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

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 ¼ 1 through l ¼ 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 T eff , the logarithmic surface gravity log g, the mass of the H-rich envelope M env , and the total mass of the star M tot . 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 T eff 41;000 K, 4:9 log g 6:4, 8 Â 10 À6 M env =M 8 Â 10 À3 , and 0:46 M tot = M 0:50. We find that both p-and g-mode periods are very sensitive to the log g parameter, while only gmodes 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-T e...

g-mode trapping and period spacings in hot B subdwarf stars

“…However, these perturbations are not uniform along the period range of interest. From radial order k = 1 to k ∼ 20 (periods less than 5 000 s for l = 1 modes), the pattern is comparable to the strong structures reported in Charpinet et al (2002), but beyond this limit the fluctuations decrease in amplitude and the period spacings become nearly uniform. Consequently, the corresponding theoreticaléchelle diagrams (central panels in Fig.…”

“…Among other properties, it was noticed that many modes seem to be nearly equally spaced in period, as one would expect for a homogeneous star showing g-mode oscillations in the asymptotic regime. This finding was in apparent contradiction with the strong g-mode trapping structures caused by the steep chemical gradients expected inside such evolved stratified stars (as illustrated in Charpinet et al 2002), leading to the claim that sdB stars may be much less stratified than previously thought (Reed et al 2011;Telting et al 2012). However, extending the study up to the g-mode cutoff period, we show that the mode trapping efficiency in current stratified models strongly decreases with increasing radial order and that the "standard" models can in fact account quite well for the observed g-mode structure.…”

A preliminary look at the empirical mass distribution of hot B subdwarf stars

“…For each target, and among other derived parameters, we list the inferred values of the surface gravity, effective temperature, total mass, and fractional mass of the outer H-rich envelope, we indicate what kind of modes (p or g) were exploited, we also indicate the known binaries, and we provide the reference to the paper in which the asteroseismological analysis was presented. Given that the mechanical structure of B subdwarfs is such that the pulsation periods are particularly sensitive to variations in surface gravity and much less so to variations in effective temperature (see, e.g., Charpinet et al 2002a), it turns out that more accurate values of log g can be derived from asteroseismological means than spectroscopic methods for these stars. Conversely, asteroseismology provides less accurate estimates of T eff than spectroscopy can, and, therefore, we retained the spectroscopic values of the effective temperature in Table 1.…”

Pulsating sdB Stars: A New Approach to Probing their Interiors

“…This results from resonant mode trapping by the He/C+O composition transition zone. At this evolutionary stage, the sdkkeele.tex; 14/11/2017; 18:42; p.6 model shows some mixed-character modes for ℓ = 2 which can have significant amplitude in the core (Charpinet et al, 2002). Figure 3 lists the computed splittings a Case B sdB model.…”