Stellar evolution with arbitrary rotation laws. I - Mathematical techniques and test cases

Deupree, R. G.

doi:10.1086/168903

Cited by 54 publications

(59 citation statements)

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“…Nevertheless, if non-axisymmetric instabilities are not important, it is possible to average the equations over the azimuthal direction, resulting in a set of 2D mean-field equations. This opens the possibility of performing stellar evolution in 2D, with an appropriate treatment of these effects (in the limit of low rotation rate due to spherical geometry), see, e.g., Deupree (1990Deupree ( , 2001 and Li et al (2006Li et al ( , 2009. The MUSIC code, which is based on time-implicit methods, provides the ideal framework for that.…”

Section: Resultsmentioning

confidence: 99%

Turbulent Convection in Stellar Interiors. Iii. Mean-Field Analysis and Stratification Effects

Viallet

Meakin

Arnett

et al. 2013

ApJ

126

213

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We present three-dimensional implicit large eddy simulations of the turbulent convection in the envelope of a 5 M red giant star and in the oxygen-burning shell of a 23 M supernova progenitor. The numerical models are analyzed in the framework of one-dimensional Reynolds-Averaged Navier-Stokes equations. The effects of pressure fluctuations are more important in the red giant model, owing to larger stratification of the convective zone. We show how this impacts different terms in the mean-field equations. We clarify the driving sources of kinetic energy, and show that the rate of turbulent dissipation is comparable to the convective luminosity. Although our flows have low Mach numbers and are nearly adiabatic, our analysis is general and can be applied to photospheric convection as well. The robustness of our analysis of turbulent convection is supported by the insensitivity of the mean-field balances to linear mesh resolution. We find robust results for the turbulent convection zone and the stable layers in the oxygen-burning shell model, and robust results everywhere in the red giant model, but the mean fields are not well converged in the narrow boundary regions (which contain steep gradients) in the oxygen-burning shell model. This last result illustrates the importance of unresolved physics at the convective boundary, which governs the mixing there.

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Section: Resultsmentioning

confidence: 99%

Turbulent Convection in Stellar Interiors. Iii. Mean-Field Analysis and Stratification Effects

Viallet

Meakin

Arnett

et al. 2013

ApJ

126

213

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“…Our stellar models are calculated using the 2D stellar structure code ROTORC (Deupree 1990(Deupree , 1995. This code takes the conservation equations for mass, energy, 3 components of momentum and the composition together with Poisson's equation and solves them implicitly on a two dimensional finite difference grid using the Henyey method (Henyey et al 1964).…”

Section: Methodsmentioning

confidence: 99%

Rotation and convective core overshoot inθOphiuchi

Lovekin¹,

Goupil²

2010

A&A

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Context. Recent work on several β Cephei stars has succeeded in constraining both their interior rotation profile and their convective core overshoot. In particular, a recent study focusing on θ Ophiuchi has shown that a convective core overshoot parameter of α ov = 0.44 is required to model the observed pulsation frequencies, significantly higher than for other stars of this type. Aims. We investigate the effects of rotation and overshoot in early type main sequence pulsators, such as β Cephei stars, and attempt to use the low order pulsation frequencies to constrain these parameters. This will be applied to a few test models and the β Cephei star θ Ophiuchi. Methods. We use the 2D stellar evolution code ROTORC and the 2D linear adiabatic pulsation code NRO to calculate pulsation frequencies for 9.5 M models evolved to an age of 15.6 Myr. We calculate low order p-modes ( ≤ 2) for models with a range of rotation rates and convective core overshoot parameters. These low order modes are the same range of modes observed in θ Ophiuchi. Results. Using these models, we find that the convective core overshoot has a larger effect on the pulsation frequencies than the rotation, except in the most rapidly rotating models considered. When the differences in radii are accounted for by scaling the frequencies by √ (GM/R(40 • ) 3 ), the effects of rotation diminish, but are not entirely accounted for. Thus, this scaling emphasizes the differences produced by changing the convective core overshoot. We find that increasing the convective core overshoot decreases the large separation, while producing a slight increase in the small separations. We created a model frequency grid which spanned several rotation rates and convective core overshoot values. We used this grid to define a modified χ 2 statistic in order to determine the best fitting parameters from a set of observed frequencies. Using this statistic, we are able to recover the rotation velocity and convective core overshoot for a few test models. We have also performed a "hare and hound" exercise to see how well 1D models can recover these parameters. Finally, we discuss the case of the β Cephei star θ Oph. Using the observed frequencies and a fixed mass and metallicity, we find a lower overshoot than previously determined, with α ov = 0.28 ± 0.05. Our determination of the rotation rate agrees well with both previous work and observations, around 30 km s −1 .

