Physical Properties of Spectroscopically-Confirmed Galaxies at z >= 6. I. Basic Characteristics from Deep HST and Spitzer Observations

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 majority of them were discovered in the Subaru Deep Field. They have extremely deep optical imaging data in a series of broad and narrow bands taken with Subaru Suprime-Cam. The near-IR images were mostly obtained from WFC3 with a typical depth of two HST orbits in the F125W and F160W bands. The Spitzer mid-IR images have a depth of 3 ~ 6 hrs in IRAC channels 1 and 2. We utilize the wealth of the multi-band data and the secure redshifts to derive the properties of their rest-frame UV continuum and Lyman-alpha emission. These galaxies have steep UV continuum slopes roughly between beta ~ -1.5 and -3.5, with a median value of beta ~ -2.3, which is slightly steeper than the slopes of photometrically-selected LBGs reported 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 ~300 \AA. The star-formation rates derived from the Lyman-alpha and UV continuum luminosities 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, we derive the UV luminosity functions (LFs) of LAEs with EW > 20 \AA\ at z ~ 5.7 and 6.5, and compare them with the UV LFs of LBGs at similar redshifts. [abridged].