Luminosity Function Of Gamma-ray Bursts Research Articles

Expected Gamma-Ray Burst Detection Rates and Redshift Distributions for the BlackCAT CubeSat Mission

We report the results of an extensive set of simulations exploring the sensitivity of the BlackCAT CubeSat to long-duration gamma-ray bursts (GRBs). BlackCAT is a NASA APRA-funded CubeSat mission for the detection and real-time subarcminute localization of high-redshift (z ≳ 3.5) GRBs. Thanks to their luminous and long-lived afterglow emissions, GRBs are uniquely valuable probes of high-redshift star-forming galaxies and the intergalactic medium. In addition, each detected GRB with a known redshift serves to localize a region of high-redshift star formation in three dimensions, enabling deep follow-on searches for host galaxies and associated local and large-scale structures. We explore two distinct models for the GRB redshift distribution and luminosity function, both consistent with Swift observations. We find that, for either model, BlackCAT is expected to detect a mean of 42 bursts per year on orbit, with 6.7% to 10% of these at z > 3.5. BlackCAT bursts will be localized to an r 90 ≲ 55″ precision and reported to the community within seconds. Due to the mission orbit and pointing scheme, bursts will be located in the night sky and well placed for deep multiwavelength follow-up observations. BlackCAT is on schedule to achieve launch readiness in 2025.

Revisiting the luminosity and redshift distributions of long gamma-ray bursts

ABSTRACT In this work, we update and enlarge the long gamma-ray burst (GRB) sample detected by the Swift satellite. Given the incomplete sampling of the faint bursts and the low completeness in redshift measurement, we carefully select a subsample of bright Swift bursts to revisit the GRB luminosity function (LF) and redshift distribution by taking into account the probability of redshift measurement. Here we also explore two general expressions for the GRB LF, i.e. a broken power-law LF and a triple power-law LF. Our results suggest that a strong redshift evolution in luminosity (with an evolution index of $\delta =1.92^{+0.25}_{-0.37}$) or in density ($\delta =1.26^{+0.33}_{-0.34}$) is required in order to well account for the observations, independent of the assumed expression of the GRB LF. However, in a one-to-one comparison using the Akaike Information Criterion, the best-fitting evolution model involving the triple power-law LF is statistically preferred over the best-fitting one involving the broken power-law LF with a relative probability of ∼94.3 per cent versus ∼5.7 per cent. Extrapolating our fitting results to the flux limit of the whole Swift sample, and considering the trigger probability of Swift/Burst Alert Telescope in detail, we find that the expectations from our evolution models provide a good representation of the observed distributions of the whole sample without the need for any adjustment of the model free parameters. This further confirms the reliability of our analysis results.

Gravitational lensing probability for the Konus-Wind gamma-ray bursts detected in the triggered mode

Although half a century has passed since the discovery of Gamma-ray bursts (GRBs), there is no evidence for any strongly lensed event. Using GRB luminosity function and GRB formation rate estimates for the Konus-Wind burst sample with known redshifts, and a Singular Isothermal Sphere as a gravitational lens model, we predict the detection rate of both GRB images being ≈ 0.02–0.05 events per year. The result is consistent with the non-detection of lensed bursts in the KW triggered GRB sample.

