Modeling Procyon A as a benchmark for F-type

Modeling Procyon A including radiative accelerations Nuno Moedas1; Maria Pia Di Mauro1; Morgan Deal2 1 - Istituto Nazionale di Astrofisica (INAF/IAPS Roma) 2–LUMP, Université de Montpellier, CNRS, Place Eufène Bataillon, 34095 Montepellier, France Introduction Procyon is a wide binary system consisting of an F-type main sequence star (Procyon A) and a white dwarf (Procyon B). Procyon A was one of the first stars for which seismic oscillations were observed displaying a large spectrum of frequencies (Bedding, 2010). Being a binary system, the stellar mass of both components is well constrained. These conditions make Procyon Aa benchmark for testing our models and characterization tools for F-type stars. In this work, we model this star by considering the effects of chemical transport mechanisms, that are usually neglected in F-type stars models due to the unrealistic surface chemical compositions that they predicted (Verma & Silva Aguirre, 2019, Semenova et al.2020). We include the effects of radiative accelerations and turbulent mixing and see how our stellar models predict the fundamental properties and the surface abundances. Also, we test how different modeling of the surface effects the inference of the stellar parameters. Procyon A Asteroseismic Data •Bedding et al. (2010) provide two sets of 50 frequencies 𝜈𝑛,ℓ , each with ℓ = 0, 1, 2. •The results of our tests indicate only one of them present consistent results. This is supported by the work of Doğan et al. (2010) and Compton et al. (2018, 2019). 1 – Bond et al. (2015) 2 –Soubiran et al. (2024) 3 –Perdelwitz et al. (2024) References Abdurro'uf et al. 2023, ApJS, 259, 35 Alecian & LeBlanc 2020, MNRAS, 498, 3420 Asplund et al. 2019, A&A, 47, 481 Ball & Gizone 2014, A&A, 568, A123 Bedding et al. 2010, AJ, 713, 935 Bond et al. 2015, AJ, 813, 106 Compton et al. 2018, MNRAS, 479, 4416 Compton et al. 2019, 0MNRAS, 485, 560 Cox & Giuli 1968 Doğan et al. 2010, AN, 331,949 Kjeldsen et al. 2008, ApJ, 683, 175 LeBlanc & Alecian 2004, MNRAS, 418, 195 Moedas et al. 2024, A&A, 695,12 Paxton et al. 2019, ApJS, 243, 10 Perdelwitz et al. 2024, A&A, 683, 125 Semenova, E., Bergemann, M., Deal, M. et al. 2020, A&A, 643,A164 Sonoi et al. 2015, A&A, 583, 11 Soubiran et al. 2024, A&A, 682, 145 Verma & Silva Aguirre 2019, MNRAS, 489, 1850 Conclusions We used ProcyonAas a test ground for our chemical transport processes and surface corrections. We conclude that: •The physics we consider allows to accurately reproduce the fundamental properties of the star (M and R). •Our results suggest that surface corrections should be avoided to model this type of stars,and a direct frequencies comparison or the use of ratios should be favored. •The most probable explanation for the observed chemical composition of the star is an initial mixture different from the solar one or an accretion event from the mass-loss phase of the companion. Both scenarios will be investigated in future works. Fig 1: Evolutionary tracks (gray lines, solar chemical abundances) for Procyon A where the blue line represents the evolution of the best model (purple circle, inferred chemical composition). The observed parameters of ProcyonA are represented by the gray star. Fig 3: The left and middle show the comparison of the element abundance between observation and model. The left panel shows the element content relative to iron, and the middle panel shows the element content relative to hydrogen. The gray stars represent the observed values (Abdurro'uf et al., 2023), and the circles represent the model estimations. The right panel shows the surface evolution of helium abundance; the circles represent our best model. For all panels, the green line represents our best model. The purple line represents a model in which turbulent mixing was reduced by 10 times, and the blue line represents a model in which turbulent mixing was reduced by 20 times. Inference •We estimated a best-fitted model with a stellar mass value compatible with the literature one (Bond et al.2015). •Our models indicate that the star is still in the final stages of the main sequence, burning the remaining hydrogen in the core. Surface corrections -There is a discrepancy between the theoretical frequencies and observed ones cause due to the unproper modelling of the surface layers (like modeling the convection and magnetic fields). Two Methods to model the frequencies: -Surface corrections are an empirical method used to adjust the discrepancy in order to compare the observed and theoretical frequencies. -Compare directly the frequencies ratios 𝑟02 =𝛿𝜈02 Δ𝜈 ,as they are less affected by this discrepancies. Results: •Some surface corrections (Ball & Gizon 2014, Kjeldsen et al. 2008) can lead to relative errors in the estimated mass up to 10%in inferred mass. Fig 2: The relative difference of the inferred parameters compared to the observed ones for different surface correction prescriptions. Surface Abundances •Only the estimated surface abundances of iron and carbon reproduce the observed ones. •We test if changing the efficiency of the chemical transport processes could improve the result. We found that changing the efficiency of turbulent mixing could help to improve the estimation of some of the elements. •Nevertheless, this changes lead to incompatible values of carbon and iron with observation, lead also to unexpected depletion of helium at the stellar surface. Inferred Parameters 𝑴 (𝐌⊙)1.447±0.031 𝑅 (R⊙)2.047±0.011 Age ( Gyr ) 1.933±0.183 𝑌 i0.295±0.013 𝑍i 0.0144 ± 0.0017 𝑌 s0.245±0.013 𝑍s 0.0126 ± 0.0015 𝑿𝐜0.169±0.038 Observed Parameters 1 𝑀 (M⊙ ) 1.478 ± 0.012 2𝐿 (L⊙) 7.049 ± 0.064 2𝑹 (𝐑⊙) 2.046 ± 0.009 3𝑻𝐞𝐟𝐟 (K) 6768.8 ± 70.0 3log 𝑔 4.056 ± 0.066 3𝐅𝐞/𝐇 0.00±0.056 We used the 𝝂𝒏,ℓ, 𝑹, 𝑻𝐞𝐟𝐟, and 𝑭𝒆/𝑯 as constraints. In addition: ●Gravitational settling 𝑔set ; ●Radiative accelerations 𝒈𝐫𝐚𝐝 computed with the Single-Valued Parameters (SVP, LeBlanc & Alecian 2004; Alecian & LeBlanc 2020) method; ●Turbulent Mixing 𝐷turb calibrated to reproduce the helium abundance in F-type stars (Verma & Silva Aguirre, 2019). Stellar Models Main Inputs: -Asplund et al. (2009) solar chemical mixture -OPAL EOS -OPAL opacity tables -Nacre Nuclear reactions -Cox & Giuli (1935) mixing length prescription We used a grid of stellar models from Moedas et al. (2024) that was computed using the MESA r12778 evolution code (Paxton et al.2019). Observational Constraints •Neglecting surface corrections provided compatible results with the observed ones. •When the surface corrections are neglected (None case) we are able to reproduce the luminosity of ProcyonA.