TRIPLE MICROLENS OGLE-2008-BLG-092L: BINARY STELLAR SYSTEM WITH A CIRCUMPRIMARY URANUS-TYPE PLANET

In strong contrast to all previous triple and the majority of binary microlensing events, the essential physics of this event can be completely understood by decomposing it into three independent point-lens events. We begin by adopting this approach not only for its didactic value but also because of its important implications for the question of free-floating planets (Sumi et al. 2011).

The flux changes F(t) in point-source/point-lens microlensing are described by five parameters, (t₀, u₀, t_E, f_s, f_b),

$$\begin{eqnarray} F(t) &=& f_sA(t) + f_b; \quad A(t) = {u^2+2\over u\sqrt{u^2+4}};\nonumber\\ u(t) &=& \sqrt{\left({t-t_0\over t_{\rm E}}\right)^2 + u_0^2}. \end{eqnarray} \tag{ 1 }$$

These are, respectively, the time of the closest approach, the impact parameter in units of the Einstein radius θ_E, the Einstein radius crossing time, the source flux, and the unmagnified (or blended) flux within the aperture.

Light curves of the form of Equation (1) fully describe both stellar subevents. However, the planetary lens transits the source, meaning that the point-source formula (1) must be convolved with the source profile in that case. This introduces an additional parameter

$$\begin{equation} \rho \equiv {\theta _*\over \theta _{\rm E}}, \end{equation} \tag{ 2 }$$

where θ_* is the angular radius of the source. The parameters of a separate fit for each subevent are shown in Table 1. Note that we have allowed f_b as a free parameter for the final subevent (due to the secondary star in OGLE-IV data), but have imposed f_b = 0 in the remaining two (OGLE-III data) subevents.

Setting f_b at zero is appropriate under the assumption that the source is the same for all three subevents. In principle, one must consider that one or both of the OGLE-III subevents results from lensing of a faint source that is blended with the principal, very bright source. However, given that less than 10% of the light comes from sources other than the one that was lensed in the OGLE-IV subevent, this implies that f_b/f_s > 10 for either of the other subevents (if it is not due to the same bright source). Imposing this constraint leads to unacceptably bad fits for both subevents. Note that Jaroszyński et al. (2010) found an acceptable binary-source fit to two OGLE-III subevents before the OGLE-IV subevent was discovered.

The Einstein timescales t_{E, i} (index i numbers consecutive subevents) are related to the masses M_i by

$$\begin{equation} t_{\rm E} ={\theta _{\rm E}\over \mu }; \quad \theta _{\rm E} = \sqrt{\kappa M \pi _{\rm rel}}; \quad \kappa \equiv {4 G\over c^2\,\rm AU} = 8.1 {\rm \frac{mas}{M_{\odot }}}, \end{equation} \tag{ 3 }$$

where μ and π_rel are the lens-source relative proper motion and parallax, respectively. Because the internal motions of the system are much smaller than the system motion across the line of sight, we approximate μ as the same for all subevents. Then the mass ratios between lenses generating subevents are q_{i, j} ≡ M_i/M_j = (t_{E, i}/t_{E, j})². We then find ratios q_{1, 2} = 2.66 × 10⁻⁴ and q_{3, 2} = 0.22. Similarly, the separation in units of θ_{E, 2} (i.e., primary) can be estimated from s_{i, j} ≃ |t_{0, i} − t_{0, j}|/t_{E, j}, yielding s_{1, 2} ≃ 5 and s_{3, 2} ≃ 17. Even θ_{E, 2} can be estimated once θ_* = 14.25 μas has been evaluated (see below) from θ_{E, 2} = (θ_*/ρ₁)(t_{E, 2}/t_{E, 1}) = 0.33 mas. This then gives an angular scale to the system and the basis to estimate the lens masses and distance (see Section 4). The planet–host separation is s_{1, 2}θ_{E, 2} ∼ 1.6 mas, which for lenses lying in the Galactic bulge corresponds to about 15 AU (projected). In the same manner, the projected separation of the primary and the secondary stars is 48 AU. The assumption of bulge lens (as opposed to disk lens) gives also the primary mass of about 0.7 M_☉, with an upper limit M < 1.2 M_☉, regardless of lens location.