Modelling the luminosity function of long gamma-ray bursts using Swift and Fermi

I have used a sample of long Gamma Ray Bursts (GRBs) common to both \emph{Swift} and \emph{Fermi} to re-derive the parameters of the Yonetoku correlation. This allowed me to self-consistently estimate pseudo redshifts of all the bursts with unknown redshifts. This is the first time such a large sample of GRBs from these two instruments are used, both individually and in conjunction, to model the long GRB luminosity function. The GRB formation rate is modelled as the product of the cosmic star formation rate and a GRB formation efficiency for a given stellar mass. An exponential cut-off powerlaw luminosity function fits the data reasonably well, with $\nu = 0.6$ and $ L_b = 5.4 \times10^{52} \, \rm{erg.s^{-1}},$ and does not require a cosmological evolution. In the case of a broken powerlaw, it is required to incorporate a sharp evolution of the break given by $L_{b}\sim0.3\times10^{52}\left(1+z\right)^{2.90} \, \rm{erg.s^{-1}},$ and the GRB formation efficiency (degenerate up to a beaming factor of GRBs) decreases with redshift as $\propto\left(1+z\right)^{-0.80}.$ However it is not possible to distinguish between the two models. The derived models are then used as templates to predict the distribution of GRBs detectable by CZTI on board \emph{AstroSat}, as a function of redshift and luminosity. This demonstrates that via a quick localization and redshift measurement of even a few CZTI GRBs, \emph{AstroSat} will help in improving the statistics of GRBs both typical and peculiar.

Collapsar γ-ray bursts: how the luminosity function dictates the duration distribution

Jets in long-duration $\gamma$-ray bursts (GRBs) have to drill through the collapsing star in order to break out of it and produce the $\gamma$-ray signal while the central engine is still active. If the breakout time is shorter for more powerful engines, then the jet-collapsar interaction acts as a filter of less luminous jets. We show that the observed broken power-law GRB luminosity function is a natural outcome of this process. For a theoretically motivated breakout time that scales with jet luminosity as $L^{-\chi}$ with $\chi\sim 1/3-1/2$, we show that the shape of the $\gamma$-ray duration distribution can be uniquely determined by the GRB luminosity function and matches the observed one. This analysis has also interesting implications about the supernova-central engine connection. We show that not only successful jets can deposit sufficient energy in the stellar envelope to power the GRB-associated supernovae, but also failed jets may operate in all Type Ib/c supernovae.

NEUTRINO AND COSMIC-RAY RELEASE FROM GAMMA-RAY BURSTS: TIME-DEPENDENT SIMULATIONS

We revisit the neutrino and ultra high-energy cosmic ray (UHECR) production from gamma-ray bursts (GRBs) with time-dependent simulations for the proton-induced cascades. This method can generate self-consistent photon, neutrino and escaped neutron spectra. To obtain the integrated background spectra, we take into account the distributions of the burst luminosity and pulse duration timescale. A benchmark case with standard GRB luminosity function, a bulk Lorentz factor $\Gamma=300$ and a proton to gamma-ray luminosity fraction $f_{\rm p}=10$, is consistent with both the neutrino upper-limits and the observed UHECR intensity at $\sim 10^{20}$ eV, while requiring a different type of UHECR source at the ankle. For the benchmark case the GRBs in the bright end of the luminosity function, which contribute most of the neutrinos, have their photon spectrum substantially distorted by secondary photons. Such bright GRBs are few in number, and reducing their $f_p$ eliminates the distortion, while reducing the neutrino production. Even if we neglect the contribution of the brightest GRBs, the UHECR production rate at GZK energies is almost unchanged. These nominal GRB models, especially with $L_{\rm iso} \lesssim 10^{53} ~\mbox{erg} ~\mbox{s}^{-1}$, appear to meet the current constraints as far as being candidate UHECR sources above the ankle energy.

A complete sample of long bright Swift gamma ray bursts

Complete samples are the basis of any population study. To this end, we selected a complete subsample of Swift long bright gamma ray bursts (GRBs). The sample, made up of 58 bursts, was selected by considering bursts with favourable observing conditions for ground-based follow-up observations and with the 15-150 keV 1 s peak flux above a flux threshold of 2.6 photons cm(-2) s(-1). This sample has a redshift completeness level higher than 90 per cent. Using this complete sample, we investigate the properties of long GRBs and their evolution with cosmic time, focusing in particular on the GRB luminosity function, the prompt emission spectral-energy correlations and the nature of dark bursts.

