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The Afterglow and Early-Type Host Galaxy of the Short GRB 150101B at z=0.1343

We present the discovery of the X-ray and optical afterglows of the short-duration GRB 150101B, pinpointing the event to an early-type host galaxy at z=0.1343 +/- 0.0030. This makes GRB 150101B the most nearby short GRB with an early-type host galaxy discovered to date. Fitting the spectral energy distribution of the host galaxy results in an inferred stellar mass of ~7x10^10 M_sol, stellar population age of ~2-2.5 Gyr, and star formation rate of <0.4 M_sol yr^-1. The host of GRB 150101B is one of the largest and most luminous short GRB host galaxies, with a B-band luminosity of ~4.3L* and half-light radius of ~8 kpc. GRB 150101B is located at a projected distance of 7.35 +/- 0.07 kpc from its host center, and lies on a faint region of its host rest-frame optical light. Its location, combined with the lack of associated supernova, is consistent with a NS-NS/NS-BH merger progenitor. From modeling the evolution of the broad-band afterglow, we calculate isotropic-equivalent gamma-ray and kinetic energies of ~1.3x10^49 erg and ~(6-14)x10^51 erg, respectively, a circumburst density of ~(0.8-4)x10^-5 cm^-3, and a jet opening angle of >9 deg. Using observations extending to ~30 days, we place upper limits of <(2-4)x10^41 erg s^-1 on associated kilonova emission. We compare searches following previous short GRBs to existing kilonova models, and demonstrate the difficulty of performing effective kilonova searches from cosmological short GRBs using current ground-based facilities. We show that at the Advanced LIGO/VIRGO horizon distance of 200 Mpc, searches reaching depths of ~23-24 AB mag are necessary to probe a meaningful range of kilonova models.