The geometry of this system is illustrated in Figure 2. In the interest of maximum precision, we carry out more rigorous calculations in the next section, but these confirm the very simple arguments outlined here.

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Binary lenses have three parameters beyond those of the single lenses: projected separation (s_{1, 2}), mass ratio (q_{1, 2}), and α_{1, 2}—the angle of the lens–source relative motion with respect to the binary axis. One can find more accurate than above (but still approximate) values of these parameters and ρ by using simple geometry, scaling to appropriate θ_E, and correcting s_{1, 2} → s_{1, 2} − 1/s_{1, 2} (Han 2006). These are compared to the results of the final modeling in Table 2. One finds very good agreement especially in the case of s_{1, 2}. For final solution, the magnification during the planetary subevent was evaluated using the "mapmaking" method (Dong et al. 2006) with modifications (Dong et al. 2009; Poleski et al. 2014). The magnification for other epochs was calculated by hexadecapole approximation (Pejcha & Heyrovský 2009; Gould 2008). Note that OGLE-2008-BLG-092 is the first microlensing event for which different photometric data sets have no overlap in time. Such an overlap typically constrains the blending ratios for different data sets. Instead, we set a prior distribution of f_b/f_s (implemented as a χ² penalty) to be Gaussian with 0 mean and dispersion equal to the uncertainty of f_b/f_s in the third subevent (Table 1). Based on Claret (2000), we assumed the source limb darkening parameter Γ_I = 0.546 (or u_I = 0.643). We checked that even a 10% change of this parameter has a negligible impact on fitted values. The model parameters indicate that the planetary caustic was very small compared to the size of the source that passed over it. The source trajectory relative to planetary caustic is illustrated in the inset in Figure 2.

Our best-fitting model predicts that the source passed the central and planetary caustics on opposite sides but this is weakly constrained. The alternative model with the source passing both caustics on the same side has χ² larger by 1.5 and the only parameter that differs significantly is α_{1, 2} = 1755(29), i.e., smaller by 044. We attempted to fit the model with the source passing relatively far away from the planetary caustic, i.e., the planetary subevent would be an almost standard point-source/point-lens light curve. In such cases, the value of ρ would be smaller leading to a very large value of μ. However, this solution is ruled out (Δχ² = 76). This conclusion is also consistent with the source star profile in the OGLE-I and OGLE-II reference images, which is circular.

Instead of full triple-lens modeling that is numerically complicated, we combine the results of the double lens model for the OGLE-III data (Table 2) and the single-lens model for the OGLE-IV data (Table 1) to obtain parameters of the triple lens. There are three additional parameters that must be estimated: q_{3, 2}—secondary to primary mass ratio, s_{3, 2}—primary–secondary projected separation (in units of primary θ_E), and ϕ_{2, 3}—the angle between the secondary and the planet as viewed from the primary. We checked that at s_{3, 2} ≈ 17 the perturbations caused by the presence of one of the stars on the microlensing signal of the other one are much smaller than the photometric errors. The Einstein timescale is proportional to the square root of the lens mass, thus q_{3, 2} is the squared ratio of primary and secondary t_E and equals 0.216(12). The values of s_{3, 2} and ϕ_{2, 3} are calculated using simple geometry and noting that the caustics of both stars are s_{3, 2} − 1/s_{3, 2} apart. The source could have passed the stellar caustics on the same or opposite sides but the data do not constrain this. If they were passed on the same side (as illustrated in Figure 2), we obtain s_{3, 2} = 16.99(38) and ϕ_{2, 3} = 15759(35). The opposite situation leads to a very similar value of s_{3, 2} = 17.03(38) and slightly smaller ϕ_{2, 3} = 15595(36).

In order to investigate the self-consistency of the triple-lens model, we checked how the presence of the secondary affects the position of the planetary caustic that is the only caustic that was approached closely. We fixed the mass ratios as well as the positions of the primary and the secondary and tried to find the position of the planet that gives the same position and size of the planetary caustic, as we have in the double-lens model. It was enough to change the planet position by as little as 0.01 to match the caustics. This is much less than the 0.11 uncertainty of s_{1, 2}. Therefore, we conclude that our approach to the triple-lens modeling is valid and available data do not require more complicated methods.

