The effect of diffusion on seismic models of SX Phoenicis stars

The effect of diffusion on seismic models of SX Phoenicis stars Paulina Góra, Jadwiga Daszyńska-Daszkiewicz, Przemysław Walczak Instytut Astronomiczny, Uniwersytet Wrocławski, Poland Star Z N/DRL M [𝐌⨀] Vrot,0 [𝐤𝐦 ∙ 𝐬−𝟏] Age [Gyrs] V194 0.000900 N 0.9762 10 4.04 V194 0.000700 N 1.0410 10 3.22 V194 0.001100 DRL 1.0250 10 3.24 V194 0.001000 DRL 1.0720 10 2.81 V220 0.003300 N 1.1320 30 2.60 V220 0.003100 N 1.1750 30 2.28 V220 0.003100 DRL 1.1000 30 2.67 V220 0.002850 DRL 1.1780 30 2.18 V225 0.002400 N 1.1300 30 2.44 V225 0.002000 N 1.1800 30 2.10 V225 0.002100 DRL 1.1300 30 2.40 V225 0.001900 DRL 1.1780 30 2.06 V237 0.001825 N 1.0175 10 3.96 V237 0.001875 N 1.1000 10 3.03 V237 0.002050 DRL 1.0500 10 3.49 V237 0.002100 DRL 1.1200 10 2.81 NV326 0.002400 N 1.0480 45 3.49 NV326 0.002100 N 1.0950 45 3.18 NV326 0.002100 DRL 1.0470 45 3.35 NV326 0.001900 DRL 1.1000 45 2.84 THE EFFECT OF ROTATION AND HYDROGEN ABUNDANCE THE EFFECT OF DIFFUSION ON MODE EXCITATION The higher rotation can cause efficient mixing and suppress the effects of diffusion. Another important parameter is the helium abundance which can be higher in the case of SX Phe stars. For the star V194, we additionally computed the DRL seismic models with the higher value of initial rotation Vrot,0 =50 kms-1 and with the higher helium abundance Y=0.33. In the left panel, the position of seismic models of V194 is marked on the HR diagram. The figures below show the dependence of age on metallicity (left) and age on mass (right). The seismic models with higher rotation are younger, more massive and have higher metallicity. Diffusion processes, in particular the competing gravitational settling and radiative levitation, can significantly modify the distribution of chemical elements in stellar interiors and thus their internal properties. These effects are especially relevant in stars with the weak envelope convection and relatively slow rotation, as they both cause efficient mixing. We study the effect of diffusion on seismic models of SX Phoenicis (SX Phe) stars which are considered to be blue straggler objects. We selected the five double-mode radially pulsating SX Phe stars in the globular cluster 𝛚 Centauri and demonstrate how their seismic masses, metallicities and ages are affected by diffusive processes. The effect of rotation and helium abundance is also discussed. Seismic modelling of these SX Phe stars without the effects of diffusion have been recently published by Daszyńska-Daszkiewicz et al. (2025, MNRAS 539, 3381). CONCLUSIONS ⚫ diffusion (gravitational settling and radiative levitation) affects seismic models of SX Phe stars ⚫ seismic models with diffusion have different masses and metallicities and, in general, they are slightly younger ⚫ higher rotation decreases the effects of diffusion ⚫ the effect of diffusion processes on mode excitation is very subtle ACKNOWLEDGEMENTS: the work was financially supported by the Polish National Science Centre grant 2023/50/A/ST9/00144 The position of seismic models of the five SX Phe stars in 𝛚 Cen (V194, V220, V225, V237, NV326) on the Hertzsprung Russell (HR) diagram (left five panels). The evolutionary models were computed with the MESA code with (DRL) and without (N) the effects of diffusion (both, gravitational settling and radiative levitation). The solar chemical composition from Asplund et al. (2009) was adopted. Opacities and the equation of state were based on OPAL and SCVH data (Rogers & Nayfonov, 2002; Saumon et al., 1995). Convection was treated using the formalism of Henyey et al. (1965). Diffusion was included based on OP data (Seaton, 2005), with radiative accelerations computed using the method of Hu et al. (2011). Rotation and angular momentum transport followed the prescriptions of Heger et al. (2000, 2005) which account for shear instabilities, Eddington–Sweet circulation, the Solberg–Hoiland criterion, and magnetic angular momentum transport via the Spruit–Tayler dynamo (Spruit, 2002). Pulsations were calculated with the linear nonadiabatic code of Dziembowski (1977), assuming the convective flux freezing approximation. The effects of rotation on pulsation frequencies were included up to second order using the perturbative approach (Pamyatnykh, 1999). The initial rotational velocity and age of seismic models are given in the above table. We constructed seismic models which reproduce the observed frequencies of two radial modes: fundamental (F) and first overtone (1O) for 4 stars and fundamental and second overtone (2O) for V237. Seismic models with diffusion and within the error box of (Teff , L) have slightly different masses and metallicities but no general trend has been found, as one can conclude from the plot M vs Z (the right-top panel). However, all seismic models with diffusion are slightly younger (the right-bottom panel). Self-excited pulsation occurs if the normalized work integral, the so-called parameter  , is greater than zero, i.e., globally, excitation prevails over damping. In the plots below, we show  as a function of metallicity Z for the radial fundamental mode (left panel) and for the first (second) overtone (right panel) for the seismic models of the five SX Phe stars. For most stars, the seismic models with diffusion have slightly lower values of  for both radial modes. The figures below show a run of the differential work integral for a radial fundamental mode, inside the models with the same mass M=1.05M but different effective temperature and chemical composition (Y0, Z). Models calculated with (DRL) and without (N) diffusion processes were compared. The model presented in the left panel is cooler and has Y0=0.298, Z=0.002. The chemical composition of the model in the right panel is Y0=0.329 and Z=0.001. As can be seen from the right panel, for certain combinations of (Teff , Y0, Z) the effect of diffusion on the excitation of pulsation modes can be completely suppressed. The frequencies of the radial modes of the five SX Phe stars Seismic models of the five SX Phe stars