An Isolated White Dwarf with a 70 s Spin Period

We report the discovery of an isolated white dwarf with a spin period of 70 s. We obtained high-speed photometry of three ultramassive white dwarfs within 100 pc and discovered significant variability in one. SDSS J221141.80+113604.4 is a 1.27 M ⊙ (assuming a CO core) magnetic white dwarf that shows 2.9% brightness variations in the BG40 filter with a 70.32 ± 0.04 s period, becoming the fastest spinning isolated white dwarf currently known. A detailed model atmosphere analysis shows that it has a mixed hydrogen and helium atmosphere with a dipole field strength of B d = 15 MG. Given its large mass, fast rotation, strong magnetic field, unusual atmospheric composition, and relatively large tangential velocity for its cooling age, J2211+1136 displays all of the signatures of a double white dwarf merger remnant. Long-term monitoring of the spin evolution of J2211+1136 and other fast-spinning isolated white dwarfs opens a new discovery space for substellar and planetary mass companions around white dwarfs. In addition, the discovery of such fast rotators outside of the ZZ Ceti instability strip suggests that some should also exist within the strip. Hence, some of the monoperiodic variables found within the instability strip may be fast-spinning white dwarfs impersonating ZZ Ceti pulsators.

EPIC 228782059: Asteroseismology of What Could Be the Coolest Pulsating Helium-atmosphere White Dwarf (DBV) Known

We present analysis of a new pulsating helium-atmosphere (DB) white dwarf, EPIC 228782059, discovered from 55.1 days of K2 photometry. The long-duration, high-quality light curves reveal 11 independent dipole and quadruple modes, from which we derive a rotational period of 34.1 ± 0.4 hr for the star. An optimal model is obtained from a series of grids constructed using the White Dwarf Evolution Code, which returns M * = 0.685 ± 0.003M ⊙, T eff = 21,910 ± 23 K, and log g = 8.14 ± 0.01 dex. These values are comparable to those derived from spectroscopy by Koester & Kepler (20,860 ± 160 K, and 7.94 ± 0.03 dex). If these values are confirmed or better constrained by other independent works, it would make EPIC 228782059 one of the coolest pulsating DB white dwarf stars known, and would be helpful for testing different physical treatments of convection, and to further investigate the theoretical instability strip of DB white dwarf stars.

Dynamical stability of giant planets: the critical adiabatic index in the presence of a solid core

ABSTRACT The dissociation and ionization of hydrogen, during the formation of giant planets via core accretion, reduce the effective adiabatic index γ of the gas and could trigger dynamical instability. We generalize the analysis of Chandrasekhar, who determined that the threshold for instability of a self-gravitating hydrostatic body lies at γ = 4/3, to account for the presence of a planetary core, which we model as an incompressible fluid. We show that the dominant effect of the core is to stabilize the envelope to radial perturbations, in some cases completely (i.e. for all γ > 1). When instability is possible, unstable planetary configurations occupy a strip of γ values whose upper boundary falls below γ = 4/3. Fiducial evolutionary tracks of giant planets forming through core accretion appear unlikely to cross the dynamical instability strip that we define.

Convection Theory and Related Problems in Stellar Structure, Evolution, and Pulsational Stability II. Turbulent Convection and Pulsational Stability of Stars

