The physics of close binaries

Introduction

Close binary systems present an interesting test case to explore the physical processes occuring in stars and their immediate environments. This includes the mass transfer and the formation of an accretion disk around the primary star, but also the role of magnetic activity and implications of stellar dynamos, as described for instance via Applegate's model. Our research on these topics concerns the post-common-envelope binaries (PCEBs) and the Double-Periodic Variables (DPVs), as well as other magnetically active binary systems. Many of these topics are jointly explored with the group of Prof. Ronald Mennickent.

Post-common-envelope binaries
Planets in post-common-envelope binaries
Magnetic activity as a potential origin of the observed period variations (Applegate's model)
Double-Periodic Variables

Post-common-envelope binaries (PCEBs)

Post-common envelope binaries are very close binary systems (typical separation: 1 solar radius) consisting of a white dwarf and a low-mass main sequence star. These systems are expected to form as a result of common envelope evolution, where the low mass companion falls into the envelope of the more massive component after it evolves and turns into a giant star. The lower-mass star may then either be engulfed by the expanding giant, or may loose angular momentum due to tidal interactions and thus fall into the giant. Due to dynamical friction, the low-mass star will spiral inward within the common envelope of the stars, and thereby deposit energy and angular momentum within the envelope. The envelope becomes thereby unbound and is ejected from the system, and the spiral-in stops once sufficiently material is removed, so that dynamical friction is no longer relevant. The typical separation between the remaining core of the giant and the low-mass star is then of the order of a solar radius, and the core of the giant will evolve quickly into a White Dwarf. The typical evolution is depicted as follows:

Fig. 1: Common envelope evolution leading to the formation of PCEB binaries (Geier et al. 2010).

An even better impression about common-envelope evolution can perhaps be obtained from 3D simulations, as pursued for instance by Jean-Claude Passy. We refer here to a video of his simulations available on his website. The ejected envelopes are expected to give rise to planetary nebulae such as NGC 6778, which is known to harbor a central binary system (Guerrero & Miranda 2012):

Fig. 2: The planetary nebula NGC 6778 - a possible outcome of common envelope evolution (Guerrero & Miranda 2012).

Planets in Post-Common-Envelope Systems

Some of the post-common-envelope binaries formed via common envelope evolution are eclipsing binaries, and their properties can therefore be studied in great detail by measuring their eclipses. A particularly well-studied system is NN Serpentis (e.g. Beuermann et al. 2013). A particulary useful quantity to study such systems is the O-C diagram, where the difference between observed and predicted times of the eclipses are shown as a function of time. The prediction in this diagram is based on the assumption that the system is strictly periodic, without deviations.

Fig. 3: The O-C diagram of NN Serpentis (Beuermann et al. 2013).

The O-C diagram mentioned above is compatible with a 2-planet solutions, with both planets having Jupiter-type masses and large separations (1-3 AU) from the central binary system. As a result, the giant planets have radii that are larger than the White Dwarf and the low-mass star, orbiting them at large distances:

Fig. 4: An illustration of the proposed planetary system in NN Ser. Credit: Warwick

As pointed out by Voelschow et al. (2014), it appears however difficult to reconcile such a system with first generation planets, which would have formed with the system itself. In particular, one would expect that the orbits should become more elliptical due to the mass loss during the common envelope phase, and they should be on large radii or become completely unbound. The probability for ejections under different assumptions for the mass loss and the initial eccentricity is depicted below:

Fig. 5: The probability for ejections depending on mass loss and initial eccentricity (Voelschow et al. 2014).

As an alternative, Schleicher & Dreizler (2014) proposed a scenario for a second-generation origin, where the planets have formed via gravitational instabilities from the ejecta of the common envelope. For this purpose, they have calculated the expected energy release during the common envelope event, from which one can infer the ejected mass and the fraction of the mass that potentially remains bound, leading to the formation of a fall-back disk. This model was recently supported by the detection of dust around NN Ser.

Fig. 6: Gravitational binding energy of the envelope vs gravitational energy released via the inspiral of the low-mass companion (Schleicher & Dreizler 2014).