The models presented above neglected the microlensing parallax (π_E) effect. We tried to incorporate π_E in the single-lens models fitted to the OGLE-IV data but the short event timescale renders the parallax effect too weak to measure. The Δχ² = 9 limit is π_E < 3.6 for negative u₀ and π_E < 3.1 for positive u₀. The low magnification of the primary event in the OGLE-III data also does not allow π_E to be measured. For similar reasons, the effect of the lens rotation was ignored.

There is one more possibility that one should consider. While three separate subevents were observed and these had to be caused by three different lenses, this does not necessarily imply that these three objects are bound. The secondary subevent could have been caused by a star that is unrelated to the planet–host system. Such an unrelated lens can give rise to microlensing of a given source with probability similar to the general event rate of 10⁻⁵ per year. For the secondary subevent happening within two years before or after the main event, the probability is about 4 × 10⁻⁵. On the other hand, the frequency of binary systems with separations equal or smaller than the deprojected separation of OGLE-2008-BLG-092L is on order of 40% (Duquennoy & Mayor 1991). However, the putative companion gives rise to the microlensing event only if the source trajectory passes close enough, i.e., u_{0, 3} < 1. In the case of OGLE-2008-BLG-092L, the source had to enter or exit (factor of two) the circle of circumference 2πs_{3, 2}θ_{E, 2} within an arc of length 2 θ_{E, 3}. Thus the probability that the secondary is detected is 4θ_{E, 3}/(2πs_{3, 2}θ_{E, 2}) = 2t_{E, 3}/(πs_{3, 2}t_{E, 2}) ≈ 0.02. In this sample of binary system most have smaller separations than considered above, which leads to higher probability of detecting the secondary, which we assume here to be 0.04. Finally, 0.4 × 0.04 = 0.016 is 400 times larger than 4 × 10⁻⁵, which makes unbound lens scenario highly unlikely.

The first step required to translate microlensing parameters to physical parameters is estimating the angular source radius (θ_*). The source has observed I-band brightness of 13.90 mag and (V − I) color of 1.88 mag and almost all stars at this part of the color–magnitude diagram (Figure 3) are located in the bulge. The red clump intrinsic (V − I) color is 1.06 mag (Bensby et al. 2011) and l = −475 implies dereddened I-band brightness of 14.61 mag (Nataf et al. 2013). This gives a source reddening corrected V-band brightness of 14.23 mag and (V − I) color of 1.28 mag. The corresponding (V − K) color is 2.88 mag (Bessell & Brett 1988). The color–surface brightness relation (Kervella et al. 2004) leads to θ_* = 14.25(60) μas. The Einstein ring radius is

$$\begin{equation} \theta _{\rm E} = \theta _{\ast }/\rho = 0.344(20)\, {\rm mas}. \end{equation} \tag{ 4 }$$

This results in

$$\begin{equation} \mu = \theta _{\rm E}/t_{\rm E} = 3.25(22)\, {\rm mas\,yr^{-1}}. \end{equation} \tag{ 5 }$$

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The baseline flux comes almost entirely from the source. Thus, we can use eight years of the OGLE-III monitoring to measure the source proper motion. Its value relative to the local red clump stars is μ_{*, αcos δ} = 0.25(31) mas yr⁻¹ and μ_{*, δ} = 1.17(31) mas yr⁻¹. This corresponds to μ_{*, lcos b} = 1.13(31) mas yr⁻¹ and μ_{*, b} = 0.39(31) mas yr⁻¹ in Galactic coordinates.

The lens parallax and mass are (Gould 2000):

$$\begin{equation} \pi _l = \pi _{\rm rel} + \pi _s, \quad \pi _{\rm rel} = \pi _{\rm E}\theta _{\rm E} \end{equation} \tag{ 6 }$$

$$\begin{equation} M = \frac{\theta _{\rm E}}{\kappa \pi _{\rm E}}, \end{equation} \tag{ 7 }$$

where M is the primary mass (because θ_E corresponds to primary lens). Both the source position in the color–magnitude diagram and proper motion are consistent with a bulge location. For some previously published planets, the value of π_E was found from the microlensing model fit. Despite three subevents observed, one of them having an Einstein timescale longer than a month, we were not able to make a meaningful measurement of π_E. The limits on π_E from OGLE-IV data translate to uninteresting limits on lens mass M > 0.012 M_☉ and distance D_l > 0.75 kpc.

