Physical Properties of Spectroscopically-Confirmed Galaxies at z >= 6.
  I. Basic Characteristics of the Rest-Frame UV Continuum and Lyman-alpha
  emission
  We present deep HST near-IR and Spitzer mid-IR observations of a large sample
of spectroscopically-confirmed galaxies at z >= 6. The sample consists of 51
Lyman-alpha emitters (LAEs) at z ~ 5.7, 6.5, and 7.0, and 16 Lyman-break
galaxies (LBGs) at 5.9 < z < 6.5. The near-IR images were mostly obtained with
WFC3 in the F125W and F160W bands, and the mid-IR images were obtained with
IRAC in the 3.6um and 4.5um bands. Our galaxies also have deep optical imaging
data from Subaru Suprime-Cam. We utilize the multi-band data and secure
redshifts to derive their rest-frame UV properties. These galaxies have steep
UV continuum slopes roughly between beta ~ -1.5 and -3.5, with an average value
of beta ~ -2.3, slightly steeper than the slopes of LBGs in previous studies.
The slope shows little dependence on UV continuum luminosity except for a few
of the brightest galaxies. We find a statistically significant excess of
galaxies with slopes around beta ~ -3, suggesting the existence of very young
stellar populations with extremely low metallicity and dust content. Our
galaxies have moderately strong rest-frame Lyman-alpha equivalent width (EW) in
a range of ~10 to ~200 \AA. The star-formation rates are also moderate, from a
few to a few tens solar masses per year. The LAEs and LBGs in this sample share
many common properties, implying that LAEs represent a subset of LBGs with
strong Lyman-alpha emission. Finally, the comparison of the UV luminosity
functions between LAEs and LBGs suggests that there exists a substantial
population of faint galaxies with weak Lyman-alpha emission (EW < 20 \AA) that
could be the dominant contribution to the total ionizing flux at z >= 6.
