Title: Stacking X-ray Observations of "Little Red Dots": Implications for their AGN Properties

Abstract: Recent {\em James Webb Space Telescope (JWST)} observations have revealed a population of compact extragalactic objects at $z\gtrsim4$ with red near-infrared colors, which have been dubbed as ``Little Red Dots" (LRDs). The spectroscopically-selected LRDs exhibit broad H$\alpha$ emission lines, which has led to the conclusion that type-I active galactic nuclei (AGN) are harbored in the galaxies' dust-reddened cores. However, other mechanisms, like strong outflowing winds, could also produce broad H$\alpha$ emission lines, and thus, the nature of LRDs is still under debate. In this work, we test the AGN hypothesis for LRDs by stacking the archival {\em Chandra} observations of 19 spectroscopically-selected LRDs. We obtain non-detections in both the soft $(0.5-2\text{ keV})$ and the hard $(2-8\text{ keV})$ X-ray band after stacking, and put upper limits on the X-ray luminosities of these LRDs. We find that the soft band upper limit is $\sim1$ dex lower than the expected level from the $L_\text{X}-L_{\text{H}\alpha}$ relation, while the hard band upper limit is consistent with this relation. This result suggests that LRDs and typical type-I AGNs have significantly different properties. We consider it unlikely that absorption is the main reason for the observed low $L_\text{X}/L_{\text{H}\alpha}$ ratios of LRDs. Alternatively, we discuss two plausible hypotheses: (1) LRDs have intrinsically weak X-ray emissions, (2) fast, galactic-scale outflows have a major contribution to the observed broad H$\alpha$ lines. Our findings indicate that empirical relations (e.g., for black hole mass measurements) established for typical type-I AGNs should be used with caution when analyzing the properties of LRDs.