Instead of finding π_E and calculating D_l and M from this, we constrain D_l and D_s using the indirect evidence based on θ_E and μ. The value of μ = 3.2 mas yr⁻¹ is comparable to the dispersion of the proper motions in the Galactic bulge in one direction (Vieira et al. 2007). This strongly suggests that the source and the lens are relatively close to each other, i.e., the lens lies in the bulge or close to its edge. We do not know the orientation of μ relative to the source proper motion μ_* = 1.2 mas yr⁻¹ but even in the most unfavorable case, the bulge lens hypothesis is preferred over a disk lens because the typical proper motions of disk stars are 6.5 mas yr⁻¹.

Noting that the lens is in the bulge, we can put the upper limit on the lens mass. The problem of the bulge highest-mass main-sequence (MS) stars was not investigated previously from observers' point of view. There are no direct mass measurements for bulge MS stars. Masses can be estimated based on the high-resolution and high signal-to-noise spectra, but these require extremely long observations even at the largest existing telescopes for bulge MS targets. This can be overcome by observing the high-magnification microlensing events with the MS sources close to the peak. Bensby et al. (2013) presented the most recent analysis of spectra from the ongoing project aimed at systematic spectroscopic observations of the microlensing events with subgiant or MS sources. In Figure 4, we present the histogram of derived masses. We see that most of the values are close to 1 M_☉ and the highest measured masses are around 1.3 M_☉. This distribution is significantly affected by the selection bias, as lower mass stars are too faint to be observed. Taking into account measurement errors in spectroscopically derived masses and the fact that these can be both subgiant and MS stars, we estimate that the bulge MS stars have masses below 1.2 M_☉ or probably even below 1.1 M_☉. The former limit corresponds to a planet mass q_{1, 2}M close to that of Saturn.

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The distances to the source and the lens were estimated using a simulation of microlensing events. Only the events with both sources and lenses in the bulge were simulated. The density of stars was modeled according to (Nataf et al. 2013) results at the vicinity of the event, i.e., with mean distance of 8.86 kpc and Gaussian distribution of distance modulus with a dispersion of 0.263 mag. The probability of observing microlensing event depends not only on the density of stars but also on the size of the θ_E, thus the simulated events were additionally weighted by $\sqrt{1/D_l-1/D_s}$. We rejected the events that resulted in lens masses above 1.2 M_☉. Integrating the lens and source distances in the rest of the simulated events leads to D_l = 8.1kpc and D_s = 9.7 kpc.

The Einstein radius in physical units is then D_lθ_E = 2.8 AU. The projected separation of the planet is 15 AU, while the secondary is at the projected separation of 48 AU. These values can be de-projected by multiplying by $\sqrt{3/2}$, which yields 18 AU and 58 AU, respectively. The adopted distances (D_l, D_s) = (8.1, 9.7) kpc yield π_rel = 20 mas and therefore $M=\theta _{\rm E}^2/\kappa \pi _{\rm rel} = 0.71\, {M_{\odot }}$. This gives the planetary mass of q_{1, 2}M = 3.3 M_Neptune = 3.9 M_Uranus. The mass of the secondary is q_{3, 2}M = 0.15 M_☉.

The ratio of the de-projected separation to the snow line distance is

$$\begin{equation} \frac{\sqrt{3/2}s_{1,2}\theta _{\rm E}D_l}{2.7\left(\frac{M}{M_{\odot }}\right)\,{\rm AU}} = 56 \times \left(1-\frac{D_l}{D_s}\right). \end{equation} \tag{ 8 }$$

For the inferred distances D_l = 8.1 kpc and D_s = 9.7 kpc, this ratio is about 9, making OGLE-2008-BLG-092LAb the first extrasolar analog of Uranus. The above ratio would be closer to values found in solar system gas giants as opposed to ice giants if D_l/D_s > 0.91. This condition is almost equivalent to already excluded values of M > 1.2 M_☉. The simulation of bulge–bulge events presented above indicates the probability of D_l/D_s > 0.91 is marginal.

