Standard GRB, Dirty Fireballs, and the Excluded Middle

arXiv:1102.0783v1 [astro-ph.HE] 3 Feb 2011 Standard GRB, Dirty Fireballs, and the Excluded Middle David Eichler 1 ABSTRACT It is shown that the contribution of faint gamma-ray bursts (GRB) to the total allsky GRB energy flux is small. The allsky flux of GRB appears to be 5.3 × 10−3 erg/cm2y, with little additional component hidden within weak or otherwise undetectable GRB. This significantly constrains physical models of GRB and dirty fireballs, suggesting a rather sharp dichotomy between them should the latter exist. Subject headings: (stars:) gamma ray bursts: general 1. Introduction Gamma-ray bursts (GRB) are understood to depend on baryon purity. With too much baryon contamination, their energy would end up in kinetic energy, and eventually after- glow. The rather stringent requirements for baryon purity needed for a successful GRB are consistent with the inference that there is only about 1 GRB per 10,000 supernovae, despite the known association between the two phenomena. One might therefore ask whether there is a continuous spectrum of ”semi-GRB” that smoothly connects normal supernovae to bright GRB. Dirty fireballs and X-ray flashes have been proposed as examples of this. As X-ray flashes are about as numerous as standard GRB, but have much smaller values for Vmax, the maximum value within which they could have been observable at our location, their rate density is probably much higher, and one might ask whether the total luminosity input in such semi-GRB’s could dominate the total. This is relevant to any question connected with GRB calorimetry and total luminosity density, e.g. the question of how much energy is available in GRB to produce ultrarelativistic cosmic rays (UHECR). There is physical motivation for asking this question as well, as it constrains models of the central engine. If, for example, the baryon purity is a function of disk cooling, so 1Physics Department, Ben-Gurion University, Be’er-Sheva 84105, Israel; eichler@bgu.ac.il – 2 – that baryons from a hot atmosphere do not extend up to the slow-Alfven critical point where they are injected into a magnetocentrifugal outflow (Levinson 2006), then one might suppose that, because this injection rate varies both with position on the disk and time, there are many GRB in which the photons are cooled by adiabatic expansion before being released beyond the gamma ray photosphere. In fact, popular models of GRB frequently invoke a saturation radius that is well within the photosphere, in which case the photons would cool adiabatically before escaping. If there is a continuous range of the extent of this adiabatic cooling, then one would expect a continuous range of GRB fluences, and perhaps a sizable contribution to the total allsky fluence from very weak, very soft, or very prolonged (i.e. low luminosity) GRB. Yet another parameter that seems quite variable in GRB is the opening angle. The larger the opening angle, the dimmer the GRB appears. Very wide GRB might thus escape detection, yet might dominate the total luminosity density of GRB. Similarly, the peripheries of ”structured jets” might conceivably contain most of the GRB energy, in which case different observers would see the peripheries as weak GRB, but with a large rate per unit comoving volume, and the product of the rate density and apparent energy of the weak GRB might conceivably dominate. In this letter we examine to what extent weak, soft, wide angle and/or high redshift GRB contribute to the present cosmic GRB radiation density. In contrast to previous works on this matter, which appear to be model dependent and give a large range of numbers, our approach is nearly model independent - we compute the total flux recorded by different GRB detectors, each with different ranges and sensitivities. We show that most of the GRB energy output comes in high fluence GRBs in the spectral range 20-5,000 KeV, independent of detector and trigger sensitivity, and such bursts could be detected by most major detectors. Moreover, these bright bursts would typically overwrite data that was being transmitted from BATSE, should they have occurred during the time such data transmission was taking place (considered ”dead time” except when overwritten [Paciesas et al., 1999]), and would not have been overlooked by BATSE (see below). We conclude from this that, in the context of total energetics, GRBs respect a law of excluded middle: There appears to be very little energy in ”semi-GRBs”, compromised GRBs, ragged GRB peripheries, and the like. Theoretical models of GRB should respect this principle of the excluded middle at a quantitative level. In other words, they should not predict that half or more of the total photon energy is sprayed or otherwise diluted in directions from which the burst would be perceived as a marginal, weak, or ”semi-” GRB. While the detectability of any given weak GRB is a function of detector sensitivity, the measured allsky flux in GRB is insensitive to it. We find from the BATSE 4B cata

This content is AI-processed based on open access ArXiv data.