Luminosity Function Of Gamma-ray Bursts Research Articles

Luminosity function of GRBs

We attempt to constrain the luminosity function of Gamma Ray Bursts (GRBs) from the observed number count{flux relation and the afterglow redshift data. We assume three classes of luminosity functions for our analysis: (a) Log-normal distribution, (b) Schechter distribution, and (c) Scale-free distribution. We assume several models of the evolution of the GRB population for each luminosity function. Our analysis shows that: (a) log-normal is the only luminosity function that is compatible with both the observations. This result is independent of the GRB evolution model, (b) for log-normal function, the average photon luminosity L0 and the width of the luminosity function that are compatible with both the observations fall in the range: 10 55 s 1 < L0 < 10 56 s 1 and 2 < < 3, (c) the agreement of observations with other luminosity functions requires the GRB population to evolve more strongly than the evolution of the star-formation rate of the universe.

Luminosity Function of Gamma‐Ray Bursts Derived without Benefit of Redshifts

We show that the Euclidean value of for gamma-ray bursts (GRBs) selected on a timescale of 1024 ms is correlated with spectral hardness. The value of ranges from ~0.42 for soft bursts to ~0.26 for the hardest bursts. Given that the Euclidean value of for cosmological objects in a well-defined sample is a distance indicator, the hard bursts must reside at larger redshifts and therefore be more luminous than the soft bursts. The resulting luminosity-hardness correlation cannot be shown explicitly as a result of the small number of observed GRB redshifts at the present time. Based on the -hardness correlation, we derive the luminosity function of GRBs without using any redshifts, but we have to make an assumption how the comoving GRB rate varies with redshift. We present luminosity functions for three models of the GRB rate as a function of redshift, based on star formation rates. The peak luminosity functions are approximately broken power laws with an isotropic-equivalent break luminosity of ~1051.5 ergs s-1 in the 50-300 keV range and total local rate densities of ~0.5 Gpc-3 yr-1. Predicted GRB counts as a function of flux and redshift are presented. Based on the GRB luminosity function, we carry out a simulation to produce the luminosity-hardness correlation, which shows that the hardest GRBs are ~20 times more luminous than the softest ones.

A Search for Nontriggered Gamma-Ray Bursts in the BATSE Continuous Records: First Results

An off-line scan for nontriggered gamma-ray bursts (GRBs) in the BATSE daily records at 1024 ms time resolution covering about 7 yr of observations gave 1353 nontriggered and 1581 triggered GRBs. The scan efficiency was measured by adding artificial test bursts to the data. The log N- log P distribution could be extended down to peak fluxes, P ~ 0.1 photons cm-2 s-1. Previous indications of a turnover at small P are not confirmed. The log N- log P distribution cannot be fitted with a standard candle model with a nonevolving GRB source population, assuming that there are no large non-GRB contaminations. It is likely that the intrinsic luminosity function of GRBs is wide.

Energetics and Luminosity Function of Gamma‐Ray Bursts

Gamma-ray bursts (GRBs) are believed to be some catastrophic event in which material is ejected at a relativistic velocity, and internal collisions within this ejecta produce the observed γ-ray flash. The angular size of a causally connected region within a relativistic flow is of the order the angular width of the relativistic beaming, γ-1. Thus, different observers along different lines of sight could see drastically different fluxes from the same burst. Specifically, we propose that the most energetic bursts correspond to exceptionally bright spots along the line of sight on colliding shells and do not represent much larger energy release in the explosion. The energy budget for an average GRB in this model is, however, same as in the uniform shell model. We calculate the distribution function of the observed fluence for random angular-fluctuation of ejecta. We find that the width of the distribution function for the observed fluence is about 2 orders of magnitude if the number of shells ejected along different lines of sight is 10 or less. The distribution function becomes narrower if number of shells along typical lines of sight increases. The analysis of the γ-ray fluence and afterglow emissions for GRBs with known redshifts provides support for our model, i.e., the large width of GRB luminosity function is not due to a large spread in the energy release but instead is due to large angular fluctuations in ejected material. We outline several observational tests of this model. In particular, for δ-function energy distribution in explosions we predict little correlation between the γ-ray fluence and the afterglow emission as in fact is observed. We predict that the early (minutes-to-hours) afterglow would depict large temporal fluctuations whose amplitude decreases with time. Finally, we predict that there should be many weak bursts with about average afterglow luminosity in this scenario.

Constraints on the luminosities of gamma-ray bursts

Constraints are found on the gamma-ray burst luminosity function from an analysis of the combined BATSE/PVO intensity distribution. If bursts originate in an extended Galactic halo, then the intrinsic luminosity range is narrow, with bursts spanning only a factor of five or less in luminosity. If bursts originate in a simple Friedmann cosmology with Ω = 1 and Λ = 0, then very few luminosity constraints exist.

On the nature of gamma-ray burst time dilations

The recent discovery that faint gamma-ray bursts are stretched in time relative to bright ones has been interpreted as support for cosmological distances: faint bursts have their durations redshifted relative to bright ones. It was pointed out, however, that the relative time stretching can also be produced by an intrinsic correlation bewteen duration and luminosity of gamma-ray bursts in a nearby, bounded distribution. While both models can explain the average amount of time stretching, we find a difference between them in the way the duration distribution of faint bursts deviates from that of bright ones, assuming the luminosity function of gamma-ray bursts is independent of distance. This allows us to distinguish between these two broad classes of model on the basis of the duration distributions of gamma-ray bursts, leading perhaps to an unambiguous determination of the distance scale of gamma-ray bursts. We apply our proposed test to the second Burst and Transient Source Experiment (BATSE) catalog and conclude, with some caution, that the data favor a cosmological interpretation of the time dilation.

Constraints on the gamma-ray burst luminosity function from Pioneer Venus Orbiter and BATSE observations

We examine the width of the gamma-ray burst luminosity function through the distribution of GRB peak fluxes as detected by the Pioneer Venus Orbiter (PVO) and the Burst and Transient Source Experiment (BATSE). The strength of the analysis is greatly enhanced by using a merged catalog of peak fluxes from both instruments with good cross-calibration of their sensitivities. The range of peak fluxes is increased by approximately a factor of 20 relative to the BATSE catalog. Thus, more sensitive investigations of the $\log N-\log P$ distribution are possible. We place constraints on the width of the luminosity function of gamma-ray bursts brighter than the BATSE completeness limit by comparing the intensity distribution in the merged catalog with those produced by a variety of spatial density and luminosity functions. For the models examined, $90\%$ of the {\em detectable\/} bursts have peak luminosities within a range of 10, indicating that the peak luminosities of gamma-ray bursts span a markedly less wide range of values than many other of their measurable properties. We also discuss for which slopes of a power-law luminosity function the observed width is at the upper end of the constrained range. This is important in determining the power-law slopes for which luminosity-duration correlations could be important.

Constraints on the luminosity function of gamma-ray bursts detected by BATSE

We have utilized the integral moment analysis technique of Horack & Emslie to extract information on the allowable form of the luminosity function for gamma-ray bursts observed by Burst and Transient Source Experiment (BATSE). Using the general properties of moments, we are able to derive constraints on the range of luminosity from which the gamma-ray bursts must be sampled. These constraints are independent of the form of the radial distribution of the gamma-ray bursts, and depend only on the assumptions that space is Euclidean and that the luminosity function phi(L) is distance independent. For power-law luminosity functions of the form phi(L) = A(sub 0)L(exp -alpha), we find that the range of luminosity from which 80% of the gamma-ray bursts must be sampled cannot exceed approximately 6.5, with a 3 sigma upper limit of 12-15, regardless of the value of alpha.