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Recent analysis of the rotation curves of a large sample of galaxies withvery diverse stellar properties reveal a relation between the radialacceleration purely due to the baryonic matter and the one inferred directlyfrom the observed rotation curves. Assuming the dark matter (DM) exists, thisacceleration relation is tantamount to an acceleration relation between DM andbaryons. This leads us to a universal maximum acceleration for all halos. Usingthe latter in DM profiles that predict inner cores implies that the centralsurface density $\mu_{DM} = \rho_s r_s$ must be a universal constant, assuggested by previous studies in selected galaxies, revealing a strongcorrelation between the density $\rho_s$ and scale $r_s$ parameters in eachprofile. We then explore the consequences of the constancy of $\mu_{DM}$ in thecontext of the ultra-light scalar field dark matter model (SFDM). We find thatfor this model $\mu_{DM} = 648 \, M_\odot {\rm pc}^{-2}$, and that theso-called WaveDM soliton profile should be an universal feature of the DMhalos. Comparing with data from the Milky Way and Andromeda satellites, we findthat they are consistent with a boson mass of the scalar field particle of theorder of $10^{-21} \, {\rm eV}/c^2$, which puts the SFDM model in agreementwith recent cosmological constraints.

physical review. d/physical review. d.

The mass discrepancy-acceleration relation: a universal maximum dark  matter acceleration and implications for the ultra-light scalar field dark  matter model