Based on this model, we calculated the expected planetary masses for a sample of PCEB systems by Zorotovic & Schreiber (2013), and compared with the proposed planetary masses based on the eclipsing time observations. The latter is illustrated here:

Fig. 7: Most massive planet in each system normalized by the primary mass, as a function of the ratio of primary to secondary mass. Diamonds show model predictions, triangles masses based on eclipsing time variations (Schleicher & Dreizler 2014).

While the model was found to naturally explain the high masses of the planets and the relatively wide orbits, the observed planetary masses in some systems were still even higher than the model predictions. It is thus conceivable that PCEB binaries harbor a mixed population, or that some of the apparent planets are due to other effects, as will be discussed below.

An alternative interpretation via Applegate's mechanism

While the planetary hypothesis seems relatively successful for NN Ser, the presence of a proposed brown dwarf in V471 Tau has been disproven through direct imaging by Hardy et al. (2015). In QS Vir, the observed eclipsing time variations also appear to be inconsistent with a planetary scenario (Parsons et al. 2010). As an alternative interpretation, one may thus consider if at least in some of the systems the observed period variations are due to magnetic activity, as proposed in Applegate's model.

The presence of such magnetic activity in the low-mass companion is highly plausible, due to the rapid rotation of the binary system. As a result of rapid synchronization via tidal torques, the low mass star will effectively rotate at the same rate as the binary system. The latter provides ideal conditions to drive a magnetic dynamo.

The presence of such a dynamo leads to regular reconfigurations of the magnetic field. Within Applegate's model, it is assumed that the magnetic fields contributes to the redistribution of angular momentum within the star, leading to regular changes in the stellar quadrupole moment on the timescale of magnetic activity. A change in the quadrupole moment in turn influences the orbit, leading to a period variation. The model specifically relates the required change in the angular momentum to the observed period variation, and quantifies the required energy to produce such a change of the quadrupole moment within the star.

While Applegate's original model considered the angular momentum exchange between a thin shell and the inner core, but without considering the change in the quadrupole moment of the core, Brinkworth et al. (2006) have shown that a more realistic model considering a finite shell as well as the quadrupole moment both in the shell and the core requires more energy to drive the period variations, but produces more realistic results. We recently extended the model and applied it to a sample of PCEBs with known eclipsing time variations (Voelschow et al. 2016).

Fig. 8: Fraction of required energy divided by energy produced in the nuclear core as a function of the orbit separation, for different masses of the companion star (Voelschow et al. 2016).

Our analysis shows that the Applegate scenario may work in the systems QS Vir, DP Leo and V471 Tau, while it can be clearly ruled out for HW Vir, NN Ser, NSVS14256825, NY Vir, RR Cae and HS 0705+6700. The situation cannot be fully decided for HU Aqr and UZ For.

Double Periodic Variables (DPVs)

The Double Periodiv Variables are a class of close binary systems consisting of two massive stars, including a cool, highly evolved component, which show clear signs of a long period in addition to the orbital period. An example based on the b and b-r light curves is given below:

Fig. 9: Mach b and b-r light curves showing a long-term period (Mennickent et al. 2003).

For this long period, a characteristic relation has been found, which indicates that it corresponds to about 33 times the orbital period of the binary:

Fig. 10: Long vs orbital period of the DPV systems (Mennickent et al. 2016).

For many of these systems, it further has been shown that the primary is surrounded by a compact, optically thick disk, as shown below for the case of V393 Sco:

Fig. 11: The inferred accretion disk arond the primary in V393 Sco (Mennickent et al. 2012).

Our group currently explores whether the observed relation between the orbital and the long period can be explained as a result of stellar magnetism, i.e. as a relation between the rotation period of the cool star and its activity cycle. In such a case, the magnetic activity of the binary could be responsible for driving variations in the mass transfer rate, both due to magnetic spots in the stellar surface, but also structural changes due to Applegate's model. The latter would give rise to a scenario with an active binary with magnetically regulated accretion.

Fig. 12: An active binary system with magnetically regulated accretion. Courtesy: M. Richards

The confirmation of this picture would be in line with other observed correlations between the rotation period and the activity cycle in single stars, as shown below:

Fig. 13: Relation between activity cycle and rotation period in single stars (Boehm-Vitense 2007).