On the Origin of Sub-subgiant Stars. III. Formation Frequencies

Sub-subgiants are a new class of stars that are optically redder than normal main-sequence stars and fainter than normal subgiant stars. Sub-subgiants, and the possibly related red stragglers (which fall to the red of the giant branch), occupy a region of the color-magnitude diagram that is predicted to be devoid of stars by standard stellar evolution theory. In previous papers we presented the observed demographics of these sources and defined possible theoretical formation channels through isolated binary evolution, the rapid stripping of a subgiant's envelope, and stellar collisions. Sub-subgiants offer key tests for single- and binary-star evolution and stellar collision models. In this paper, we synthesize these findings to discuss the formation frequencies through each of these channels. The empirical data, our analytic formation rate calculations, and analyses of sub-subgiants in a large grid of Monte Carlo globular cluster models suggest that the binary evolution channels may be the most prevalent, though all channels appear to be viable routes to sub-subgiant creation (especially in higher-mass globular clusters). Multiple formation channels may operate simultaneously to produce the observed sub-subgiant population. Finally, many of these formation pathways can produce stars in both the sub-subgiant and red straggler (and blue straggler) regions of the color-magnitude diagram, in some cases as different stages along the same evolutionary sequence.