Out-of-equilibrium Relaxation of a Time-dependent Effective Temperature

Context. The possible existence of warm (Teff ∼ 19 000 K) pulsating DA white dwarf (WD) stars, hotter than ZZ Ceti stars, was predicted in theoretical studies more than 30 yr ago. These studies reported the occurrence of g-mode pulsational instabilities due to the κ mechanism acting in the partial ionization zone of He below the H envelope in models of DA WDs with very thin H envelopes (MH/M⋆ ≲ 10−10). However, to date, no pulsating warm DA WD has been discovered, despite the varied theoretical and observational evidence suggesting that a fraction of WDs should be formed with a range of very low H content. Aims. We re-examine the pulsational predictions for such WDs on the basis of new full evolutionary sequences. We analyze all the warm DAs observed by the TESS satellite up to Sector 9 in order to search for the possible pulsational signal. Methods. We computed WD evolutionary sequences of masses 0.58 and 0.80 M⊙ with H content in the range −14.5 ≲ log(MH/M⋆)≲ − 10, appropriate for the study of pulsational instability of warm DA WDs. Initial models were extracted from progenitors that were evolved through very late thermal pulses on the early cooling branch. We use LPCODE stellar code into which we have incorporated a new full-implicit treatment of time-dependent element diffusion to precisely model the H–He transition zone in evolving WD models with very low H content. The nonadiabatic pulsations of our warm DA WD models were computed in the effective temperature range of 30 000 − 10 000 K, focusing on ℓ = 1 g modes with periods in the range 50 − 1500 s. Results. We find that traces of H surviving the very late thermal pulse float to the surface, eventually forming thin, growing pure H envelopes and rather extended H–He transition zones. We find that such extended transition zones inhibit the excitation of g modes due to partial ionization of He below the H envelope. Only in the cases where the H–He transition is assumed much more abrupt than predicted by diffusion do models exhibit pulsational instability. In this case, instabilities are found only in WD models with H envelopes in the range of −14.5 ≲ log(MH/M⋆)≲ − 10 and at effective temperatures higher than those typical for ZZ Ceti stars, in agreement with previous studies. None of the 36 warm DAs observed so far by TESS satellite are found to pulsate. Conclusions. Our study suggests that the nondetection of pulsating warm DAs, if WDs with very thin H envelopes do exist, could be attributed to the presence of a smooth and extended H–He transition zone. This could be considered as indirect proof that element diffusion indeed operates in the interior of WDs.

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Spectroscopic properties of a two-dimensional time-dependent Cepheid model

Astronomy and Astrophysics ◽

10.1051/0004-6361/201732201 ◽

2018 ◽

Vol 611 ◽

pp. A19 ◽

Cited By ~ 6

Author(s):

V. Vasilyev ◽

H.-G. Ludwig ◽

B. Freytag ◽

B. Lemasle ◽

M. Marconi

Keyword(s):

Effective Temperature ◽

Spectroscopic Properties ◽

Variable Stars ◽

Time Dependent ◽

Surface Gravity ◽

Current Standard ◽

Static Approximation ◽

Cepheid Variables ◽

Microturbulent Velocity ◽

1D Model

Context. Standard spectroscopic analyses of variable stars are based on hydrostatic 1D model atmospheres. This quasi-static approach has not been theoretically validated. Aim. We aim at investigating the validity of the quasi-static approximation for Cepheid variables. We focus on the spectroscopic determination of the effective temperature Teff, surface gravity log g, microturbulent velocity ξt, and a generic metal abundance log A, here taken as iron.Methods. We calculated a grid of 1D hydrostatic plane-parallel models covering the ranges in effective temperature and gravity that are encountered during the evolution of a 2D time-dependent envelope model of a Cepheid computed with the radiation-hydrodynamics code CO5BOLD. We performed 1D spectral syntheses for artificial iron lines in local thermodynamic equilibrium by varying the microturbulent velocity and abundance. We fit the resulting equivalent widths to corresponding values obtained from our dynamical model for 150 instances in time, covering six pulsational cycles. In addition, we considered 99 instances during the initial non-pulsating stage of the temporal evolution of the 2D model. In the most general case, we treated Teff, log g, ξt, and log A as free parameters, and in two more limited cases, we fixed Teff and log g by independent constraints. We argue analytically that our approach of fitting equivalent widths is closely related to current standard procedures focusing on line-by-line abundances.Results. For the four-parametric case, the stellar parameters are typically underestimated and exhibit a bias in the iron abundance of ≈−0.2 dex. To avoid biases of this type, it is favorable to restrict the spectroscopic analysis to photometric phases ϕph ≈ 0.3…0.65 using additional information to fix the effective temperature and surface gravity.Conclusions. Hydrostatic 1D model atmospheres can provide unbiased estimates of stellar parameters and abundances of Cepheid variables for particular phases of their pulsations. We identified convective inhomogeneities as the main driver behind potential biases. To obtain a complete view on the effects when determining stellar parameters with 1D models, multidimensional Cepheid atmosphere models are necessary for variables of longer period than investigated here.

