Little Red and Blue Dots: AGN-excited narrow lines, Lyman-$\alpha$ emission, and resemblance to standard quasars

We present an analysis of a sample of 36 Little Red and Blue Dots (LRDs and LBDs) at $2.26<z<7.89$, identified by JWST in the GOODS fields. While both categories are selected to have broad Balmer lines, both of them are extremely X-ray weak. Both classes share the same location on various diagnostic diagrams, consistent with AGN excitation (with some deviations which can be ascribed to low metallicity), although their weak HeII emission suggests a generally softer ionizing spectrum than ordinary AGN. LRDs display Ly$\alpha$ emission stronger than normal star-forming galaxies, and with a broad component consistent with the broad component of H$\alpha$. Overall, these findings indicate that LRDs and LBDs are both powered by growing black holes and their ionizing radiation escapes to ionize the surrounding interstellar medium (ISM). The broad Balmer lines ($H\alpha_b$ and $H\beta_b$) have different apparent properties: LBDs have EW(H$\alpha _b$) and $H\alpha_b/H\beta_b$ broadly consistent with normal AGN, while LRDs have higher values of both quantities, although still in the tail of the quasars distribution. LRD models in which a gas envelope completely encases the black hole, are inconsistent with these results -- these scenarios need modification to include clumpiness, or a (classical) equatorial geometry, letting ionizing photons reach the ISM. The different broad Balmer properties imply that LBDs cannot simply be LRDs with more galaxy contribution. Scenarios in which LRDs are simply dust-obscured LBDs seem broadly consistent with the observations. Finally, these results indicate that LRDs' bolometric luminosities estimated assuming isotropic emission and complete covering by the absorber are inadequate. The few X-ray-detected LRDs suggest no deviation from the standard AGN bolometric corrections, once absorption is accounted for.