Unraveling year-long radial velocity variations in red clump region. I. Comprehensive analysis of a K0 giant star, 2 Draconis

Abstract Slow-rotating evolved stars frequently exhibit radial velocity (RV) variations on annual timescales, complicated by instrumental systematics and aliasing in the one-year regime. Here, we investigate the origin of the near-yearly periodicity in 2 Dra, a star located in the red-clump region, assessing possible causes between stellar activity, instrumental profile (IP) effects, sampling alias, and planetary companions. We applied two independent approaches: (1) constraining diagnostic signals and performing a correlation analysis (r) between period-confined signals and (2) evaluating phase stability by partitioning Keplerian fits. These methods enabled us to examine the physical connections and phase coherence among stellar activity indicators, RV measurements, and IP diagnostics. Our analysis suggests a stellar rotation period of ${\simeq }270\!-\!320$ d for 2 Dra. The 340 d RV signal does not appear to originate from stellar activity in this chromospherically quiet star ($|r| \lesssim 0.33$), nor from instrumental systematics near the annual period ($|r| \lesssim 0.1$). This conclusion is supported by contrasting phase behavior: the RV and stellar activity phases remain stable, whereas the IP phases do not. We therefore propose that the 340 d variation likely arises from either a small-amplitude intrinsic variability or a tentative gas giant companion with potential weak activity-induced modulation. The case of 2 Dra provides a framework for distinguishing the origins of $\sim$1 yr RV variations in other evolved stars.