P. Brassard

A DRIVING MECHANISM FOR THE NEWLY DISCOVERED CLASS OF PULSATING SUBDWARF B STARS

We present new calculations that strongly reinforce the idea—originally proposed by Charpinet et al.—that pulsation modes are driven through an opacity bump due to a local enhancement of the iron abundance in the envelopes of sdB stars. Our improved models incorporate nonuniform iron abundance distributions obtained through the condition of diffusive equilibrium between gravitational settling and radiative levitation. They also include special Rosseland opacity tables that take into account the large variations of the iron abundance about the cosmic value that are predicted by equilibrium radiative levitation theory. For representative models with M = 0.48 M☉ and log g = 5.8, we find strong instabilities for low-order radial and nonradial (p and f) pulsation modes in the range 36,500 K Teff 29,000 K. The four pulsating sdB stars currently known all have effective temperatures in that range. In addition, one of our models with Teff = 34,000 K has a band of unstable modes with periods in the range 116-195 s, in excellent agreement with those of the known pulsators. We therefore claim that our proposed iron bump mechanism provides a natural explanation for the instabilities found in the newly discovered class of pulsating sdB stars.

The Potential of Asteroseismology for Hot, Subdwarf B Stars: A New Class of Pulsating Stars?

We present key sample results of a systematic survey of the pulsation properties of models of hot B subdwarfs. We use equilibrium structures taken from detailed evolutionary sequences of solar metallicity (Z = 0.02) supplemented by grids of static envelope models of various metallicities (Z = 0.02, 0.04, 0.06, 0.08, and 0.10). We consider all pulsation modes with l = 0, 1, 2, and 3 in the 80-1500 s period window, the interval currently most suitable for fast photometric detection techniques. We establish that significant driving is often present in hot B subdwarfs and is due to an opacity bump associated with heavy-element ionization. We find that models with Z ≥ 0.04 show low radial order unstable modes; both radial and nonradial (p, f, and g) pulsations are excited. The unstable models have Teff 30,000 K and log g 5.7, depending somewhat on the metallicity. We emphasize that metal enrichment need only occur locally in the driving region. On this basis, combined with the accepted view that local enrichments and depletions of metals are commonplace in the envelopes of hot B subdwarfs, we predict that some of these stars should show luminosity variations resulting from pulsational instabilities.

Discovery and Asteroseismological Analysis of the Pulsating sdB Star PG 0014+067*

We report the discovery of low-amplitude, short-period, multiperiodic luminosity variations in the hot B subdwarf PG 0014+067. This star was selected as a potential target in the course of our ongoing survey to search for pulsators of the EC 14026 type. Our model atmosphere analysis of the time-averaged Multiple Mirror Telescope (MMT) optical spectrum of PG 0014+067 indicates that this star has Teff = 33,550 ± 380 K and log g = 5.77 ± 0.10, which places it right in the middle of the theoretical EC 14026 instability region in the log g-Teff plane. A standard analysis of our Canada-France-Hawaii Telescope (CFHT) light curve reveals the presence of at least 13 distinct harmonic oscillations with periods in the range 80-170 s. Fine structure (closely spaced frequency doublets) is observed in three of these oscillations, and five high-frequency peaks due to nonlinear cross frequency superpositions of the basic oscillations are also possibly seen in the Fourier spectrum. The largest oscillation has an amplitude 0.22% of the mean brightness of the star, making PG 0014+067 the EC 14026 star with the smallest intrinsic amplitudes so far. On the basis of the 13 observed periods, we carry out a detailed asteroseismological analysis of the data starting with an extensive search in parameter space for a model that could account for the observations. To make this search efficient, objective, and reliable, we use a newly developed period matching technique based on an optimization algorithm. This search leads to a model that can account remarkably well for the 13 observed periods in the light curve of PG 0014+067. A detailed comparison of the theoretical period spectrum of this optimal model with the distribution of the 13 observed periods leads to the realization that 10 other pulsations, with lower amplitudes than the threshold value used in our standard analysis, are probably present in the light curve of PG 0014+067. Altogether, we tentatively identify 23 distinct pulsation modes in our target star (counting the frequency doublets referred to above as single modes). These are all low-order acoustic modes with adjacent values of k and with l = 0, 1, 2, and 3. They define a band of unstable periods, in close agreement with nonadiabatic pulsation theory. Furthermore, the average relative dispersion between the 23 observed periods and the periods of the corresponding 23 theoretical modes of the optimal model is only 0.8%, a remarkable achievement by asteroseismological standards. On the basis of our analysis, we infer that the global structural parameters of PG 0014+067 are log g = 5.780 ± 0.008, Teff = 34,500K ± 2690 K, M*/M☉ = 0.490 ± 0.019, log(Menv/M*) = -4.31 ± 0.22, and R/R☉ = 0.149 ± 0.004. If we combine these estimates of the surface gravity, total mass, and radius with our value of the spectroscopic temperature (which is more accurately evaluated than its asteroseismological counterpart, in direct contrast to the surface gravity), we also find that PG 0014+067 has a luminosity L/L☉ = 25.5 ± 2.5, has an absolute visual magnitude MV = 4.48 ± 0.12, and is located at a distance d = 1925 ± 195 pc (using V = 15.9 ± 0.1). If we interpret the fine structure (frequency doublets) observed in three of the 23 pulsations in terms of rotational splitting, we further find that PG 0014+067 rotates with a period of 29.2 ± 0.9 hr and has a maximum rotational broadening velocity of V sin i 6.2 ± 0.4 km s-1.

