  The O9IV star HD 57682, discovered to be magnetic within the context of the
MiMeS survey in 2009, is one of only eight convincingly detected magnetic
O-type stars. Among this select group, it stands out due to its sharp-lined
photospheric spectrum. Since its discovery, the MiMeS Collaboration has
continued to obtain spectroscopic and magnetic observations in order to refine
our knowledge of its magnetic field strength and geometry, rotational period,
and spectral properties and variability. In this paper we report new ESPaDOnS
spectropolarimetric observations of HD 57682, which are combined with
previously published ESPaDOnS data and archival H{\alpha} spectroscopy. This
dataset is used to determine the rotational period (63.5708 \pm 0.0057 d),
refine the longitudinal magnetic field variation and magnetic geometry (dipole
surface field strength of 880\pm50 G and magnetic obliquity of 79\pm4\circ as
measured from the magnetic longitudinal field variations, assuming an
inclination of 60\circ), and examine the phase variation of various lines. In
particular, we demonstrate that the H{\alpha} equivalent width undergoes a
double-wave variation during a single rotation of the star, consistent with the
derived magnetic geometry. We group the variable lines into two classes: those
that, like H{\alpha}, exhibit non-sinusoidal variability, often with multiple
maxima during the rotation cycle, and those that vary essentially sinusoidally.
Based on our modelling of the H{\alpha} emission, we show that the variability
is consistent with emission being generated from an optically thick, flattened
distribution of magnetically-confined plasma that is roughly distributed about
the magnetic equator. Finally, we discuss our findings in the magnetospheric
framework proposed in our earlier study.
