Nonadiabatic Stability Research Articles

Instabilities in the yellow hypergiant domain

ABSTRACT Yellow hypergiants (YHGs) are massive stars that are commonly interpreted to be in a post-red supergiant evolutionary state. These objects can undergo outbursts on time-scales of decades, which are suspected to be due to instabilities in the envelope. To test this conjecture, the stability of envelope models for YHGs with respect to infinitesimal, radial perturbations is investigated. Violent strange mode instabilities with growth rates in the dynamical regime are identified if the luminosity-to-mass ratio exceeds ≈104 in solar units. For the observed parameters of YHGs, we thus predict instability. The strange mode instabilities persist over the entire range of effective temperatures from red to blue supergiants. Due to short thermal time-scales and dominant radiation pressure in the envelopes of YHGs, a non-adiabatic stability analysis is mandatory and an adiabatic analysis being the basis of the common perception is irrelevant. Contrary to the prevailing opinion, the models considered here do not exhibit any adiabatic instability.

Instabilities and pulsations in models of the B-type supergiant κ Cassiopeiae (HD 2905)

ABSTRACTFor the B-type supergiant κ Cassiopeiae (HD 2905), variabilities with periods between several hours and a few days have been observed both photometrically and spectroscopically. A recent study of this star by Simón-Díaz et al. has revealed variability with a dominant period of 2.7 d. To understand this variability, we present a linear non-adiabatic stability analysis with respect to radial perturbations for models of κ Cassiopeiae. Instabilities associated with the fundamental mode and the first overtone are identified for models with masses between 27 and 44 M⊙. For selected models, the instabilities are followed into the nonlinear regime by numerical simulations. As a result, finite amplitude pulsations with periods between 3 and 1.8 d are found. The model with a mass of 34.5 M⊙ exhibits a pulsation period of 2.7 d consistent with the observations. In the nonlinear regime, the instabilities may cause a substantial inflation of the envelope.

Damping rates and frequency corrections of Kepler LEGACY stars

ABSTRACT Linear damping rates and modal frequency corrections of radial oscillation modes in selected LEGACY main-sequence stars are estimated by means of a non-adiabatic stability analysis. The selected stellar sample covers stars observed by Kepler with a large range of surface temperatures and surface gravities. A non-local, time-dependent convection model is perturbed to assess stability against pulsation modes. The mixing-length parameter is calibrated to the surface-convection-zone depth of a stellar model obtained from fitting adiabatic frequencies to the LEGACY observations, and two of the non-local convection parameters are calibrated to the corresponding LEGACY linewidth measurements. The remaining non-local convection parameters in the 1D calculations are calibrated so as to reproduce profiles of turbulent pressure and of the anisotropy of the turbulent velocity field of corresponding 3D hydrodynamical simulations. The atmospheric structure in the 1D stability analysis adopts a temperature–optical–depth relation derived from 3D hydrodynamical simulations. Despite the small number of parameters to adjust, we find good agreement with detailed shapes of both turbulent pressure profiles and anisotropy profiles with depth, and with damping rates as a function of frequency. Furthermore, we find the absolute modal frequency corrections, relative to a standard adiabatic pulsation calculation, to increase with surface temperature and surface gravity.

Calibrating damping rates with LEGACY* linewidths

Linear damping rates of radial oscillation modes in selected $Kepler$ stars are estimated with the help of a nonadiabatic stability analysis. The convective fluxes are obtained from a nonlocal, time-dependent convection model. The mixing-length parameter is calibrated to the surface-convection-zone depth of a stellar model obtained from fitting adiabatic frequencies to the LEGACY observations, and two of the three nonlocal convection parameters are calibrated to the corresponding LEGACY linewidth measurements. The atmospheric structure in the 1D stability analysis adopts a temperature-optical-depth relation derived from 3D hydrodynamical simulations. Results from 3D simulations are also used to calibrate the turbulent pressure and to guide the functional form of the depth-dependence of the anisotropy of the turbulent velocity field in the 1D stability computations.

KIC 7582608: a newKeplerroAp star with frequency variability

We analyse the fifth roAp star reported in the Kepler field, KIC 7582608, discovered with the SuperWASP project. The object shows a high frequency pulsation at 181.7324d−1 (P = 7.9 min) with an amplitude of 1.45 mmag, and low frequency rotational modulation corresponding to a period of 20.4339 d. Spectral analysis confirms the Ap nature of the target, with characteristic lines of rare earth elements present. From our spectral observations we derive a lower limit on the mean magnetic field modulus of 〈B 〉 =3.05 ± 0.23 kG. Long Cadence Kepler observations show a frequency quintuplet split by the rotational period of the star, typical for an oblique pulsator. We suggest the star is a quadrupole pulsator with a geometry such that i ~ 66° and β ~ 33°. We detect frequency variations of the pulsation in both the WASP and Kepler data sets on many time scales. Linear, non-adiabatic stability modelling allows us to constrain a region on the HR diagram where the pulsations are unstable, an area consistent with observations.

