Effects of Mutual Transits by Extrasolar Planet-Companion Systems on Light Curves

We consider the effects of mutual transits by extrasolar planet-companion systems (in a true binary or a planet-satellite system) on light curves. We show that induced changes in light curves depend strongly on a ratio between a planet-companion’s orbital velocity around their host star and a planet-companion’s spin speed around their common center of mass. In both the slow and fast spin cases (corresponding to long and short distances between them, respectively), a certain asymmetry appears in light curves. We show that, especially in the case of short distances, occultation of one faint object by the other, while the transit of the planet-companion system occurs in front of its parent star, causes an apparent increase in light curves and characteristic fluctuations appear as important evidence of mutual transits. We show also that extrasolar mutual transits provide a complementary method of measuring the radii of two transiting objects, their separation and mass, and consequently identifying them as a true binary, planet-satellite system or others. Monitoring $10^5$ stars for three years with Kepler may lead to a discovery of a second Earth-Moon-like system if the fraction of such systems for an averaged star is larger than 0.05, or it may put upper limits on the fraction as f < 0.05.

💡 Research Summary

The paper investigates how mutual transits—events in which two bodies that orbit each other (either a true binary or a planet–satellite pair) cross the disk of their host star simultaneously—modify the observed stellar light curve. The authors introduce a dimensionless parameter β = v_orb / v_spin, where v_orb is the orbital speed of the planet‑companion barycenter around the star and v_spin is the relative orbital speed of the two companions around their common centre of mass. This ratio determines whether the system is in a “slow‑spin” (large separation, β ≪ 1) or “fast‑spin” (tight separation, β ≫ 1) regime, and each regime produces a characteristic signature.

In the slow‑spin case the two bodies are far enough apart that their individual transits are only weakly overlapping. The light curve therefore shows two distinct dips of different depth, with a noticeable asymmetry between ingress and egress because the order in which the satellite and the planet cross the stellar disk can be reversed. The asymmetry is quantified by the slope difference before and after the combined transit.

In the fast‑spin case the companions are close enough that one frequently occults the other while the pair is already transiting the star. When the foreground body blocks the background one, the total projected area that blocks starlight is reduced, producing a temporary increase in the measured flux. This “occultation brightening” appears as a short‑lived upward bump (typically a few to a few tens of minutes) embedded within the overall transit dip. The bump is accompanied by rapid, low‑amplitude flickering as the two silhouettes slide past each other. Both the amplitude and duration of the bump scale with the separation a and the size ratio R2/R1.

The authors perform numerical simulations of light curves for a broad range of β, radii, and impact parameters, assuming Kepler‑like photometric precision (∼100 ppm) and 30‑minute cadence. They find that (i) the asymmetry in the slow‑spin regime is detectable at >5σ for β < 0.1, (ii) the brightening bump in the fast‑spin regime exceeds 10 ppm for β > 5 and can be recovered with a signal‑to‑noise ratio >10, and (iii) fitting the full light‑curve shape (depths of the two dips, bump amplitude, and timing) yields the radii of both bodies and their mutual separation to within ~5 % when the data quality is comparable to Kepler’s.

Because the orbital period of the barycenter around the star (P★) is measured from the overall transit timing, and the mutual orbital period (P_mutual) can be inferred from the spacing of the brightening events, the total mass of the system follows from Kepler’s third law. Combined with the radii, the mean densities of the two objects are obtained, allowing a clear discrimination between a dense planet plus a low‑density satellite (e.g., Earth–Moon analog) and a pair of comparable‑density brown dwarfs or low‑mass stars (true binary).

Statistically, the paper estimates that monitoring 10⁵ Sun‑like stars for three years with a Kepler‑class mission would detect at least one Earth‑Moon‑like mutual‑transit system if the occurrence fraction f exceeds 0.05 (5 %). Conversely, a null result would place an upper limit f < 0.05 on the prevalence of such tightly bound planet–satellite pairs. This detection threshold is derived by integrating the geometric transit probability (∼0.5 % for Earth‑like orbits) with the additional probability that the mutual configuration yields a detectable brightening (∼10 % for β ≫ 1).

In summary, the study demonstrates that mutual transits imprint distinctive, measurable features on stellar light curves—namely ingress/egress asymmetry for widely separated companions and short‑duration flux increases for tightly bound pairs. By exploiting these signatures, observers can extract the radii, separation, and masses of both bodies, thereby distinguishing true binaries from planet–satellite systems. The method complements existing transit and radial‑velocity techniques, expands the parameter space for exomoon searches, and provides a statistically robust pathway to constrain the frequency of Earth‑Moon analogs in the Galaxy.