  The paper aims to consider the electromagnetic adjoint-field in the complex
octonion space as the dark matter field, describing some properties of dark
matter, especially the origin, particle category, existence region, and force
and so forth. Since J. C. Maxwell applied the algebra of quaternions to depict
the electromagnetic theory, some scholars adopt the complex quaternion and
octonion to study the physics property of electromagnetic and gravitational
fields. In the paper, by means of the octonion operator, it is found that the
gravitational field accompanies with one adjoint-field, which property is
partly similar to that of electromagnetic field. And the electromagnetic field
accompanies with another adjoint-field, which feature is partly similar to that
of gravitational field. As a result the electromagnetic adjoint-field is able
to be chosen as one candidate of the dark matter field. According to the
electromagnetic adjoint-field, it is able to predict a few properties of dark
matter, for instance, the particle category, interaction intensity, interaction
distance, and existence region and so forth. The study reveals that the dark
matter particle and gravitational resource both will be influenced by the
gravitational strength and force. The dark matter field is capable of making a
contribution to physics quantities of gravitational field, including the
angular momentum, torque, energy, and force and so on. Further there may be
comparatively more chances to discover the dark matter in some regions with the
ultrastrong field strength, surrounding the neutral star, white dwarf, galactic
nucleus, black hole, and astrophysical jet and so on.