Uranus and Neptune formed closer to the Sun and migrated outward because of the interaction with Jupiter and Saturn. The key factors that led to this conclusion were planetary masses and separations. If the properties of OGLE-2008-BLG-092LAb are taken at face value and combined with a host mass that is smaller than the Sun, they suggest in situ planet formation is not possible. However, the density of the protoplanetary nebula of OGLE-2008-BLG-092LA could be higher than the solar one. This would lead not only to formation of OGLE-2008-BLG-092LAb, but also other massive planets in this system. The sensitivity for detecting such additional planets was very low, thus we cannot rule out the hypothesis of much denser protoplanetary nebula.

The planet could be also formed closer to the host and migrated outward. In a hierarchical triple system, the Lidov–Kozai effect (Lidov 1962; Fabrycky & Tremaine 2007) changes the eccentricity of the inner orbit in an oscillatory way. For a short period of time, the eccentricity of the inner binary is very large, resulting in short pericenter distance. During the pericenter passage, the tidal forces can only shrink the orbit, not expand it. Alternatively, the system may contain more planets whose role might then have been similar to Jupiter and Saturn in the solar system. It is also possible that the planetary orbit has significant eccentricity. This would affect the relation between the semi-major axis and observed projected separation, leading to a semi-major axis that is overestimated. With more examples of similar planets observed in the future, a more definitive answer to the question of their origin could be derived.

Detecting cold ice giants that, like Uranus and Neptune, are many AU away from their hosts is extremely difficult for techniques other than microlensing. In the case of the radial velocity method, a very long survey would be required to accomplish this. Currently, the longest period transiting planet is Kepler-421b with a period of nearly two years (Kipping et al. 2014). This period is still about 40 times shorter than required to find a Uranus analog. There are a few candidates for longer orbital periods found by the Kepler satellite (Burke et al. 2014). For some stars, even the longest observing campaigns conducted reveal only one transit. Although the orbital period cannot be estimated based on photometry alone, combining transit timing with radial velocity measurements may constrain the orbital period (Yee & Gaudi 2008). Such a combination of transit and radial velocity methods is still limited by the low probability that a planet on a very wide orbit transits in front of the host star. Ice giants orbiting nearby stars can have angular separations larger than the resolution achieved by direct imaging. However, the problem lies in detecting the light from the planet, which cannot be done by any of the instruments that are currently working or planned for the near future.

We showed above that microlensing is capable of discovering planets on very wide orbits. There are a few different channels that can lead to microlensing planet discoveries. First, the source may approach very close to the lens. This gives rise to very large magnification and the event is sensitive to even small perturbations in the magnification pattern caused by the presence of the lens companions (Griest & Safizadeh 1998). Such close proximity can be predicted while the event is ongoing, and intensified observations lead to greater sensitivity for planets (e.g., Udalski et al. 2005; Gould et al. 2010). This channel led to most of the planets published to date (Zhu et al. 2014), but its sensitivity drops for planets with large s. The size of central caustic is w = (4 q)/((s − s⁻¹)²) (Chung et al. 2005) and for OGLE-2008-BLG-092, it would result in w = 3.8 × 10⁻⁵ if the secondary star were not present. Such small caustics cannot be detected by current microlensing experiments because the signal is smeared by the much larger source (Chung et al. 2005). Second, the planet can be revealed if the source approaches a resonant caustic, which is large and forms if s ≈ 1. This requires that the Einstein ring has a size larger than 10 AU, which is highly unlikely. Third, the source may approach the planetary caustic that is located close to the planet (Mao & Paczyński 1991; Gould & Loeb 1992; Di Stefano & Scalzo 1999). Such approaches are unpredictable and well separated in time from the host lensing event. Follow-up photometry can be obtained after the anomaly is detected or by routine monitoring of many events after the peak, which is not done currently. This shows that the microlensing surveys that cover significant part of the bulge with high cadence are the only efficient way to investigate the population of extrasolar ice giants.

There are further obstacles to detecting microlensing planets at large separations. The typical microlensing event has t_E ≈ 25 days, which means that a significant number of planetary caustic approaches are a few months before or after the main peak. They may be unobservable because of the conjunction of the Sun and the bulge. They may also happen when the Sun is relatively close to the bulge so that 24 hour per day observations are not possible. We showed that even a few years ago, the OGLE survey had cadence good enough to identify such an anomaly. At present, the OGLE-IV survey has sufficient cadence to observe events similar to OGLE-2008-BLG-092 in 26 deg² of bulge. The survey observing strategy is well defined, therefore, a larger sample of similar planetary caustic approaches would allow one to estimate the frequency of such planets.

