Nicole M. Lloyd

Cosmological versus Intrinsic: The Correlation between Intensity and the Peak of the νFν Spectrum of Gamma-Ray Bursts

We present results of correlation studies, examining the association between the peak of the nu F_nu spectrum of gamma ray bursts, E_p, with the bursts energy fluence and photon peak flux. We discuss methods to account for data truncation in E_p and fluence or flux when performing the correlation analyses. However, because bursts near the detector threshold are not usually able to provide reliable spectral parameters, we focus on results for the brightest bursts in which we can better understand the selection effects relevant to E_p and burst strength. We find that there is a strong correlation between total fluence and E_p. We discuss these results in terms of both cosmological and intrinsic effects. In particular, we show that for realistic distributions of the burst parameters, cosmological expansion alone cannot account for the correlation between E_p and total fluence; the observed correlation is likely a result of an intrinsic relation between the burst rest-frame peak energy and the total radiated energy. We investigate this latter scenario in the context of synchrotron radiation from external and internal shock models of GRBs. We find that the internal shock model is consistent with our interpretation of the correlation, while the external shock model cannot easily explain this intrinsic relation between peak energy and burst radiated energy.

Distribution of Spectral Characteristics and the Cosmological Evolution of Gamma-Ray Bursts

We investigate the cosmological evolution of GRBs, using the total gamma ray fluence as a measure of the burst strength. This involves an understanding of the distributions of the spectral parameters of GRBs as well as the total fluence distribution - both of which are subject to detector selection effects. We present new non-parametric statistical techniques to account for these effects, and use these methods to estimate the true distribution of the peak of the nu F_nu spectrum, E_p, from the raw distribution. The distributions are obtained from four channel data and therefore are rough estimates. Here, we emphasize the methods and present qualitative results. Given its spectral parameters, we then calculate the total fluence for each burst, and compute its cumulative and differential distributions. We use these distributions to estimate the cosmological rate evolution of GRBs, for three cosmological models. Our two main conclusions are the following: 1) Given our estimates of the spectral parameters, we find that there may exist a significant population of high E_p bursts that are not detected by BATSE, 2) We find a GRB co-moving rate density quite different from that of other extragalactic objects; in particular, it is different from the recently determined star formation rate.

Synchrotron emission as the source of GRB spectra, Part II: Observations

We test the models of synchrotron emission presented in Part I of this series (Lloyd & Petrosian, these proceedings [8]) against the distributions and evolution of GRB spectral parameters (particularly the low energy index, α). With knowledge of the Ep distribution and the correlation between α and Ep presented in [8], we show how to derive the expected distribution of α from fits to optically thin synchrotron spectra, and compare this with the observed distribution. We show that there is no difficulty explaining bursts below the “line of death,” α<−2/3, and that these bursts indicate that the spectrum of accelerated electrons must flatten or decline at low energies. Bursts with low energy spectral indices that fall above this limit are explained by the synchrotron self-absorption frequency entering the lower end of the BATSE window. Finally, we discuss a variety of spectral evolution behavior seen in GRBs and explain this behavior in the context of synchrotron emission from internal shocks.

Synchrotron radiation as the source of GRB spectra, Part I: Theory

We investigate synchrotron emission models as the source of gamma-ray burst spectra. We show that allowing for synchrotron self absorption and a “smooth cutoff” to the electron energy distribution produces a wide range of low-energy spectral behavior. We show that there exists a correlation between the value of the peak of the νFν spectrum, Ep, and the low-energy spectral index α as determined by spectral fits over a finite bandwidth. Finally, we discuss the implications of synchrotron emission from internal shocks for GRB spectral evolution.

Cosmological signatures in intensity and break energy correlations

We examine the association between the peak of the νFν spectrum of gamma ray bursts, Ep, and the burst’s energy fluence. Because bursts near the detector threshold are not usually able to provide reliable spectral parameters, we analyze the results for the brightest bursts in which we can better understand the selection effects relevant to Ep and burst strength. We find that there is a strong correlation between total fluence and Ep. We discuss these results in terms of both cosmological and intrinsic effects. In particular, we show that for realistic distributions of the burst parameters, cosmological expansion alone cannot account for the correlation between Ep and total fluence; the observed correlation is likely a result of an intrinsic relation between the burst rest-frame peak energy and the total radiated energy, as expected in an internal shock model.

Distribution of fluences versus peak fluxes and the cosmological density evolution of the rate of GRBs

We argue that recent observations of afterglows and some theoretical considerations indicate that the gamma-ray fluence may be a better measure of strength of a burst than its peak flux. We discuss how the distribution of the fluence, or any physical quantity related to the peak counts (or flux), can be obtained with proper correction for threshhold effects. Using this method, we compare the cumulative and differential distributions of flux and fluence. We find some differences between these distributions, but more remarkable are the similarities between these distributions. The other striking feature is how different these distributions are from those of other extragalactic objects. Using the fluence distributions, we derive the expected comoving density rate evolution for different assumed total luminosity; we compare this with the GRB rate expected from the recently determined star formation rate.