The binarity or binary fraction, f, is defined as the ratio of the number of binary or higher-order systems, Nbin, to the total number of systems, Nsys. Here, the term system includes multiple systems and singles (their number being noted as Nsng) as well. Then
6For the star-like population, we apply the binary DPS method developed by Marks etÂ al. (2011) and Marks & Kroupa (2011), hereafter referred to as dynamical or DPS pairing. In DPS the binary stars are formed in a population of embedded clusters, within which they are dynamically processed to yield the Galactic disk stellar single-plus-binary population. An attractive feature of this theory is its underlying assumption of the universality of binary properties of late-type stars being consistent with observational data (Marks & Kroupa 2012; Leigh etÂ al. 2014). For initial binaries with intermediate to large separations, the DPS pairing method applies random pairing11M. Marks etÂ al. (2014, in preparation) show that random pairing with subsequent dynamical processing does indeed reproduce at least the observed low-mass stellar population (see also Kroupa 1995).
below a primary mass of 5âM and ordered pairing (such that q â©¾ 0.9) above. Here, q = mcomp/mprim â©½ 1, where mcomp is the companion mass and mprim is the mass of the primary star. This initial binary population is then altered by dynamical evolution. Close binaries with orbital periods below about 10Â days undergo eigenevolution (Kroupa 1995) and tend to equalize the companion masses. Note that this eigenevolution term alters the very-low-mass end of the star-like IMF. For the purpose of this work, however, these effects only play a negligible role. Here, the initial or primordial binary fraction is 100%; that is, it is assumed that all stars form in binaries. The final (after dynamical processing in the embedded cluster) overall binary fraction is about 40% (i.e., f = 0.4) but varies as a function of the primary-star mass. For M dwarfs, in particular, it is as low as 25%, whereas G dwarfs show about 56% binarity. The binary fraction approaches 90% for O stars. For the BD-like population, we chose an overall binary fraction of 20% (i.e., f = 0.20), in accordance with TK07 and TK08. About half of the members of observed average stellar populations are binaries, most of them remaining unresolved in typical star-cluster surveys. However, very young and likely dynamically unevolved populations like the TaurusâAuriga association exhibit almost 100% binarity (Kroupa etÂ al. 2013; DuchÃªne & Kraus 2013; Reipurth etÂ al. 2014). The number of systems must not be confused with the number of individual bodies: Nbod = Nsng + 2Nbin. Because higher-order multiples are relatively rare (Goodwin & Kroupa 2005), they are summarized within the binary population in this work, so the total number of bodies is
7The CMRD describes the relative number of binaries as a function of the companion-to-primary mass ratio. Observations reveal a continuous decline of f as a function of the primary-object mass, which has been interpreted as a continuous transition from the stellar to the substellar regime (Joergens 2008; Kraus & Hillenbrand 2012; but see Thies & Kroupa 2008). There is also a shift toward more equal-mass binaries (q = 1) for VLMSs and BDs (Dieterich etÂ al. 2012). These properties of the stellar population are well reproduced by DPS such that the origin and properties of binary populations are well understood.
Citation: Kroupa 1995; Kroupa 1995
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