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Register a new userThe Luminosity Function of Long Gamma-Ray Bursts and their rate at z>6
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We compute the luminosity function (LF) and the formation rate of long gamma ray bursts (GRBs) in three different scenarios: i) GRBs follow the cosmic star formation and their LF is constant in time; ii) GRBs follow the cosmic star formation but the LF varies with redshift; iii) GRBs form preferentially in low-metallicity environments. We then test model predictions against the Swift 3-year data, showing that scenario i) is robustly ruled out. Moreover, we show that the number of bright GRBs detected by Swift suggests that GRBs should have experienced some sort of luminosity evolution with redshift, being more luminous in the past. Finally we propose to use the observations of the afterglow spectrum of GRBs at z>5.5 to constrain the reionization history and we applied our method to the case of GRB 050904.
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We study the luminosity function (LF), the comoving rate and the detection rate of Long Gamma-Ray Burst (LGRBs) to high redshift, using galaxy catalogues constructed by combining high-resolution N-body simulations with semi-analytic models of galaxy formation. We assume the collapsar model and different metallicity thresholds, and conclude that LGRBs are not good tracers of the star formation history in the universe. Then using the log N-log P diagram for BATSE bursts, we determine the LF (with and without evolution with redshift) and the formation rate of LGRBs, obtaining constraints on the slope of the power-law. We check the resulting redshift distribution with SWIFT data updated to 2009 August, finding that models where LGRBs have as progenitors stars with Z<0.3Z_sun and without evolution of the LF are in agreement with the data. We also predict that there are about ~1% of GRBs at redshift z>6.
The structure of Gamma Ray Burst (GRB) jets impacts on their prompt and afterglow emission properties. The jet of GRBs could be uniform, with constant energy per unit solid angle within the jet aperture, or it could instead be structured, namely with energy and velocity that depend on the angular distance from the axis of the jet. We try to get some insight about the still unknown structure of GRBs by studying their luminosity function. We show that low (1e46-1e48 erg/s) and high (i.e. with L > 1e50 erg/s) luminosity GRBs can be described by a unique luminosity function, which is also consistent with current lower limits in the intermediate luminosity range (1e48-1e50} erg/s). We derive analytical expressions for the luminosity function of GRBs in uniform and structured jet models and compare them with the data. Uniform jets can reproduce the entire luminosity function with reasonable values of the free parameters. A structured jet can also fit adequately the current data, provided that the energy within the jet is relatively strongly structured, i.e. E propto theta^{-k} with k > 4. The classical E propto theta^{-2} structured jet model is excluded by the current data.
Motivated by the recent observational and theoretical evidence that long Gamma-Ray Bursts (GRBs) are likely associated with low metallicity, rapidly rotating massive stars, we examine the cosmological star formation rate (SFR) below a critical metallicity Z_crit Z_sun/10 - Z_sun/5, to estimate the event rate of high-redshift long GRB progenitors. To this purpose, we exploit a galaxy formation scenario already successfully tested on a wealth of observational data on (proto)spheroids, Lyman break galaxies, Lyman alpha emitters, submm galaxies, quasars, and local early-type galaxies. We find that the predicted rate of long GRBs amounts to about 300 events/yr/sr, of which about 30 per cent occur at z>~6. Correspondingly, the GRB number counts well agree with the bright SWIFT data, without the need for an intrinsic luminosity evolution. Moreover, the above framework enables us to predict properties of the GRB host galaxies. Most GRBs are associated with low mass galaxy halos M_H<~10^11 M_sun, and effectively trace the formation of small galaxies in such halos. The hosts are young, with age smaller than 5*10^7 yr, gas rich, but poorly extincted (A_V<~0.1) because of their chemical immaturity; this also implies high specific SFR and quite extreme alpha-enhancement. Only the minority of hosts residing in large halos with M_H>~10^12 M_sun have larger extinction (A_V~0.7-1), SFRs exceeding 100 M_sun/yr and can be detected at submm wavelengths. Most of the hosts have UV magnitudes in the range -20 <~M_1350<~ -16, and Lyman alpha luminosity in the range 2*10^40 <~L_Lya<~2*10^42 erg/s. GRB hosts are thus tracing the faint end of the luminosity function of Lyman break galaxies and Lyman alpha emitters.
The complete Swift Burst Alert Telescope and X-Ray Telescope light curves of 118 gamma-ray bursts (GRBs) with known redshifts were fitted using the physical model of GRB pulses by Willingale et al. to produce a total of 607 pulses. We compute the pulse luminosity function utilizing three GRB formation rate models: a progenitor that traces the cosmic star formation rate density (CSFRD) with either a single population of GRBs, coupled to various evolutionary parameters, or a bimodal population of high- and low-luminosity GRBs, and a direct fit to the GRB formation rate excluding any a priori assumptions. We find that a single population of GRB pulses with an evolving luminosity function is preferred over all other univariate evolving GRB models, or bimodal luminosity functions in reproducing the observed GRB pulse L-z distribution and that the magnitude of the evolution in brightness is consistent with studies that utilize only the brightest GRB pulses. We determine that the appearance of a GRB formation rate density evolution component is an artifact of poor parametrization of the CSFRD at high redshifts rather than indicating evolution in the formation rate of early epoch GRBs. We conclude that the single brightest region of a GRB light curve holds no special property, by incorporating pulse data from the totality of GRB emission we boost the GRB population statistics by a factor of 5, rule out some models utilized to explain deficiencies in GRB formation rate modelling, and constrain more tightly some of the observed parameters of GRB behaviour.
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=2.3pm 0.6) or in density (d_d=1.7pm 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.
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