The nature of the progenitor systems of type?Ia supernovae (SNe?Ia) is still unclear. One way to distinguish between the single-degenerate scenario and double-degenerate scenario for their progenitors is to search for the surviving companions (SCs). Using a technique that couples the results from multi-dimensional hydrodynamics simulations with calculations of the structure and evolution of main-sequence- (MS-) and helium-rich SCs, the color and magnitude of MS- and helium-rich SCs are predicted as functions of time. The SC candidates in Galactic type?Ia supernova remnants (Ia SNR) and nearby extragalactic Ia SNRs are discussed. We find that the maximum detectable distance of MS SCs (helium-rich SCs) is 0.6-4?Mpc (0.4-16?Mpc), if the apparent magnitude limit is 27 in the absence of extinction, suggesting that the Large and Small Magellanic Clouds and the Andromeda Galaxy are excellent environments in which to search for SCs. However, only five Ia SNRs have been searched for SCs, showing little support for the standard channels in the singe-degenerate scenario. To better understand the progenitors of SNe?Ia, we encourage the search for SCs in other nearby Ia SNRs.
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