Abstract
We show that ultra-light scalar dark matter (fuzzy dark matter) in galaxies has a quantum mechanical typical acceleration scale about 10−10ms−2, which leads to the baryonic Tully-Fisher relation. Baryonic matter at central parts of galaxies acts as a boundary condition for dark matter wave equation and influences stellar rotation velocities in halos. Without any modification of gravity or mechanics this model also explains the radial acceleration relation and MOND-like behavior of gravitational acceleration found in galaxies having flat rotation curves. This analysis can be extended to the Faber-Jackson relation.
Highlights
The baryonic Tully-Fisher relation (BTFR) [1] is a tight empirical correlation between the total baryonic mass (Mb) of a disk galaxy and its asymptotic rotation velocity vf ; Mb ∼ vf4
Semi-analytic models for BTFR based on baryonic processes in a cold dark matter (CDM) cosmology predict significant scatter from individual galaxy formation history, but observed BTFR is largely independent of baryonic processes and has small scatter [2]
There are models [4] based on CDM paradigm explaining radial acceleration relation (RAR), but it is unclear whether this tight relation can survive chaotic processes of galaxy formation and mergering
Summary
The baryonic Tully-Fisher relation (BTFR) [1] is a tight empirical correlation between the total baryonic mass (Mb) of a disk galaxy and its asymptotic rotation velocity vf ; Mb ∼ vf4. 300pc that ξ to be is not the typical a constant mass and the size of the core of but almost independent of other properties of the galaxy except for Mc. We suggest that ξ and the uncertainty principle lead to a natural acceleration scale g† = GMc/ξ2 ≃ 2/m2ξ3 ≃ O(10−10)ms−2 of SFDM.
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