The BINGO Project IX: Search for Fast Radio Bursts -- A Forecast for the BINGO Interferometry System

The Baryon Acoustic Oscillations (BAO) from Integrated Neutral Gas Observations (BINGO) radio telescope will use the neutral Hydrogen emission line to map the Universe in the redshift range $0.127 \le z \le 0.449$, with the main goal of probing BAO. In addition, the instrument optical design and hardware configuration support the search for Fast Radio Bursts (FRBs). In this work, we propose the use of a BINGO Interferometry System (BIS) including new auxiliary, smaller, radio telescopes (hereafter \emph{outriggers}). The interferometric approach makes it possible to pinpoint the FRB sources in the sky. We present here the results of several BIS configurations combining BINGO horns with and without mirrors ($4$ m, $5$ m, and $6$ m) and 5, 7, 9, or 10 for single horns. We developed a new {\tt Python} package, the {\tt FRBlip}, which generates synthetic FRB mock catalogs and computes, based on a telescope model, the observed signal-to-noise ratio (S/N) that we used to compute numerically the detection rates of the telescopes and how many interferometry pairs of telescopes (\emph{baselines}) can observe an FRB. FRBs observed by more than one baseline are the ones whose location can be determined. We thus evaluate the performance of BIS regarding FRB localization. We found that BIS will be able to localize 23 FRBs yearly with single horn outriggers in the best configuration (using 10 outriggers of 6 m mirrors), with redshift $z \leq 0.96$; the full localization capability depends on the number and the type of the outriggers. Wider beams are best to pinpoint FRB sources because potential candidates will be observed by more baselines, while narrow beams look deep in redshift. The BIS can be a powerful extension of the regular BINGO telescope, dedicated to observe hundreds of FRBs during Phase 1. Many of them will be well localized with a single horn + 6 m dish as outriggers.(Abridged)