A Complete Sample of Long BrightSwiftGRBs

Starting from the Swift sample we defined a complete sub-sample of 58 bright long Gamma Ray Bursts (GRB), 52 of them (90%) with a redshift determination, in order to characterize their properties. This complete sample of bright long- GRBs allowed us to investigate their evolution with cosmic time and properties. We focused in particular on the GRB luminosity function, on the spectral-energy correlations of their prompt emission, on the nature of dark bursts and on possible correlations between the prompt and the X-ray afterglow properties.

Gamma-ray bursts: the isotropic-equivalent-energy function and the cosmic formation rate

Gamma-ray bursts (GRBs) are brief but intense emission of soft $\gamma-$rays, mostly lasting from a few seconds to a few thousand seconds. For such kind of high energy transients, their isotropic-equivalent-energy ($E_{\rm iso}$) function may be more scientifically meaningful when compared with GRB isotropic-equivalent-luminosity function ($L_{\rm iso}$), as the traditional luminosity function refers to steady emission much longer than a few thousand seconds. In this work we for the first time construct the isotropic-equivalent-energy function for a sample of 95 bursts with measured redshifts ($z$) and find an excess of high-$z$ GRBs. Assuming that the excess is caused by a GRB luminosity function evolution in a power-law form, we find a cosmic evolution of $E_{\rm iso}\propto(1+z)^{1.80^{+0.36}_{-0.63}}$, which is comparable to that between $L_{\rm iso}$ and $z$, i.e., $L_{\rm iso}\propto(1+z)^{2.30^{+0.56}_{-0.51}}$ (both $1\sigma$). The evolution-removed isotropic-equivalent-energy function can be reasonably fitted by a broken power-law, in which the dim and bright segments are $\psi(E_{\rm iso})\propto E_{\rm iso}^{-0.27\pm0.01}$ and $\psi(E_{\rm iso})\propto E_{\rm iso}^{-0.87\pm0.07}$, respectively ($1\sigma$). For the cosmic GRB formation rate, it increases quickly in the region of $0 \leq z \lesssim 1$, and roughly keeps constant for $1\lesssim z \lesssim 4$, and finally falls with a power index of $-3.80\pm2.16$ for $z\gtrsim 4$, in good agreement with the observed cosmic star formation rate so far.

A COMPLETE SAMPLE OF BRIGHTSWIFTLONG GAMMA-RAY BURSTS. I. SAMPLE PRESENTATION, LUMINOSITY FUNCTION AND EVOLUTION

We present a carefully selected sub-sample of Swift Long Gamma-ray Bursts (GRBs), that is complete in redshift. The sample is constructed by considering only bursts with favorable observing conditions for ground-based follow-up searches, that are bright in the 15-150 keV Swift/BAT band, i.e. with 1-s peak photon fluxes in excess to 2.6 ph s^-1 cm^-2. The sample is composed by 58 bursts, 52 of them with redshift for a completeness level of 90%, while another two have a redshift constraint, reaching a completeness level of 95%. For only three bursts we have no constraint on the redshift. The high level of redshift completeness allows us for the first time to constrain the GRB luminosity function and its evolution with cosmic times in a unbiased way. We find that strong evolution in luminosity (d_l=2.3\pm 0.6) or in density (d_d=1.7\pm 0.5) is required in order to account for the observations. The derived redshift distribution in the two scenarios are consistent with each other, in spite of their different intrinsic redshift distribution. This calls for other indicators to distinguish among different evolution models. Complete samples are at the base of any population studies. In future works we will use this unique sample of Swift bright GRBs to study the properties of the population of long GRBs.