KIC 7582608: a new Kepler roAp star with frequency variability

We analyse the fifth roAp star reported in the Kepler field, KIC 7582608, discovered with the SuperWASP project. The object shows a high frequency pulsation at 181.7324 d$^{-1}$ (P=7.9 min) with an amplitude of 1.45 mmag, and low frequency rotational modulation corresponding to a period of 20.4339 d with an amplitude of 7.64 mmag. Spectral analysis confirms the Ap nature of the target, with characteristic lines of Eu II, Nd III and Pr III present. The spectra are not greatly affected by broadening, which is consistent with the long rotational period found from photometry. From our spectral observations we derive a lower limit on the mean magnetic field modulus of <B> = 3.05$\pm$0.23 kG. Long Cadence Kepler observations show a frequency quintuplet split by the rotational period of the star, typical for an oblique pulsator. We suggest the star is a quadrupole pulsator with a geometry such that $i\sim66^\circ$ and $\beta\sim33^\circ$. We detect frequency variations of the pulsation in both the WASP and Kepler data sets on many time scales. Linear, non-adiabatic stability modelling allows us to constrain a region on the HR diagram where the pulsations are unstable, an area consistent with observations.

Linear analyses for the stability of radial and non-radial oscillations of massive stars

In order to understand the periodic and semi-periodic variations of luminous O- B- A-type stars, linear nonadiabatic stability analyses for radial and nonradial oscillations have been performed for massive evolutionary models ($8M_\odot - 90M_\odot$). In addition to radial and nonradial oscillations excited by the kappa-mechanism and strange-mode instability, we discuss the importance of low-degree oscillatory convection (nonadiabatic g$^-$) modes. Although their kinetic energy is largely confined to the convection zone generated by the Fe opacity peak near $2\times10^5$K, the amplitude can emerge to the photosphere and should be observable in a certain effective temperature range. They have periods longer than those of the radial strange modes so that they seem to be responsible for some of the long-period microvariations of LBVs (S Dor variables) and $\alpha$ Cyg variables. Moreover, monotonously unstable radial modes are found in some models whose initial masses are greater than or equal to $60M_\odot$ with $Z=0.02$. The monotonous instability probably corresponds to the presence of an optically thick wind. The instability boundary roughly coincides with the Humphreys-Davidson limit.

PULSATIONS IN HYDROGEN BURNING LOW-MASS HELIUM WHITE DWARFS

Helium core white dwarfs (WDs) with mass M <~ 0.20 Msun undergo several Gyrs of stable hydrogen burning as they evolve. We show that in a certain range of WD and hydrogen envelope masses, these WDs may exhibit g-mode pulsations similar to their passively cooling, more massive carbon/oxygen core counterparts, the ZZ Cetis. Our models with stably burning hydrogen envelopes on helium cores yield g-mode periods and period spacings longer than the canonical ZZ Cetis by nearly a factor of 2. We show that core composition and structure can be probed using seismology since the g-mode eigenfunctions predominantly reside in the helium core. Though we have not carried out a fully nonadiabatic stability analysis, the scaling of the thermal time in the convective zone with surface gravity highlights several low-mass helium WDs that should be observed in search of pulsations: NLTT 11748, SDSS J0822+2753, and the companion to PSR J1012+5307. Seismological studies of these He core WDs may prove especially fruitful, as their luminosity is related (via stable hydrogen burning) to the hydrogen envelope mass, which eliminates one model parameter.

Accuracy of stellar parameters of exoplanet-host stars determined from asteroseismology

In the context of the space-based mission CoRoT, devoted to asteroseismology and search for planet transits, we analyse the accuracy of fundamental stellar parameters (mass, radius, luminosity) that can be obtained from asteroseismological data.} Our work is motivated by the large uncertainties on planetary radius determination of transiting planets which are mainly due to uncertainties on the stellar parameters. Our goal is to analyse uncertainties of fundamental stellar parameters for a given accuracy of oscillation frequency determination. We generate grids of equilibrium models of stars and compute their pulsation spectra based on a linear nonadiabatic stability analysis. Using differents methods of comparison of oscillation mode spectra, we derive uncertainties on fundamental stellar parameters and analyse the effect of varying the number of considered modes.} The limits obtained depend strongly on the adapted method to compare spectra. We find a degeneracy in the stellar parameter solutions, up to a few % in mass (from less than 1% to more than 7% depending on the method used and the number of considered modes), luminosity (from 2% to more than 10%) or radius (from less than 1% to 3%), for a given pulsation spectrum.

