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Asteroseismic Modelling of the Red Giant HD222404 (γCephei A) Introduction Key stellar parameters like mass and radius are essential in astronomy, helping us understand individual stars and their possible exoplanets. Asteroseismology, the study of solar-like oscillations, allows for precise measurements of these attributes. Red giant stars signify a crucial phase in stellar evolution, arising after the depletion of hydrogen fuel. In this stage, nuclear fusion ignites in a shell around an inert helium core. The star’s cooling outer envelope forms a vast convection zone, rendering red giants nearly fully convective. This unique structure produces a steep, vertical path on the Hertzsprung-Russell diagram, marking them distinct in stellar evolution. Why γCep A is important? γCep A is a K-type red giant branch star characterized by Malla et al. (2020) and Knudstrup et al. (2023). As a solar-like oscillator, it provides insights into stellar interiors through p-mode spectra. This star, hosting a confirmed exoplanet, makes accurate stellar characterization essential for understanding planetary properties (Hatzes et al., 2003). We aim to ⋆Obtain high-resolution spectra (R∼67,000) with the TLS Coudé-Echelle Spectrograph. ⋆Measure radial velocities and line-profile variations to extract νmax and ∆ν. ⋆Compare observed global parameters (M, R, log g, Teff) with models using MESA and GYRE. Observations & Data Reduction ⋆Instrument: Coudé-Echelle Spectrograph at the TLS 2-meter Alfred Jensch Telescope. ⋆Wavelength coverage: 470 – 740 nm. ⋆Data reduction (in progress): bias, dark, flat-field correction (TLS pipeline). ⋆Wavelength calibration using ThAr lamp. Figure 1: The 2-meter Alfred Jensch Telescope (AJT) at the TLS, Tautenburg. Asteroseismic Modeling & Preliminary Results MESA modeling is crucial for simulating stellar evolution by optimizing input physics. We utilize the GYRE pulsation code to calculate adiabatic oscillation frequencies, allowing us to estimate the large frequency separation ∆νand the frequency of maximum power, νmax, using seismic scaling relations. We computed a grid of MESA models with stellar masses from 1.20 to 1.35 M⊙and metallicities from Z= 0.0165 to Z= 0.0210. The model shows ∆ν= 13.64 µHz (target range: 14.3–14.6 µHz) and νmax = 165.8µHz, which is lower than the observed ∼185 µHz. This serves as an intermediate step in our parameter space exploration, with final calibration using seismic constraints ongoing. Our best-fit model has M= 1.23 M⊙,Z= 0.0165, and mixing-length parameter α= 1.6. Global Parameter Comparison Comparison of global parameters. Values are mean ±uncertainty. Source M[M⊙]R[R⊙]log g[cgs] Teff [K] νmax [µHz] MESA (this work) 1.23 ±0.05 5.06 ±0.15 3.12 ±0.05 4628 ±80 165.8 ±1.5 Malla et al. (2020) 1.32 ±0.20 4.88 ±0.22 3.34 ±0.02 4800 ±80 185.0 ±5.0 Knudstrup et al. (2023) 1.28 ±0.04 4.94 ±0.12 3.34 ±0.01 4855 ±60 185.4 ±1.5 Figure 2: Left: The Echelle diagram of radial p-modes (ℓ= 0) presents a frequency comb pattern with a spacing of ∆ν= 13.64 µHz. This spacing confirms the solar-like oscillation of γCep A, enabling accurate asteroseismic parameter determination.; Right: The plot effectively illustrates the relationship between frequency and fractional radius (r/R⋆), featuring the Brunt–Väisälä frequency (N) as a solid black line. The Lamb frequencies for spherical harmonic degrees ℓ= 1, 2, and 3 are shown as dashed lines in blue, orange, and green, respectively. Notably, the gray shaded regions represent convective zones where N2<0, highlighting areas of significant convective instability. Discussion & Future Work Once measurements are complete, we will align our MESA model to redetermine key parameters like mass and radius, in particular as the temperature offsets and surface gravity differences drive us to refine our modelling approach. Spectroscopic validation should clarify uncertainties in effective temperature, surface gravity, and metallicity. The ongoing analysis from TLS Tautenburg is expected to provide independent constraints on these atmospheric parameters, helping us address discrepancies between our model predictions and asteroseismic observations. This multi-method approach enhances our understanding of stellar structure and evolution. Next Steps & Outlook ⋆Spectroscopic validation is currently ongoing with high-resolution TLS data. ⋆Fit individual mode frequencies to enable detailed modelling. ⋆Extend analysis to include line profiles for non-radial modes. ⋆Incorporate TLS 2 m results into the ensemble of red giant asteroseismology. References Malla, P. et al. 2020, MNRAS, 496, 5423; Knudstrup, E. et al. 2023, A&A, 675, A197; Hatzes et al. 2003, ApJ, 599, 1383; Paxton, B., et al. (2011, 2013, 2015, 2018, 2019), ApJS, MESA stellar evolution code; Townsend, R. Teitler, S. (2013), MNRAS, GYRE stellar oscillation code Aashana Tripathi & Markus Roth Thüringer Landessternwarte (TLS) Tautenburg, Germany
