Context: We present a newly discovered class of low-luminosity, dusty, evolved objects in the Magellanic Clouds. These objects have dust excesses, stellar parameters, and spectral energy distributions similar to those of dusty post-asymptotic giant branch (post-AGB) stars. However, they have lower luminosities and hence lower masses. We suggest that they have evolved off the red giant branch (RGB) instead of the AGB as a result of binary interaction. Aims: In this study we aim to place these objects in an evolutionary context and establish an evolutionary connection between RGB binaries (such as the sequence E variables) and our new sample of objects. Methods: We compared the theoretically predicted birthrates of the progeny of RGB binaries to the observational birthrates of the new sample of objects. Results: We find that there is order-of-magnitude agreement between the observed and predicted birthrates of post-RGB stars. The sources of uncertainty in the birthrates are discussed; the most important sources are probably the observational incompleteness factor and the post-RGB evolution rates. We also note that mergers are relatively common low on the RGB and that stars low on the RGB with mid-IR excesses may recently have undergone a merger. Conclusions: Our sample of dusty post-RGB stars most likely provides the first observational evidence for a newly discovered phase in binary evolution: post-RGB binaries with circumstellar dust.
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