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Register a new userIron and nickel diffusion in subdwarf B stars
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Haili Hu
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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 as 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.
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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 pulsations 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 short 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 horizontal 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.
In 2007, a companion with planetary mass was found around the pulsating subdwarf B star V391 Pegasi with the timing method, indicating that a previously undiscovered population of substellar companions to apparently single subdwarf B stars might exist. Following this serendipitous discovery, the EXOTIME (http://www.na.astro.it/~silvotti/exotime/) monitoring program has been set up to follow the pulsations of a number of selected rapidly pulsating subdwarf B stars on time-scales of several years with two immediate observational goals: 1) determine Pdot of the pulsational periods P 2) search for signatures of substellar companions in O-C residuals due to periodic light travel time variations, which would be tracking the central stars companion-induced wobble around the center of mass. These sets of data should therefore at the same time: on the one hand be useful to provide extra constraints for classical asteroseismological exercises from the Pdot (comparison with local evolutionary models), and on the other hand allow to investigate the preceding evolution of a target in terms of possible binary evolution by extending the otherwise unsuccessful search for companions to potentially very low masses. While timing pulsations may be an observationally expensive method to search for companions, it samples a different range of orbital parameters, inaccessible through orbital photometric effects or the radial velocity method: the latter favours massive close-in companions, whereas the timing method becomes increasingly more sensitive towards wider separations. In this paper we report on the status of the on-going observations and coherence analysis for two of the currently five targets, revealing very well-behaved pulsational characteristics in HS 0444+0458, while showing HS 0702+6043 to be more complex than previously thought.
We present photometric and spectroscopic analyses of gravity (g-mode) long-period pulsating hot subdwarf B (sdB) stars. We perform a detailed asteroseismic and spectroscopic analysis of five pulsating sdB stars observed with {it TESS} aiming at the global comparison of the observations with the model predictions based on our stellar evolution computations coupled with the adiabatic pulsation computations. We apply standard seismic tools for mode identification, including asymptotic period spacings and rotational frequency multiplets. We calculate the mean period spacing for $l = 1$ and $l = 2$ modes and estimate the errors by means of a statistical resampling analysis. For all stars, atmospheric parameters were derived by fitting synthetic spectra to the newly obtained low-resolution spectra. We have computed stellar evolution models using {tt LPCODE} stellar evolution code, and computed $l = 1$ g-mode frequencies with the adiabatic non-radial pulsation code {tt LP-PUL}. Derived observational mean period spacings are then compared to the mean period spacings from detailed stellar evolution computations coupled with the adiabatic pulsation computations of g-modes. The atmospheric parameters derived from spectroscopic data are typical of long-period pulsating sdB stars with the effective temperature ranging from 23,700,K to 27,600,K and surface gravity spanning from 5.3,dex to 5.5,dex. In agreement with the expectations from theoretical arguments and previous asteroseismological works, we find that the mean period spacings obtained for models with small convective cores, as predicted by a pure Schwarzschild criterion, are incompatible with the observations. We find that models with a standard/modest convective boundary mixing at the boundary of the convective core are in better agreement with the observed mean period spacings and are therefore more realistic.
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