The BINGO Project IX. Search for fast radio bursts - A forecast for the BINGO interferometry system

Context. 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 <= z <= 0.449, with the main goal of probing BAO. In addition, the instrument's optical design and hardware configuration support the search for fast radio bursts (FRBs). Aims. In this work, we propose the use of a BINGO Interferometry System (BIS) including new auxiliary, smaller radio telescopes (hereafter outriggers). The interferometric approach makes it possible to pinpoint the FRB sources in the sky. We present the results of several BIS configurations combining BINGO horns with and without mirrors (4 m, 5 m, and 6 m) and five, seven, nine, or ten for single horns. Methods. We developed a new Python package, the FRBlip, which generates mock catalogs of synthetic FRB and computes, based on a telescope model, the observed signal-to-noise ratio, which we use to numerically compute the detection rates of the telescopes and how many interferometry pairs of telescopes (baselines) can observe an FRB. The FRBs observed by more than one baseline are the ones whose location can be determined. We thus evaluated the performance of BIS regarding FRB localization. Results. We found that BIS would be able to localize 23 FRBs yearly with single horn outriggers in the best configuration (using ten outriggers of 6-m mirrors), with redshift z <= 0.96. The full localization capability depends on the number and type of the outriggers. Wider beams are best for pinpointing FRB sources because potential candidates will be observed by more baselines, while narrow beams search deep in redshift. Conclusions. The BIS can be a powerful extension of the BINGO telescope, dedicated to observe hundreds of FRBs during Phase 1. Many of FRBs will be well localized with a single horn and a 6-m dish as outriggers.