We study solitonic cores in the Thomas–Fermi regime of self-interacting scalar field dark matter (SI-SFDM) and assess whether strong gravitational lensing by galaxy clusters can detect or constrain them. We build composite halo profiles that join a solitonic core to an outer Navarro-Frenk-White (NFW) profile at fixed total mass, and compute their lensing signatures—the deflection angle and the excess surface mass density—for two halos of typical cluster scale, $M_{200}=2\times {10}^{15}$ and $2\times {10}^{14}{M}_{\odot }$. The soliton radius is fixed by the microphysics ($m$, ${\lambda }_4$), while its mass is not fixed by these parameters but is constrained by the halo mass budget. Lensing constrains only the radius, and hence the combination ${\lambda }_4/m^4$; combined with the independent bound on the self-interaction cross section, this places an indirect upper bound on the scalar field mass, $m\lesssim \mathrm{few}\times {10}^{-5}\mathrm{eV}$, and correspondingly ${\lambda }_4\sim {10}^{-18}$. Taking the NFW profile as reference, we quantify the deflection-angle difference produced by the soliton and confront our predictions with the cluster A2390 and with the stacked DES weak-lensing profile to assess when an SI-SFDM core can be distinguished from NFW.

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• Dark matter
• Gravitational lenses