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Na I D absorbing systems toward Type Ia supernovae (SNe Ia) have beenintensively studied over the last decade with the aim of finding circumstellarmaterial (CSM), which is an indirect probe of the progenitor system. However,it is difficult to deconvolve CSM components from non-variable, and oftendominant, components created by interstellar material (ISM). We present aseries of high-resolution spectra of SN Ia 2014J from before maximum brightnessto ~250 days after maximum brightness. The late-time spectrum provides uniqueinformation for determining the origin of the Na I D absorption systems. Thedeep late-time observation allows us to probe the environment around the SN ata large scale, extending to ~40 pc. We find that a spectrum of diffuse light inthe vicinity, but not directly in the line-of-sight, of the SN has absorbingsystems nearly identical to those obtained for the "pure" SN line-of-sight.Therefore, basically all Na I D systems seen toward SN 2014J must originatefrom foreground material that extends to at least ~40 pc in projection and noneat the CSM scale. A fluctuation in the column densities at a scale of ~20 pc isalso identified. After subtracting the diffuse, "background" spectrum, thelate-time SN Na I D profile along the SN line-of-sight is consistent with theprofile in the near-maximum brightness spectra. The lack of variability on a ~1year timescale is consistent with the ISM interpretation for the gas.

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