Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userCalibration of the mixing-length parameter $alpha$ for the MLT and FST models by matching with CO$^5$BOLD models
83
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The CoRoT and Kepler missions provided a wealth of high-quality data for solar-like oscillations. To make the best of such data for seismic inferences, we need theoretical models with precise near-surface structure, which has significant influence on solar-like oscillation frequencies. The mixing-length parameter, $alpha$, is a key factor for the near-surface structure. In the convection formulations used in evolution codes, the $alpha$ is a free parameter that needs to be properly specified. We calibrated $alpha$ values by matching entropy profiles of 1D envelope models with those of 3D CO$^5$BOLD models. For such calibration, previous works concentrated on the classical mixing-length theory (MLT). Here we also analyzed the full spectrum turbulence (FST) models. For the atmosphere part in the 1D models, we use the Eddington grey $T(tau)$ relation and the one with the solar-calibrated Hopf-like function. For both the MLT and FST models with a mixing length $l=alpha H_p$, calibrated $alpha$ values increase with increasing $g$ or decreasing $T_{rm eff}$. For the FST models, we also calibrated values of $alpha^*$ defined as $l=r_{rm top}-r+alpha^*H_{p,{rm top}}$. $alpha^*$ is found to increase with $T_{rm eff}$ and $g$. As for the correspondence to the 3D models, the solar Hopf-like function gives a photospheric-minimum entropy closer to a 3D model than the Eddington $T(tau)$. The structure below the photosphere depends on the convection model. However, not a single convection model gives the best correspondence since the averaged 3D quantities are not necessarily related via an EOS. Although the FST models with $l=r_{rm top}-r+alpha^*H_{p,{rm top}}$ are found to give the frequencies closest to the solar observed ones, a more appropriate treatment of the top part of the 1D convective envelope is necessary.
rate research
Read More
We present evolutionary models for solar-like stars with an improved treatment of convection that results in a more accurate estimate of the radius and effective temperature. This is achieved by improving the calibration of the mixing-length parameter, which sets the length scale in the 1D convection model implemented in the stellar evolution code. Our calibration relies on the results of 2D and 3D radiation hydrodynamics simulations of convection to specify the value of the adiabatic specific entropy at the bottom of the convective envelope in stars as a function of their effective temperature, surface gravity and metallicity. For the first time, this calibration is fully integrated within the flow of a stellar evolution code, with the mixing-length parameter being continuously updated at run-time. This approach replaces the more common, but questionable, procedure of calibrating the length scale parameter on the Sun, and then applying the solar-calibrated value in modeling other stars, regardless of their mass, composition and evolutionary status. The internal consistency of our current implementation makes it suitable for application to evolved stars, in particular to red giants. We show that the entropy calibrated models yield a revised position of the red giant branch that is in better agreement with observational constraints than that of standard models.
Red giants in the updated APOGEE-Kepler catalogue, with estimates of mass, chemical composition, surface gravity and effective temperature, have recently challenged stellar models computed under the standard assumption of solar calibrated mixing length. In this work, we critically reanalyse this sample of red giants, adopting our own stellar model calculations. Contrary to previous results, we find that the disagreement between the effective temperature scale of red giants and models with solar calibrated mixing length disappears when considering our models and the APOGEE-Kepler stars with scaled solar metal distribution. However, a discrepancy shows up when alpha-enhanced stars are included in the sample. We have found that assuming mass, chemical composition and effective temperature scale of the APOGEE-Kepler catalogue, stellar models generally underpredict the change of temperature of red giants caused by alpha-element enhancements at fixed [Fe/H]. A second important conclusion is that the choice of the outer boundary conditions employed in model calculations is critical. Effective temperature differences (metallicity dependent) between models with solar calibrated mixing length and observations appear for some choices of the boundary conditions, but this is not a general result
The granulation background seen in the power spectrum of a solar-like oscillator poses a serious challenge for extracting precise and detailed information about the stellar oscillations. Using a 3D hydrodynamical simulation of the Sun computed with CO$^5$BOLD, we investigate various background models to infer, using a Bayesian methodology, which one provides the best fit to the background in the simulated power spectrum. We find that the best fit is provided by an expression including the overall power level and two characteristic frequencies, one with an exponent of 2 and one with a free exponent taking on a value around 6. We assess the impact of the 3D hydro-code on this result by repeating the analysis with a simulation from Stagger and find that the main conclusion is unchanged. However, the details of the resulting best fits differ slightly between the two codes, but we explain this difference by studying the effect of the spatial resolution and the duration of the simulation on the fit. Additionally, we look into the impact of adding white noise to the simulated time series as a simple way to mimic a real star. We find that, as long as the noise level is not too low, the results are consistent with the no-noise case.
Stellar convection is customarily described by Mixing-Length Theory, which makes use of the mixing-length scale to express the convective flux, velocity, and temperature gradients of the convective elements and stellar medium. The mixing-length scale is taken to be proportional to the local pressure scale height, and the proportionality factor (the mixing-length parameter) must be determined by comparing the stellar models to some calibrator, usually the Sun. No strong arguments exist to suggest that the mixing-length parameter is the same in all stars and at all evolutionary phases. The aim of this study is to present a new theory of stellar convection that does not require the mixing length parameter. We present a self-consistent analytical formulation of stellar convection that determines the properties of stellar convection as a function of the physical behaviour of the convective elements themselves and of the surrounding medium. This new theory is formulated starting from a conventional solution of the Navier-Stokes/Euler equations, i.e. the Bernoulli equation for a perfect fluid, but expressed in a non-inertial reference frame co-moving with the convective elements. In our formalism the motion of stellar convective cells inside convectively-unstable layers is fully determined by a new system of equations for convection in a non-local and time-dependent formalism. We obtain an analytical, non-local, time-dependent sub-sonic solution for the convective energy transport that does not depend on any free parameter. The theory is suitable for the outer convective zones of solar type stars and stars of all mass on the main sequence band. The predictions of the new theory are compared with those from the standard mixing-length paradigm for the most accurate calibrator, the Sun, with very satisfactory results.
The bright, nearby binary $alpha$ Centauri provides an excellent laboratory for testing stellar evolution models, as it is one of the few stellar systems for which we have high-precision classical (mass, radius, luminosity) and asteroseismic ($p$-mode) observations. Stellar models are created and fit to the classical and seismic observations of both stars by allowing for the free variation of convective mixing length parameter $alpha_{text{MLT}}$. This system is modeled using five different sets of assumptions about the physics governing the stellar models. There are 31 pairs of tracks (out of ${sim} 150,000$ generated) which fit the classical, binary, and seismic observational constraints of the system within $3,sigma$. Models with each tested choice of input physics are found to be viable, but the optimal mixing lengths for Cen A and Cen B remain the same regardless of the physical prescription. The optimal mixing lengths are $alpha_{text{MLT,A}} /alpha_{odot}= 0.932$ and $alpha_{text{MLT,B}}/alpha_{odot} = 1.095$. That Cen A and Cen B require sub- and super-solar mixing lengths, respectively, to fit the observations is a trend consistent with recent findings, such as in Kervella et al. (2017), Joyce and Chaboyer (2018), and Viani et al. (2018). The optimal models find an age for $alpha$ Centauri of $5.3 pm 0.3$ Gyr.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
