Transit probabilities in secularly evolving planetary systems

Abstract

This paper considers whether the population of known transiting exoplanets provides evidence for additional outer planets on inclined orbits, due to the perturbing effect of such planets on the orbits of inner planets. As such, we develop a semi-analytical method for calculating the probability that two mutually inclined planets are observed to transit. We subsequently derive a simplified analytical form to describe how the mutual inclination between two planets evolves due to secular interactions with a wide orbit inclined planet and use this to determine the mean probability that the two inner planets are observed to transit. From application to Kepler-48 and HD-106315 we constrain the inclinations of the outer planets in these systems (known from RV). We also apply this work to the so called Kepler Dichotomy, which describes the excess of single transiting systems observed by Kepler. We find 3 different ways of explaining this dichotomy: some systems could be inherently single, some multi-planet systems could have inherently large mutual inclinations, while some multi-planet systems could cyclically attain large mutual inclinations through interaction with an inclined outer planet. We show how the different mechanisms can be combined to fit the observed populations of Kepler systems with one and two transiting planets. We also show how the distribution of mutual inclinations of transiting two planet systems constrains the fraction of two planet systems that have perturbing outer planets, since such systems should be preferentially discovered by Kepler when the inner planets are coplanar due to an increased transit probability.

Long-period Jovian Tilts the Orbits of Two sub-Neptunes Relative to Stellar Spin Axis in Kepler-129

“…If the orbit of Kepler-129 d is inclined with respect to those of the inner planets, it could have imposed a torque on the inners and excited them out of the equatorial plane of the host star. In addition to exciting the spin-orbit angle, an inclined outer giant planet could also excite mutual inclinations between inner planets, possibly preventing them from transiting together (Becker & Adams 2017;Lai & Pu 2017;Read et al 2017). The fact that we observe both Kepler-129 b and c to be transiting places an additional constraint on the inclination of Kepler-129 d. In other words, the inclination of d must be large enough that a spin-orbit angle of ∼38°can be produced, while small enough that both planets b and c have a large probability of transiting together.…”

“…In order to quantify whether the simulated inner planets transit together as observed, we define the parameter doubletransit pprobability (DTP) for Kepler-129 b and c (e.g., Becker & Adams 2017; Read et al 2017). DTP is the fraction of time when two inner planets can both be observed to transit from any line of sight along their mutual ecliptic.…”

Shaping HR8799’s outer dust belt with an unseen planet

“…Nevertheless, the detection of wide orbit giant planets can place stringent constraints on the architecture of the inner planets (e.g. Becker & Adams 2016;Read & Wyatt 2016;Mustill et al 2016;Hansen 2017;Lai & Pu 2017;Read et al 2017), and the existence of unseen planets invoked to explain structure observed in debris belts (e.g. β Pic Lagrange et al 2009).…”

The signatures of the parental cluster on field planetary systems

“…They also point out, however, that dynamical evolution due to the outer planets alone is insufficient to explain the excess of Kepler 's single-transit systems. Read et al (2017) also suggest that single-transit systems may have inclined/non-transiting outer planets. On the other hand, a recent study by Izidoro et al (2017) suggests that when the gas disk is present, planetary embryos grow and migrate inward.…”