The Local Group galaxy M33 exhibits a regular spiral structure and is close enough to permit high resolution analysis of its kinematics , making it an ideal candidate for rotation curve studies of its inner regions .
Previous studies have claimed the galaxy has a dark matter halo with an NFW profile , based on statistical comparisons with a small number of other profiles .
We apply a Bayesian method from our previous paper to place the dark matter density profile in the context of a continuous , and more general , parameter space .
For a wide range of initial assumptions we find that models with inner log slope \gamma _ { in } < 0.9 are strongly excluded by the kinematics of the galaxy unless the mass-to-light ratio of the stellar components in the 3.6 \mu m band satisfies \Upsilon _ { 3.6 } \geq 2 .
Such a high \Upsilon _ { 3.6 } is inconsistent with current modelling of the stellar population of M33 .
This suggests that M33 is a galaxy whose dark matter halo has not been significantly modified by feedback .
We discuss possible explanations of this result , including ram pressure stripping during earlier interactions with M31 .