Physical Properties of Spectroscopically-Confirmed Galaxies at $z\ge6$.
  III. Stellar Populations from SED Modeling with Secure Ly$\alpha$ Emission
  and Redshifts
  We present a study of stellar populations in a sample of
spectroscopically-confirmed Lyman-break galaxies (LBGs) and Ly$\alpha$ emitters
(LAEs) at $5.7<z<7$. These galaxies have deep optical and infrared images from
Subaru, $HST$, and $Spitzer$/IRAC. We focus on a subset of 27 galaxies with
IRAC detections, and characterize their stellar populations utilizing galaxy
synthesis models based on the multi-band data and secure redshifts. By
incorporating nebular emission estimated from the observed Ly$\alpha$ flux, we
are able to break the strong degeneracy of model spectra between young galaxies
with prominent nebular emission and older galaxies with strong Balmer breaks.
The results show that our galaxies cover a wide range of ages from several to a
few hundred million years (Myr), and a wide range of stellar masses from
$\sim10^8$ to $\sim10^{11}$ $M_{\odot}$. These galaxies can be roughly divided
into an `old' subsample and a `young' subsample. The `old' subsample consists
of galaxies older than 100 Myr, with stellar masses higher than $10^9$
$M_{\odot}$. The galaxies in the `young' subsample are younger than $\sim$30
Myr, with masses ranging between $\sim10^8$ and $\sim3\times10^9$ $M_{\odot}$.
Both subsamples display a correlation between stellar mass and star-formation
rate (SFR), but with very different normalizations. The average specific SFR
(sSFR) of the `old' subsample is 3--4 Gyr$^{-1}$, consistent with previous
studies of `normal' star-forming galaxies at $z\ge6$. The average sSFR of the
`young' subsample is an order of magnitude higher, likely due to starburst
activity. Our results also indicate little or no dust extinction in the
majority of the galaxies, as already suggested by their steep rest-frame UV
slopes. Finally, LAEs and LBGs with strong Ly$\alpha$ emission are
indistinguishable in terms of age, stellar mass, and SFR.
