Classically and Asteroseismically Constrained 1D Stellar Evolution Models of α Centauri A and B Using Empirical Mixing Length Calibrations

Over the past decades various forms of the mixing length theory (MLT) have been used to describe convection in stellar atmospheres. Recent advances in turbulence theory now allow for major improvements in modelling thermal convection. We review several models for convection which have been derived from turbulence theory, and describe one of them, the “CM model”, in detail. The CM model has been used in several stellar evolution and helioseismology codes during the last four years and has now been applied to model atmospheres. An overwiew comparing stellar atmosphere models based on the CM formulation with its MLT predecessors indicates improvements on model atmospheres for A and F stars.

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Testing the entropy calibration of the radii of cool stars: models of α Centauri A and B

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz2465 ◽

2019 ◽

Cited By ~ 2

Author(s):

Federico Spada ◽

Pierre Demarque

Keyword(s):

Stellar Evolution ◽

Ad Hoc ◽

Calibration Method ◽

Radiation Hydrodynamics ◽

Mixing Length ◽

Specific Entropy ◽

Cool Stars ◽

Host Stars ◽

Comparable Quality ◽

Temperature Surface

Abstract We present models of α Centauri A and B implementing an entropy calibration of the mixing-length parameter αMLT, recently developed and successfully applied to the Sun (Spada et al. 2018, ApJ, 869, 135). In this technique the value of αMLT in the 1D stellar evolution code is calibrated to match the adiabatic specific entropy derived from 3D radiation-hydrodynamics simulations of stellar convective envelopes, whose effective temperature, surface gravity, and metallicity are selected consistently along the evolutionary track. The customary treatment of convection in stellar evolution models relies on a constant, solar-calibrated αMLT. There is, however, mounting evidence that this procedure does not reproduce the observed radii of cool stars satisfactorily. For instance, modelling α Cen A and B requires an ad-hoc tuning of αMLT to distinct, non-solar values. The entropy-calibrated models of α Cen A and B reproduce their observed radii within $1\%$ (or better) without externally adjusted parameters. The fit is of comparable quality to that of models with freely adjusted αMLT for α Cen B (within 1 σ), while it is less satisfactory for α Cen A (within ≈2.5 σ). This level of accuracy is consistent with the intrinsic uncertainties of the method. Our results demonstrate the capability of the entropy calibration method to produce stellar models with radii accurate within $1\%$. This is especially relevant in characterising exoplanet-host stars and their planetary systems accurately.

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Recent Advances in Convection Theory and Modelling

Highlights of Astronomy ◽

10.1017/s1539299600011618 ◽

1995 ◽

Vol 10 ◽

pp. 433-434

Author(s):

S. Sofia

Keyword(s):

Stellar Evolution ◽

Numerical Models ◽

Spatial Scales ◽

Stellar Structure ◽

Wave Number ◽

The Sun ◽

Mixing Length ◽

Number Range ◽

Wide Range ◽

Non Locality

This Joint Discussion (Number 13), took place on August 22, 1994 at The Hague, in connection with the XXII General Assembly of the IAU. At the one-day long meeting, there were presentations by 15 invited speakers and 15 posters.The Joint Discussions had been organized in response to the considerable progress made in this field of research during the previous decade. Although it had long been known that the prevailing mixing length theory (MLT), used extensively and very successfully in Astrophysics for several decades had become needlessly limited, until recently it was impractical to contemplate more realistic approaches. The situation has changed recently as a consequence of advances in numerical techniques and computational capabilities, and thus JD 13 was organized to discuss the advances, and perhaps to understand the strengths and weaknesses of each approach.There were two presentations which addressed the main issues in convection theory (E. Schatzman), and the astrophysical implications (P. Demarque). Several talks covered current numerical codes, which included deep convection in a rotating reference frame (K. Chan), convection in the presence of magnetic fields (P. Fox), and shallower solar convection simulations on a wide range of spatial scales (A. Nordlund). Although these approaches have enriched (and are continuing to enrich) our understanding of the physics of convective fluids, they are much too detailed (both in space and in time) to be integrated in the study of stellar evolution. To overcome this shortcoming, S. Sofia described a technique developed together with Lydon and Fox to use relationships between dynamical and thermodynamic properties of convective flows derived in numerical models to be applied in stellar structure and evolution codes by performing small modifications of the standard MLT formalism. The advantage of this technique is that it does not contain a mixing length or any other arbitrary parameter, and it was used successfully in modeling the evolution of the Sun and other solar analogues. V. Canuto also presented a formulation of convection both amenable to be used in stellar evolution studies, and not requiring an arbitrary mixing length-like parameter. His formulation uses the Reynolds stress method, which has the advantage of modeling the full eddy spectrum of the turbulence, rather than the narrow wave number range for energy containing eddies assumed in the MLT. Additionally, this technique can address the problems of non-locality and overshoot. M. Stix also addressed non-locality and overshoot by presenting results of a non-local mixing length model of the Sun derived from the Shaviv and Salpeter model.

