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 $1{{\ \rm per\ cent}}$ (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 1σ), while it is less satisfactory for α Cen A (within 2.5σ). 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 $1{{\ \rm per\ cent}}$. This is especially relevant in characterizing exoplanet-host stars and their planetary systems accurately.
The development of two-dimensional and three-dimensional simulations of solar convection has lead to a picture of convection quite unlike the usually assumed Kolmogorov spectrum turbulent flow. We ...investigate the impact of this changed structure on the dissipation properties of the convection zone, parameterized by an effective viscosity coefficient. We use an expansion treatment developed by Goodman & Oh, applied to a numerical model of solar convection, to calculate effective viscosity as a function of frequency and compare this to currently existing prescriptions based on the assumption of Kolmogorov turbulence. The results quite closely match a linear scaling with period, even though this same formalism applied to a Kolmogorov spectrum of eddies gives a scaling with a power-law index of 5/3.
ABSTRACT
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 modelling 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.
Using synthetic horizontal-branch models, we have investigated the origin of the systematic variation in horizontal-branch (HB) morphology with galactocentric distance (R(sub G)) among globular ...clusters. The variations in He abundance, CNO abundance, and core mass required separately to explain this effect are inconsistent with either the observed properties of the RR Lyrae variables or the observed main-sequence turnoffs in the clusters. There is also no clear evidence that the trend with R(sub G) is related to the central concentrations, central densities, or absolute magnitudes of the clusters. The variations in cluster age required to explain this effect are not in conflict with any observations. A detailed comparison of our synthetic HB calculations with pairs of clusters of very different HB morphology but similar (Fe/H) reveals reasonably good agreement between the age differences inferred from HB morphology and the main-sequence turnoff. The major source of uncertainty is the need for ad hoc hypotheses in the modeling of the HB morphologies of a few peculiar clusters (e.g., NGC 6752). Nonetheless, there is firm evidence for age variations of several gigayears (as much as approximately 5 Gyr) among the halo globular clusters. Our results support the hypothesis of Searle & Zinn that the inner halo is more uniform in age and is older in the mean than the outer halo, and we estimate this difference to be approximately 2 Gyr.
ABSTRACT
Supernova (SN) cosmology is based on the assumption that the width–luminosity relation (WLR) and the colour–luminosity relation (CLR) in the type Ia SN luminosity standardization would not ...show absolute magnitude differences with progenitor age. Unlike this expectation, recent age datings of stellar populations in host galaxies have shown significant correlations between progenitor age and Hubble residual (HR). Here, we show that this correlation originates from a strong progenitor age dependence of the zero-points of the WLR and the CLR, in the sense that SNe from younger progenitors are fainter each at given light-curve parameters x1 and c. This 4.6σ result is reminiscent of Baade’s discovery of the zero-point variation of the Cepheid period–luminosity relation with age, and, as such, causes a serious systematic bias with redshift in SN cosmology. Other host properties show substantially smaller and insignificant offsets in the WLR and CLR for the same data set. We illustrate that the differences between the high-$z$ and low-$z$ SNe in the WLR and CLR, and in HR after the standardization, are fully comparable to those between the correspondingly young and old SNe at intermediate redshift, indicating that the observed dimming of SNe with redshift may well be an artefact of overcorrection in the luminosity standardization. When this systematic bias with redshift is properly taken into account, there is little evidence left for an accelerating universe, in discordance with other probes, urging the follow-up investigations with larger samples at different redshift bins.
In the second paper of this series we pursue two objectives. First, in order to make the code more sensitive to small effects, we remove many approximations made in Paper I. Second, we include ...turbulence and rotation in the two-dimensional framework. The stellar equilibrium is described by means of a set of five differential equations, with the introduction of a new dependent variable, namely the perturbation to the radial gravity, that is found when the nonradial effects are considered in the solution of the Poisson equation. Following the scheme of the first paper, we write the equations in such a way that the two-dimensional effects can be easily disentangled. The key concept introduced in this series is the equipotential surface. We use the underlying cause-effect relation to develop a recurrence relation to calculate the equipotential surface functions for uniform rotation, differential rotation, rotation-like toroidal magnetic fields, and turbulence. We also develop a more precise code to numerically solve the two-dimensional stellar structure and evolution equations based on the equipotential surface calculations. We have shown that with this formulation we can achieve the precision required by observations by appropriately selecting the convergence criterion. Several examples are presented to show that the method works well. Since we are interested in modeling the effects of a dynamo-type field on the detailed envelope structure and global properties of the Sun, the code has been optimized for short timescales phenomena (down to 1 yr). The time dependence of the code has so far been tested exclusively to address such problems.
We examine how metallicity affects convection and overshoot in the superadiabatic layer of main sequence stars. We present results from a grid of three-dimensional radiation hydrodynamic simulations ...with four metallicities (Z = 0.040, 0.020, 0.010, 0.001), and spanning a range in effective temperature (4950 < T sub(eff) < 6230). We show that changing the metallicity alters properties of the convective gas dynamics, and the structure of the superadiabatic layer and atmosphere. Our grid of simulations shows that the amount of superadiabaticity, which tracks the transition from efficient to inefficient convection, is sensitive to changes in metallicity. We find that increasing the metallicity forces the location of the transition region to lower densities and pressures, and results in larger mean and turbulent velocities throughout the superadiabatic region. We also quantify the degree of convective overshoot in the atmosphere, and show that it increases with metallicity as well.
PDF
