Possible gamma-ray burst radio detections by the Square Kilometre Array. New perspectives

Abstract

The next generation interferometric radio telescope, the Square Kilometre Array (SKA), which will be the most sensitive and largest radio telescope ever constructed, could greatly contribute to the detection, survey and characterization of Gamma Ray Bursts (GRBs). By the SKA, it will be possible to perform the follow up of GRBs even for several months. This approach would be extremely useful to extend the Spectrum Energetic Distribution (SED) from the gamma to the to radio band and would increase the number of radio detectable GRBs. In principle, the SKA could help to understand the physics of GRBs by setting constraints on theoretical models. This goal could be achieved by taking into account multiple observations at different wavelengths in order to obtain a deeper insight of the sources. Here, we present an estimation of GRB radio detections, showing that the GRBs can really be observed by the SKA. The approach that we present consists in determining blind detection rates derived by a very large sample consisting of merging several GRB catalogues observed by current missions as Swift, Fermi, Agile and INTEGRAL and by previous missions as BeppoSAX, CGRO, GRANAT, HETE-2, Ulysses and Wind. The final catalogue counts 7516 distinct sources. We compute the fraction of GRBs that could be observed by the SKA at high and low frequencies, above its observable sky. Considering the planned SKA sensitivity and through an extrapolation based on previous works and observations, we deduce the minimum fluence in the range 15–150 keV. This is the energy interval where a GRB should emit to be detectable in the radio band by the SKA. Results seem consistent with observational capabilities.

Appendices

Appendix A

Table 2 is the merging of catalogues mentioned and explained in part in Sec. 3.1. For each row there are seven columns. The first two columns are GRB coordinates (RA J2000 and DEC J2000) in decimal degrees; the third, fourth and fifth are the acquisition time with year, month, day (days are decimal and contain information about hours, minutes and seconds); the sixth column is the referring mission and, finally, the source name.

In the sixth column, only one of the missions which detected GRBs is reported. As previously mentioned, some GRBs have been detected by more than one mission, hence they could be reported in more than one catalogue.

As for source name, we reported the same name of the catalogue considered in the sixth column. No official names were found for the BNT GRBs, therefore only “GRB” has been written in the last column. Furthermore, BT source names are the same used in the HEASARC web table, with a final dash instead of the standard progressive letters. However, sources have been sorted by detection time, so it is possible to read all GRBs in a time sequence.

The references used for every mission are reported in Table 2:

• GRANAT satellite (cat. GRA)

  References in the phebus catalogue (Terekhov et al. 1994, 1995; Tkachenko et al. 1998, 2002).

• BATSE/CGRO (t) (cat. BT)

  references in the batsegrb catalogue (Meegan et al. 1998, 1996) and (Stern et al. 2001).

• BATSE/CGRO (nt) (cat. BNT)

  references in the Stern et al. (2001) and Kommers et al. (2001).

• Konus/Wind (cat. K/W)

  references in the Pal’shin et al. (2013).

• BeppoSAX (cat. BeS)

  references in the Frontera et al. (2009).

• HETE-2 (cat. HET)

  references in the “hete2grb: HETE-2 Gamma-Ray Bursts” by MIT (Massachusetts Institute of Technology) and “hete2gcn: HETE-2 GCN Triggers Catalog”.

• INTEGRAL (cat. INT)

  references in the Minaev et al. (2014), Bošnjak et al. (2014) and Mereghetti (2013). We matched with the “Swift GRB Table and Lookup” (selecting INTEGRAL mission).

• Swift (cat. Swi)

  references in Sakamoto et al. (2011) and “Swift GRBTable and Lookup”.

• Agile (cat. Agi)

  references in Galli et al. (2013), Pal’shin et al. (2013), Longo et al. (2012) and Hurley et al. (2013) and I matched them with “Swift GRB Table and Lookup” (selecting Agile mission).

• Fermi (cat. Fer)

  references in Paciesas et al. (2012), von Kienlin et al. (2014) and the fermigbrst catalogue in HEASARC archive.

The following list explains how matchings among catalogues have been achieved. As mentioned in Sec. 3.1, different GRB catalogues, gathering in each list only a single mission (the only exception is CGRO with two different catalogues). Equal events from various tables have been made as one. For this purpose, lists have been matched each other, using the following criteria:

• The Agile list is matched with all other lists. A GRB is the same if it exploded within 0.005 days with respect to another one, and if they have a difference $\leq 90^{\circ }$ in RA and in DEC each other. Even if the Agile angular resolution is within a few arcmin, many GRBs are localized by satellite triangulations and other satellite are not so fine in localization accuracy. As a check, a larger angular range has been used. More details about this mission can be read at the ASI web site.

