On the mass of ultra-light bosonic dark matter from galactic dynamics

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We consider the hypothesis that galactic dark matter is composed of ultra-light scalar particles and use internal properties of dwarf spheroidal galaxies to establish a preferred range for the mass m of these bosonic particles. We re-investigate the problem of the longevity of the cold clump in Ursa Minor and the problem of the rapid orbital decay of the globular clusters in Fornax and dwarf ellipticals. Treating the scalar field halo as a rigid background gravitational potential and using N-body simulations, we have explored how the dissolution timescale of the cold clump in Ursa Minor depends on m. It is demonstrated that for masses in the range 0.3x10-22 eV < m <1x10-22 eV, scalar field dark halos without self-interaction would have cores large enough to explain the longevity of the cold clump in Ursa Minor and the wide distribution of globular clusters in Fornax, but small enough to make the mass of the dark halos compatible with dynamical limits. It is encouraging to see that this interval of m is consistent with that needed to suppress the overproduction of substructure in galactic halos and is compatible with the acoustic peaks of cosmic microwave radiation. On the other hand, for self-interacting scalar fields with coupling constant l, values of m⁴/l <= 0.55x10³ eV⁴ are required to account for the properties of the dark halos of these dwarf spheroidal galaxies.