Nonadiabatic asteroseismology of GW vir stars

We present results from nonadiabatic stability calculation to determine the position of the GW Vir band in the log g -Teff diagram. With this method, we calculate the position of seven GW Vir stars. The results are consistent with and complementary to the spectroscopic determination of atmospheric parameters and the chemical compositions of these stars except for the newly discover GW Vir star VV 47. This discrepancy is discussed.

ASTEROSEISMOLOGICAL MODELING OF THE MULTIPERIODIC λ BOOTIS STAR 29 CYGNI

The present work focuses on the discussion of the λ Bootis nature of the multiperiodic δ Scuti star HD 192640 (29 Cyg), through a comprehensive asteroseismic modeling. Some of the most recent asteroseismic tools are used to check whether the observed low metallicity is internal, i.e., intrinsic, present throughout the star, or due to superficial processes as accretion, diffusive settling, radiative levitation, mass loss, etc. The modeling method uses some of the most recent tools, including: (1) effects of rotation on equilibrium models, on the adiabatic oscillation spectrum, and its influence in multicolor observables, (2) nonadiabatic stability of radial and nonradial modes, (3) inclusion of the atmosphere-pulsation interaction for a more accurate multicolor mode identification, and (4) ratio between radial modes n = 4 and n = 5 in the framework of Petersen diagrams. The analysis performed reveals that the models fulfilling all the constraints are those in the middle of the main sequence (MS), with subsolar metallicity, except some other unlikely possibilities. Therefore, this study does not support the idea of the λ Bootis stars being zero-age MS or pre-MS stars interacting with their primordial cloud of gas and dust, but suggest the explanation of their nature as submetallic MS objects. Nevertheless, more accurate multicolor photometric observations are required for a more conclusive study using the procedure presented here, since the observational errors are too large for a definitive rejection of any of the possible explanations.

Nonradial Oscillations in Cepheids

We analyse the presence of nonradial oscillations in Cepheids, a problem that has not been theoretically revised since the work of Dziembowsky (1977, Acta Astron., 27, 95) and Osaki (1977, Publ. Astron. Soc. Japan, 29, 235). Our analysis is motivated by a work of Moskalik et al. (2004, ASPC, 310, 498), which reports the detection of low-amplitude periodicities in a few Cepheids of the large Magellanic cloud. These newly discovered periodicities were interpreted as nonradial modes. Based on linear nonadiabatic stability analysis, our goal is to reanalyse the presence and stability of nonradial modes, taking into account improvement in the main input physics required for the modelling of Cepheids.

Nonadiabatic asteroseismology of GW Vir stars

We present and explore a new method involving a nonadiabatic stability calculation to determine the position of the GW Vir band in the log g — Teff diagram. With this method, we calculate the position of two GW Vir stars, PG 1159-035, log g = 6.80, Teff = 144, 500 K and PG 1707+427, log g = 7.38, Teff = 81, 500 K. The results are consistent with and complementary to the spectroscopic determination of atmospheric parameters and the chemical compositions of these stars.

Nonradial oscillations in classical Cepheids: the problem revisited

Context. We analyse the presence of nonradial oscillations in Cepheids, a problem that has not been theoretically revised since the work of Dziembowski (1977, Acta Astron., 27, 95) and Osaki (1977, PASJ, 29, 235). Our analysis is motivated by a work of Moskalik et al. (2004, ASPC, 310, 498), which reports the detection of low-amplitude periodicities in a few Cepheids of the large Magellanic cloud. These newly discovered periodicities were interpreted as nonradial modes. Aims. Based on linear nonadiabatic stability analysis, our goal is to reanalyse the presence and stability of nonradial modes, taking into account improvement in the main input physics required for the modelling of Cepheids. Methods. We compare the results obtained from two different numerical methods used to solve the set of differential equations: a matrix method and the Ricatti method. Results. We show the limitation of the matrix method for finding low-order p-modes (l < 6), because of their dual character in evolved stars such as Cepheids. For higher order p-modes, we find excellent agreement between the two methods. Conclusions. No nonradial instability is found below l = 5, whereas many unstable nonradial modes exist for higher orders. We also find that nonradial modes remain unstable, even at hotter effective temperatures than the blue edge of the Cepheid instability strip, where no radial pulsations are expected.

