The study focuses on characterizing planet-hosting stars and their planets, particularly those discovered by the K2 mission. With approximately 5500 confirmed exoplanets orbiting over 4250 stars (mostly detected via transit methods), understanding host star properties is crucial for accurate planetary characterization. Previous research has unveiled significant patterns: a correlation between stellar metallicity and the frequency of giant planets; the presence of a radius valley (a dearth of planets with radii between super-Earths and sub-Neptunes); and a dependence of the radius valley on orbital period. These findings provide key constraints on planetary formation theories. Precise stellar parameters, including effective temperature (Teff), surface gravity (logg), and metallicity ([Fe/H]), are vital for deriving accurate planetary radii from transit depth measurements. This study addresses the critical need for high-precision spectroscopic analysis of planet-hosting stars to improve planetary radius determinations. Moreover, the research acknowledges that stellar magnetic activity can influence the derived stellar and planetary radii, as magnetic activity affects stellar parameters. This study will determine stellar parameters for a sample of K2 planet-hosting stars using high-resolution spectroscopic analysis, paying special attention to the potential influence of stellar activity on the parameters derived.

The introduction cites several key papers that laid the groundwork for this research. Gonzalez (1997), Fischer & Valenti (2005), and Ghezzi et al. (2018) established the correlation between stellar metallicity and the frequency of giant planets. The discovery of the radius valley, a gap in the distribution of exoplanet radii, is attributed to Fulton et al. (2017) and Fulton & Petigura (2018). The dependence of the radius valley on orbital period is detailed in Van Eylen et al. (2018) and Martinez et al. (2019). These studies highlight the importance of accurate stellar parameters for understanding exoplanet formation. The paper also notes previous work investigating the influence of stellar magnetic activity on derived parameters, such as the work by Yana Galarza et al. (2019) and Spina et al. (2020). The influence of stellar activity is an important consideration, affecting the derived stellar and planetary parameters. The paper references studies using various methodologies including high-precision spectroscopy and asteroseismology for stellar parameter determination (e.g., Huber et al. 2016).

This study analyzes optical spectra of 109 K2 planet-hosting stars obtained from the California Planet Search (CPS) program using the High Resolution Echelle Spectrometer (HIRES) on the Keck I telescope. Spectroscopic parameters (Teff, logg, A(Fe), and ξ) are derived using equivalent width measurements of Fe I and Fe II lines, assuming Local Thermodynamic Equilibrium (LTE) and employing Kurucz model atmospheres. The ARES code (Sousa et al. 2015) is used for continuum setting and equivalent width measurements. The analysis initially excludes lines sensitive to magnetic activity. Stellar masses and radii are then calculated using the PARAM code (da Silva et al. 2006) which combines spectroscopic parameters with Gaia DR3 parallaxes, V-magnitudes, and PARSEC isochrones. Planetary radii are calculated using the transit depth (ΔF) from various sources (Kruse et al. 2019; Barros et al. 2016; Pope et al. 2016; Christiansen et al. 2017) and the derived stellar radii using a formula from Seager & Mallén-Ornelas (2003). To assess stellar activity, the chromospheric activity index S_HK is measured from Ca II H and K lines, following Isaacson & Fischer (2010), using IRAF's sbands task. For this activity determination, the V-coefficient in the S_HK equation was adjusted on a spectrum-by-spectrum basis to equalize mean fluxes in the R and V continuum bandpasses. A total of 725 spectra (from both ExoFop and the Keck Observatory Archives) are used. This S_HK is then converted to log R_HK using the method of Noyes et al. (1984) to account for photospheric contribution. The impact of stellar activity on the derived parameters is evaluated by repeating the analysis, this time including magnetically sensitive Fe I lines.

The study achieved high precision in its stellar and planetary radius measurements, with median internal uncertainties of 1.8% and 2.3%, respectively. A radius gap near 1.9 R⊕ was identified in the planetary radius distribution, confirming previous findings and supporting theories of planet formation. Chromospheric activity analysis revealed a distribution of S_HK indices similar to those in literature compilations. The relation between S_HK and (B-V) color followed expected trends found in previous studies. Analysis of log R_HK versus rotational period (Prot) and projected rotational velocity (v sin i) indicated a general decrease in activity with increasing Prot or v sin i but demonstrated significant scatter, consistent with findings by Böhm-Vitense (2007) and Metcalfe & van Saders (2017). The study found evidence for a Vaughan-Preston gap in the log R_HK distribution for F and G dwarfs, a scarcity of stars with intermediate activity levels. A comparison of stellar parameters derived with and without activity-sensitive lines showed only small systematic differences, with the more active stars showing larger scatter in the differences of Teff and [Fe/H].

The high precision achieved in the stellar and planetary radius determinations validates the methodology employed. The detection of the radius gap reinforces the significance of this feature in understanding planetary formation. The findings on chromospheric activity confirm earlier observations and highlight the complexities in the relationship between stellar activity and rotation. The presence of the Vaughan-Preston gap in this sample supports the robustness of this observational feature in characterizing stellar populations. The lack of significant differences in derived stellar parameters with and without activity-sensitive lines suggests that this specific line list minimizes activity effects. The increased scatter in T_eff and [Fe/H</sub> differences for active stars indicates the importance of considering activity when high accuracy is required.

This research provides high-precision stellar and planetary characterization for a sample of K2 stars, revealing the radius gap and exhibiting the Vaughan-Preston gap in chromospheric activity. The impact of stellar activity on parameter determinations is limited when using the specific line list selected. Future studies could expand this analysis to larger samples or incorporate additional data sources (like asteroseismology) to further refine our understanding of the interplay between stellar activity and planetary formation.

The sample size, while substantial for a detailed spectroscopic analysis, is relatively small compared to some larger surveys. The reliance on literature values for certain parameters (e.g., rotational periods, transit depths) introduces potential uncertainties. The study mainly focuses on FGK stars, limiting the generalizability to other spectral types.