  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 ~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 ~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 ~40 pc in projection and none
at the CSM scale. A fluctuation in the column densities at a scale of ~20 pc is
also identified. After subtracting the diffuse, "background" spectrum, the
late-time SN Na I D profile along the SN line-of-sight is consistent with the
profile in the near-maximum brightness spectra. The lack of variability on a ~1
year timescale is consistent with the ISM interpretation for the gas.

Solar and Stellar Astrophysics