Using our non-local and time-dependent theory of convection and a fixed set of convective parameters (C1, C2/C1 , C3)= (0.70, 0.50, 3.0) calibrated against the Sun, the linear non-adiabatic oscillations for evolutionary models with masses 1–20 M⊙ are calculated. The results show that almost all the classical instability strips can be reproduced. The theoretical instability strips of δ Scuti and γ Doradusvariables agree well with Kepler spacecraft observations. There is no essential difference in the excitation mechanism for δ Scuti and γ Doradus stars. They are excited by the combined effects of the radiative κ-mechanism and coupling between convection and oscillations. They represent two subgroups of a broader type of δ Scuti and γ Doradus stars, located in the lower part of the Cepheid instability strip. δ Scuti is the p-mode subgroup and γ Doradus is the g-mode subgroup. The luminous variable red giants observed by MACHO and OGLE are low-order radial pulsators among low-mass red giant and asymptotic giant branch stars. The excitation and damping mechanism of oscillations for low-temperature stars is studied in detail. Convective flux and turbulent viscosity are consistent damping mechanisms. The damping effect of the convective enthalpy flux is inversely proportional to the frequency of the modes, so it plays an important role in stabilizing the low-order modes and defining the red edge of the Cepheid instability strip. The damping effect of turbulent viscosity reaches its maximum at 3ωτc/16∼1, where τc is the dynamic time scale of turbulent convection and ω is the angular frequency of the modes. Turbulent viscosity is the main damping mechanism for stabilizing the high-order modes of low-temperature variables. The turbulent pressure is, in general, an excitation mechanism; it reaches maximum at 3ωτc/4∼1, and it plays an important role for the excitation of red variables. Convection is not, in fact, a pure damping effect for stellar oscillations. The relative contributions of turbulent pressure, turbulent viscosity, and convective enthalpy flux for excitation and damping effects change with stellar parameters (mass, luminosity, effective temperature) and with the radial order and spherical harmonic degree of the oscillation mode; therefore, the combined effect of convection is sometimes damping, and sometimes the excitation of oscillations. Our research shows that, for low-luminosity red giants, the low-order modes are pulsationally stable, while the intermediate- and high-order modes are unstable. Toward higher luminosity, the range of unstable modes shifts gradually toward the lower order. All of the intermediate- and high-order modes become stable, and a few low-order modes become unstable for high-luminosity red giants. They show the typical pulsational characteristics of Mira-like variables. The variable red giants are, at least for the high-luminosity RGs, self-excited. For red giants, the frequency of the maximally unstable modes predicted by our theory is similar to that given by the semi-empirical scaling relation.

Evolutionary and pulsation properties of Type II Cepheids

We discuss the observed pulsation properties of Type II Cepheids (TIICs) in the Galaxy and in the Magellanic Clouds. We found that period (P) distributions, luminosity amplitudes, and population ratios of the three different sub-groups (BL Herculis [BLH, P < 5 days], W Virginis [WV, 5 ≤ P < 20 days], RV Tauri [RVT, P > 20 days]) are quite similar in different stellar systems, suggesting a common evolutionary channel and a mild dependence on both metallicity and environment. We present a homogeneous theoretical framework based on horizontal branch (HB) evolutionary models, showing that TIICs are mainly old (t ≥ 10 Gyr) low-mass stars. The BLH stars (BLHs) are predicted to be post-early asymptotic giant branch (PEAGB) stars (double shell burning) on the verge of reaching their AGB track (first crossing of the instability strip), while WV stars (WVs) are a mix of PEAGB and post-AGB stars (hydrogen shell burning) moving from the cool to the hot side (second crossing) of the Hertzsprung-Russell Diagram. This suggests that they are a single group of variable stars. The RVT stars (RVTs) are predicted to be a mix of post-AGB stars along their second crossing (short-period tail) and thermally pulsing AGB stars (long-period tail) evolving towards their white dwarf cooling sequence. We also present several sets of synthetic HB models by assuming a bi-modal mass distribution along the HB. Theory suggests, in agreement with observations, that TIIC pulsation properties marginally depend on metallicity. Predicted period distributions and population ratios for BLHs agree quite well with observations, while those for WVs and RVTs are almost a factor of two smaller and higher than observed, respectively. Moreover, the predicted period distributions for WVs peak at periods shorter than observed, while those for RVTs display a long-period tail not supported by observations. We investigate several avenues to explain these differences, but more detailed calculations are required to address these discrepancies.

