  We report magnetic and spectroscopic observations and modeling of the Of?p
star CPD -28 2561. Using more than 75 new spectra, we have measured the
equivalent width variations and examined the dynamic spectra of photospheric
and wind-sensitive spectral lines. A period search results in an unambiguous
73.41 d variability period. High resolution spectropolarimetric data analyzed
using Least-Squares Deconvolution yield a Zeeman signature detected in the mean
Stokes V profile corresponding to phase 0.5 of the spectral ephemeris.
Interpreting the 73.41 d period as the stellar rotational period, we have
phased the equivalent widths and inferred longitudinal field measurements. The
phased magnetic data exhibit a weak sinusoidal variation, with maximum of about
565 G at phase 0.5, and a minimum of about -335 G at phase 0.0, with extrema
approximately in phase with the (double-wave) Halpha equivalent width
variation. Modeling of the Halpha equivalent width variation assuming a
quasi-3D magnetospheric model produces a unique solution for the ambiguous
couplet of inclination and magnetic obliquity angles: (i, beta) or (beta,
i)=(35 deg,90 deg). Adopting either geometry, the longitudinal field variation
yields a dipole polar intensity Bd=2.6\pm 0.9~kG, consistent with that obtained
from direct modelling of the Stokes V profiles. We derive a wind magnetic
confinement parameter eta*\simeq 100, leading to an Alfv\'en radius RA\simeq
3-5~R*, and a Kepler radius RK\simeq 20~R*. This supports a physical scenario
in which the Halpha emission and other line variability have their origin in an
oblique, co-rotating 'dynamical magnetosphere' structure resulting from a
magnetically channeled wind. Nevertheless, the details of the formation of
spectral lines and their variability within this framework remain generally
poorly understood.
