Structural parameters of the hot pulsating B subdwarf PG 1219+534 from asteroseismology

Over the last several years, we have embarked on a long term effort to exploit the strong potential that hot B subdwarf (sdB) pulsators have to offer in terms of asteroseismology. This effort is multifaceted as it involves, on the observational front, the acquisition of high sensitivity photometric data supplemented by accurate spectroscopic measurements, and, on the theoretical and modeling fronts, the development of appropriate numerical tools dedicated to the asteroseismological interpretation of the seismic observations. In this paper, we report on the observations and thorough analysis of the rapidly pulsating sdB star (or EC 14026 star) PG 1219+534. Our model atmosphere analysis of the time averaged optical spectrum of PG 1219+534 obtained at the new Multiple Mirror Telescope (MMT) leads to estimates of T{eff}= 33 600 ± 370 K and log g=5.810 ± 0.046 (with log N(He)/N(H)=-1.49 ± 0.08), in good agreement with previous spectroscopic measurements of its atmospheric parameters. This places PG 1219+534 right in the middle of the EC 14026 instability region in the log g-Teff 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 122{-}172 s, a significant improvement over the original detection of only four periods by Koen et al. (1999, MNRAS, 305, 28). On this basis, we have carried out a detailed asteroseismic analysis of PG 1219+534 using the well-known forward method and assuming that the observed modes have ℓ&leq 3. Our analysis leads objectively to the identification of the (k, ℓ) indices of the nine periods observed in the star PG 1219+534, and to the determination of its structural parameters. The periods all correspond to low-order acoustic modes with adjacent values of k and with ℓ=0, 1, 2, and 3. They define a band of unstable modes, in close agreement with nonadiabatic pulsation theory. Furthermore, the average dispersion between the nine observed periods and the periods of the corresponding nine theoretical modes of the optimal model is only 0.6%, comparable to the results of a similar analysis carried out by Brassard et al. (2001) on the rapid sdB pulsator PG 0014+067. On the basis of our combined spectroscopic and asteroseismic analysis, the inferred global structural parameters of PG 1219+534 are Teff= 33 600 ± 370 K, log g=5.8071 ± 0.0057, log Menv/M*=-4.254 ± 0.147, M*=0.457 ± 0.012 M⊙, R/R⊙=0.1397 ± 0.0028, and L/L⊙=22.01 ± 1.85. Combined with detailed model atmosphere calculations, we estimate, in addition, that this star has an absolute visual magnitude M_V=4.62 ± 0.06 and is located at a distance d=531 ± 23 pc (using V=13.24 ± 0.20). Finally, if we interpret the absence of fine structure (frequency multiplets) as indicative of a slow rotation rate of that star, we further find that PG 1219+534 rotates with a period longer than 3.4 days, and has a maximum rotational broadening velocity of V sin i 2.1 km s-1