# Eccentric Companions to Kepler-448b and Kepler-693b: Clues to the Formation of Warm Jupiters

## TL;DR

This paper reports the discovery of non-transiting companions to two warm Jupiters, Kepler-448b and Kepler-693b, using transit timing and duration variations, providing insights into their formation and migration processes.

## Contribution

It presents the first detection of massive, eccentric, non-transiting companions to warm Jupiters via dynamical modeling of TTVs and TDVs, suggesting possible in situ formation or high-eccentricity migration.

## Key findings

- Companions have masses of 22 and 150 Jupiter masses.
- Both companions are on eccentric orbits with high eccentricities.
- Mutual inclinations suggest potential eccentricity oscillations affecting migration.

## Abstract

I report the discovery of non-transiting close companions to two transiting warm Jupiters (WJs), Kepler-448/KOI-12b (orbital period $P=17.9\,\mathrm{days}$, radius $R_{\rm p}=1.23^{+0.06}_{-0.05}\,R_{\rm Jup}$) and Kepler-693/KOI-824b ($P=15.4\,\mathrm{days}$, $R_{\rm p}=0.91\pm0.05\,R_{\rm Jup}$), via dynamical modeling of their transit timing and duration variations (TTVs and TDVs). The companions have masses of $22^{+7}_{-5}\,M_{\rm Jup}$ (Kepler-448c) and $150^{+60}_{-40}\,M_{\rm Jup}$ (Kepler-693c), and both are on eccentric orbits ($e=0.65^{+0.13}_{-0.09}$ for Kepler-448c and $e=0.47^{+0.11}_{-0.06}$ for Kepler-693c) with periastron distances of $1.5\,\mathrm{au}$. Moderate eccentricities are detected for the inner orbits as well ($e=0.34^{+0.08}_{-0.07}$ for Kepler-448b and $e=0.2^{+0.2}_{-0.1}$ for Kepler-693b). In the Kepler-693 system, a large mutual inclination between the inner and outer orbits ($53^{+7}_{-9}\,\mathrm{deg}$ or $134^{+11}_{-10}\,\mathrm{deg}$) is also revealed by the TDVs. This is likely to induce a secular oscillation of the inner WJ's eccentricity that brings its periastron close enough to the host star for tidal star-planet interactions to be significant. In the Kepler-448 system, the mutual inclination is weakly constrained and such an eccentricity oscillation is possible for a fraction of the solutions. Thus these WJs may be undergoing tidal migration to become hot Jupiters (HJs), although the migration via this process from beyond the snow line is disfavored by the close-in and massive nature of the companions. This may indicate that WJs can be formed in situ and could even evolve into HJs via high-eccentricity migration inside the snow line.