Kepler and the Behemoth: Three Mini-Neptunes in a 40 Million Year Old
  Association
  Stellar positions and velocities from Gaia are yielding a new view of open
cluster dispersal. Here we present an analysis of a group of stars spanning
Cepheus to Hercules, hereafter the Cep-Her complex. The group includes four
Kepler Objects of Interest: Kepler-1643 b ($2.32 \pm 0.14$ Earth-radii, 5.3 day
orbital period), KOI-7368 b ($2.22 \pm 0.12$ Earth-radii, 6.8 days), KOI-7913
Ab ($2.34 \pm 0.18$ Earth-radii, 24.2 days), and Kepler-1627 Ab ($3.85 \pm
0.11$ Earth-radii, 7.2 days). The latter Neptune-sized planet is in part of the
Cep-Her complex called the $\delta$ Lyr cluster (Bouma et al. 2022). Here we
focus on the former three systems, which are in other regions of the
association. Based on kinematic evidence from Gaia, stellar rotation periods
from TESS, and spectroscopy, these three objects are also approximately 40
million years (Myr) old. More specifically, we find that Kepler-1643 is
$46^{+9}_{-7}$ Myr old, based on its membership in a dense sub-cluster of the
complex called RSG-5. KOI-7368 and KOI-7913 are $36^{+10}_{-8}$ Myr old, and
are in a diffuse region that we call CH-2. Based on the transit shapes and high
resolution imaging, all three objects are most likely planets, with false
positive probabilities of $6 \times 10^{-9}$, $4 \times 10^{-3}$, and $1 \times
10^{-4}$ for Kepler-1643, KOI-7368, and KOI-7913 respectively. These planets
demonstrate that mini-Neptunes with sizes of approximately 2 Earth radii exist
at ages of 40 million years.