Effect of Coulomb diffusion of ions on the pulsational properties of DA white dwarfs

Context. Element diffusion is a key physical process that substantially affects the superficial abundances, internal structure, pulsation properties, and evolution of white dwarfs. Aims. We study the effect of Coulomb separation of ions on the cooling times of evolving white dwarfs, their chemical profiles, the Brunt–Väisälä (buoyancy) frequency, and the pulsational periods at the ZZ Ceti instability strip. Methods. We followed the full evolution of white dwarf models in the range 0.5 − 1.3 M⊙ derived from their progenitor history on the basis of a time-dependent element diffusion scheme that incorporates the effect of gravitational settling of ions due to Coulomb interactions at high densities. We compared the results for the evolution and pulsation periods of ZZ Ceti stars with the case where this effect is neglected. Results. We find that Coulomb sedimentation profoundly alters the chemical profiles of ultra-massive (M⋆ ≳ 1 M⊙) white dwarfs throughout their evolution, preventing helium from diffusing inward toward the core, and thus leading to much narrower chemical transition zones. As a result, significant changes in the g-mode pulsation periods as high as 15% are expected for ultra-massive ZZ Ceti stars. For lower mass white dwarfs, the effect of Coulomb separation is much less noticeable. It causes period changes in ZZ Ceti stars that are below the period changes that result from uncertainties in progenitor evolution, but larger than the typical uncertainties of the observed periods. Conclusions. Coulomb diffusion of ions profoundly affects the diffusion flux in ultra-massive white dwarfs, driving the gravitational settling of ions with the same A/Z (mass to charge number). We show that it strongly alters the period spectrum of such white dwarfs, which should be taken into account in detailed asteroseismological analyses of ultra-massive ZZ Ceti stars.

A theoretical framework for BL Her stars – I. Effect of metallicity and convection parameters on period–luminosity and period–radius relations

ABSTRACT We present a new grid of convective BL Herculis models using the state-of-the-art 1D non-linear radial stellar pulsation tool mesa-rsp. We investigate the impact of metallicity and four sets of different convection parameters on multiwavelength properties. Non-linear models were computed for periods typical for BL Her stars, i.e. 1 ≤ P(d) ≤ 4 covering a wide range of input parameters – metallicity (−2.0 dex ≤ [Fe/H] ≤ 0.0 dex), stellar mass (0.5–0.8 M⊙), luminosity (50–300 L⊙), and effective temperature (full extent of the instability strip; in steps of 50 K). The total number of BL Her models with full-amplitude stable pulsations used in this study is 10 280 across the four sets of convection parameters. We obtain their multiband (UBVRIJHKLL′M) light curves and derive new theoretical period–luminosity (PL), period–Wesenheit (PW), and period–radius (PR) relations at mean light. We find that the models computed with radiative cooling show statistically similar slopes for PL, PW, and PR relations. Most empirical relations match well with the theoretical PL, PW, and PR relations from the BL Her models computed using the four sets of convection parameters. However, PL slopes of the models with radiative cooling provide a better match to empirical relations for BL Her stars in the Large Magellanic Cloud in the HKS bands. For each set of convection parameters, the effect of metallicity is significant in U and B bands and negligible in infrared bands, which is consistent with empirical results. No significant metallicity effects are seen in the PR relations.

ANALYSIS OF A SHORT PERIODIC PULSATOR: SX PHOENICIS STAR XX CYG

Photometric observations were made of the SX Phoenicis star XX Cyg between September and October 2019, using the 1.88-m Kottamia reflector telescope in Egypt. We used 340 CCD observations with blue-visible-red (BVR) filters to derive light curves. In addition, we obtained 9540 visual magnitudes for XX Cyg from the literature to prepare an observed-minus-calculated (O-C) diagram. 85 new times of maximum for XX Cyg are presented. We did not detect a bump in the descending portion of the light curve of maximum light for XX Cyg. However, we did detect a secular bump in the phased light curves, which changes with phase in some SuperWASP observations. We found the change in period of XX Cyg to be dP/dt = 15.5 × 10-5 s/yr, with its amplitude decreasing at a rate of 0.7 mmag/year. Stellar parameters of XX Cyg and its position in the instability strip of the Hertzsprung Russell stellar evolution diagram are presented.

