There is overwhelming evidence that binary interactions play a major role in the evolu- tion of massive stars, and hence the formation of some fraction of WR stars. Not only does the high observed binary fraction and distribution of orbital parameters in massive binaries point to this (Sana et al., 2012), but several observations require it. The ob- served binary fraction amongst Galactic WR stars is ∼40 % (van der Hucht, 2001), not accounting for observational bias towards easily detectable systems. The present-day orbital parameters of many of these can only be explained by previous mass and angular momentum exchanges (Petrovic et al.,2005). Indirectly, the observed rate of H-free ccSN
(assumed to come from WR stars) is too high to arise exclusively from massive single
WR stars (Smith et al., 2011), and the cosmic long-GRB rate is easier to reproduce with models including a binary channel (Bissaldi et al., 2007; Trenti et al., 2015). The qualitative evolutionary scenario for WR stars as a result of binary interaction was in- troduced byPaczy´nski(1967). Compared to single-star models, however, the addition of extra variables (orbital period, eccentricity, mass ratio, etc.), complicates binary models considerably. Furthermore, important uncertainties exist, including the efficiency of the mass-transfer process (Cantiello et al., 2007; de Mink et al., 2007), and the subsequent response of the secondary to gaining mass and angular momentum (de Mink et al.,2013) As the primary star in a binary system expands (see Section 1.2.1), its outer layers might extend beyond the Roche Lobe, inside which material is gravitationally bound to the star. Material will subsequently flow through the inner Lagrangian point (L1)
towards the less-evolved secondary. This process is known as Roche Lobe Over-Flow (RLOF). Kippenhahn & Weigert (1967) categorise these events according to the evolu- tionary state of the primary at the onset of mass transfer; Case A during theMS, Case B during H-shell burning, and Case C during core/shell He-burning. Case A will occur in binaries with periods of a few days, Case B up to ∼ 1000 days assuming a circular orbit and one component expanding to RSG proportions, and Case C up to a few thousand days (Podsiadlowski et al.,1992). If both stars fill their Roche Lobes - as a result of mass gained by the secondary or its own evolutionary expansion - a Common Envelope (CE) phase will result. The orbit will decay due to dynamical friction, and a merger may occur before the primary explodes (Podsiadlowski et al., 1992).
Mass transfer may be conservative (mass transfer efficiency=1) or non-conservative (mass transfer efficiency < 1), depending on how amenable the secondary is to accepting mass. The rotation rate of the secondary is an important determining factor for mass transfer efficiency. Significant amounts of angular momentum may be transferred with
the mass, such that the mass gainer can be spun up to a substantial fraction of its critical rotation rate (gef f= 0 at equator) after increasing in mass by as little as 5–
10% (Packet, 1981). Depending on the secondary radius (evolutionary stage), and the orbital separation, material flowing through L1 may form an accretion disk capable of
spinning-up the whole star to critical velocity, effectively halting accretion. Mass transfer efficiency is therefore expected to decrease for wider systems, which are more likely to form accretion disks, and lower mass ratios (q = M2/M1), where a smaller fraction of
primary mass is required to spin-up the secondary (cf. Langer 2012). The latter has been proven by observations of massive WR binaries (Petrovic et al., 2005). These spun-up secondaries may display CNO enhancements, due to the accreted material and rotational mixing (Section 1.2.1). The efficiency of mass transfer remains a crucial unknown in binary modelling.
I will now assess the likelihood of H-depleted He-burning stars, i.e.,WR stars, being produced by each case, as either primaries or secondaries. Case A mass transfer occurs on a nuclear timescale, and systems with periods . 2d and q < 0.6 may evolve into contact (CE) (Pols, 1994), causing a probable merger in & 50 % of Case A systems (de Mink et al., 2011). Case A primaries that avoid such a CE phase will promptly lose their H envelopes upon ignition of H-shell burning, resulting in a H-depleted primary with a potentially more luminous secondary, in a close (of order ∼ 10d) orbit.
Mass transfer in Case B systems is less well understood due to the large convective envelopes involved. For periods up to ∼ 100 days, mass transfer may lead to a CE
phase - as proposed for the progenitor of SN 1987A (Podsiadlowski et al., 1992) - and a subsequent merger is favourable for low mass ratios. The merger product will not be a rejuvenated star, as Hydrogen is unable to mix into the primary’s He core. Instead, the resulting star will be core He-burning with an under-massive core for its total mass. This type of star stays blue, and reaches core collapse as a BSG, or WR if sufficiently massive (Braun & Langer, 1995; Claeys et al., 2011). CE evolution is highly uncertain, but it is thought that if a merger does not result from Case B interaction, theCEcan be ejected at the expense of orbital energy (Paczy´nski,1967), leading to a close binary with a H-deficient core He-burning component (Taam & Sandquist,2000). If a Case B system remains detached, the primary will become a H-deficient He-burning star, retaining an envelope with anything up to a few M of hydrogen. It is possible that the secondary
star will outshine the primary at this point, as it will be rejuvenated due to gained mass (assuming it is still core H-burning), and mimic a higher mass star. However, as noted by
Figure 1.11: (Left ) Average duration ofRSG,WNL, WNEand WCphases (labelled) as a function of initial mass, for a population of non-rotating single stars at approximately solar metallicity (Z = 0.02). (Right ) As left, for primary stars in binary systems, averaged over a range of orbital parameters. Adapted fromEldridge et al. (2008).
to lower luminosities, as > 30 M stars are not expected to expand to RSG dimensions.
In summary, core He-burning stars with H-depleted surfaces (essentially WR stars) are most likely to arise from i ) Case A systems which avoid merging, resulting in a close binary (P < 10d) with a similarly (if not more) luminous less-evolved companion, ii ) post-CE Case B systems, resulting in a close binary with a relatively low-luminosity primary (log(L/L ) . 5.6), potentially with surrounding nebula containing the ejected
envelope, iii ) Case B systems with P & 100 d which avoid aCE phase, resulting in WR- like primaries of luminosity similar to (ii ), and secondaries whose luminosities are heavily dependent on the mass transfer efficiency.
Population synthesis models taking binary evolution into account (e.g., Vanbeveren et al. 1998) predict very different relative numbers of massive star types than those based solely on single stars (e.g., Meynet 1995). Outstanding problems to single-star population synthesis include the BSG/RSG ratio (Langer & Maeder, 1995; Massey & Olsen, 2003), the RSG/WR ratio (Massey, 2003), and to a lesser extent the WC/WN
ratio; the lack of a complete sample larger than those of theLMCand SMChas limited comparison of the latter to observations. In Figure1.11I show average lifetimes predicted forRSGand WR(divided intoWNE,WNLandWC) stars as a function of initial mass, for single stars (as in Figure 1.8a) and the primary stars of binary systems, according to the population synthesis models of Eldridge et al. (2008). In the binary scenario, average WR lifetimes moderately increase and RSG lifetimes are dramatically reduced.
This is due to RLOF assisting the removal of H-rich layers, revealing CNO products with a larger fraction of tHe remaining. The most significant difference is a decrease
in the minimum initial masses producing a WR star, from ∼27 M to ∼15 M . The
lengthening of averageWR lifetimes is manifest mainly in the WN phase, in qualitative agreement with other studies (Vanbeveren et al., 2007).