  In this paper we examine the profiles of the complex Na I D-lines in the Red
Rectangle. The spectra were acquired with the ARCES \'{e}chelle spectrograph R
= 38,000 on the 3.5-m telescope at the Apache Point Observatory. Additional
spectra taken with STIS were acquired from the Hubble Legacy Archive (HLA) and
were used to independently confirm the spatial origin of the spectral features.
The profile of a single D-line consists of double-peaked emission, red-shifted
absorption and blue-shifted absorption. We find that the double-peaked emission
originates from the bipolar outflow, the red-shifted absorption feature is due
to the photospheric line, and the blue-shifted absorption arises from the
bipolar outflow as seen against the photosphere of the luminous post-AGB
component in HD 44179. In order to better understand the Na I D-line profile,
we examined the periodically variable asymmetric photospheric absorption lines.
The asymmetric lines are interpreted as a signature of slow self-accretion
following enhanced mass-loss around periastron. An empirical model was
constructed to remove the photospheric component from the Na I D-line profile
in order to study the nebular emission and absorption of sodium along the
line-of-sight to the primary. This paper also discusses the different origins
of the single-peaked emission, the double-peaked emission and the blue-shifted
and red-shifted absorption components.
