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

We present observations followed by a thorough analysis of the rapidly pulsating subdwarf B star (or EC14026 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 EC14026 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, 1105; Reed et al. 2004, MNRAS, 348, 1164). Out of these nine periods, only four turn out to be independent modes having different k and/or l indices suitable for detailed asteroseismology. The remaining periods can be interpreted as rotationally split components of modes with the same (k, l) 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, l) 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 l = 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 similar to 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-circle dot (i.e., close to the canonical mass of extreme horizontal branch stars), R/R-circle dot = 0.2147 +/- 0.0034, and L/L-circle dot = 31.62 +/- 2.58. Combined with detailed model atmosphere calculations, we estimate, in addition, that this star has an absolute visual magnitude M-V = 3.961 +/- 0.062 and is located at a distance d = 794 +/- 30 pc (using V = 13.46 +/- 0.02). Finally, the analysis of the fine structure indicate a rotation period of P = 9.44 +/- 1.18 h, leading to an equatorial velocity of V-eq = 27.6 +/- 3.9 km s(-1). Wit a V-eq sin i less than or similar to 5 km s(-1) limit set by Heber et al. (2000, A&A, 363, 198), this result means that Feige 48 is a moderate rotator which, with an inclination angle i less than or similar to 10.4 +/- 1.7 degrees, is seen nearly pole-on.