Galactic history is written in the white dwarf stars. Their surface properties hint at interiors composed of matter under extreme conditions. In the forty years since their discovery, pulsating white dwarf stars have moved from side-show curiosities to center stage as important tools for unraveling the deep mysteries of the Universe. Innovative observational techniques and theoretical modeling tools have breathed life into precision asteroseismology. We are just learning to use this powerful tool, confronting theoretical models with observed frequencies and their time rate-of-change. With this tool, we calibrate white dwarf cosmochronology; we explore equations of state; we measure stellar masses, rotation rates, and nuclear reaction rates; we explore the physics of interior crystallization; we study the structure of the progenitors of Type Ia supernovae, and we test models of dark matter. The white dwarf pulsations are at once the heartbeat of galactic history and a window into unexplored and exotic physics.

Pulsating White Dwarf Stars and Precision Asteroseismology

We present the observed pulsation spectra of all known noninteracting ZZ Ceti stars (hydrogen atmosphere white dwarf variables [DAVs]) and examine changes in their pulsation properties across the instability strip. We confirm the well-established trend of increasing pulsation period with decreasing effective temperature across the ZZ Ceti instability strip. We do not find a dramatic order-of-magnitude increase in the number of observed independent modes in ZZ Ceti stars, traversing from the hot to the cool edge of the instability strip; we find that the cool DAVs have one more mode on average than the hot DAVs. We confirm the initial increase in pulsation amplitude at the blue edge and find strong evidence of a decline in amplitude prior to the red edge. We present the first observational evidence that ZZ Ceti stars lose pulsation energy just before pulsations shut down at the empirical red edge of the instability strip.

https://www.lume.ufrgs.br/bitstream/handle/10183/108923/000538161.pdf?sequence=1

Ensemble Characteristics of the ZZ Ceti Stars

Understanding differential rotation of Sun-like stars is of great importance for insight into the angular momentum transport in these stars. One means of gaining such information is that of asteroseismology. By a forward modeling approach we analyze in a qualitative manner the impact of different differential rotation profiles on the splittings of p-mode oscillation frequencies. The optimum modes for inference on differential rotation are identified along with the best value of the stellar inclination angle. We find that in general it is not likely that asteroseismology can be used to make an unambiguous distinction between a rotation profile such as a conical Sun-like profile and a cylindrical profile. In addition, it seems unlikely that asteroseismology of Sun-like stars will result in inferences on the radial profile of the differential rotation, such as can be done for red giants. At best, one could possibly obtain the sign of the radial differential rotation gradient. Measurements of the extent of the latitudinal differential from frequency splitting are, however, more promising. One very interesting aspect that could likely be tested from frequency splittings is whether the differential rotation is solar-like or anti-solar-like in nature, in the sense that a solar-like profile has an equatormore » rotating faster than the poles.« less

http://iopscience.iop.org/article/10.1088/0004-637X/790/2/121/pdf

Differential rotation in main-sequence solar-like stars: Qualitative inference from asteroseismic data

We analyse 2.75 yr of Kepler spacecraft observations of the pulsating subdwarf B star KIC 10670103. These 1.4 million measurements have an impressive duty cycle of 93.8 per cent, a frequency resolution of 0.017 μHz, and a 5σ detection limit of 0.1 parts-per-thousand (ppt). We detect 278 periodicities, making KIC 10670103 the richest pulsating subdwarf B star to date. Frequencies range from 23 to 673 μHz (0.4 and 11.8 h), with amplitudes from the detection limit up to 14 ppt. Follow-up spectroscopic data were obtained from which it was determined that KIC 10670103 does not show significant radial velocity variations. Updated atmospheric model fits determined Teff = 21 485 ± 540 K, log g = 5.14 ± 0.05, and log N(He)/N(H) = −2.60 ± 0.04. We identify pulsation modes using asymptotic period spacings and frequency multiplets. The frequency multiplets indicate a spin period of 88 ± 8 d. Of the 278 periodicities detected in KIC 10670103, 163 (59 per cent) have been associated with low-degree ( ≤ 2) pulsation modes, providing tight constraints for model fitting. While the data are exquisite, amplitudes (and some frequencies) are not stable over the course of the observations, requiring tools which are non-standard for compact pulsators such as sliding Fourier transforms and Lorentzian fitting. Using the 163 identified pulsation modes, it is possible to make detailed examinations of the pulsation structure; including where the pulsation power is concentrated in radial order, over what frequency range mode trapping is inefficient, and how power switches between multiplet members.

/pdf/analysis-of-the-rich-frequency-spectrum-of-kic-10670103-56bde9lmk9.pdf

Analysis of the rich frequency spectrum of KIC 10670103 revealing the most slowly rotating subdwarf B star in the Kepler field

Context: PG 1159-035, a pre-white dwarf with Teff? 140 000 K, is the prototype of both two classes: the PG 1159 spectroscopic class and the DOV pulsating class. Previous studies of PG 1159-035 photometric data obtained with the Whole Earth Telescope (WET) showed a rich frequency spectrum allowing the identification of 122 pulsation modes. Analyzing the periods of pulsation, it is possible to measure the stellar mass, the rotational period and the inclination of the rotation axis, to estimate an upper limit for the magnetic field, and even to obtain information about the inner stratification of the star. Aims: We have three principal aims: to increase the number of detected and identified pulsation modes in PG 1159-035, study trapping of the star's pulsation modes, and to improve or constrain the determination of stellar parameters. Methods: We used all available WET photometric data from 1983, 1985, 1989, 1993 and 2002 to identify the pulsation periods. Results: We identified 76 additional pulsation modes, increasing to 198 the number of known pulsation modes in PG 1159-035, the largest number of modes detected in any star besides the Sun. From the period spacing we estimated a mass M/M_? = 0.59 ± 0.02 for PG 1159-035, with the uncertainty dominated by the models, not the observation. Deviations in the regular period spacing suggest that some of the pulsation modes are trapped, even though the star is a pre-white dwarf and the gravitational settling is ongoing. The position of the transition zone that causes the mode trapping was calculated at r_c/R_star = 0.83 ± 0.05. From the multiplet splitting, we calculated the rotational period P_rot = 1.3920 ± 0.0008 days and an upper limit for the magnetic field, B < 2000 G. The total power of the pulsation modes at the stellar surface changed less than 30% for ? = 1 modes and less than 50% for ? = 2 modes. We find no evidence of linear combinations between the 198 pulsation mode frequencies. PG 1159-035 models have not significative convection zones, supporting the hypothesis that nonlinearity arises in the convection zones in cooler pulsating white dwarf stars. Tables [see full textsee full text]-[see full textsee full text] are only available in electronic form at http://www.aanda.org

/pdf/the-pulsation-modes-of-the-pre-white-dwarf-pg-1159-035-vjgr5bx34f.pdf

The pulsation modes of the pre-white dwarf PG 1159-035

On presente les spectres de puissance theoriques des variations lumineuses et de vitesse radiale d'une etoile pulsante non radialement, en incluant les effets de rotation. Application au cas d'une naine blanche a hydrogene et d'une etoile B de la sequence principale

W. D. Pesnell

Papers

Observable quantities of nonradial pulsations in the presence of slow rotation