Stellar Characterization and a Chromospheric Activity Analysis of a K2 Sample of Planet-Hosting Stars

The study addresses precise characterization of K2 planet-hosting stars to improve determinations of planetary radii and to assess how stellar magnetic activity affects spectroscopically derived stellar parameters. With thousands of confirmed exoplanets, accurate stellar effective temperatures, surface gravities, and metallicities are essential because planetary radii scale with host-star radii derived from these parameters. Magnetic activity can bias stellar characterization through effects on spectral lines and chromospheric emission. The purpose is to derive homogeneous stellar parameters for a K2 sample, compute precise stellar and planetary radii, measure chromospheric activity via Ca II H and K lines, and evaluate the impact of activity on derived stellar parameters and on observed exoplanet radius distributions.

The paper situates its work within findings that metallicity correlates with giant-planet frequency and that the small-planet radius distribution shows a valley (Fulton gap) around ~1.9 R⊕, with a period dependence, informing planet formation and evolution theories (e.g., core-powered mass loss and photoevaporation). The importance of precise spectroscopic parameters to resolve the radius valley is emphasized. Stellar magnetic activity diagnostics, especially Ca II H and K cores, are reviewed as sensitive tracers of chromospheric activity tied to magnetic fields. Prior works have transformed S-index measurements to the Mt. Wilson scale and related activity to rotation and stellar type, including the Vaughan-Preston gap among F–G dwarfs. Studies indicate activity can affect Fe-line based parameter determinations, particularly for active stars, motivating a careful line selection and tests including activity-sensitive lines.

- Data: High-resolution optical spectra from Keck I/HIRES (CPS program), with wavelength coverage including Ca II H&K. 145 spectra from ExoFOP were inspected; 109 had sufficient S/N for parameter derivation. An additional 725 HIRES spectra from KOA enabled multi-epoch Ca II H&K measurements for activity. - EW measurements: EWs of Fe I and Fe II lines measured with ARES v2. Continuum placement used line-free windows at 5764–5766 Å, 6047–6052 Å, and 6068–6076 Å. - Line list and model atmospheres: Fe line list from Yana Galarza et al. (2019) based on Meléndez et al. (2014), with classification of activity sensitivity via Landé g and EW. LTE analysis with 1D plane-parallel Kurucz ATLAS9 ODFNEW models. - Spectroscopic parameters: q2 (qoyllur-quipu) interfaced with MOOG (2019) to iteratively enforce excitation/ionization balance of Fe I/Fe II and remove trends with reduced EW to determine Teff, log g, A(Fe), and microturbulence ξ. Initial analysis used only activity-insensitive lines; a parallel analysis including sensitive lines assessed activity impacts. Solar-proxy (asteroid Iris) HIRES spectra validated methodology. - Stellar masses and radii: Derived via PARAM v1.3 (Bayesian) using PARSEC isochrones with inputs Teff, [Fe/H], and MV from Gaia DR3 parallaxes and V magnitudes. Cross-check with q2/Yonsei-Yale isochrones showed close agreement. - Planetary radii: Computed from transit depths ΔF of confirmed K2 planets combined with derived stellar radii using Rpl [R⊕] = 109.1979 × sqrt(ΔF) × 10^-6 × Rstar. ΔF values from Kruse et al. (2019), Barros et al. (2016), Pope et al. (2016), Christiansen et al. (2017). - Ca II H&K activity measurements: S-index (SHK) measured per Isaacson & Fischer (2010) using triangular H/K core bandpasses (FWHM 1.09 Å) and 20 Å rectangular V/R continua. The V-bandpass coefficient was adjusted per spectrum (mean ~2.28) to equalize mean R and V fluxes, placing SHK close to the Mt. Wilson scale; comparisons with literature showed near 1:1 correspondence (fit slope ~1.10, negligible intercept), so no further transformation applied. - Conversion to R′HK: Photospheric correction and color-dependent bolometric factor Ccf computed using Noyes et al. (1984) and Rutten (1984), with distinct Ccf polynomials for main-sequence and evolved stars. log R′HK computed from SHK and (B–V). - Ancillary rotation data: v sin i from APOGEE DR17 and Petigura et al. (2018); photometric rotation periods from Reinhold & Hekker (2020), de Leon et al. (2021), and Rampalli et al. (2021). Assessed relations between activity, rotation, and v sin i. - Uncertainties: Formal errors from q2 following Epstein et al. (2010) and Bensby et al. (2014). Error budget propagated to Mstar, Rstar, and Rpl, including contributions from V magnitude and Gaia parallax; median internal precisions: Rstar 1.79%, ΔF 2.79%, Rpl 2.33%.

