Structural parameters of the hot pulsating B subdwarf Feige 48 from asteroseismology

Abstract

We present observations followed by a thorough analysis of the rapidly pulsating subdwarf B star (or EC 14026 star) Feige 48. This work is part of a long term multifaceted effort to exploit the strong asteroseismological potential of sdB pulsators which involves high sensitivity photometric observations, accurate spectroscopic measurements, and the development of appropriate modelling tools dedicated to the interpretation of the seismic data. Our model atmosphere analysis of the time averaged optical spectrum of Feige 48 obtained at the new Multiple Mirror Telescope (MMT) leads to estimates of T eff = 29 580 ± 370 K and log g = 5.480 ± 0.046 (with log N(He)/N(H) = −2.95 ± 0.08), in excellent agreement with previous spectroscopic measurements of its atmospheric parameters. This places Feige 48 close to the red edge of the EC 14026 instability region in the log g − T eff plane. A standard Fourier analysis of our high signal-to-noise ratio Canada-France-Hawaii Telescope (CFHT) light curves reveals the presence of nine distinct harmonic oscillations with periods in the range 343−383 s, a significant improvement over previous reported observations that recovered only five periods (Koen et al. 1998, MNRAS, 300, 1105Reed et al. 2004, MNRAS, 348, 1164. Out of these nine periods, only four turn out to be independent modes having different k and/or indices suitable for detailed asteroseismology. The remaining periods can be interpreted as rotationally split components of modes with the same (k, ) values, but different m indices that bear the signature of the rotation of the star. On the basis of the four independent periods, we have carried out a detailed asteroseismic analysis of Feige 48 using the well-known forward method. Our analysis leads objectively to the identification of the (k, ) indices of the four independent periods identified in the star, and to the determination of its structural parameters. The periods correspond to low-order modes with adjacent values of k and with = 0, 1, and 2. They define a band of unstable modes, in agreement with nonadiabatic pulsation theory. Furthermore, the average dispersion between the observed periods and the periods of the corresponding theoretical modes of the optimal model is only ∼0.005%, quite close to the actual accuracy of the observations. We emphasise that radiative levitation is a key ingredient in the determination of accurate pulsation periods for sdB stars, and that standard models with uniform metallicity fail to reproduce the observed periods in Feige 48 because they do not incorporate this key piece of constitutive physics. On the basis of our combined spectroscopic and asteroseismic analysis, the inferred global structural parameters of Feige 48 are T eff = 29 580±370 K, log g = 5.4365±0.0060, log M env /M * = −2.97±0.09, M * = 0.460±0.008 M (i.e., close to the canonical mass of extreme horizontal branch stars), R/R = 0.2147±0.0034, and L/L = 31.62±2.58. Combined with detailed model atmosphere calculations, we estimate, in addition, that this star has ...

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

“…The case of Feige 48 is different. Both Charpinet et al (2005c) and Van Grootel et al (2008a) used 2G models and the same data set, but with the important difference that Van Grootel et al (2008a) fitted all the nine available frequency components in terms of rotationally-split modes with indices k, l, and m, while Charpinet et al (2005c) fitted only the four frequencies identified a priori as the central m = 0 components of rotationally-split multiplets. While the approach of Van Grootel et al (2008a) is to be preferred as a matter of principle, the rather different value of the derived mass, 0.519 ± 0.009 M versus 0.460 ± 0.008 M , heavily hinges on the reality of the lowamplitude f − 4 and f + 4 components of the f 4 triplet reported in Table 1 of Van Grootel et al (2008a).…”

“…In the light of the still unpublished results of a recent extended observational photometric campaign on Feige 48, we are forced at this stage to question the reality of this "triplet", however. For the present needs, we prefer the earlier estimate of the mass provided by Charpinet et al (2005c), which does not depend on whether or not a f 4 triplet exists in the light curve of Feige 48. Billères & Fontaine (2005) analyzed the p-mode pulsator EC 05217−3914 in the same manner as in the previous studies, but could not find time to produce an error analysis.…”

A Quantitative Analysis of the Available Multicolor Photometry for Rapidly Pulsating Hot B Subdwarfs

“…This model has been refined subsequently by Charpinet et al (2005b), who exploited a higher quality (white light) data set and found the same mode identification. In both cases, in the search in parameter space for the optimal model, it was explicitly assumed that the observed modes had to belong to degree indices from l ¼ 0 up to and including l ¼ 3.…”

“…3 are excited to visible levels in that star. Except for the restriction to l-values from 0 to 3, no a priori constraints were imposed in the asteroseismological exercises carried out by Brassard et al (2001) and Charpinet et al (2005b), and the actual mode identification (the determination of both the radial order k and the degree index l for each observed pulsation) came out as a natural by-product of the method.…”

“…Indeed, by combining the forward method with high S/ N ratio spectroscopy, it has been possible to carry out complete asteroseismological analyses for four EC 14026 pulsators so far: PG 0014+067 , PG 1047+003 (Charpinet et al 2003), PG 1219+534 (Charpinet et al 2005c), and Feige 48 (Charpinet et al 2005a). The ultimate product of these analyses is the determination of the global structural properties of the stars, but complete mode identification (i.e., a determination of the radial order k and the degree index l of each pulsation mode) is a by-product of the method.…”