Benchmarking the fundamental parameters of Ap stars with optical long-baseline interferometric measurements

Context. The variety of physical processes at play in chemically peculiar stars makes it difficult to determine their fundamental parameters. In particular, for the magnetic ones, called Ap stars, the strong magnetic fields and the induced spotted stellar surfaces may lead to biased effective temperatures when these values are derived through spectro-photometry. Aims. We propose to benefit from the exquisite angular resolution provided by long-baseline interferometry in the visible to determine the accurate angular diameters of a number of Ap stars, and thus estimate their radii by a method that is as independent as possible of atmospheric models. Methods. We used the visible spectrograph VEGA at the CHARA interferometric array to complete the sample of Ap stars currently observable with this technique. We estimated the angular diameter and radius of six new targets. We estimated their bolometric flux based solely on observational spectroscopic and photometric data to derive nearly model-independent luminosities and effective temperatures. Results. We extend to 14 the number of Ap stars for which interferometric angular diameters have been measured. The fundamental parameters we derived for the complete Ap sample are compared with those obtained through a self-consistent spectroscopic analysis. Based on a model fitting approach of high-resolution spectra and spectro-photometric observations over a wide wavelength range, this method takes into account the anomalous chemical composition of the atmospheres and the inhomogeneous vertical distribution for different chemical elements. Regarding both the radii and the effective temperatures, the derived values from our interferometric observations and from self-consistent modelling are consistent within better than 2σ for nine targets out of ten. We thus benchmark nine Ap stars for effective temperatures ranging from 7200 and 9100 K, and luminosities ranging between 7 L⊙ and 86 L⊙. Conclusions. These results will be key for the future derivation of accurate radii and other fundamental parameters of fainter peculiar stars for which both the sensitivity and the angular resolution of the current interferometers are not sufficient. Within the context of the observations of Ap stars with the Transiting Exoplanet Survey Satellite (TESS), these interferometric measurements are crucial for testing the mechanism of pulsation excitation at work in these peculiar stars. In particular, our interferometric measurements provide accurate locations in the Hertzsprung-Russell diagram for hot Ap stars among which pulsations may be searched for with TESS, putting to test the blue edge of the theoretical instability strip. These accurate locations could be used to derive masses and ages of these stars through a specific grid of models, and to test correlations between the properties of these peculiar stars and their evolutionary state.

On the first δ Sct–roAp hybrid pulsator and the stability of p and g modes in chemically peculiar A/F stars

ABSTRACT Strong magnetic fields in chemically peculiar A-type (Ap) stars typically suppress low-overtone pressure modes (p modes) but allow high-overtone p modes to be driven. KIC 11296437 is the first star to show both. We obtained and analysed a Subaru spectrum, from which we show that KIC 11296437 has abundances similar to other magnetic Ap stars, and we estimate a mean magnetic field modulus of 2.8 ± 0.5 kG. The same spectrum rules out a double-lined spectroscopic binary, and we use other techniques to rule out binarity over a wide parameter space, so the two pulsation types originate in one δ Sct–roAp hybrid pulsator. We construct stellar models depleted in helium and demonstrate that helium settling is second to magnetic damping in suppressing low-overtone p modes in Ap stars. We compute the magnetic damping effect for selected p and g modes, and find that modes with frequencies similar to the fundamental mode are driven for polar field strengths ≲4 kG, while other low-overtone p modes are driven for polar field strengths up to ∼1.5 kG. We find that the high-order g modes commonly observed in γ Dor stars are heavily damped by polar fields stronger than 1–4 kG, with the damping being stronger for higher radial orders. We therefore explain the observation that no magnetic Ap stars have been observed as γ Dor stars. We use our helium-depleted models to calculate the δ Sct instability strip for metallic-lined A (Am) stars, and find that driving from a Rosseland mean opacity bump at ∼5 × 104 K caused by the discontinuous H-ionization edge in bound-free opacity explains the observation of δ Sct pulsations in Am stars.