- Spectroscopic parameters were obtained for 109 K2 host stars using Fe I/Fe II EWs under LTE with Kurucz models; median internal errors: Teff ≈ 42 K, log g ≈ 0.09 dex, [Fe/H] ≈ 0.03 dex. - Stellar masses and radii (PARAM/PARSEC) show most stars have Rstar < 2 R⊙ and Mstar < 1.2 M⊙; medians: Rstar ≈ 0.92 R⊙ (16th–84th: 0.70–1.35), Mstar ≈ 0.92 M⊙ (0.74–1.05). PARAM vs q2 radii and masses agree within −0.03 ± 0.02 R⊙ and −0.01 ± 0.01 M⊙. - Comparison to asteroseismic results (Huber et al. 2016): small systematics with median differences (H16 − this work) of +0.06 ± 0.12 R⊙ and +0.04 ± 0.06 M⊙; a few notable outliers discussed with literature context. - Planetary radii for 93 confirmed planets orbiting 69 stars computed with 2.3% median internal precision. The radius gap (Fulton gap) is detected at ~1.9 R⊕ for Rpl < 4 R⊕. Cross-comparisons with literature show small median differences: ~+0.08 R⊕ (Petigura 2018), −0.13 R⊕ (Mayo 2018), +0.01 R⊕ (Kruse 2019), −0.08 R⊕ (Hardegree-Ullman 2020), +0.07 R⊕ (Loaiza-Tacuri 2023). - S-index (SHK) measured for 144 stars (725 spectra total) aligns closely to Mt. Wilson scale (fit slope ~1.10). The sample’s SHK distribution peaks near ~0.15–0.18, similar to solar values; a few stars exhibit SHK ~2–3 (very active). SHK increases toward redder (B−V) along the lower envelope in agreement with Isaacson & Fischer (2010). - Conversion to log R′HK shows activity generally decreases with increasing rotation period, but with large scatter (~0.5 dex) at fixed Prot. Stars with P/sin i ≲ 30–40 days tend to show higher activity; above this threshold, activity is low (log R′HK ~ −5.5). Rapid rotators (v sin i > 10 km s−1) are predominantly active (≈83%). - The Vaughan–Preston gap is evident among main-sequence stars and F–G dwarfs as a deficit of intermediate-activity objects in the log R′HK distribution. - Including activity-sensitive Fe lines yields small systematic differences relative to the insensitive-line analysis: ΔTeff = −46 ± 51 K, Δ[Fe/H] = −0.034 ± 0.047 dex, Δξ = +0.10 ± 0.28 km s−1 (non-sensitive − sensitive). No clear correlation of these differences with log R′HK beyond increased scatter for more active stars (log R′HK > −5.0).

The work demonstrates that high-precision spectroscopic characterization of K2 planet hosts, combined with Gaia parallaxes and isochrones, delivers percent-level stellar radii that propagate to similarly precise planetary radii. This precision is sufficient to reliably recover population-level features such as the ~1.9 R⊕ radius gap in the K2 sample, confirming its robustness beyond the original Kepler field. By calibrating HIRES-based SHK to the Mt. Wilson scale and converting to log R′HK across FGK types (including evolved stars), the study maps chromospheric activity in the sample and links it to rotation. The observed decrease of activity with increasing rotational period, but with substantial dispersion at a given period, aligns with prior findings that stellar activity depends on multiple factors (e.g., mass, age, Rossby number) and may follow distinct active/inactive sequences. The detection of the Vaughan–Preston gap among F–G dwarfs reinforces bimodality in chromospheric activity distributions. Importantly, a controlled test including activity-sensitive Fe lines indicates that, for this dataset and methodology, activity introduces only small systematic shifts within the measurement uncertainties; however, more active stars show larger scatter in Teff and [Fe/H], cautioning that activity phase and line selection can impact precision for active targets. Overall, the results support the reliability of spectroscopic parameters for exoplanet studies while highlighting the nuanced role of stellar activity.

- A uniform high-resolution spectroscopic analysis of 109 K2 host stars yielded precise stellar parameters and radii; planetary radii for 93 confirmed planets achieved a median internal precision of 2.3% and reproduced the radius gap at ~1.9 R⊕. - Chromospheric activity indices from Ca II H&K (725 HIRES spectra, 144 stars) were placed on the Mt. Wilson scale and converted to log R′HK, revealing expected trends with color and rotation, a large scatter at fixed period, and the Vaughan–Preston gap among F–G dwarfs. - Comparisons against literature and asteroseismic constraints show small systematics and validate the approach. Including activity-sensitive Fe lines causes only modest parameter shifts within errors, though active stars display larger scatter. Future directions include multi-epoch monitoring to sample activity cycles, improved rotational period coverage, incorporating convective turnover times to assess Rossby numbers, and expanding samples (especially K dwarfs) to refine activity–rotation relations and their impact on spectroscopic parameter determinations.

- Many stars have only a single or few HIRES observations, so SHK/log R′HK represent snapshots rather than phase-averaged activity over cycles; activity variability can be significant for some targets. - Photometric rotation periods are available for only 44 stars; v sin i measurements mix instruments and have detection floors (~2–3 km s−1), complicating interpretation for slow rotators and low inclinations. - The analysis assumes 1D LTE and plane-parallel model atmospheres; non-LTE/3D effects are not explored and could introduce systematics. - The activity impact assessment, while informative, is limited by the line list and sample size; the largest effects occur in more active stars and may depend on activity phase. - Asteroseismic comparisons show a few outliers; some literature radii/masses have large uncertainties, and discrepancies persist for certain targets. - The K-dwarf subsample is small, limiting conclusions about their activity distribution; the overall sample selection is constrained by S/N and archival availability. - Planetary radii rely on external transit depth measurements with their own uncertainties and potential systematic differences between sources.