Contact binaries can be variously described as two stars witha single envelope, or one star with two cores. Either way it is somewhat like a peanut. The larger component is usually something like an F or G dwarf, and the orbital periods are usually 0.3-0.5 d, although some inhabit the extremes of the wider range 0.2-1.0 d. The smaller component has much the same temperature as the larger, and yet usually has a much lower mass, more typical of a K or M dwarf.I believe that they are one of the two great unsolved problems of stellar astrophysics, the other being common envelope evolution.
At any rate I
Let us address the following four questions:
(A) How are contact binaries formed?
(B) What is their structure?
(C) How do they evolve?
(D) What is their end-point?
I will start with a series of assertions, and only justify them?to the extent that I can, and that time allows?after putting them all down.
(A1) Protostars condense within a star-forming region (SFR) by a process of hierarchical contraction and fragmentation into binaries and higher multiples. The shortest periods are ~1 yr, and periods range up to 104 yr or more.
(A2) Independent binaries and triples 'collide' gravitationally, and the shorter periods are shortened further, some to ~months; longer ones are lengthened. Triples are often formed from two binaries, with the fourth star ejected and the inner pair becoming rathert ight. Inner and outer orbit will be typically highly inclined to each other.
(A4) During the close periastra tidal friction takes energy from the inner orbit, thus reducing a and
(A5) F/G/K dwarfs in 2-3 d binaries are rapidly rotating, and so magnetically active. This causes erratic mass loss, which coupled to the magnetic field causes magnetic braking; and this couples with tidal friction (magnetic braking with tidal friction [MTBF]) to reduce
(B1) In contact, heat flows in the common envelope from the hotter to the cooler component, until the temperatures are nearly equal. The mechanism of heat transfer is the differential rotation that is observed on the Sun, with equatorial material flowing prograde round
(B2) Heating of the less massive component makes it fill its Roche lobe more than the other, causing a slight flow of mass in the opposite direction. This sets up a cyclic behaviour, which because of (a) continued MBTF, and (b) possible nuclear evolution (NCEV) in star 1, is superimposed on a slight evolutionary trend towards more unequal masses.
(B3) The light curve cycles between rather equal eclipses during the contact portion of the cycle and less equal eclipses during the (probably rather brief) semi-detached portion (‘near-contact binaries’). But in both cases the light curve is badly perturbed by starspots consequent on the magnetic activity, so that it can be difficult to reach aunique conclusion about the geometry.
(C) On a longish timescale, determined by NCEV or MBTF or both, the system evolves towards very unequal masses (10 to 1, and even 15 to 1, have been observed). At some extreme mass ratio, depending quite a lot on the internal structure of star 1?i.e. on whether it is substantially evolved across the main sequence band or not?the system becomes unstable to the Darwin instability, whose timescale may be a few years or even days.
(D1) The Darwin instability leads rapidly to a merger, as in V1309 Sco in 2008. After the merger the star relaxes to something like a red giant or an evolved MS star, rapidly rotating. But magnetic activity and consequential mass loss brake the star fairly rapidly.
(D2) The system, formerly a triple, is now a (fairly) wide binary. It may be a rather odd binary, whose two components do not appear coeval, i.e. on the same isochrone. An example may be γ Per, whose A-type subgiant secondary is apparently quite evolved despite the fact that it is only two-thirds the mass of the primary, a G giant. Perhaps the G giant is the merged remnant of a former binary, whose sub-primary was nearer in mass to the A star.
Regarding process (A1), the issue is whether very close binaries (VCBs, say P< 3d) can condense directly out of an SFR, or whether the SFR produces in the first instance, by fragmentation, only rather wide binaries (the 'angular momentum problem' or AMP, Bodenheimer 1978). Note that VCBs are about 2% (Eggleton & Tokovinin 2008) of the stars in the Bright Star Catalogue. One requires that a subcloud of gas and dust that ends up as a
Regarding (A2) and (A3), the important point to note is that there are proportionately
We do not require KCTF to reduce the period below ~2 - 3 d, because even before that period is reached MBTF (process A5) is capable, for magnetically active stars, of reducing the period right down to the value, 0.25 - 0.4 d, at which RLOF sets in. Note that it is only necessary that
That dynamical interactions?process (A2)?take place and produce remarkable results, unlikely to be produced directly by process (A1), is suggested by a few examples:
(i) in DI Her, a 10 d binary of two B5 stars,
For me, a difficult issue is that with late-A/F/G stars (and F/G/K companions) having periods of 0.4 to 3 d it is very likely that NCEV on the one hand and activity-generated MBTF?process (A5)?on the other are very competitive in timescale. When I try to model such systems I get results that vary alarmingly depending on only modest changes in the formalism that I adopt for the dynamo model which generates the mass loss driven by magnetic dissipation, and angular momentum loss driven by the mass loss in collaboration with the overall magnetic field. Thus in an example like δ Cap mentioned above it is very unclear to me whether the primary will evolve nuclearly to fill its Roche lobe before the Roche lobe shrinks down on it as a result of the secondary’s activity. One way or the other I would expect that the system reaches RLOF, but it could be at a period of say 0.9 d if NCEV is stronger and 0.4 d if MBTF is stronger. The systems XY Boo (0.37 d) at spectral type A9 and V2388 Oph (0.80 d) at F0 probably reflect this substantial range.Although there is not much doubt about the rate of NCEV, there is much uncertainty about the rate of MBTF, and so it is difficult to model this process convincingly.
