Sodium Absorption Systems towards SN Ia 2014J Originate on Interstellar Scales

Na I. D absorbing systems toward Type Ia supernovae (SNe Ia) have been intensively studied over the last decade with the aim of finding circumstellar material (CSM), which is an indirect probe of the progenitor system. However, it is difficult to deconvolve CSM components from non-variable, and often dominant, components created by interstellar material (ISM). We present a series of high-resolution spectra of SN. Ia. 2014J from before maximum brightness to greater than or similar to 250. days after maximum brightness. The late-time spectrum provides unique information for determining the origin of the Na I. D absorption systems. The deep late-time observation allows us to probe the environment around the SN at a large scale, extending to greater than or similar to 40 pc. We find that a spectrum of diffuse light in the vicinity, but not directly in the line of sight, of the SN has absorbing systems nearly identical to those obtained for the "pure" SN line of sight. Therefore, basically all Na I. D systems seen toward SN. 2014J must originate from foreground material that extends to at least similar to 40 pc in projection and none at the CSM scale. A fluctuation in the column densities at a scale of similar to 20 pc is also identified. After subtracting the diffuse, "background" spectrum, the late-time Na I. D profile along the SN line of sight is consistent with profiles near maximum brightness. The lack of variability on a similar to 1. year timescale is consistent with the ISM interpretation for the gas.