Very High-energy Gamma-ray Emission from LS I +61$^\circ$ ~303 Binary

LS I +61$^\circ$ ~303 is one of around ten gamma-ray binaries detected so far which has a spectral energy distribution dominated by MeV-GeV photons. It is located at a distance of 2 kpc and consists of a compact object (black hole or neutron star) in an eccentric orbit around a 10-15 $M_{\odot}$ Be star, with an orbital period of 26.496 days. The binary orbit modulates the emission ranging from radio to TeV energies. A second, longer, modulation period of 1667 days (the super-orbital period) has also been detected from radio to TeV observations. The VERITAS imaging atmospheric Cherenkov telescope array has been observing LS I +61$^\circ$ ~303 since 2006, and has accumulated a dataset that fully covers the entire orbit. Increased coverage of the source in the very-high-energy band is currently underway to provide more results on the modulation pattern, super-orbital period, and orbit-to-orbit variability at the highest energies. The spectral measurements at the highest energies will reveal more information about gamma-ray production/absorption mechanisms, the nature of the compact object, and the particle acceleration mechanism. Using >150 hrs of VERITAS data, we present a detailed study of the spectral energy distribution and periodic behavior of this rare gamma-ray source type at very-high energy.