Eruptive variables, another type of intrinsic variables, exhibit irregular violent outbursts and brightness variations associated with their chromospheres and coronae, often accompanied by mass outflows and interaction with the inter- stellar medium. A common type are the so-called Orion variables (3.9% of the GCVS), which are mainly protostellar objects such as T Tauri or FU Ori stars, moving towards the main sequence. Outflows and jets seem to be associated with the protoplanetary/accretion disks surrounding these young stars, produc- ing light curves such as in Fig. 2.15 (Krautter, 1996b). Another common eruptive group are flare stars (3.8% of the GCVS) or UV Ceti-type variables; these seem to be late-main sequence, low-mass stars undergoing magnetic reconnection (sim- ilar to solar flares but at far higher energies). Fig. 2.16 illustrates such a flare across multiple wavelengths (Krautter, 1996a).
Explosive or cataclysmic variables include extremely violent transients (super- novae and novae of various kinds) whose outbursts are caused by thermonuclear processes. Many are close binary systems containing at least one post-main se-
Figure 2.17: Light curve for SS Cygni-type dwarf nova U Gem (P = 0.17690618 d, from Vogt (1996), Fig. 5.24). The extended maximum corresponds to a hot spot on the accretion disk, where a stream of material strikes the disk; the minimum occurs when the disk is partially eclipsed by the secondary.
quence object. The commonest type in the GCVS (1.0%) are dwarf novae (or U Geminorum stars), which consist of a white dwarf primary accreting matter via a disk from a main sequence secondary filling its Roche lobe. If eclipsing, the or- bital period (on the order of hours) may be revealed in the light curve (Fig. 2.17). Semi-regular outbursts of much greater magnitude also occur (Fig. 2.18), which “can be understood as the limit cycle evolution of an unstable accretion disc that alternates between a hot, high-viscosity state and a cool, low-viscosity state” (Kolb, 2010).
Figure 2.18: Light curve for dwarf nova SS Cygni showing semi-regular outbursts over nearly 100 y (from Kolb (2010), Fig. 4.5, constructed from observations made by the American Association of Variable Star Observers, courtesy John Cannizzo).
Chapter 3
Questions of interest
In this chapter, the background will be set out to a number of specific research questions which might be addressed using SuperWASP archive data on eclipsing binaries and their orbital period variations. These questions motivated several of the focused studies to be described in Part III, and were either suggested in the original proposal for this research project, or emerged during its course. The first three are related.
3.1
The short-period binary limit
When the period distributions of contact binary systems are plotted (Figures 3.1 and 3.2) a number of interesting features emerge. There is a peak at around 0.4 d, a long tail to the right, and a fairly sharp cut-off at around 0.2 d, below which no objects have been observed. (Here we are considering binary systems containing main sequence stars only; systems containing one or more compact objects such as a white dwarf, neutron star or black hole can have shorter periods.) The cause of this short-period limit is a matter of continuing debate.
Rucinski (1992) proposed a theory linking the short-period limit of W UMa systems to the limit of full convection for low-mass stars. He derived a formula
Figure 3.1: Period distributions of contact binaries observed by OGLE in two fields (from Szyma´nski et al. (2001), Fig. 9).
Figure 3.2: Period distributions of eclipsing binaries observed by ASAS (from Paczy´nski et al. (2006), Fig. 6). Contact systems are shown with a solid line; semidetached systems dot- ted; detached systems dashed.
for possible configurations of stellar parameters in a contact binary:
f (Q1) ∝ K(Teff)M −1/3 1 R
−1 1
where f is a very steeply rising function of Q1, the ratio of core radius to total stellar radius, and K was calibrated using stellar models. Using these constraints, he argued that “there cannot exist dynamically stable contact binaries with ef- fective temperatures lower [. . . ] than the Hayashi limit” i.e. the low-temperature limit for fully-convective stars on the Hertzsprung-Russell diagram. Since there is an observed relationship between binary period and stellar colour, his sug- gestion was that the temperature limit would correspond to a period limit for contact binaries.
