Strong Constraints on Superfluid Dark Matter from Milky Way Dynamics

Many well-known correlations between dark matter and baryons exist on galactic scales. These can essentially be encompassed by a simple scaling relation between observed and baryonic accelerations, historically known as the Mass Discrepancy Acceleration Relation (MDAR). This relation has prompted many theories that attempt to explain the correlations by invoking additional fundamental forces on baryons. Since a collisionless cold dark matter (CDM) model is desirable on scales of clusters and above, the standard lore has been that a theory which reduces to the MDAR on galaxy scales but behaves like CDM on larger scales provides an excellent fit to data. However, this statement should be revised in light of recent results showing that a fundamental force that reproduces the MDAR is often challenged at accommodating Milky Way dynamics. In this study, we test this claim on the  example of Superfluid Dark Matter. We find that a standard CDM model is strongly preferred over a static superfluid profile.  This is due to the fact that the superfluid model over-predicts vertical accelerations, even while reproducing galactic rotation curves.  Our results establish an important criterion that any dark matter model must satisfy within the Milky Way.