orders of magnitude in L , and the slope of the correlation is positive with a probability of 1 [ (9.3 ] 10~7) (4.9 p). In either case, the luminosity estimator yields best-estimate luminosities that are accurate to a factor of B4, or best-estimate luminosity distances that are accurate to a factor of B2. Regardless of whether GRB 980425 should be included in the Ðt, its light curve is unique in that it is much less variable than the other B17 light curves of bursts in our sample for which the signal-tonoise ratio is reasonably good.

Peak Luminosity–Spectral Lag Relation Caused by the Viewing Angle of the Collimated Gamma-Ray Bursts

“…Surprisingly enough, a simple subjet model happens to reproduce the observation quite well, including GRB 980425, which has the extremely dim luminosity and large spectral lag. The subjet model might be compatible with the luminosityvariability relation that more complex bursts tend to be brighter Reichart et al 2001;Schaefer et al 2001). According to Plaga (2001), when the power density spectrum of the GRB time histories is (Belo- Stern, & Svensson 1998Shaviv & Dar 1995), the variability relates to the pulse width as priate offsets.…”

“…(2001) found that the luminosities of seven bursts with known redshifts are correlated with the variabilities of the bursts (see also Reichart et al 2001). If both relations are correct, there should be a relation between the variability and the spectral lag.…”

Correlation between peak energy and Fourier power density spectrum slope in gamma-ray bursts

“…On the temporal side, we need to determine how Γ may be related to the fast component in the observed light curves. In early attempts to explain the luminosity-variability correlation (Fenimore & Ramirez-Ruiz 2000;Reichart et al 2001;Guidorzi et al 2005;Rizzuto et al 2007), it was shown that the e ± pair photosphere created by the IS synchrotron photons contributes to suppress the short-timescale variability in GRBs with the pl PDS is the result of the superposition of different pulses with different timescales, so that no break stands out in the total PDS, which looks like a power-law with a shallow index (α = 1.5 in this example, thick dashed line).…”

Thermalization in Relativistic Outflows and the Correlation between Spectral Hardness and Apparent Luminosity in Gamma‐Ray Bursts

“…In some models of the engine, e.g., those in which the outflow is driven by a magnetic field threading the horizon of a black hole ( Blandford & Znajek 1977;Mészáros & Rees 1997), it is not obvious why should correlate strongly with L iso . Recently, Firmani et al (2006) have pointed out that a rather tight correlation exists between three observed quantities that are derived from measurements of the prompt emission, namely, L iso , E pk , and t 0:45 , where L iso / E 1:62 pk t À0:49 0:45 and t 0:45 is essentially a measure of the duration of the prompt emission above a certain level (originally used for measuring the variability or spikiness of the prompt emission, by Fenimore 2000 andReichart et al 2001). Assuming that t 0:45 $ t j and that the energy output rate is L iso ' E iso /t j , the Firmani relation can be written as E iso / E 5 = 3 pk t 1 = 2 j .…”