Origins of the UV continuum and Balmer emission lines in Little Red Dots: observational validation of dense gas envelope models enshrouding the AGN

We present a statistical study on the origins of the UV continuum and narrow/broad emission lines in little red dots (LRDs), presumably involving active galactic nuclei (AGNs). Leveraging all archived JWST/NIRSpec data, we build a sample of 27 spectroscopically-confirmed LRDs at $5<z_{\rm spec}<7.2$, by requiring broad H$\alpha$ emission, blue UV colors, V-shaped continua, and compact morphology. We define a control sample of 7 blue, compact, broad-line AGNs without red optical continua (hereafter little blue dots; LBDs), and examine correlations between rest UV and the narrow/broad H$\alpha$ luminosities in these populations. In LRDs, both narrow and broad H$\alpha$ components are tightly correlated with the UV continuum, and the luminosity ratios are consistent with those in young starburst galaxies. In contrast, the UV to broad H$\alpha$ ratios in LBDs closely match local unobscured AGNs and are statistically different from LRDs. The Ly$\alpha$ occurrence rates and strengths do not differ between LRDs and LBDs and are comparable to normal star-forming galaxies. These results are consistent with a scenario where the central BH in LRDs is enshrouded by a dense opaque gas envelope -- in this model, the UV continuum as well as narrow and even broad H$\alpha$ emissions are not powered by AGNs but predominantly by young massive stars surrounding the envelope, while the envelope radiates as a $\sim 5000$ K blackbody. As the envelope dissipates, direct AGN emission can emerge, potentially transforming LRDs into LBDs and marking the end of a short-lived phase of rapid black hole growth.