Extended main-sequence turnoffs in the double cluster $h$ and $\chi$
  Persei: The complex role of stellar rotation
  Using {\sl Gaia} Data Release 2 photometry, we report the detection of
extended main-sequence turnoff (eMSTO) regions in the color--magnitude diagrams
(CMDs) of the $\sim 14$ Myr-old double clusters $h$ and $\chi$ Persei (NGC 869
and NGC 884). We find that stars with masses below $\sim$1.3 $M_{\odot}$ in
both $h$ and $\chi$ Persei populate narrow main sequences (MSs), while more
massive stars define the eMSTO, closely mimicking observations of young
Galactic and Magellanic Cloud clusters (with ages older than $\sim$30 Myr).
Previous studies based on clusters older than $\sim$30 Myr find that rapidly
rotating MS stars are redder than slow rotators of similar luminosity,
suggesting that stellar rotation may be the main driver of the eMSTO. By
combining photometry and projected rotational velocities from the literature of
stars in $h$ and $\chi$ Persei, we find no obvious relation between the
rotational velocities and colors of non-emission-line eMSTO stars, in contrast
with what is observed in older clusters. Similarly to what is observed in
Magellanic Cloud clusters, most of the extremely rapidly rotating stars,
identified by their strong H$\alpha$ emission lines, are located in the red
part of the eMSTOs. This indicates that stellar rotation plays a role in the
color and magnitude distribution of MSTO stars. By comparing the observations
with simulated CMDs, we find that a simple population composed of coeval stars
that span a wide range of rotation rates is unable to reproduce the color
spread of the clusters' MSs. We suggest that variable stars, binary
interactions, and stellar rotation affect the eMSTO morphology of these very
young clusters.