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Modelling the solar twin 18 Scorpii

Astronomy and Astrophysics ◽

10.1051/0004-6361/201834058 ◽

2018 ◽

Vol 619 ◽

pp. A172 ◽

Cited By ~ 5

Author(s):

M. Bazot ◽

O. Creevey ◽

J. Christensen-Dalsgaard ◽

J. Meléndez

Keyword(s):

Chemical Composition ◽

Stellar Evolution ◽

Seismic Data ◽

Gaussian Mixture Models ◽

Gaussian Mixture ◽

Mixing Length ◽

Posterior Density ◽

Initial Chemical Composition ◽

Probability Densities ◽

Set Up

Context. Solar twins are objects of great interest in that they allow us to understand better how stellar evolution and structure are affected by variations of the stellar mass, age and chemical composition in the vicinity of the commonly accepted solar values. Aims. We aim to use the existing spectrophotometric, interferometric and asteroseismic data for the solar twin 18 Sco to constrain stellar evolution models. 18 Sco is the brightest solar twin and is a good benchmark for the study of solar twins. The goal is to obtain realistic estimates of its physical characteristics (mass, age, initial chemical composition, mixing-length parameter) and realistic associated uncertainties using stellar models. Methods. We set up a Bayesian model that relates the statistical properties of the data to the probability density of the stellar parameters. Special care is given to the modelling of the likelihood for the seismic data, using Gaussian mixture models. The probability densities of the stellar parameters are approximated numerically using an adaptive MCMC algorithm. From these approximate distributions we proceeded to a statistical analysis. We also performed the same exercise using local optimisation. Results. The precision on the mass is approximately 6%. The precision reached on X0 and Z0 and the mixing-length parameter are respectively 6%, 9%, and 35%. The posterior density for the age is bimodal, with modes at 4.67 Gyr and 6.95 Gyr, the first one being slightly more likely. We show that this bimodality is directly related to the structure of the seismic data. When asteroseismic data or interferometric data are excluded, we find significant losses of precision for the mass and the initial hydrogen-mass fraction. Our final estimates of the uncertainties from the Bayesian analysis are significantly larger than values inferred from local optimization. This also holds true for several estimates of the age encountered in the literature.

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Calibration of mixing-length parameter α for MLT and FST models by matching with CO5BOLD models

Astronomy and Astrophysics ◽

10.1051/0004-6361/201833495 ◽

2019 ◽

Vol 621 ◽

pp. A84 ◽

Cited By ~ 5

Author(s):

T. Sonoi ◽

H.-G. Ludwig ◽

M.-A. Dupret ◽

J. Montalbán ◽

R. Samadi ◽

...

Keyword(s):

Surface Structure ◽

Stellar Evolution ◽

Effective Temperature ◽

3D Models ◽

Surface Gravity ◽

Mixing Length ◽

Convective Envelope ◽

Near Surface ◽

Convection Model ◽

Oscillation Frequencies

Context. Space observations by the CoRoT and Kepler missions have provided a wealth of high-quality seismic data for a large number of stars from the main sequence to the red giant phases. One main goal of these missions is to take advantage of the rich spectra of solar-like oscillations to perform precise determinations of stellar characteristic parameters. To make the best of such data, we need theoretical stellar models with a precise near-surface structure since a near-surface structure of a solar-like star has significant influence on solar-like oscillation frequencies. The mixing-length parameter is a key factor to determine the near-surface structure of stellar models. In current versions of the convection formulations used in stellar evolution codes, the mixing-length parameter is a free parameter that needs to be properly specified. Aims. We aim at determining appropriate values of the mixing-length parameter, α, to be used consistently with the adopted convection formulation when computing stellar evolution models across the Hertzsprung–Russell diagram. This determination is based on 3D hydrodynamical simulation models. Methods. We calibrated α values by matching entropy profiles of 1D envelope models with those of hydrodynamical 3D models of solar-like stars produced by the CO5BOLD code. For such calibration, previous works concentrated on the classical mixing-length theory (MLT). We also analyzed full spectrum turbulence (FST) models. To construct the atmosphere in the 1D models, we used the Eddington gray T(τ) relation and that with the solar-calibrated Hopf-like function. Results. For both MLT and FST models with a mixing length l = αHp, calibrated α values increase with increasing surface gravity or decreasing effective temperature. For the FST models, we carried out an additional calibration using an α* value defined as l = rtop − r + α*Hp, top, where α* is found to increase with surface gravity and effective temperature. We provide tables of the calibrated α values across the Teff–log g plane for solar metallicity. By computing stellar evolution with varying α based on our 3D α calibration, we find that the change from solar α to varying α shifts evolutionary tracks particularly for the FST model. As for the correspondence to the 3D models, the solar Hopf-like function generally gives a photospheric-minimum entropy closer to a 3D model than the Eddington T(τ). The structure below the photosphere depends on the adopted convection model. However, we cannot obtain a definitive conclusion about which convection model gives the best correspondence to the 3D models. This is because each 1D physical quantity is related via an equation of state (EoS), but it is not the case for the averaged 3D quantities. Although the FST models with l = rtop − r + α*Hp, top are found to give the oscillation frequencies closest to the solar observed frequencies, their acoustic cavities are formed with compensatory effects between deviating density and temperature profiles near the top of the convective envelope. In future work, an appropriate treatment of the top part of the 1D convective envelope is necessary, for example, by considering turbulent pressure and overshooting.

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Stellar Evolution

Transactions of the International Astronomical Union ◽

10.1017/s0251107x00022343 ◽

1962 ◽

Vol 11 (02) ◽

pp. 137-143

Author(s):

M. Schwarzschild

Keyword(s):

Solar System ◽

Stellar Evolution ◽

Space Craft ◽

New Techniques ◽

Substantial Body ◽

Individual Stars ◽

The Past ◽

Evolution Of Galaxies ◽

History Of ◽

Fast Flow

It is perhaps one of the most important characteristics of the past decade in astronomy that the evolution of some major classes of astronomical objects has become accessible to detailed research. The theory of the evolution of individual stars has developed into a substantial body of quantitative investigations. The evolution of galaxies, particularly of our own, has clearly become a subject for serious research. Even the history of the solar system, this close-by intriguing puzzle, may soon make the transition from being a subject of speculation to being a subject of detailed study in view of the fast flow of new data obtained with new techniques, including space-craft.

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