Unfortunately, when plotted on a period-colour graph (Fig. 3.3), the full convection limit lies some distance from observed contact systems, and he himself acknowledged that the theory could not provide a complete explanation of the period limit. However, we might note that many more contact binaries have been
Figure 3.3: Period-colour relationship for observed W UMa systems, with lines indicating the limit of full convection for systems with various total masses (from Rucinski (1992), Fig. 5).
observed since 1992, and the inclusion of these extra data points on the graph, together with a potentially improved determination of K, might narrow the gap and make Rucinski’s model more tenable.
Stepie´n (2006) proposed a totally different explanation. He obtained a for- mula for the angular momentum loss (AML) rate in a close detached binary due to magnetic braking: dHorb dt = −4.9 × 10 41ωR21M1+ R22M2 Porb ,
(where masses and radii are in solar units, Porb is in days, t is in years and Horb is in cgs units), which implies that lower-mass binaries will lose angular momentum more slowly than higher-mass systems, and so will take longer to reach a small- separation, short-period contact orbit. (The assumption must be that the AML ceases once a contact configuration is achieved.) By his calculations, “[b]inaries with initial component masses lower than 0.7 M⊙have not lost enough AM within
Figure 3.4: Orbital periods of detached binaries plotted against age, using Stepie´n’s model for mass-related AML (from Stepie´n (2006), Fig. 2). The mass ratio q=1; the different lines indicate calculations for systems with different total masses, decreasing left to right.
the age of the Universe to form contact systems and they remain [. . . ] detached”, and this then provides a reason for the period limit: the Universe simply has not existed long enough for any binaries to evolve to an orbital period below 0.2 d (Fig. 3.4). We may note that this model implies a changing short-period limit: in the far future, astronomers could expect to observe contact systems with a period cut-off below 0.2 d, as more low-mass systems evolve into stable contact configurations at small separations.
A problem with this theory is that a number of recent observations conflict with it, as pointed out by Jiang et al. (2012), who collected published parameters for a number of short-period binaries. GSC 01387-00475 is a contact system with period 0.2178 d and primary mass 0.638 M⊙: according to Stepie´n, such a low- mass binary should not have had time yet to evolve into contact, even if it was one of the first stars to form in the Universe (which is most unlikely). The shortest- period binary known is GSC 2314-0530 (Figure 6.3), a semidetached system
Figure 3.5: Two binary evolution cal- culations with different initial pri- mary masses and initial mass ra- tio 0.79 (from Jiang et al. (2012), Fig. 1). On the left, a system with initial primary mass 0.79 M⊙ un- dergoes mass (lower panel) and ra- dius (upper panel) changes over sev- eral million years, reaching a sta- ble contact configuration at the point marked by the star. On the right, a system with initial primary mass 0.71 M⊙ undergoes mass and radius changes so rapid as to appear instan- taneous on this scale, reaching an un- stable state at the point marked by the cross, at which point it may be expected to merge into a single star.
Figure 3.6: Binary evolution out- comes in an initial primary mass– mass ratio plane (from Jiang et al., Fig. 2). Filled stars indicate sta- ble systems; crosses indicate unsta- ble systems. The notional diagonal line separating the two regions corre- sponds to the short-period limit.
with period 0.192 d and primary mass just 0.51 M⊙; if Stepie´n’s evolutionary calculations are remotely correct, a system of such low mass should have a much greater separation and longer period at the current time, rather than being on the brink of contact and actually below the short-period cut-off.
suite of calculations for binaries with various initial primary masses and mass ratios, using an evolutionary code of Eggleton. They found (Figs. 3.5 and 3.6) that systems with particular combinations of low primary mass and low mass ratio evolved into unstable states and did not reach contact at all; rather, they would be expected to undergo rapid mass transfer and merge on a dynamic timescale. We would expect in general to observe only those systems where stable mass transfer is possible within a long-term contact configuration: these will have primary mass/mass ratio combinations corresponding to periods greater than ∼0.20 d. This, then, provides an explanation for the short-period limit which is consistent with observation, at least for the moment.
Given the uncertainties inherent in all these models, and the lack of reliable parameters available for W UMa-type systems, it would be unwise to completely rule out any of the three explanations at this stage, or indeed other explanations not yet thought of. It might be that multiple factors combine to produce the observed period limit. In any case, further identifications and investigations of short-period contact binaries close to the limit (as in Norton et al. (2011)), especially those undergoing period changes, would be expected to make a useful contribution to resolving the issue.