Little red dots as obscured little blue dots: relative abundances, luminosities, and black-hole masses

We test whether ``little red dots'' (LRDs) are the dust-reddened, high-inclination counterparts of bluer compact broad-line active galactic nuclei, here referred to as ``little blue dots'' (LBDs), by modeling their relative number densities and luminosities. Using the observed UV luminosity function (LF) of broad-line active galactic nuclei (BLAGNs) at z>4 as the parent distribution, we forward-model the effects of accretion rate, anisotropic emission, orientation, and dust obscuration within our super-Eddington unification framework. We show that a model with a geometrically thick accretion flow, an equatorially concentrated broad-line region, and a dusty circumnuclear cloud population reproduces the LRD LF over the luminosity range currently constrained by JWST. The predicted LRD/BLAGN fraction is strongly luminosity dependent, rising from 3% at M_1500=-21 to a peak value of 20% near M_1500=-19. The model also predicts a larger apparent LRD fraction at rest-frame optical wavelengths, reaching 26% at M_4500=-20 mag and 35% at M_6500=-21. The best-fitting solutions imply a characteristic per-cloud extinction <A_V>=2.8^{+0.0}_{-0.4} mag and a mean dust covering factor <C_dust>= 0.23^{+0.27}_{-0.00} at 68% confidence, with the asymmetric uncertainties reflecting the degeneracy between cloud extinction and covering factor. These results may support an orientation-based unification of little dots and identify the LRD LF as a key demographic test of rapid accretion onto infant black holes at cosmic dawn. Within this same framework, UV-selected LRDs are predicted to host systematically more massive black holes than unobscured LBDs, not because they represent a distinct parent population, but because dust attenuation preferentially removes lower-mass obscured systems from the observed UV sample.