A compact system of small planets around a former red-giant star

Planets that orbit their parent star at less than about one astronomical unit (1 au is the Earth–Sun distance) are expected to be engulfed when the star becomes a red giant. Previous observations have revealed the existence of post-red-giant host stars with giant planets orbiting as close as 0.116 au or with brown dwarf companions in tight orbits, showing that these bodies can survive engulfment. What has remained unclear is whether planets can be dragged deeper into the red-giant envelope without being disrupted and whether the evolution of the parent star itself could be affected. Here we report the presence of two nearly Earth-sized bodies orbiting the post-red-giant, hot B subdwarf star KIC 05807616 at distances of 0.0060 and 0.0076 au, with orbital periods of 5.7625 and 8.2293 hours, respectively. These bodies probably survived deep immersion in the former red-giant envelope. They may be the dense cores of evaporated giant planets that were transported closer to the star during the engulfment and triggered the mass loss necessary for the formation of the hot B subdwarf, which might also explain how some stars of this type did not form in binary systems.

Spectroscopic Studies of DB White Dwarfs: The Instability Strip of the Pulsating DB (V777 Herculis) Stars

We have secured optical spectra for the eight currently known variable DB, or V777 Her, stars. With the help of a new generation of synthetic spectra, spectroscopic effective temperatures are derived for these objects, as well as for 15 other DB or DBA stars above 20,000 K. We find that the location of the boundaries of the instability strip is sensitive to the atmospheric hydrogen abundance assumed for DB stars: the strip covers the range 22,400-27,800 K if atmospheres of pure helium are used and the range 21,800-24,700 K if undetectable traces of hydrogen are allowed for in the DB models. These determinations provide independent constraints for current seismological analyses of the V777 Her stars. More sensitive searches for weak hydrogen features in hot DB stars should help decide between the two temperature scales.

Kepler observations of the beaming binary KPD 1946+4340

The Kepler Mission has acquired 33.5 d of continuous 1-min photometry of KPD 1946+4340, a short-period binary system that consists of a subdwarf B star (sdB) and a white dwarf. In the light curve, eclipses are clearly seen, with the deepest occurring when the compact white dwarf crosses the disc of the sdB (0.4 per cent) and the more shallow ones (0.1 per cent) when the sdB eclipses the white dwarf. As expected, the sdB is deformed by the gravitational field of the white dwarf, which produces an ellipsoidal modulation of the light curve. Spectacularly, a very strong Doppler beaming (also known as Doppler boosting) effect is also clearly evident at the 0.1 per cent level. This originates from the sdB’s orbital velocity, which we measure to be 164.0 ± 1. 9k m s −1 from supporting spectroscopy. We present light-curve models that account for all these effects, as well as gravitational lensing, which decreases the apparent radius of the white dwarf by about 6 per cent, when it eclipses the sdB. We derive system parameters and uncertainties from the light curve using Markov chain Monte Carlo simulations. Adopting a theoretical white dwarf mass–radius relation, the mass of the subdwarf is found ,

A Theoretical Exploration of the Pulsational Stability of Subdwarf B Stars

In this paper, we first review the main steps of a purely theoretical exploration of the pulsation properties of subdwarf B (sdB) stars that led us, ultimately, to postulate the existence of a new class of pulsating stars. Using both detailed evolutionary and static models of sdB stars, we were able to establish that a potent oscillation driving mechanism exists in these objects. This mechanism results from the κ-effect associated with a local enrichment of iron in the stellar envelope caused by diffusion. On this basis, we reached the conclusion that a fraction of hot B subdwarf stars should show observable pulsational instabilities, a theoretical prediction that was confirmed observationally by the independent discovery of real sdB pulsators by a team of astronomers at the South African Astronomical Observatory. We also review the current status of sdB star seismology, a field that has been growing at a fast pace following this key discovery. For that purpose, we present sample results obtained from more recent pulsation computations based on improved stellar models—our so-called second-generation models—which include a detailed treatment for gravitational settling and radiative levitation of iron. These clearly reveal that the theoretical expectations built upon the recognition of the iron driving mechanism in pulsating sdB stars reproduce remarkably well the observational data currently available. Such results confirm the basic ideas that we developed and that explain the origin of pulsations in sdB stars. They also pave the way for the future exploitation of the full asteroseismological potential of these stars.

Adiabatic properties of pulsating DA white dwarfs. II - Mode trapping in compositionally stratified models

As part of a series of investigations aimed at understanding the adiabatic gravity-mode period structure of models of pulsating DA white dwarfs, we examine qualitatively and quantitatively the phenomenon of mode trapping caused by compositional layering in these stars. This is motivated by the real possibility that the pulsation modes detected in ZZ Ceti stars are actually trapped in the outer hydrogen layer. We first discuss the various manifestations of compositional layering on the pulsational properties of a representative ZZ Ceti star model

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 theoret- ical 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 Teff = 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 � ≤ 3. Our analysis leads ob- jectively to the identification of the (k, � ) 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 � = 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 MV = 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. 1k m s −1 .

Adiabatic properties of pulsating DA white dwarfs. IV - an extensive survey of the period structure of evolutionary models

The results of a detailed adiabatic survey of the pulsation properties of evolutionary models of pulsating DA white dwarfs are presented. Pulsation periods, kinetic energies, and first-order rotation coefficients were calculated for all g-modes with l ≤ 3 in the period window 0-1000 s. The survey was carried out with the help of a new, high-performance adiabatic pulsation code based on the Galerkin finite-element method of weighted residuals. A very large volume of parameter space was explored in order to obtain a complete picture of the fundamental asteroseismological properties of DA white dwarfs