Planets that orbit their parent star at less than about one astronomical unit (1 au is the Earth–Sun distance) are expected to be engulfed when the star becomes a red giant1. Previous observations have revealed the existence of post-red-giant host stars with giant planets2, 3, 4 orbiting as close as 0.116 au or with brown dwarf companions5, 6 in tight orbits, showing that these bodies can survive engulfment. What has remained unclear is whether planets can be dragged deeper into the red-giant envelope without being disrupted and whether the evolution of the parent star itself could be affected7, 8, 9. Here we report the presence of two nearly Earth-sized bodies orbiting the post-red-giant, hot B subdwarf star KIC 05807616 at distances of 0.0060 and 0.0076 au, with orbital periods of 5.7625 and 8.2293 hours, respectively. These bodies probably survived deep immersion in the former red-giant envelope. They may be the dense cores of evaporated giant planets that were transported closer to the star during the engulfment and triggered the mass loss necessary for the formation of the hot B subdwarf, which might also explain how some stars of this type did not form in binary systems.
At a glance
KIC 05807616 (also known as KPD 1943+4058) is a seemingly isolated pulsating hot B subdwarf (sdB) star that has been monitored by the Kepler satellite primarily for the study of its oscillations10, 11, 12. It is at an evolved stage of thermonuclear fusion of helium in its core, and belongs to the so-called extreme horizontal branch. This star shows a rich pulsation spectrum mostly composed of gravity (g-)modes13, 14. Its main structural parameters are well determined through asteroseismic means based on one month of Kepler exploratory data (Table 1)15. We focus here on additional Kepler time-series photometry obtained for this star after the exploratory phase.
The analysis of these data revealed many frequencies, most being associated with stellar oscillations (Fig. 1 and Supplementary Information section A1). However, we also found two very weak periodic modulations in the low-frequency range whose nature is most intriguing. The timescales involved for these variations are 5.7625 ± 0.0001 h (F1, with an amplitude of 52 ± 6 parts per million, p.p.m.) and 8.2293 ± 0.0003 h (F2, with an amplitude of ~47 p.p.m.; see Supplementary Information sections A2 and E). The phase folded curves show that these variations repeat at a coherent phase throughout the entire light curve (Fig. 1b and c). We determined that contamination from a nearby star, stellar pulsations, or rotational modulations (for example, through surface spots) cannot account for these variations, leaving orbital modulations as the most plausible interpretation (Fig. 1 and Supplementary Information sections B and C). Compact binary systems with an sdB star as the primary and having comparable orbital periods are indeed not atypical. However, in the present case, the very subtle modulations and the suggested presence of more than one companion raise the question of the eventual substellar nature of these objects. In this context, the period ratio F2/F1 ≈ 1.43, which is close to a 3:2 resonance, is also intriguing.
We explored this possibility by evaluating the properties (in particular the radius) that these objects would need to have in order to produce the observed variations in the light curve. There are two main sources of modulation involving small bodies. The first is reflection by the surface of each planet of the light emitted by the star; such reflection would be modulated by the orbital motions, as we see the planets in different phases of illumination. The second source is a possible thermal imbalance between the heated day-side and cooler night-side hemisphere of each planet. Assuming the rotation of each planet is tidally synchronized to its orbital motion (a very likely situation for a compact system like KIC 05807616), we would see a thermal emission that was modulated along their orbits16. Both effects depend on unknown properties of the orbiting bodies. These are the amount of light reflected and absorbed at their surface (characterized by the Bond albedo, α) and how the absorbed heat is redistributed before being re-emitted. For this latter effect, we adopted a simple approach involving average temperatures on the day and night sides, assuming radiative equilibrium and black-body re-emission. Heat redistribution is then characterized by a parameter, β, being the ratio of the mean temperature in the dark hemisphere to the mean temperature in the heated hemisphere. The magnitude of these variations also depends on the inclination angle of the system relative to the observer.
