Pulsations in subdwarf B stars are attributed to radiative levitation of iron-group elements in the stellar envelope. Until now, only iron diffusion is accounted for in stellar models used for sdB seismology. However, nickel has also been suggested a
s a contributor to the opacity bump that drives the pulsation modes. Stellar models including time-dependent atomic diffusion, as we compute here, are needed to evaluate the importance of different iron-group elements for mode driving. We perform detailed calculations of radiative accelerations of H, He, C, N, O, Ne, Mg, Fe and Ni and include these in Burgers diffusion equations. We compute the evolution and non-adiabatic pulsations of a typical subdwarf B star. We show that, despite its lower initial abundance, nickel accumulates to comparable mass fractions as iron in the sdB envelope. For accurate determination of pulsation frequencies and mode instability, it is essential that diffusion of both metals are included in stellar models. The role of other iron-group elements remain to be evaluated.
Subdwarf B stars show chemical peculiarities that cannot be explained by diffusion theory alone. Both mass loss and turbulence have been invoked to slow down atomic diffusion in order to match observed abundances. The fact that some sdB stars show pu
lsations gives upper limits on the amount of mass loss and turbulent mixing allowed. Consequently, non-adiabatic asteroseismology has the potential to decide which process is responsible for the abundance anomalies. We compute for the first time seismic properties of sdB models with atomic diffusion included consistently during the stellar evolution. The diffusion equations with radiative forces are solved for H, He, C, N, O, Ne, Mg, Fe and Ni. We examine the effects of various mass-loss rates and mixed surface masses on the abundances and mode stability. It is shown that the mass-loss rates needed to simulate the observed He abundances (10^{-14}<=Mdot [Msun/yr]<=10^{-13}) are not consistent with observed pulsations. We find that for pulsations to be driven the rates should be Mdot<=10^{-15} Msun/yr. On the other hand, weak turbulent mixing of the outer 10^{-6} Msun can explain the He abundance anomalies while still allowing pulsations to be driven. The origin of the turbulence remains unknown but the presence of pulsations gives tight constraints on the underlying turbulence model.
Diffusion of atoms can be important during quiescent phases of stellar evolution. Particularly in the very thin inert envelopes of subdwarf B stars, diffusive movements will considerably change the envelope structure and the surface abundances on a s
hort timescale. Also, the subdwarfs will inherit the effects of diffusion in their direct progenitors, namely giants near the tip of the red giant branch. This will influence the global evolution and the pulsational properties of subdwarf B stars. We investigate the impact of gravitational settling, thermal diffusion and concentration diffusion on the evolution and pulsations of subdwarf B stars. Our diffusive stellar models are compared with models evolved without diffusion. We constructed subdwarf B models with a mass of 0.465 Msun from a 1 and 3 Msun ZAMS progenitor. The low mass star ignited helium in an energetic flash, while the intermediate mass star started helium fusion gently. For each progenitor type we computed series with and without atomic diffusion. Atomic diffusion in red giants causes the helium core mass at the onset of helium ignition to be larger. We find an increase of 0.0015 Msun for the 1 Msun model and 0.0036 Msun for the 3 Msun model. The effects on the red giant surface abundances are small after the first dredge up. The evolutionary tracks of the diffusive subdwarf B models are shifted to lower surface gravities and effective temperatures due to outward diffusion of hydrogen. This affects both the frequencies of the excited modes and the overall frequency spectrum. Especially the structure and pulsations of the post-non-degenerate sdB star are drastically altered, proving that atomic diffusion cannot be ignored in these stars.
Realistic stellar models are essential to the forward modelling approach in asteroseismology. For practicality however, certain model assumptions are also required. For example, in the case of subdwarf B stars, one usually starts with zero-age horizo
ntal branch structures without following the progenitor evolution. We analyse the effects of common assumptions in subdwarf B models on the g-mode pulsational properties. We investigate if and how the pulsation periods are affected by the H-profile in the core-envelope transition zone. Furthermore, the effects of C-production and convective mixing during the core helium flash are evaluated. Finally, we reanalyse the effects of stellar opacities on the mode excitation in subdwarf B stars. We find that helium settling causes a shift in the theoretical blue edge of the g-mode instability domain to higher effective temperatures. This results in a closer match to the observed instability strip of long-period sdB pulsators, particularly for l<=3 modes. We show further that the g-mode spectrum is extremely sensitive to the H-profile in the core-envelope transition zone. If atomic diffusion is efficient, details of the initial shape of the profile become less important in the course of evolution. Diffusion broadens the chemical gradients, and results in less effective mode trapping and different pulsation periods. Furthermore, we report on the possible consequences of the He-flash for the g-modes. The outer edge of a flash-induced convective region introduces an additional chemical transition in the stellar models, and the corresponding spike in the Brunt-Vaisala frequency produces a complicated mode trapping signature in the period spacings.
There are many unknowns in the formation of subdwarf B stars. Different formation channels are considered to be possible and to lead to a variety of helium-burning subdwarfs. All seismic models to date, however, assume that a subdwarf B star is a pos
t-helium-flash-core surrounded by a thin inert layer of hydrogen. We examine an alternative formation channel, in which the subdwarf B star originates from a massive (>~2 Msun) red giant with a non-degenerate helium-core. Although these subdwarfs may evolve through the same region of the log g-Teff diagram as the canonical post-flash subdwarfs, their interior structure is rather different. We examine how this difference affects their pulsation modes and whether it can be observed. Using detailed stellar evolution calculations we construct subdwarf B models from both formation channels. The iron accumulation in the driving region due to diffusion, which causes the excitation of the modes, is approximated by a Gaussian function. The pulsation modes and frequencies are calculated with a non-adiabatic pulsation code. A detailed comparison of two subdwarf B models from different channels, but with the same log g and Teff, shows that their mode excitation is different. The excited frequencies are lower for the post-flash than for the post-non-degenerate subdwarf B star. This is mainly due to the differing chemical composition of the stellar envelope. A more general comparison between two grids of models shows that the excited frequencies of most post-non-degenerate subdwarfs cannot be well-matched with the frequencies of post-flash subdwarfs. In the rare event that an acceptable seismic match is found, additional information, such as mode identification and log g and Teff determinations, allows us to distinguish between the two formation channels.
The formation of subdwarf B (sdB) stars is not well understood within the current framework of stellar single and binary evolution. In this study, we focus on the formation and evolution of the pulsating sdB star in the very short-period eclipsing bi
nary PG1336-018. We aim at refining the formation scenario of this unique system, so that it can be confronted with observations. We probe the stellar structure of the progenitors of sdB stars in short-period binaries using detailed stellar evolution calculations. Applying this to PG1336-018 we reconstruct the common-envelope phase during which the sdB star was formed. The results are interpreted in terms of the standard common-envelope formalism (the alpha-formalism) based on the energy equation, and an alternative description (the gamma-formalism) using the angular momentum equation. We find that if the common-envelope evolution is described by the alpha-formalism, the sdB progenitor most likely experienced a helium flash. We then expect the sdB mass to be between 0.39 and 0.48 Msun, and the sdB progenitor initial mass to be below ~2 Msun. However, the results for the gamma-formalism are less restrictive, and a broader sdB mass range (0.3 - 0.8 Msun) is possible in this case. Future seismic mass determination will give strong constraints on the formation of PG1336-018 and, in particular, on the CE phase.
