  Context: The complex system HD 100453 AB with a ring-like circumprimary disk
and two spiral arms, one of which is pointing to the secondary, is a good
laboratory to test spiral formation theories. Aims: To quantify the interaction
of HD 100453 B with the circumprimary disk. Methods: Using ALMA band 6 dust
continuum and CO isotopologue observations we study the HD 100453 AB system
with a spatial resolution of 0.09" x 0.17" at 234 GHz. We use SPH simulations
and orbital fitting to investigate the tidal influence of the companion on the
disk. Results: We resolve the continuum emission around HD 100453 A into a disk
between 0.22" and 0.40" with an inclination of 29.5 deg. and a position angle
of 151.0 deg., an unresolved inner disk, and excess mm emission cospatial with
the northern spiral arm which was previously detected using scattered light
observations. We also detect CO emission from 7 au (well within the disk
cavity) out to 1.10", i.e., overlapping with HD 100453 B at least in
projection. The outer CO disk PA and inclination differ by up to 10 deg. from
the values found for the inner CO disk and the dust continuum emission, which
we interpret as due to gravitational interaction with HD 100453 B. Both the
spatial extent of the CO disk and the detection of mm emission at the same
location as the northern spiral arm are in disagreement with the previously
proposed near co-planar orbit of HD 100453 B. Conclusions: We conclude that HD
100453 B has an orbit that is significantly misaligned with the circumprimary
disk. Because it is unclear whether such an orbit can explain the observed
system geometry we highlight an alternative scenario that explains all detected
disk features where another, (yet) undetected, low mass close companion within
the disk cavity, shepherds a misaligned inner disk whose slowly precessing
shadows excite the spiral arms.
