  It is well known that the polarized continuum emission from magnetically
aligned dust grains is determined to a large extent by local magnetic field
structure. However, the observed significant anticorrelation between
polarization fraction and column density may be strongly affected, perhaps even
dominated by variations in grain alignment efficiency with local conditions, in
contrast to standard assumptions of a spatially homogeneous grain alignment
efficiency. Here we introduce a generic way to incorporate heterogeneous grain
alignment into synthetic polarization observations of molecular clouds, through
a simple model where the grain alignment efficiency depends on the local gas
density as a power-law. We justify the model using results derived from
radiative torque alignment theory. The effects of power-law heterogeneous
alignment models on synthetic observations of simulated molecular clouds are
presented. We find that the polarization fraction-column density correlation
can be brought into agreement with observationally determined values through
heterogeneous alignment, though there remains degeneracy with the relative
strength of cloud-scale magnetized turbulence and the mean magnetic field
orientation relative to the observer. We also find that the dispersion in
polarization angles-polarization fraction correlation remains robustly
correlated despite the simultaneous changes to both observables in the presence
of heterogeneous alignment.