The luminosity function of Swift long gamma-ray bursts

The accumulation of Swift observed gamma-ray bursts (GRBs) has gradually made it possible to directly derive a GRB luminosity function (LF) from the observational luminosity distribution. However, two complexities are involved: (i) the evolving connection between GRB rate and cosmic star formation rate; and (ii) observational selection effects due to telescope thresholds and redshift measurements. With a phenomenological investigation of these two complexities, we constrain and discriminate two popular competing LF models (i.e. the broken-power-law LF and the single-power-law LF with an exponential cut-off at low luminosities). As a result, we find that the broken-power-law LF may be more favoured by observations, with a break luminosity Lb= 2.5 × 1052 erg s−1 and prior- and post-break indices ν1= 1.72 and ν2= 1.98. Regarding an extra evolution effect expressed by a factor (1 +z)δ, if the metallicity of GRB progenitors is lower than ∼0.1 Z⊙ as expected by some collapsar models, then there may be no extra evolution effect other than the metallicity evolution (i.e. δ approaches zero). Alternatively, if we remove the theoretical metallicity requirement, then a relationship between the degenerate parameters δ and Zmax can be found, very roughly, δ∼ 2.4(Zmax /Z⊙− 0.06). This indicates that extra evolution could become necessary for relatively high metallicities.

Trigger Simulations for GRB Detection with the Swift Burst Alert Telescope

AbstractUnderstanding the intrinsic cosmic long gamma-ray burst (GRB) rate is essential in many aspects of astrophysics and cosmology, such as revealing the connection between GRBs, supernovae (SNe), and stellar evolution. Swift, a multi-wavelength space telescope, is quickly expanding the GRB category by observing hundreds of GRBs and their redshifts. However, it remains difficult to determine the intrinsic GRB rate due to the complex trigger algorithm adopted by Swift. Current studies of the GRB rate usually approximate the Swift trigger algorithm by a single detection threshold. Nevertheless, unlike the previously flown GRB instruments, Swift has over 500 trigger criteria based on count rates and additional thresholds for localization. To investigate possible systematic biases and further explore the intrinsic GRB rate as a function of redshift and the GRB luminosity function, we adopt a Monte Carlo approach by simulating all trigger criteria used by Swift. A precise estimation of the intrinsic GRB rate is important to reveal the GRB origins and their relation to the black-hole forming SNe. Additionally, the GRB rate at high redshifts provides a strong probe of the star formation history in the early universe, which is hard to measure directly through other methods.

GAMMA-RAY BURST LUMINOSITY FUNCTIONS BASED ON A NEWLY DISCOVERED CORRELATION BETWEEN PEAK SPECTRAL ENERGY ANDV/Vmax

We have discovered a correlation between the observed peak spectral energy E_(pk,obs) and the Euclidean value of of gamma-ray bursts (GRBs). We present the evidence for the correlation in the GUSBAD catalog and use it to derive the luminosity function of GRBs without using any redshifts. The procedure involves dividing GUSBAD GRBs into five spectral classes based on their E_(pk,obs). The overall luminosity function is derived assuming that each of the spectral classes contributes a Gaussian luminosity function. Their central luminosity is derived from the observed Euclidean . We explore various forms for the GRB rate function GR(z) in predicting redshift distributions of GRBs detected by Swift. We find that GR(z) peaks at a higher redshift than the typical star formation history currently favored in the literature. We consider two examples of GR(z) that successfully predict the observed redshift distribution of Swift GRBs. With the luminosity functions in hand, we convert the E_(pk,obs) – V/V_(max) correlation into an E_(pk,obs) – L_(iso) correlation and a rest-frame E_(pk) – L_(iso) correlation. By comparing the E_(pk) – L_(iso) correlation with a published correlation based on GRBs with known E_(pk,obs) and redshifts, we discuss the effect of Malmquist bias.

Evidence for luminosity evolution of long gamma-ray bursts inSwiftdata

We compute the luminosity function (LF) and the formation rate of long gamma ray bursts (GRBs) by fitting the observed differential peak flux distribution obtained by the BATSE experiment in two different scenarios: i) the GRB luminosity evolves with redshift and ii) GRBs form preferentially in low-metallicity environments. In both cases, model predictions are consistent with the Swift number counts and with the number of detections at z>2.5 and z>3.5. To discriminate between the two evolutionary scenarios, we compare the model results with the number of luminous bursts (i.e. with isotropic peak luminosity in excess of 10^53 erg s^-1) detected by Swift in its first three years of mission. Our sample conservatively contains only bursts with good redshift determination and measured peak energy. We find that pure luminosity evolution models can account for the number of sure identifications. In the case of a pure density evolution scenario, models with Z_th>0.3 Zsun are ruled out with high confidence. For lower metallicity thresholds, the model results are still statistically consistent with available lower limits. However, many factors can increase the discrepancy between model results and data, indicating that some luminosity evolution in the GRB LF may be needed also for such low values of Z_th. Finally, using these new constraints, we derive robust upper limits on the bright-end of the GRB LF, showing that this cannot be steeper than ~2.6.

