A search for a surviving companion in SN 1006

Multiple channels have been proposed to produce Type Ia supernovae, with many scenarios suggesting that the exploding white dwarf accretes from a binary companion pre-explosion. In almost all cases, theory suggests that this companion will survive. However, no such companion has been unambiguously identified in ancient supernova remnants - possibly falsifying the accretion scenario. Existing surveys, however, have only looked for stars as faint as {≈ } 0.1 L_{⊙} and thus might have missed a surviving white dwarf companion. In this work, we present very deep DECam imaging (u, g, r, z) of the Type Ia supernova remnant SN 1006 specifically to search for a potential surviving white dwarf companion. We find no object that is consistent with a relatively young cooling white dwarf within the inner half of the SN 1006 remnant. We find that if there is a companion white dwarf, it must be redder than the standard white dwarf cooling track, or it must have formed long ago and cooled undisturbed for >10^8 yr. We conclude that our findings are consistent with the complete destruction of the secondary (such as in a merger) or an anomalously red or very dim surviving companion white dwarf.