Ultraviolet diversity of Little Red Dots as a probe for direct-collapse black hole ages

Little Red Dots (LRDs) uncovered by the James Webb Space Telescope have been proposed as candidate galaxies hosting embedded accreting direct-collapse black holes (DCBHs), yet the relative ultraviolet (UV) emission of their host galaxy remains highly uncertain and diverse across the population. Using a large-scale cosmological hydrodynamical simulation from the MELI\(\odot\)RA suite, we investigate the contribution of PopIII stars and accreting DCBHs in LRD candidates at \(z>8.5\), in the rest-frame \(0.2-0.6~\mu\mathrm{m}\) band. We find that the UV emission from the host galaxy evolves rapidly over the first \(\sim 30~\mathrm{Myr}\) following DCBH formation, reflecting the build-up of stellar mass and metal enrichment. This evolution consists of a rapid transition from initially BH-dominated systems, with negligible stellar mass, low metallicity, and high accretion rates, to progressively more developed hosts in which rapid star formation enhances the UV output and metallicity increases. After \(\sim 30~\mathrm{Myr}\), the stellar continuum typically overwhelms the accreting DCBH contribution, producing bluer colours and more extended stellar distributions. As a result, UV-bright LRDs are predicted to host older DCBHs, have higher gas-phase metallicities, lower BH-to-stellar mass ratios, and lower Eddington ratios. The short-lived nature of the LRD phase places strong constraints on their emergence over cosmic time. Overall, our results suggest that DCBH ages can be constrained from the host galaxy contribution to the UV-optical spectrum of LRDs, relative to that of the accreting DCBH, and support the picture in which a DCBH evolutionary sequence is systematically encoded in emission line properties, gas-phase metallicities, and accretion states.