On the Redshift Distribution of Gamma‐Ray Bursts in theSwiftEra

A simple physical model for long-duration gamma ray bursts (GRBs) is used to fit the redshift (z) and the jet opening-angle distributions measured with earlier GRB missions and with Swift. The effect of different sensitivities for GRB triggering is sufficient to explain the difference in the z distributions of the pre-Swift and Swift samples, with mean redshifts of <z> ~1.5 and <z>~2.7, respectively. Assuming that the emission properties of GRBs do not change with time, we find that the data can only be fitted if the comoving rate-density of GRB sources exhibits positive evolution to z >~ 3-5. The mean intrinsic beaming factor of GRBs is found to range from ~34-42, with the Swift average opening half-angle <\theta_j> ~10 degree, compared to the pre-Swift average of <\theta_j> ~7 degree. Within the uniform jet model, the GRB luminosity function is proportional to L^{-3.25}_*, as inferred from our best fit to the opening angle distribution. Because of the unlikely detection of several GRBs with z <~ 0.25, our analysis indicates that low redshift GRBs represent a different population of GRBs than those detected at higher redshifts. Neglecting possible metallicity effects on GRB host galaxies, we find that ~1 GRB occurs every 600,000 yrs in a local L_* spiral galaxy like the Milky Way. The fraction of high-redshift GRBs is estimated at 8-12% and 2.5-6% at z >= 5 and z >= 7, respectively, assuming continued positive evolution of the GRB rate density to high redshifts.

Contribution of GRB Emission to the GeV Extragalactic Diffuse Gamma‐Ray Flux

TeV gamma rays emitted by gamma-ray bursts (GRBs) are converted into electron-positron pairs via interactions with the extragalactic infrared radiation fields. In turn, the pairs produced, whose trajectories are randomized by magnetic fields, will inverse Compton scatter off the cosmic microwave background photons. The beamed TeV gamma-ray flux from GRBs is thus transformed into a GeV isotropic gamma-ray flux, which contributes to the total extragalactic gamma-ray background emission. Assuming a model for the extragalactic radiation fields, the GRB redshift distribution, and the GRB luminosity function, we evaluate the contribution of the GRB prompt and scattered emissions to the measured extragalactic gamma-ray flux. To estimate this contribution we optimistically require that the energy flux at TeV energies is about 10 times stronger than the energy flux at MeV energies. The resulting gamma-ray diffuse background is only a small fraction of what is observed, allowing blazars and other sources to give the dominant contribution.

The Gamma-Ray Burst Luminosity Function in the Light of the Swift 2 Year Data

We compute the luminosity function (LF) and the formation rate of long gamma-ray bursts (GRBs) by fitting the observed differential peak flux distribution obtained by BATSE in three different scenarios: (1) GRBs follow the cosmic star formation, and their LF is constant in time; (2) GRBs follow the cosmic star formation, but the LF varies with redshift; and (3) GRBs form preferentially in low-metallicity environments. We find that the differential peak flux number counts obtained by BATSE and by Swift can be reproduced using the same LF and GRB formation rate, indicating that the two satellites are observing the same GRB population. We then check the resulting redshift distributions in light of Swift 2 year data, focusing in particular on the relatively large sample of GRBs detected at z > 2.5. We show that models in which GRBs trace the cosmic star formation and are described by a constant LF are ruled out by the number of high-z Swift detections. This conclusion does not depend on the redshift distribution of bursts that lack optical identification, nor on the existence of a decline in star formation rate at z > 2, nor on the adopted faint end of the GRB LF. Swift observations can be explained by assuming that the LF varies with redshift and/or that GRB formation is limited to low-metallicity environments.

