Why variable AGB stars with Long Secondary Periods aren't binaries, but   are dusty
  Roughly 30% of variable AGB stars show a Long Secondary Period, or LSP. These LSPs have posed something of a problem in recent years and their cause remains a mystery. By combining VLT-derived velocity curves with MACHO and OGLE light curves we were able to examine many properties of these stars and test the theory that LSPs are caused by binarity. We show why we concluded that the binary model for LSPs is unlikely. Examining mid-infrared SAGE observations for stars with LSPs shows that these stars are surrounded by a significant amount of cool dust in a nonspherical distribution, e.g. a disk or clumps. The unlikeliness of binarity in these stars forces us to conclude that the dust is not in a disk. We are left without an acceptable explanation for Long Secondary Periods in AGB stars. 
C. P. Nicholls
astro-ph.SR