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“…The 2D structure models were calculated with the rotorc code (Deupree 1990(Deupree , 1995. This code solves the conservation equations for mass, momentum, energy and composition, as well as Poisson's equation on a 2D spherical grid using a Henyey method.…”

Section: D Rotational Deformation: Rotorcmentioning

confidence: 99%

“…This allows us to calculate mode frequencies and amplitudes for each given stellar model. We chose to use classical stellar structure models for the target structures, adding a perturbative Chandrasekhar expansion (Lee & Baraffe 1995) to model stars flattened by the centrifugal force, as well as 2D stellar models (Deupree 1990(Deupree , 1995 that take into account the flattening in a non-perturbative way.…”

Section: Introductionmentioning

confidence: 99%

Seismic modelling of the late Be stars HD 181231 and HD 175869 observed with CoRoT: a laboratory for mixing processes

Neiner

Mathis

Saio

et al. 2012

A&A

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Context. HD 181231 and HD 175869 are two late rapidly rotating Be stars, which have been observed using high-precision photometry with the CoRoT satellite during about five consecutive months and 27 consecutive days, respectively. An analysis of their light curves, by Neiner and collaborators and Gutiérrez-Soto and collaborators respectively, showed that several independent pulsation g-modes are present in these stars. Fundamental parameters have also been determined by these authors using spectroscopy. Aims. We aim to model these results to infer seismic properties of HD 181231 and HD 175869, and constrain internal transport processes of rapidly rotating massive stars. Methods. We used an adiabatic (NRO) and a non-adiabatic (Tohoku) oscillation code that accounts for the combined action of Coriolis and centrifugal accelerations on stellar pulsations as needed for rapid rotator modelling. We coupled these codes with a 2D (ROTORC) stellar structure model to take the rotational deformation of the star into account. The action of transport processes was parametrised with the mixing parameter α ov , which represents the "non-standard" extension of the convective core, and determined by matching observed pulsation frequencies assuming a single star evolution scenario. In a second step, we used (Geneva) evolution models to evaluate the contribution of the secular rotational transport and mixing processes in the radiative envelope. A Monte Carlo analysis of spectropolarimetric data was also performed to examine the role of a potential fossil magnetic field. Finally, based on state-of-the-art modelling of penetrative convection and internal waves, we unravelled their respective contribution to the needed "non-standard" mixing.Results. We find that extra mixing of α ov = 0.3−0.35H p is needed in HD 181231 and HD 175869 to match the observed frequencies with those of prograde sectoral g-modes. We also detect the possible presence of r-modes. We investigated the respective contributions of several transport processes to this mixing: the hydrodynamical processes in particular the meridional circulation and shear-induced turbulence caused by the radiative envelope differential rotation, the possible magnetic field, the penetrative convection at the top of the convective core, and the transport by internal waves. Conclusions. We showed that the extension of the convective core needed to match observations and models may be explained by mixing induced by the penetrative movements at the bottom of the radiative envelope and by the secular hydrodynamical transport processes induced by the rotation in the envelope. We showed how asteroseismology opens a new door to probe transport processes in stellar interiors.

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Stellar evolution with arbitrary rotation laws. I - Mathematical techniques and test cases

Cited by 54 publications

References 0 publications

Turbulent Convection in Stellar Interiors. Iii. Mean-Field Analysis and Stratification Effects

Turbulent Convection in Stellar Interiors. Iii. Mean-Field Analysis and Stratification Effects

Rotation and convective core overshoot inθOphiuchi

Seismic modelling of the late Be stars HD 181231 and HD 175869 observed with CoRoT: a laboratory for mixing processes

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