• The BeppoSAX list is matched with all CGRO lists, as explained previously (time delay of 0.005 and angular range ${\leq} 146^{\circ }$).

• Among BATSE/CGRO lists no change is adopted for the criterion used by Stern et al. (2001).

• Swift list is matched with Fermi one, with a delay of 0.005 days and angular range of $45^{\circ }$.

• The GRANAT list is matched with all other lists, using only a time delay of 0.005 days.

• The HETE-2 list is matched with BeppoSAX and Swift lists: angular range of $83^{\circ }$ and time delay of 0.005 days.

• The INTEGRAL list is matched with Hete-2, Fermi and Swift lists. Time delay 0.005 and angular range $90^{\circ }$.

• The Konus/Wind list is matched with all other lists, with a delay 0.005 and angular range $90^{\circ }$.

It is worth noticing that the RA and DEC difference thresholds depend on the largest pointing-range error among different satellites. For example, by matching three catalogues from BeppoSAX, Swift and HETE-2, where the worst pointings has a range error respectively of $85^{\circ}$, $67'$ and $11.9^{\circ}$, the value $85^{\circ}$ is the threshold range. One has to choose this value in order to have the worst case. However, in the reported cases, the most important threshold is the time threshold. The time delay of 0.005 days (that is ${\sim} 7$ minutes between an explosion and the next) is in common. We changed angular ranges instrument by instrument, depending on their error positions, or FoV, or angular resolution. These angular values are probably large, but a conservative case has been preferred. However, the most relevant matching filter was the time delay and, that other criteria could be used.

Appendix B

GRBs are observed in different bands and there is a preferred measure of unit for each band. A measure can usually be given either in luminosity $L$ (erg s⁻¹ Hz⁻¹), fluence $S$ (erg cm⁻²), flux $F$ (erg cm⁻² s⁻¹) or flux density $F_{\nu }~(\mbox{W}\,\mbox{m}^{-2}\,\mbox{Hz}^{-1})$. Since we want to compare different wavelengths to each other, we must have the same measure unit. For convenience, the relations among there units is written here:

$$\begin{aligned} &L = \frac{4 \pi F_{\nu }d_{L}^{2}}{1 + z}, \end{aligned}$$

(20)

$$\begin{aligned} &F= F_{\nu } \Delta \nu, \end{aligned}$$

(21)

$$\begin{aligned} &S = F \Delta t , \end{aligned}$$

(22)

where $\Delta \nu$ and $\Delta t$ are respectively the bandwidth and the integration time during the acquisition.

In order to plot the SED of the 95 GRBs detected by Chandra and Frail (2012), we choose to convert everything into fluxes. Taking into account tables 1 and 4 in that work, from the fluence at 15–150 keV we can obtain the flux by dividing by the $T_{90}$. Furthermore, from data in flux density, we can calculate the flux of the source knowing the bandwidth (100 MHz at radio band and R-band¹⁵ at optical wavelengths). The conversion from energies into frequencies, or wavelengths, is given by using the Planck constant

$$ E = h \nu = h c \lambda. $$

(23)

Finally, the flux density is expressed in μ Jy, so, in cgs system, it is

$$ 1~\upmu \,\mbox{Jy} = 10^{-6}~\mbox{Jy} = 10^{-32} \frac{\mathrm{W}}{ \text{m}^{2}\,\mbox{Hz}} = 10^{-29} \frac{\text{erg}}{\text{s}\,\text{cm}^{2}\text{Hz}}. $$

(24)

In practice, if one has the R-band flux density $F_{\nu }= 6.5~\upmu \,\mbox{Jy}$, it has be multiplied by the bandwidth 138 nm (converted into cgs system and frequency, it is $138 \cdot 10^{-7}~\text{cm} \times 3 \cdot 10^{10}~\text{cm}/\text{s}$) and the conversion factor is $10^{-29}~\mbox{erg}\,\mbox{s}^{-1}\,\mbox{cm}^{-2}\,\mbox{Hz}^{-1}$. Thus the result in flux is $F = 2.691 \cdot 10^{-23}~\mbox{erg}\,\mbox{cm}^{-2}\,\mbox{s}^{-1}$.