# Planets in binary systems

THE BASICS FACTS:

This graph presents an overview of the architecture of all binary systems harboring a *confirmed* exoplanet on an S-type orbit, that is, a planet orbiting *one* of the two stars in the system. This list is exhaustive for all binaries of separation <500AU (fig. 1) and 200 AU (fig. 2) updated on 15/12/2017.

Figure 1: All systems with at least one confirmed exoplanet and one confirmed stellar companion with projected separation <500au. Figure from Thebault & Haghighipour (2014), updated on 15/12/2017.

Figure 2: All systems with at least one confirmed exoplanet and one confirmed stellar companion with projected separation <200au. Figure from Thebault & Haghighipour (2014), updated on 15/12/2017.

The blue circles' location shows the semi-major axis of the exoplanet while the yellow circles show the location of the companion star. The radius of the blue circle is proportional to the estimated radius of the planet (or the cubic root of its mass when only a mass estimate is available). The radius of the yellow circle is proportional to the cubic root of the *mass ratio* between the companion and the central star (for the sake of visibility, the sizes of the planets have been inflated by a factor 20 with respect to the sizes of the yellow stars).
For both the planets and the stars, the horizontal purple line represents the radial excursion due to the object's eccentricity. Note that, for most stellar systems of separation > 30-50AU, the semi-major axis of the binary is unknown and the only available information is the projected separation between the stellar components. These cases are indicated by a "I" symbol overlaid onto the companion star.
The black vertical line plotted between the planet and the stellar companion represents the outer limit for long-term orbital stability as estimated with the widely used empirical formula of Holman & Wiegert (1999), assuming that the planet and the binary are *coplanar*. For systems where only the projected separation of the binary is known, the stability limit is computed assuming that the companion star is on a circular orbit whose radius is equal to the projected separation.

Some of the presented cases are in fact higher-order multiple systems, mostly triple or even quadruple stellar systems. However, almost all of these systems are highly hierarchical, meaning that the third star does not significantly impact the dynamical evolution of the planet. This is why, for the sake of clarity and simplicity, we chose to present them as "binaries", labelling them with an additional "*" at the end of the system's name, with a brief explanation presenting the system's specificity. Most of these hierarchical cases fall into 2 categories:
- 1) Systems where either the central or the companion star is itself a very tight spectroscopic binary. In this case, the dynamical stability of the planet is computed by merging the two stars into one "effective" central or companion star
- 2) Systems where the third star is very distant from the central binary, typically more than 10 times the distance of the closer companion star. In this case, the gravitational pull of the third star is ignored when estimating the planet's stability.

OTHER SPECIAL CASES:

For most cases, the planet orbits the more massive component (usually labelled as "A") of the binary. In this case, we simply give the stellar name without adding the "A". For the few systems where the planet orbits the lower mass ("B") binary component, we specify it be adding the "B" at the end of the stellar name.

For a few systems (2 so far), there are planets orbiting each member of the binary. In this case, the system is divided into two "binaries", one where the first star is the "central star" and the other star is the perturbing companion, and another one where the roles are reversed.

We chose a rather conservative policy of excluding all systems with « planetary » objects having a mass (or a minimum mass) higher than 13 M_Jup. However, we display the > 13 M_Jup companions for the few systems (2 so far) for which an exoplanet has been detected *in addition* to them. These >13M_jup objects are drawn in orange instead of blue.

A FEW WORDS OF CAUTION:

As already pointed out, for the vast majority of systems where only the projected separation between the stars is known while the actual orbit of the binary reamains unconstrained, we consider the fiducial configuration of a binary having a circular orbit equal to the projected separation. The estimated stability limit thus only gives a first-order estimate and should be taken with caution. However, it can be reasonably considered as a rather conservative assumption with respect to the planet's orbital stability, as it corresponds to the smallest possible physical separation between the stars.

On a related note, for most systems there is another unknown parameter, which is the relative inclination between the planetary and binary orbital planes. We have considered the simplest possible case of a coplanar configuration, which might hold for the tightest binaries, since observations of young binaries have shown that proptoplanetary discs tend to be aligned with stellar equatorial planes for separations up to 30-40AU (see Hale, 1994). But significant inclination values, possibly entailing complex effects such as the Kozai mechanism, cannot be ruled out for most systems. As a matter of fact, some detailed numerical studies have shown that large i values could increase the odds for long term orbital stability for some specific planets observed at the limit (or even beyond the limit) of the coplanar orbital stability (HD196885, HD59686).

STATISTICAL SIGNIFICANCE:

Although it might be tempting to do so, it is difficult to straightforwardly derive statistics regarding the incidence of planets in binary systems, because the available list of systems is affected by several strong biases. The first one is that, until relatively recently, observational surveys, especially those relying on the radial velocity method, had been strongly biased *against* binaries, excluding known multiple systems from their potential targets. Another issue is that, for many cases, the binarity of the system was not known at the time of the exoplanet's discovery and was established by later observational campaigns. This means that there should still be a potentially large population of exoplanet hosting "single" stars that are in fact members of a (yet undetected) multiple system. To alleviate this problem, several large-scale adaptive optics surveys are currently underway in order to assess the presence of stellar companions around exoplanet hosts. These surveys have already detected a large number of potential stellar companions (albeit mostly around yet-unconfirmed KOIs ("Kepler Object of Interest")), but the physical link between stellar components (as opposed to chance alignment with background stars) of each individual system remains yet to be established (see, for instance, Wang et al., 2015a,2015b, Kraus et al., 2016, or Ziegler et al., 2017). However, since the background star scenario should be very unlikely for binaries of separations <500-1000AU, we are presenting an additional graph that includes all the <500AU companion stars detected by the Kraus et al.(2016) survey, albeit limiting it to companions to *confirmed* Kepler exoplanet systems.

N.B. : The graphs might be freely re-used, as long as properly credited to Philippe Thebault and referring to the original Thebault & Haghighipour (2014) article.