The Century Survey Galactic Halo Project III: A Complete 4300 deg^2 Survey of Blue Horizontal Branch Stars in the Metal-Weak Thick Disk and Inner Halo

We present a complete spectroscopic survey of 2414 2MASS-selected blue horizontal branch (BHB) candidates selected over 4300 deg^2 of the sky. We identify 655 BHB stars in this non-kinematically selected sample. We calculate the luminosity function of field BHB stars and find evidence for very few hot BHB stars in the field. The BHB stars located at a distance from the Galactic plane |Z|<4 kpc trace what is clearly a metal-weak thick disk population, with a mean metallicity of [Fe/H]= -1.7, a rotation velocity gradient of dv_{rot}/d|Z|= -28+-3.4 km/s in the region |Z|<6 kpc, and a density scale height of h_Z= 1.26+-0.1 kpc. The BHB stars located at 5<|Z|<9 kpc are a predominantly inner-halo population, with a mean metallicity of [Fe/H]= -2.0 and a mean Galactic rotation of -4+-31 km/s. We infer the density of halo and thick disk BHB stars is 104+-37 kpc^-3 near the Sun, and the relative normalization of halo to thick-disk BHB stars is 4+-1% near the Sun.