The coincidental detection of the gravitational wave event GW 170817 and the associated gamma-ray burst GRB 170817A marked the advent of multi-messenger astronomy and represented a milestone in the study of GRBs. In this context, the launch of SVOM in mid-2022, with its two wide-field high-energy instruments ECLAIRs and GRM, will foster the possibilities of coincidental transient detection with gravitational waves and gamma-rays events. The purpose of this paper is to assess the ability of SVOM/ECLAIRs to detect and quickly characterize high-energy transients in the local Universe (z<0.3), and to discuss the contribution of this instrument to multi-messenger astronomy and to gamma-ray burst(GRB) astrophysics in the 2020s. A list of local HE transients, along with their main characteristics, is constructed through an extensive literature survey. The detectability of these transients with ECLAIRs is assessed with detailed simulations using tools developed for the SVOM mission, including a GEANT4 simulation of the energy response and a simulated trigger algorithm representative of the onboard trigger algorithm. The SNR for almost all detections will be sufficiently high to allow the on-board ECLAIRs trigger algorithm to detect and derive the localisation of the transient, transmitting it to the SVOM satellite and ground-based instruments. Coupled with the anti-solar pointing strategy of SVOM, this will enable an optimal follow-up of the events, allowing the observation of their afterglows, supernovae/kilonovae counterparts, and host galaxies. We conclude the paper with a discussion of the unique contribution expected from SVOM and of the possibility of simultaneous GW detection for each type of transient in our sample.
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