Gravitational lensing effects on the gamma-ray burst Hubble diagram

Gamma-ray bursts (GRBs) offer a potential way to extend the Hubble diagram to very high redshifts and to constrain the nature of dark energy in a way complementary to distant type Ia supernovae. However, gravitational lensing systematically brightens distant GRBs through the magnification bias, in addition to increasing the dispersions of distance measurements. We investigate how the magnification bias limits the cosmological usage of GRBs. We perform Monte-Carlo simulations of Swift GRBs assuming a cosmological constant dominated universe and then constrain the dark energy equation of state neglecting gravitational lens effects. The originally assumed model is recovered with 68% confidence limit even when the dispersion of inferred luminosities is comparable to that of type Ia supernovae. This implies that the bias is not so drastic for Swift GRBs as to change constraints on dark energy and its evolution. However, the precise degree of the bias in cosmological parameter determinations depends strongly on the shape of the luminosity function of GRBs. Therefore, an accurate determination of the shape of the luminosity function is required to remove the effect of gravitational lensing and to obtain an unbiased Hubble diagram.

Microlensing of Gamma‐Ray Bursts by Stars and MACHOs

The microlensing interpretation of the optical afterglow of GRB 000301C seems naively surprising, since a simple estimate of the stellar microlensing rate gives less than one in 400 for a flat ΩΛ = 0.7 cosmology, whereas one event was seen in about 30 afterglows. Assuming baryonic MACHOs making up one-half the baryons in the universe, the microlensing probability per burst can be roughly 5% for a gamma-ray burst at redshift z = 2. We explore two effects that may enhance the probability of observing microlensed gamma-ray burst afterglows: binary lenses and double magnification bias. We find that the consideration of binary lenses can increase the rate only at the ~15% level. On the other hand, because gamma-ray bursts for which afterglow observations exist are typically selected on the basis of fluxes at widely separated wave bands that are not necessarily well correlated (e.g., localization in X-ray, afterglow in optical/infrared), magnification bias can operate at an enhanced level compared to the usual single-bias case. Using a simple model for the selection process in two bands, we compute the enhancement of the microlensing rate due to magnification bias in two cases: perfect correlation and complete independence of the flux in the two bands. We find that existing estimates of the slope of the luminosity function of gamma-ray bursts, while as yet quite uncertain, point to enhancement factors of more than 3 above the simple estimates of the microlensing rate. We find that the probability of observing at least one microlensing event in the sample of 27 measured afterglows can be 3%-4% for stellar lenses, or as much as 25 Ωlens for baryonic MACHOs. We note that the probability of observing at least one event over the available sample of afterglows is significant only if a large fraction of the baryons in the universe are condensed in stellar-mass objects.

On the Structure of Quasi‐universal Jets for Gamma‐Ray Bursts

The idea that gamma-ray bursts (GRBs) originate from uniform jets has been used to explain numerous observations of breaks in the GRB afterglow light curves. We explore the possibility that GRBs instead originate from a structured jet that may be quasi-universal, where the variation in the observed properties of GRBs is due to the variation in the observer viewing angle. We test how various models reproduce the jet data of Bloom, Frail, & Kulkarni, which show a negative correlation between the isotropic energy output and the inferred jet opening angle (in a uniform jet configuration). We find, consistent with previous studies, that a power-law structure for the jet energy as a function of angle gives a good description. However, a Gaussian jet structure can also reproduce the data well, particularly if the parameters of the Gaussian are allowed some scatter. We place limits on the scatter of the parameters in both the Gaussian and power-law models needed to reproduce the data and discuss how future observations will better distinguish between these models for the GRB jet structure. We also discuss the predictions each model makes for the observed luminosity function of GRBs and compare these predictions with the existing data.