Multiple stellar populations at less evolved stages-II: no evidence of
  significant helium spread among NGC 1846 dwarfs
  The detection of star-to-star chemical variations in star clusters older than
2 Gyr has changed the traditional view of star clusters as canonical examples
of "simple stellar populations" (SSPs) into the so-called "multiple stellar
populations" (MPs). Although the significance of MPs seems to correlate with
cluster total mass, it seems that the presence of MPs is determined by cluster
age, however. In this article, we use deep photometry from the Hubble Space
Telescope to investigate whether the FG-type dwarfs in the $\sim$1.7 Gyr-old
cluster NGC 1846, have helium spread. By comparing the observation with the
synthetic stellar populations, we estimate a helium spread of
$\Delta{Y}\sim0.01\pm0.01$ among the main-sequence stars in NGC 1846. The
maximum helium spread would not exceed $\Delta{Y}\sim0.02$, depending on the
adopted fraction of helium-enriched stars. To mask the color variation caused
by such a helium enrichment, a nitrogen enrichment of at least $\Delta{\rm
[N/Fe]}$=0.8 dex is required, which is excluded by previous analyses of the
red-giant branch in this cluster. We find that our result is consistent with
the $\Delta{Y}$--mass relationship for Galactic globular clusters. To examine
whether or not NGC 1846 harbors MPs, higher photometric accuracy is required.
We conclude that under the adopted photometric quality, there is no extreme
helium variation among NGC 1846 dwarfs.
