Stephane Charpinet

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.

Detection of p-Mode Pulsations and Possible Ellipsoidal Luminosity Variations in the Hot Subdwarf B Star KPD 1930+2752

We report the discovery of multiperiodic luminosity variations in the hot B subdwarf KPD 1930+2752. 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 optical spectrum of KPD 1930+2752 indicates that this star has Teff 33,280 K and log g 5.61, which places it well within the theoretical EC 14026 instability strip. At least 44 harmonic oscillations are seen in the light curve, with periods in the range 145-332 s, and amplitudes in the range 0.064%-0.451% of the mean brightness of the star. In addition, the light curve is dominated by a nearly sinusoidal variation with a period of ~4108.9 s and amplitude of ~1.39%. This latter variation is unique among the known EC 14026 stars. We argue that this relatively slow luminosity variation is likely due to the ellipsoidal deformation of the sdB star in a close binary system containing a faint invisible companion (possibly a white dwarf). Using a new period-matching technique based on a genetic algorithm, we demonstrate that the dense observed period spectrum in the 145-332 s interval is compatible with a theoretical low-degree p-mode spectrum that is rotationally split in a star rotating with a period of ~8217.8 s, the value expected from the ellipsoidal effect invoked to explain the observed long-period variation. This interpretation awaits the test of time-resolved spectroscopy. If confirmed, the potential of KPD 1930+2752 as a laboratory for EC 14026 seismology will become immense.

Discovery of p-Mode Instabilities in the Hot Subdwarf B Star PG 1047+003

We report the discovery of multiperiodic luminosity variations in the hot B subdwarf PG 1047+003. At least five periodicities are seen in the light curve, from 104.2 s to 161.9 s, but others are also present at lower amplitudes in that interval. The largest oscillation has an amplitude of 9.2 millimag in white light and a period of 142.2 s. With atmospheric parameters Teff ~ 34,370 K and log g ~ 5.7 for PG 1047+003, these variations are identified with low-order radial and nonradial (p and f) pulsation modes. The similarity of periods and derived stellar parameters indicate that PG 1047+003 is a genuine member of the EC 14026 class, the latest and newest family of pulsators in the field of asteroseismology. However, it shows no evidence of a binary companion, implying that the mechanism for driving pulsations is internal to the star. We also report on the current status of our ongoing survey to search for additional sdB pulsators.

Detection of p-Mode Pulsations in the Hot Subdwarf B Star KPD 2109+4401

We report the discovery of multiperiodic luminosity variations in the hot B subdwarf KPD 2109+4401. At least five periodicities are seen in the light curve, from 182.5 to 198.4 s. The largest oscillation has an amplitude 8.6 mmag in white light and a period 196.3 s. Our model atmosphere analysis of the time-averaged optical spectrum of KPD 2109+4401 indicates that this star has Teff 31,200 K and log g 5.84. A comparison with pulsation periods computed from stellar models having similar atmospheric parameters implies that the observed brightness variations must be identified with low-order radial and nonradial (p and f) pulsation modes. The overall similarity of periods and derived stellar parameters shows that KPD 2109+4401 is a genuine member of the EC 14026 class, the most recent family of pulsators uncovered in the field of asteroseismology. We note, however, that KPD 2109+4401 is slightly but significantly cooler than the previously known members of this class, thus widening significantly the empirical instability strip. Interestingly, theory predicts that a cooler EC 14026 pulsator (of a given surface gravity) should show larger excited periods, and this is indeed what KPD 2109+4401 shows, with periods reaching values as large as 198 s, not seen previously in other pulsators of the class. We also report on the current status of our ongoing survey to search for additional EC 14026 pulsators.

Gravity-Mode Instabilities in Models of Post-Extreme Horizontal Branch Stars: Another Class of Pulsating Stars?

We present new results of a stability analysis of realistic models of post-extreme horizontal branch stars. We find that g-mode instabilities develop in some of these models as a result of a potent -mechanism associated with the presence of an active H-burning shell. The -process drives low-order and low-degree g modes with typical periods in the range 40-125 s. The unstable models populate a broad instability strip covering the interval 76,000 K Teff 44,000 K and are identified with low-mass DAO white dwarfs. They descend from stars that reach the zero-age extended horizontal branch with H-rich envelope masses Menv0.0010 M☉. Our computations indicate that some DAO stars should show luminosity variations resulting from pulsational instabilities. We suggest looking for brightness variations in six particularly promising candidates.

The Potential of Asteroseimology for Hot, B Subdwarfs: A New Class of Pulsating Stars?

In the last two decades, considerable progress has been made in our understanding of the physical properties and evolutionary status of hot, hydrogenrich subdwarfs B stars (see, e.g., Saffer et al. 1994). It is now currently believed (e.g., Heber et al. 1984) that sdB stars are ~ 0.5 M ⊙ objects belonging to the so-called extended horizontal branch (EHB), which never evolve toward the asymptotic giant branch (AGB) after core helium exhaustion (their hydrogen envelope masses being too small) (see, e.g., Dorman 1995 for a review). They remain at high effective temperatures (T e f f ≥ 20000K) throughout their core-burning evolution and ultimately contribute to a small fraction of the total white dwarf population (Bergeron et al. 1994).

Outstanding Issues for Post-Main Sequence Evolution

We review the question of the empirical and theoretical instability regions in the HR diagram for evolved, compact stars. These include the three families of pulsating white dwarfs (g- mode pulsators excited through mechanisms associated with partial ionization and convection in the stellar envelope), the pulsating subdwarf B stars (p-mode variables excited through a classic kappa mechanism associated with the radiative levitation of iron in the stellar envelope), and the Betsy stars, the brand new class of long-period, g-mode pulsators of the subdwarf B type discovered recently.