Population Synthesis of Common Envelope Mergers: I. Giant Stars with Stellar or Substellar Companions

Using a population synthesis technique, we have calculated detailed models of the present-day field population of objects that have resulted from the merger of a giant primary and a main-sequence or brown dwarf secondary during common-envelope evolution. We used a grid of 116 stellar and 32 low-mass/brown dwarf models, a crude model of the merger process, and followed the angular momentum evolution of the binary orbit and the primary's rotation prior to merger, as well as the merged object's rotation after the merger. We find that present-day merged objects that are observable as giant stars or core-helium burning stars in our model population constitute between 0.24% and 0.33% of the initial population of ZAMS binaries, depending upon the input parameters chosen. The median projected rotational velocity of these merged objects is ~16 km/sec, an order of magnitude higher than the median projected rotational velocity in a model population of normal single stars calculated using the same stellar models and initial mass function. The masses of the merged objects are typically less than ~2 solar masses, with a median mass of 1.28 solar masses, which is slightly more than, but not significantly different from, their normal single star counterparts. The luminosities in our merged object population range from ~10-100 solar luminosities, with a strong peak in the luminosity distribution at ~60 solar luminosities, since the majority of the merged objects (57%) lie on the horizontal branch at the present epoch. The results of our population synthesis study are discussed in terms of possible observational counterparts either directly involving the high rotational velocity of the merger product or indirectly, via the effect of rotation on envelope abundances and on the amount and distribution of circumstellar matter.