Adiabatic Survey of Subdwarf B Star Oscillations. II. Effects of Model Parameters on Pulsation Modes

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Abstract
We present additional results obtained from a systematic adiabatic survey of the pulsation properties of extreme horizontal branch models identified with the subdwarf B stars. This survey is aimed at providing the most basic theoretical tools with which to analyze the asteroseismological characteristics of the recently discovered class of pulsating sdB stars (the EC 14026 stars). In this paper, the second of a series of three, we use an adiabatic pulsation code to compute the low-order, radial and nonradial (from l = 1 through l = 3) p, f, and g oscillation modes of a large grid of static envelope models of subdwarf B stars in order to explore thoroughly parameter space. We first demonstrate that such static models are sufficiently reliable for computations of the pulsation mode properties in these stars. This step is necessary if we are to understand the effects of various model parameters on the pulsation periods of sdB stars, effects that remain hopelessly tangled in evolutionary models. We show, in particular, that low-order radial and nonradial p-modes obtained from static structures do not experience significant period variations compared to modes computed with evolutionary models. This is not surprising because the acoustic modes probe mainly the envelope and are not sensitive to the details of the deep core, which are, of course, ignored in static models. In contrast, we find that the g-mode periods computed with static models are systematically overestimated, and we provide a detailed explanation of this phenomenon. We note, however, that the qualitative behaviors of the g-mode properties are still very well reproduced with static models. Moreover, because the pulsation periods observed in the vast majority of the known EC 14026 stars can be unambiguously identified with low-order acoustic modes, we conclude that static envelope models are valuable additions to the tools that we have at our disposal for carrying out asteroseismological analyses of these stars. On this basis, and in the light of the results presented in the first paper of this series, we next discuss and interpret the pulsation mode behaviors as functions of the main model parameters: the effective temperature Teff, the logarithmic surface gravity log g, the mass of the H-rich envelope Menv, and the total mass of the star Mtot. To achieve this goal, a large grid of 11,200 static envelope models is built and some 1,256,600 adiabatic modes (including p-, f-, and g-modes) are computed. The grid covers the whole volume of parameter space where real subdwarf B stars are expected: 22,000 ≤ Teff ≤ 41,000K, 4.9 ≤ log g ≤ 6.4, 8 × 10-6 ≤ Menv/M⊙ ≤ 8 × 10-3, and 0.46 ≤ Mtot/M⊙ ≤ 0.50. We find that both p- and g-mode periods are very sensitive to the log g parameter, while only g-modes respond significantly to variations of the effective temperature. We stress, however, that mode bumping and avoided crossing phenomena blur somewhat the differences between nonradial acoustic and gravity modes (in effect, these become mixed modes) in the high-Teff, low-gravity part of the explored log g-Teff plane. We show that changing the mass of the H-rich envelope has a significant impact, through the trapping and microtrapping effects, on both the g-mode and, more importantly from a practical point of view, the p-mode period spectra. This raises the exciting possibility of using the signature of the Menv parameter on the acoustic mode periods to constrain the H-rich envelope mass of the EC 14026 stars from their observed period spectra. We also find that the Mtot parameter has a slight, although noticeable, impact on the p- and g-mode periods within the narrow mass range considered in this survey.