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Out-of-equilibrium Relaxation of a Time-dependent Effective Temperature

Jamming, Yielding, and Irreversible Deformation in Condensed Matter - Lecture Notes in Physics ◽

10.1007/11581000_8 ◽

2006 ◽

pp. 129-136

Author(s):

A. Lemaítre

Keyword(s):

Effective Temperature ◽

Time Dependent

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Irregularity Interpreted as Low Dimension Chaos for Convective Models of W VIR Variables

International Astronomical Union Colloquium ◽

10.1017/s0252921100011751 ◽

1989 ◽

Vol 111 ◽

pp. 267-267

Author(s):

S. Ami Glasner ◽

J. Robert Buchler

Keyword(s):

Effective Temperature ◽

Control Parameter ◽

Chaotic Behavior ◽

Time Dependent ◽

Special Cases ◽

Low Dimension ◽

Rv Tau Stars ◽

Linear And Nonlinear ◽

Stellar Envelopes ◽

Irregular Behavior

AbstractLinear and nonlinear pulsational properties of convective stellar envelopes relevant for W Vir and RV Tau stars are surveyed. All models show the same trend to pass from regular to irregular behavior when a control parameter is changed (the effective temperature). The transition to irregular pulsation follows well known systematic routes to chaos (as in the radiative case). Some rich structures were found in special cases; they deserve further research. We show that the chaotic behavior is sustained even when convection is taken into account. The effect of the inclusion of time dependent convection shows up mostly as a shift of Kovacs and Buchler (Ap.J 1988) results in the parameters plane (L,Teff) towards more realistic models.

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Nonlinear Models of Miras, Including Time-Dependent Convection

International Astronomical Union Colloquium ◽

10.1017/s0252921100117361 ◽

1993 ◽

Vol 139 ◽

pp. 208-208

Author(s):

Dale A. Ostlie ◽

Arthur N. Cox

Keyword(s):

Effective Temperature ◽

Fundamental Mode ◽

Chaotic Behavior ◽

Nonlinear Models ◽

Variable Stars ◽

Time Dependent ◽

Phase Lag ◽

Spatial Averaging ◽

Mira Variable ◽

Turbulent Pressure

AbstractNonlinear calculations of Mira variable stars of Population I are presented. Each model is 1 M⊙, with a luminosity of 5000 L⊙ and an effective temperature near 3000 K. These models incorporate our theory of time-dependent convection, which is based on a convective phase lag formalism and includes spatial averaging of convective eddies from adjacent zonal interfaces. The theory also includes turbulent pressure, energy, and viscosity terms and allows for negative convective luminosities in subadiabatic regions where overshooting occurs.Results of the present study suggest that based upon the dynamic behavior of the models, fundamental mode pulsations are the preferred mode of oscillation. In particular, we do not obtain the chaotic behavior that has been noted in previous nonlinear studies of the fundamental mode oscillations of Miras.

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White Dwarf and Pre-White Dwarf Oscillations

International Astronomical Union Colloquium ◽

10.1017/s0252921100117038 ◽

1993 ◽

Vol 139 ◽

pp. 107-115

Author(s):

Arthur N. Cox

Keyword(s):

Effective Temperature ◽

White Dwarf ◽

Time Scale ◽

Convection Zone ◽

Scale Effects ◽

Asymptotic Giant Branch ◽

Compact Stars ◽

Time Dependent ◽

Short Time Scale ◽

Surface Layers

AbstractCompact stars that result from extreme mass loss on the asymptotic giant branch and planetary nebula formation are observed to pulsate in a very large surface effective temperature range as they cool to become the classical white dwarfs. The hottest and most luminous of these display periods in excess of 1000 seconds because they are large, but when the stars arrive on the cooling line on the Hertzsprung-Russell diagram, their periods become generally less than 1000 seconds. Then the stars have masses near 0.6 M⊙ and radii near 109 cm. Their luminosity depends then almost entirely on the surface effective temperature as the entire star with its legacy of complicated internal luminosity peaks cools to the classical simple electron degenerate structure. Very thin surface layers of hydrogen and helium cover the bulk of the carbon- and oxygen-rich mass that results from hydrogen and helium burning in earlier intermediate mass stellar evolution. The cause of the nonradial pulsations of low angular degree, but rather high radial order, for the most luminous of these stars is the cyclical ionization of carbon and oxygen in layers not too deep that their effectiveness is limited by a long luminosity time scale. Thus the surface hydrogen and helium must be thin, probably thinner than the current period spacings interpretation for PG 1159-035 suggests. For the classical DBV and DAV pulsators, it appears that neither the hydrogen ionization K and γ effects or convection blocking at the bottom of a hydrogen convection zone can destabilize the observed pulsations when the overriding short time scale effects of time-dependent convection are included. It appears, however, that a thin CO convection shell can produce pulsations by its time-dependent effects, but again only very thin H and He surface layers are allowed. This new pulsation mechanism can alleviate the serious problem that DAV variables are observed hotter than the hydrogen K and γ effects and convection blocking can predict. The appearance of non-pulsators in the DAV and DBV instability strips can be explained by a too-thick hydrogen and helium surface layer that interferes with (poisons) the CO ionization convection zone. Finally time-dependent convection predicts that only a few of the many possible modes exist due to their internal amplitude structure that can result in both strong driving and strong damping. Thus actually observed pulsating modes can assist in mapping individual internal white dwarf composition structures, not only by their periods but also the fact that they pulsate.

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