Unraveling Year-Long Radial Velocity Variations in Red Clump Region -- I: Comprehensive analysis of a K0 Giant star, 2 Draconis

TL;DR

The paper tackles the challenge of distinguishing genuine long-period companions from stellar and instrumental sources in RV data for evolved stars, focusing on 2 Dra. It deploys two complementary diagnostics (periodogram-based coherence tests and phase-stability analyses) along with a thorough examination of stellar activity, IP systematics, and sampling effects, supported by Keplerian orbit fitting. The main finding is that a robust $\sim340$-day RV signal in 2 Dra is unlikely to originate from activity or IP drift, though a definitive planetary confirmation remains cautious due to potential subtle stellar contributions; an outer $\sim1540$-day signal appears to be sampling-related. This work provides a practical framework for disentangling year-long RV variations in GK giants and informs interpretation of similar signals in other evolved stars, with implications for planet searches around red giants and the assessment of alternative intrinsic variability mechanisms such as oscillatory convective modes.

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 $\simeq270\text{--}320$\,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 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.

Figures (18)

• Figure 1: Power spectrum density (PSD) diagrams of TESS lightcurve of 2 Dra. Main panel: The original PSD is shown in gray curve, while the smoothed PSD is a black curve. The oscillation hump is represented in the Gaussian red curve, the two granulation terms are present in the two green curves, the white noise is a brown line, and the sum of MCMC fit components is for the blue curve. Top right panel is the non-smoothed background (granulation and white noise)-removed PSD (in unit of dex in power).
• Figure 2: Asteroseismic diagnostic plots of 2 Dra. Top panel: the smoothed PSD with the oscillation peak at $\nu_{\text{max}}=35.98 \pm 0.55\,\mu\rm{Hz}$ and background (same line colors as main Figure \ref{['fig: Power Spectrum']}). Middle panel: Échelle diagram (ED) showing the radial oscillation modes with the highest power at $\nu_{\text{max}}$ (darkgreen). Bottom panel: Collapsed échelle diagram showing the highest peak with its uncertainty at $\Delta\nu = 4.23 \pm 0.06\,\mu\rm{Hz}$ (following darkgreen grid in ED), as the frequency width of radial modes.
• Figure 3: Evolutionary tracks (HR diagram) of the evolved intermediate-mass giant stars around solar-masses ($1-2M_{\odot}$) in different stages: main sequence (MS), red giant branch (RGB), core-He burning (CHeB), and asymptotic red giant branch (ARGB), between the margin of metal-poor $(\text{[Fe/H]} = -0.5$; dashed line) and metal-rich content $(\text{[Fe/H]} = 0.0$; solid line). 2 Dra is located with a white star with errorbar.
• Figure 4: GLS-Ps of 2 Dra's RV variations (left panels) with RV residuals (right panels), WF (bottom left panel), and $S_{H}$ (bottom right panel). In RV residual panel, $\rm{O-C}_{1}$ is the $\rm{1^{st}}$ RV residual after 340-d RV peak removed, and subsequently, $\rm{O-C}$ is the last RV residual after 1540-d RV peak removed. Three FAP levels are represented by green (0.1%), yellow (1%), and red (10%) dot-dash lines in each indicator, respectively. Vertical skyblue band is a hypothetical outer period errorbar. The alias signals ($\times$ marker) are indicated at the zero baseline ($P_{\rm{alias}} [\text{yr}] = 1 / |1/P_{\text{peak}} \pm 1|$; dumusque2012earth).
• Figure 5: SBGLS-P of RV variations of 2 Dra. Central colormap signifies SBGLS-P power (i.e., the significance probability) across the signal periods over observation time. Left vertical plot is the projected SBGLS-P probability at the significant periods (e.g., 340-d and 1540-d RV, respectively). Right vertical plot is the max-likelihood signal-to-noise ratio over the number of observational data given input jitters $s_{\rm{inst}}$ computed by radvel in each instrument.