IACT observations of gamma-ray bursts: prospects for the Cherenkov Telescope Array

Abstract

Gamma rays at rest frame energies as high as 90 GeV have been reported from gamma-ray bursts (GRBs) by the Fermi Large Area Telescope (LAT). There is considerable hope that a confirmed GRB detection will be possible with the upcoming Cherenkov Telescope Array (CTA), which will have a larger effective area and better low-energy sensitivity than current-generation imaging atmospheric Cherenkov telescopes (IACTs). To estimate the likelihood of such a detection, we have developed a phenomenological model for GRB emission between 1 GeV and 1 TeV that is motivated by the high-energy GRB detections of Fermi-LAT, and allows us to extrapolate the statistics of GRBs seen by lower energy instruments such as the Swift-BAT and BATSE on the Compton Gamma-ray Observatory. We show a number of statistics for detected GRBs, and describe how the detectability of GRBs with CTA could vary based on a number of parameters, such as the typical observation delay between the burst onset and the start of ground observations. We also consider the possibility of using GBM on Fermi as a finder of GRBs for rapid ground follow-up. While the uncertainty of GBM localization is problematic, the small field-of-view for IACTs can potentially be overcome by scanning over the GBM error region. Overall, our results indicate that CTA should be able to detect one GRB every 20–30 months with our baseline instrument model, assuming consistently rapid pursuit of GRB alerts, and provided that spectral breaks below ~100 GeV are not a common feature of the bright GRB population. With a more optimistic instrument model, the detection rate can be as high as 1 to 2 GRBs per year.

Appendices

Appendix A: Other properties of detected GRBs

In this section, we examine how the population of GRBs that pass our detection criteria compares to the entire population of simulated GRBs. This will give us some insight as to the properties that might be expected of a burst with a confident CTA detection. It will also be useful to look at how the assumption of different effective area functions can affect results.

The distribution of integration timescales that maximize detection significance is shown in Fig. 20. The two spectral models produce similar results in this distribution. This result suggests that a integration timescale of 100–500 s after the commencement of ground-based observation will be favored for GRB detection in most cases, assuming a universal t ^− 1.5 falloff in the afterglow lightcurve. A small subset of bright GRBs however are still visible against the background some hours after the event trigger (10⁴ s in the longest timescale considered here), and nonzero results are found for all bins in Fig. 20. On the right hand side of this plot, we show how detection efficiency varies with GRB T90 duration, as determined by BATSE. Not surprisingly, longer bursts always have a better chance of being detected, but the majority of detected GRBs have T90 values from 30 to 100 s, due to the scarcity of bursts with T90 > 100 s.

Fig. 20

Left The distribution of integration timescales that maximize detection significance for detected GRBs, for the bandex (solid black) and fixed (broken blue) models. Right Comparison of T90 for detected GRBs with the whole population, for 3×10⁴ simulated GRBs. In the top panel, the thin line is the distribution of the full population, and the solid black and broken blue lines are the number of detected GRBs for the bandex and fixed models, respectively. The bottom panel shows the fraction of GRBs detected in each bin

The differences between the fixed and bandex models become most apparent when we consider the distribution in high energy fluences predicted by each, as are shown in Fig. 21. In general, the bandex model has a much wider distribution in high energy fluence, because the beta parameter introduces another degree of freedom into the extrapolation, and steep beta indices lead to a subset of the bursts in the sample having extremely low levels of high energy emission. Conversely, the brightest bandex GRBs are brighter than the brightest bursts in the fixed model, as the latter are limited to a fluence ratio of 0.1 between ~1 MeV and ~1 GeV, while the corresponding ratio in the bandex model can be as high as 1.0, with β = − 2. This accounts for our somewhat unexpected result that while overall detection rates predicted by the bandex model are lower, detected GRBs in this model tend to be brighter than for the fixed model. Figure 22 shows the distribution of β indices for detected GRBs in the bandex model. Only GRBs with fairly hard extrapolated spectra, $\beta \gtrsim -2.5$, are capable of being detected.

Fig. 21

High energy fluence distribution of GRBs in our bandex (left) and fixed (right) models, together with the distribution for detected GRBs. Lower panels are the detected fraction of GRBs in a given bin. Solid black and dashed blue lines are distributions for baseline effective area, while dotted lines are the corresponding values for the optimistic area function. The thin solid lines in the top panels are the distribution for the full population

Fig. 22

The distribution of beta parameters from the bandex model. As in previous figures, the thin line is for the whole population, the thick solid line shows the GRBs detected using a baseline effective area, and the dotted line shows detections using an optimistic effective area function. The lower panel shows the fraction of detected GRBs in each bin. The rightmost bin in each panel designates GRBs that had β > − 2 in the BATSE sample, and have been reset to −2 for this calculation

Figure 23 shows how the probability of detecting a GRB varies with the zenith angle θ _zen at which it is observed. GRBs in our model are assumed to be observed at a single instantaneous point relative to zenith. While motion on the sky over the observation period T _obs will change θ _zen over the course of longer integrations, the effect is small enough that we ignore it here. Detection efficiency at a given angle is found to decrease roughly linearly with decreasing cos(θ _zen). However, GRBs can in principle be detected out to angles as large as 70°, where the energy threshold is raised by a factor of 25 (3). These would have to be at low redshift, so as not to be completely obscured by EBL opacity combined with the elevated energy threshold of the telescope.

Fig. 23

The fraction of GRBs detected as a function of cosine (zenith angle) for the bandex model with baseline (solid) and optimistic (dotted) effective area functions. Results for the fixed model are qualitatively similar

Appendix B: Prompt phase observations

GRB detection in our calculation is heavily reliant on emission during the early afterglow phase. Only about 21 % of GRBs in our sample have prompt emission (T90) phases longer than 60 s, which we assume as a typical delay time for observations with the LSTs. The majority of GRBs are therefore completely inaccessible during the prompt phase for the standard assumption of a 60 s time delay. As shown in Fig. 20, there is a definite bias toward longer duration GRBs in the detected portion of the population. Figure 24 summarizes the amount of fluence in detected GRBs that arises from $t<\mbox{T90}$. About 57 % of bursts detected with a baseline effective area have no prompt phase fluence, while only about 10 % have more than half the detected fluence arising from emission during the prompt period. With an optimistic effective area function, the fraction of GRBs seen purely in the afterglow period is slightly higher.

Fig. 24

Top The integral distribution of photon counts arising from the prompt phase for detected GRBs in our bandex model. The solid line is for a baseline effective area function, while the dotted line is for the optimistic. Note that the y-axis intercept indicates the fraction of GRBs for which any photons are detected during the prompt phase; the majority of GRBs are detected purely on the basis of afterglow fluence. Results with the fixed model are qualitatively similar. Bottom The integral distribution of the fraction of high-energy fluence collected during the T90 period for detected GRBs; the remainder of the fluence being due to the burst afterglow

We can also consider an extreme possibility in our detection efficiency calculation: one in which no high energy emission emerges after the prompt phase, or equivalently, the light curve index γ in (2) is taken to + ∞. This is found to reduce detection efficiencies to about one-fourth their values in the standard calculation: 0.021 and 0.029 for the bandex and fixed model with baseline effective area (0.044 and 0.079 in the optimistic case). Figure 25 shows the distribution of sigma values and counts for detected GRBs in such a case. These can be compared to those predicted in Fig. 8.

Fig. 25

The integral distributions of detection significances (left) and photon counts for detected GRBs (right), in a scenario in which GRBs only emit during the prompt (T90) phase. Line types are as in Fig. 8