Theoretical Distribution of Cepheid Periods in the SMC and LMC

AbstractWe have computed stellar evolutionary models for stars in a mass range characteristic of Cepheid variables for metallicities representative of the Magellanic Clouds populations. These calculations are coupled to a linear non-adiabatic stability analysis in order to get self-consistent mass-period-luminosity relationships. We construct period histograms taking into account a mass function and evolutionary time scales, and we compare them to those given by the microlensing surveys EROSl and OGLE.

Cepheid Models Based on Self-Consistent Stellar Evolution and Pulsation Calculations: The Right Answer?

We have computed stellar evolutionary models for stars in a mass range characteristic of Cepheid variables (3<m/M<12) for different metallicities representative of the Galaxy and the Magellanic Clouds populations. The stellar evolution calculations are coupled to a linear nonadiabatic stability analysis in order to get self-consistent mass-period-luminosity relations. The period-luminosity (PL) relation as a function of metallicity is analyzed and compared with the recent EROS observations in the Magellanic Clouds. The models reproduce the observed width of the instability strips for the SMC and LMC. We determine a statistical PL relationship, taking into account the evolutionary timescales and a mass distribution given by a Salpeter mass function. Excellent agreement is found with the SMC PL relationship determined by Sasselov et al. The models reproduce the change of slope in the PL relationship near P~2.5 days discovered recently by the EROS collaboration (Bauer; Bauer et al.) and thus explain this feature in terms of stellar evolution. Some discrepancy, however, remains for the LMC Cepheids. The models are also in good agreement with beat Cepheids observed by the MACHO and EROS collaborations. We show that most of the first-overtone/second-overtone beat Cepheids have not yet ignited central helium burning; they are just evolving off the main sequence toward the red giant branch.

Sakurai’s Object: Constraints from its Variability?

The peculiar outburst of the star baptized Sakurai’s Object (SO) is a conceivable example of a late He shell flash in a post-AGB object. The new source of nuclear energy forces such objects toward high luminosities and eventually low effective temperatures; they cross the HR diagram in a comparable fashion as FG Sge did in the past - i.e., they move noticeably on the HR diagram on human timescales. From monitoring campaigns of SO during the last year, first estimates of its cooling rate were derived and in particular cyclic light variability was established. We present first results from attempts to model stellar envelopes appropriate for SO. As we hypothesize the light variability to be attributable to stellar pulsations, we aim at constraining the basic stellar parameters based on stability analyses of our envelope models. Radial, nonadiabatic stability computations provided predictions of the modal content which should be observable as SO evolves. The particular components in such mode spectra of SO as they are to appear in the coming years should indeed help to constrain basic stellar parameters such as mass and luminosity.

On non-radial oscillations of B-type stars

The excitation mechanisms behind the slow pulsations―with periods of the order of one day―of OB stars are discussed on the basis of numerical computations. Non-radial, non-adiabatic stability analysis is performed on a set of evolutionary models with masses between 5.2 M ○ . and 12.1 M ○ .. The long-period oscillations in stellar models below the newly recovered β Cephei region are found to be excited by the iron bump in the newly available OPAL opacities. For more massive stars exhibiting oscillations with periods of the order of one day, however, another excitation mechanism must be sought

Exciting Alpha Cygni

The excitation of the possible non-radial oscillations of supergiant stars is still a puzzle. A non-radial, non-adiabatic stability analysis is performed on a series of stellar envelope models of varying mass. A number of excited low-order modes is found. The modes are excited by mode interaction which is found in luminous stars with extended envelopes. Observational consequences are discussed

Analytic solutions of the radial pulsation equation for rotating and magnetic star models

Eddington's (1926) form of wave equation for small-amplitude, radial, adiabatic stellar pulsations of spherically symmetric, gaseous stars is generalized to include the effects of axial rotation and tangled magnetic fields. Equilibrium quantities possessing dimensions are affected, and the relative importance of rotation and magnetism in affecting pulsation characteristics of the models depends on the choices of gamma and the type of model. Solutions are obtained in closed form for adiabatic pulsation periods of fine analytic stellar models, and nonadiabatic stability criteria are determined by means of the one-zone stellar model. Results are discussed for a range of physical parameters such as rotational angular momenta, central condensations, and magnetic energies; and applications are made to the case of classical Cepheids and other variable giant stars.