Xin Zhou, Ji Yang, Yang Su, Xuepeng Chen, Yang Chen, Yan Sun, Qing-Zeng Yan, Shaobo Zhang

We investigate the relationships between LHAASO TeV gamma-ray sources and various kinds of objects, including pulsar wind nebulae (PWNe), supernova remnants (SNRs), HII regions, microquasars, and OB associations. We propose a Randomization-Adjusted Overlap Correlation (RAOC) method to statistically assess association probabilities and evaluate association proportions across catalogs. The results reveal statistically significant overlaps between LHAASO sources and SNRs, PWNe, and microquasars, supporting their role as important contributors to TeV gamma-ray emission. The estimated association proportions of LHAASO sources are 0.19$\pm$0.08 with SNRs, 0.20$\pm$0.04 with PWNe, and 0.027$\pm$0.008 with microquasars. The proportion of the gamma-ray sources associated with the subsample of shell-type SNRs is ~0.1. While HII regions also show potential association, particularly with the KM2A component, their large self-overlap ratio complicates precise estimation. In contrast, OB associations exhibit a high probability of chance coincidence, suggesting their limited contribution to TeV gamma-ray emission. Our analysis of TeV gamma-ray emission capabilities shows that ~60% of PWNe are gamma-ray bright in both the WCDA and KM2A energy ranges. For SNRs and microquasars, the TeV gamma-ray bright fraction is ~10%. The subsample of PWNe associated with molecular clouds (MCs) shows enhanced gamma-ray emission. Furthermore, positional analysis reveals a systematic offset of the gamma-ray sources overlapping with PWNe toward the associated MCs. These findings imply a role for MCs in PWN gamma-ray production. Additionally, self-correlation analysis indicates that about 70% of the WCDA and KM2A gamma-ray components share a common origin. The study also identifies selection effects in existing SNR catalogs and notes clustering among approximately 30% of HII regions within larger star-forming regions.