Scalar-Assisted Growth of Supermassive Black Holes: Boson-Mass Windows and Observational Constraints

We study a phenomenological cosmological model of black-hole growth in which a finite baryonic reservoir and a bosonic scalar cloud feed the black hole simultaneously. The baryonic component accretes through an Eddington-like channel, while the scalar cloud transfers mass through an effective quasibound-state decay rate. Evolving the system directly in redshift within a flat $\mathrm{\Lambda }$CDM background, we scan over $\mu$, $M_0$, $M_{c,0}$, and $M_{b,0}$ to assess whether scalar-assisted accretion can accelerate the formation of ${10}^9{M}_{\odot }$ supermassive black holes. We find that the scalar contribution is highly selective in parameter space. For the mass scales explored here, scalar transfer is most efficient for $\mu \sim {10}^{-19}-{10}^{-16}\mathrm{e}\mathrm{V}$, producing rapid cloud depletion and significantly earlier black-hole growth, while outside this interval the evolution remains mainly baryonic. More generally, this efficient window reflects a preferred range of the dimensionless coupling $\alpha =\mu M_{\mathrm{B}\mathrm{H}}$ and therefore shifts approximately as $\mu \propto M_{\mathrm{B}\mathrm{H}}^{-1}$. Comparison with observed quasar masses and luminosities instead favors lower boson masses, broadly around $\mu \sim {10}^{-21}-{10}^{-20}\mathrm{e}\mathrm{V}$. These results are not necessarily in tension, since the boson mass that maximizes early growth depends on the characteristic black-hole mass and evolutionary stage. This separation between dynamical efficiency and observational compatibility leaves open complementary roles for different bosonic mass scales in supermassive black hole growth and dark-matter phenomenology.