ATLAS. I. A Scaling Relation of LRDs between Broad H alpha and Bolometric Luminosities: Enhanced Broad H alpha Emission Relative to Low- z Type 1 AGN

We investigate the demography of little red dots (LRDs) using 37 objects at z about3 - 7 with JWST/NIRSpec PRISM and grating spectra compiled from various JWST programs. We focus on spectroscopic quantities of the broad H α luminosity L Hα,broad (and the broad H β luminosity L Hβ,broad where available) and the bolometric luminosity L bol represented by modified blackbody emission, avoiding quantities contaminated by host-galaxy emission (e.g., total H α luminosity). We identifiy a tight scaling relation between L Hα,broad and L bol, supporting the interpretation that these emissions are primarily powered by the central engine. Interestingly, the L Hα,broad - L bol scaling relation of LRDs is enhanced by a factor of about40 in L Hα,broad relative to that of low- z Type 1 AGN. A similar trend is found in the L Hβ,broad - L bol relation, although the enhancement in L Hβ,broad is smaller, only by a factor of about10. We explore the physical origin of these enhancements and find that Cloudy photoionization modeling within the classic locally optimally-emitting cloud (LOC) framework can explain them through an increase in the covering factor from about20 % (Type 1 AGN) to about100 % (LRDs), together with an increase in the hydrogen column density from N H about10 23, cm-2 to 10 24, cm-2, with a preferred gas density of about10 10, cm-3, successfully reproducing the modified blackbody emission. Such a nearly unity covering factor without requiring a gas density increase may result from a significant increase in the BLR filling factor or size, corresponding to a ``stuffed BLR" or ``giant BLR," respectively.