After the sequence of processes which leads to contact, we are still faced with the challenge of how stars evolve further, during contact. Several investigators in the 1970s (Flannery 1976, Robertson & Eggleton 1977, Lucy 1976) concluded that the evolution would have a non-linear, cyclic character, a relaxation cycle or thermal relaxation oscillation (TRO). In this process, the transfer of heat from the hotter to the cooler slightly contracts the hotter, and slightly expands the cooler, thus causing the cooler to overfill its Roche lobe
Yakut & Eggleton (2005) followed a binary through the detached phase, with orbit shrinking in response to MBTF, and through a few dozen TROs. The numerical modeling of heat transport in contact was somewhat ad hoc, but reasonably robust and reproducible. Shortly after RLOF began the system was rather like an Algol; that is, the initial primary, significantly more evolved nuclearly than the secondary, lost sufficient mass before coming into contact that it became the less massive star. The mass ratio was however not far from unity, which makes it somewhat unlike most contact binaries since these usually have mass ratios far from unity. But in the course of a few dozen TROs the mass ratio gradually moved further from unity, and so in the direction one would hope for.
My expectation is that as the mass ratio diverges further from unity, the TROs will become more asymmetric, with long contact portions and (relatively) short near-contact portions. This is what we need in order to agree with the fact that near-equal-temperature contact binaries are substantially more common than the so-called 'near-contact binaries’ that presumably represent the semidetached part of the TRO. Long-term evolution, whether driven mainly by NCEV or MBTF,
However, near-contact binaries (NCBs) are not as rare as was once thought. Yakut & Eggleton (2005) listed 25 likely objects. Several of these have at some time been believed to be ‘contact but with unequal temperatures’; for example W Crv (Lucy & Wilson 1979), but this was shown to be more probably an Algol-like semidetached system (Rucinski & Lu 2000). It is entirely possible that W Crv is
A problem with determining the ‘geometrical’ status of a VCB is that such systems often have light curves distorted with spots. And even if no asymmetric distortion is particularly evident, it is quite feasible that there is a distortion which happens to be fairly symmetric. For instance, if I am right in believing that it is differential rotation which drives luminosity transfer, then there may well be an equatorial belt that is at a (slightly) different temperature from the polar regions of either star.
I have already argued that it seems inevitable that systems evolve on balance?and despite TROs in the short term?towards very unequal masses. The limit of this must be a merger, and it will probably be triggered by the Darwin instability. Enough has been said about this elsewhere; I summarise it in Eggleton (2006). The instability happens when the spin angular momentum of the more massive star (taking the less massive to be a point mass, for convenience) exceeds one third of the orbital angular momentum.This requires a mass ratio that may range between ~7 if the primary is a convective dwarf to 15 or 20 if the primary is radiative, and with a dense core as on the evolved side of the main sequence band. It can be even larger if the primary gets into the Hertzsprunggap, but it suddenly becomes much smaller again once the primary is a largely convective red subgiant.
This may be what happened to the binary V1309 Sco, which was observed (Tylenda et al. 2011) to:
(a) have been a contact binary with a period of 1.4 d before 2008
(b) to have undergone a 10 mag. eruption lasting ~ 2 yr starting in 2008; and
(c) to have subsequently appeared to be a
I think this must have been a system with intense competition between NCEV and MBTF: enough NCEV for the primary to reach the end of the MS and a little beyond, yet enough MBTF to avoid the usual widening of the orbit that we expect in a legitimate Algol when its mass ratio becomes extreme.
Some might see that as the end of the story. But I think there is still another chapter. How do we recognise a former contact binary that has merged? Not easily. Probably it is rapidly rotating, but it may lose mass and angular momentum sufficiently rapidly that it soon becomes ‘normal.’ However, I have already suggested that it probably?even dare I say certainly?was in a triple, and so after the merger it will be in a
The formation and evolution of contact binaries seem to require a considerable variety of astrophysical processes, ranging from gravitational interactions to tidal friction and finally the Darwin instability and a merger. A triple system may be a necessary stage, involving Kozai cycles and tidal friction. The pre-contact phase may involve a few Mega years to a Giga year or more, and the contact phase may be of similar duration. The merger needs only a couple of years, but perhaps a further few Mega years to settle down. The long-term result may be a somewhat anomalous long-period binary.