We calculated the planets’ properties as functions of the parameters mentioned above and explored all plausible situations (Supplementary Information section D). Our findings from this thorough analysis are as follows: (1) in all configurations except for very small inclination angles (i < 20°), the derived radii for the orbiting objects are in the planetary range. (2) If efficient heat redistribution occurs (β > 0.90), the objects would be in the giant planet range of sizes, similar to Neptune or Jupiter in size. However, in most situations (when β < 0.80), the day/night temperature contrast effect dominates, and nearly Earth-sized planets are predicted. As this system is extremely compact and orbits a very hot star, the temperature contrast between the two hemispheres should be large, and therefore the value of β small, and the small-planet solution is preferred. (3) The assumed albedo has a limited influence on the above results and does not qualitatively change the conclusions. A low albedo, α ≈ 0.10, is generally observed for hot gaseous planets17, 18, 19 and Mercury, in our Solar System, has a comparable albedo (but, admittedly, it may not be representative of the hottest telluric worlds). The last unknown is the inclination angle of the system, and its effect is illustrated in Fig. 2. At very small inclinations (i < 3°), the derived radius could still be in the giant-planet range. However, the pulsations detected in KIC 05807616 provide valuable indications that small angles (i < 20°) are improbable, suggesting instead that i ≈ 65°. This additional constraint relies on the reasonable assumption that the orbits of the planets are most probably coplanar with the star's equatorial plane (see Supplementary Information sections A3 and A4).
On the basis of these considerations, we have derived the parameters for the two planet candidates, named KOI 55.01 and KOI 55.02, from the most probable configuration for this system (Table 1). These parameters suggest that the two planets are smaller than Earth, which would make them the smallest planets so far found around a star still undergoing nuclear fusion. Considering their sizes and orbital parameters, their nature is most probably telluric. This conclusion may be further supported by a possible brightness excess (but only a 1.9σ detection at this stage) at phase zero in the phase curve of KOI-55.01 (Fig. 1). This excess, if real, could be associated with an opposition surge, a phenomenon observed with solid bodies having a tenuous (or no) atmosphere20. The two planet candidates are also remarkable for the very high temperatures expected at their surfaces, indicating that they must be undergoing significant evaporation. However, these atypical properties, compared with those of known planets orbiting main-sequence stars, should not be surprising, considering the nature of the parent star. Planets in extreme environments have been reported previously21.
Our two planets were most probably swallowed by their parent star when it became a red giant, a stage that ended only ~18 million years ago15. They were probably orbiting further away and may have been dragged deep into the red-giant envelope to their current positions22. The fact that they are of equivalent size with orbits close to a 3:2 resonance may be an important factor explaining their survival. Indeed, preliminary N-body calculations (not shown) suggest that this system is dynamically stable, as long as the planet masses remain lower than several Earth masses; the system may also be stable when a third small planet is present between KOI 55.01 and KOI 55.02. This is consistent with our finding that small bodies should be involved.
This discovery suggests that planets may influence stellar evolution9. The increased envelope mass ejection required to form sdB stars from red giants is expected to occur in close interacting binaries, where the companion can transfer some of its orbital momentum to the expanded red-giant envelope, speeding up its rotation and thus triggering its enhanced dissipation23. However, this does not explain how about half of the sdB stars that, like KIC 05807616, appear to be single or in well detached binaries24, could be produced. In the present case, the planets may have contributed to the dissipation of the envelope to the point of making KIC 05807616 become an extreme horizontal branch star instead of a normal horizontal branch star with a thicker residual envelope25. A plausible scenario would be that these bodies were originally giant planets immersed in the red-giant envelope and massive enough to survive engulfment and trigger the enhanced mass loss necessary for the formation of a hot B subdwarf star26. During that episode, the planets may have been stripped down, losing their gaseous layers and being left only with their inner rocky/iron cores, which would be exposed. The small detected bodies would then be these cores, also named Chthonian planets27, which are dense enough to lie beyond their Roche limit (see Table 1), thus avoiding disruption by the strong tides generated by the parent star.
Alternative scenarios may also be considered. Another way to form single sdB stars is through the merger of two helium white dwarfs23, and planet formation following this event may be possible28. We could speculate that the collapse of the extended envelope resulting from this merger could produce a circumstellar disk, where second generation planets may form. However, it seems unlikely that new, sufficiently dense, planets could have formed within a rather short period of time (less than ~18 Myr) in an environment that close to this hot star.
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S.C. thanks the Programme National de Physique Stellaire (PNPS, CNRS/INSU, France) for support. G.F. acknowledges the support of the NSERC of Canada and the contribution of the Canada Research Chair Program. MMT spectra for KIC 05807616 were obtained at the MMT Observatory, a joint facility of the University of Arizona and the Smithsonian Institution. A.S.B. acknowledges funding from the Polish Ministry of Science and Higher Education. S.C. thanks R. Gilliland for help in managing Kepler's procedures. We acknowledge the Kepler team and all who have contributed to making this mission possible. Funding for the Kepler mission is provided by NASA’s Science Mission Directorate.
- Supplementary Information (2.3M)
This file comprises Supplementary Sections A-E, which contain Supplementary Text and Data, Supplementary Figures with legends Supplementary Tables and additional references – see Contents on page 1 for more details.