Detectability of double white dwarfs in the Local Group with LISA

Detached double white dwarf (DWD) binaries are one of the main science case for the Laser Interferometer Space Antenna (LISA). As the most numerous LISA sources, they will provide important contributions towards understanding binary evolution, Supernovae Type Ia (SNIa) formation channels and the structure of the Milky Way. So far only detection prospects for the Milky Way have been computed. In this letter we show that LISA has the potential to detect DWDs in neighboring galaxies up to the border of the Local Group. In particular, we compute quantitative estimates for the number of detections in M31. We expect between a dozen to several tens of DWDs above the nominal detection threshold, for a mission duration between 4 and 10$\,$yr. We show that extra-galactic DWDs detectable by LISA are those with the shortest orbital periods and with the highest chirp masses, that are candidates SNIa progenitor, virtually undetectable at those distances in optical. This implies that LISA will be the only instrument able to provide SNIa merger rates across the Local Group.