One of the important outcomes of the microlensing experiments was the detection of an excess of the events with very short t_E of one to two days (Sumi et al. 2011). Since t_E is proportional to the square root of the lens mass, these events should be produced by planetary mass objects. Sumi et al. (2011) presented 10 events with very short t_E and no signs of other lenses and therefore interpreted them as free-floating planets with abundance of $1.8^{+1.7}_{-0.8}$ per MS star. There are other possible interpretations of these events. Some of them may involve bound planets on very wide orbits, for which the presence of the host was not revealed based on either additional bump in photometry (Han et al. 2005) or distortion of planetary event (Ryu et al. 2013). Based on the direct imaging upper limits on the abundance of Jupiter-mass planets on 10–250 AU wide orbits (Lafrenière et al. 2007), Sumi et al. (2011) estimated that no more than 25% of detected short events are caused by bound planets. However, we find a significant observational bias in detecting the stellar hosts for these planets. Even if the microlensing planet is bound, the signal from the host may be too weak to be measured. In the case of OGLE-2008-BLG-092, even a 1% signal would be revealed because the source is very bright. This corresponds to u_{0, 2} < 3.5 for host lensing. For source trajectories crossing the planetary caustic with randomly selected angle relative to the planet–host axis, the probability that the source would make a closer approach to the host is 0.49. For 10% magnification (u_{0, 2} < 1.7), the corresponding probability is 0.21. These numbers ignore the lack of data due to seasonal gaps. It is harder to detect host subevent if the photometric accuracy is lower. The source stars in Sumi et al. (2011) sample were at least 3.3 mag fainter than OGLE-2008-BLG-092S and 1% signals could be easily missed.

We note that the events similar to OGLE-2008-BLG-092 but with fainter sources (i.e., smaller ρ) and different α_{1, 2} would not pass the selection criteria used by Sumi et al. (2011). One of their requirements was u₀ < 1 and we measured u_{0, 1} = 1.51(20) in single-lens approximation.

Sumi et al. (2011) presented also 2σ detection limits for hosts of each presented planet based on the light curve distortions. Only 2 out of 10 cases are inconsistent with a planet that is similar to OGLE-2008-BLG-092LAb, i.e., with s = 5.26. These are MOA-ip-1 and MOA-ip-10. The third case (MOA-ip-7) is marginally consistent (s > 5.2). We note that there are two other events that showed separate subevents by planetary microlensing. First, Skowron et al. (2009) analyzed the event OGLE-2002-BLG-045. The best-fitting model was a binary lens with s = 4.0 and q = 0.008. However, the analyzed data were very limited. Even though the mass ratio was found to be in the planetary regime, this event is not considered a secure planet detection. Second, Bennett et al. (2012) presented event MOA-bin-1 that is best fitted by a planet with s = 2.10 and q = 0.0049. In this case, the host lensing signal was not detected, but the evidence for its presence is a distortion of the planetary anomaly.

We have discovered a relatively compact triple system and thus its long-term dynamical stability should be investigated. Holman & Wiegert (1999) investigated the conditions under which a massless planet orbiting one component of a stellar binary is a stable configuration. The initial planetary orbit was assumed to be circular, prograde, and coplanar with the stellar binary. A wide range of stellar binary eccentricities (e) was tested. Based on results of Holman & Wiegert (1999) and q_{3, 2} in OGLE-2008-BLG-092L, we obtain the following stability criterion (a_c—critical planet semi-major axis, a_b—stellar binary semi-major axis):

$$\begin{equation} \frac{a_c}{a_b} = 0.397(7)-0.527(36) e + 0.115(43)\, e^2, \end{equation} \tag{ 9 }$$

where the quoted uncertainties take into account the uncertainty of q_{3, 2} as well as those from the formula in Holman & Wiegert (1999). We have measured s_{1, 2}/s_{3, 2} = 0.3096(95), thus the system is stable if the measured projected separation ratio represents the semi-major axis ratio and the stellar orbit is circular. However, we must note that s_{1, 2} and s_{3, 2} correspond to two different epochs. The planetary orbit remains stable for binary eccentricities up to 0.17. If the stellar binary is at its apoastron, then the planetary orbit is stable for e < 0.11.