Extent Of Overshooting Research Articles

Significant uncertainties from calibrating overshooting with eclipsing binary systems

The precise measurement of the masses and radii of stars in eclipsing binary systems provides a window into uncertain processes in stellar evolution, especially mixing at convective boundaries. Recently, these data have been used to calibrate models of convective overshooting in the cores of main sequence stars. In this study we have used a small representative sample of eclipsing binary stars with 1.25 ≤ M/M⊙ < 4.2 to test how precisely this method can constrain the overshooting and whether the data support a universal stellar mass–overshooting relation. We do not recover the previously reported stellar mass dependence for the extent of overshooting and in each case we find there is a substantial amount of uncertainty, that is, the same binary pair can be matched by models with different amounts of overshooting. Models with a moderate overshooting parameter 0.013 ≤ fos ≤ 0.014 (using the scheme from Herwig et al. 1997, A&A, 324, L81) are consistent with all eight systems studied. Generally, a much larger range of f is suitable for individual systems. In the case of main sequence and early post-main sequence stars, large changes in the amount of overshooting have little effect on the radius and effective temperature, and therefore the method is of extremely limited utility.

A Large Eddy Model Study on the Effect of Overshooting Convection on Lower Stratospheric Water Vapor

AbstractUsing a cloud‐resolving large eddy model (LEM), we investigate how overshooting convection affects the water vapor content in the lower stratosphere. We design and conduct a series of sensitivity experiments to diagnose the effects of dynamical and thermodynamical background conditions on the transport of water vapor into the lower stratosphere associated with overshooting convection. The three‐dimensional LEM simulations capture the bulk properties of the target case and track microphysical processes using a three‐phase microphysical parameterization. The model results indicate that the net effect of overshooting convection on lower stratospheric water content is moistening, primarily due to gravity wave breaking and ice sublimation. The contributions of small‐scale turbulent mixing to water vapor transport from the overshooting turret into the stratosphere are relatively weak. Sensitivity experiments show that convective intensity (as measured by updraft velocity) is directly related to the effect of overshooting convection on lower stratospheric humidity. This impact is quantified for the idealized target case. Changes in vertical wind shear near the tropopause have no significant impact on the extent of overshooting but have important impacts on cross‐tropopause water vapor exchange via their modulation of gravity wave breaking. Larger vertical wind shear in the tropopause layer inhibits the transport of water vapor and ice into the lower stratosphere by overshooting convection.

Confronting uncertainties in stellar physics: calibrating convective overshooting with eclipsing binaries

As part of a larger program aimed at better quantifying the uncertainties in stellar computations, we attempt to calibrate the extent of convective overshooting in low to intermediate mass stars by means of eclipsing binary systems. We model 12 such systems, with component masses between 1.3 and 6.2 solar masses, using the detailed binary stellar evolution code STARS, producing grids of models in both metallicity and overshooting parameter. From these, we determine the best fit parameters for each of our systems. For three systems, none of our models produce a satisfactory fit. For the remaining systems, no single value for the convective overshooting parameter fits all the systems, but most of our systems can be well described with an overshooting parameter between 0.09 and 0.15, corresponding to an extension of the mixed region above the core of about 0.1-0.3 pressure scale heights. Of the nine systems where we are able to obtain a good fit, seven can be reasonably well fit with a single parameter of 0.15. We find no evidence for a trend of the extent of overshooting with either mass or metallicity, though the data set is of limited size. We repeat our calculations with a second evolution code, MESA, and we find general agreement between the two codes. For the extension of the mixed region above the convective core required by the MESA models is about 0.15-0.4 pressure scale heights. For the system EI Cep, we find that MESA gives an overshooting region that is larger than the STARS one by about 0.1 pressure scale heights for the primary, while for the secondary the difference is only 0.05 pressure scale heights.

New PARSEC evolutionary tracks of massive stars at low metallicity: testing canonical stellar evolution in nearby star-forming dwarf galaxies

We extend the {\sl\,PARSEC} library of stellar evolutionary tracks by computing new models of massive stars, from 14\Msun to 350\Msun. The input physics is the same used in the {\sl\,PARSEC}~V1.1 version, but for the mass-loss rate which is included by considering the most recent updates in literature. We focus on low metallicity, $Z$=0.001 and $Z$=0.004, for which the metal poor dwarf irregular star forming galaxies, Sextans A, WLM and NCG6822, provide simple but powerful workbenches. The models reproduce fairly well the observed CMDs but the stellar colour distributions indicate that the predicted blue loop is not hot enough in models with canonical extent of overshooting. In the framework of a mild extended mixing during central hydrogen burning, the only way to reconcile the discrepancy is to enhance the overshooting at the base of the convective envelope (EO) during the first dredge-UP. The mixing scales required to reproduce the observed loops, EO=2\HP or EO=4\HP, are definitely larger than those derived from, e.g., the observed location of the RGB bump in low mass stars. This effect, if confirmed, would imply a strong dependence of the mixing scale below the formal Schwarzschild border, on the stellar mass or luminosity. Reproducing the features of the observed CMDs with standard values of envelope overshooting would require a metallicity significantly lower than the values measured in these galaxies. Other quantities, such as the star formation rate and the initial mass function, are only slightly sensitive to this effect. Future investigations will consider other metallicities and different mixing schemes.

ASTEROSEISMIC ANALYSIS OF THECoRoTTARGET HD 49933

The frequency ratios and of HD 49933 exhibit an increase at high frequencies. This behavior also exists in the ratios of other stars, which is considered to result from the low signal-to-noise ratio and the larger line width at the high-frequency end and could not be predicted by stellar models in previous work. Our calculations show that the behavior not only can be reproduced by stellar models, but can be predicted by asymptotic formulas of the ratios. The frequency ratios of the Sun, too, can be reproduced well by the asymptotic formulas. The increased behavior derives from the fact that the gradient of mean molecular weight at the bottom of the radiative region hinders the propagation of p-modes, while the hindrance does not exist in the convective core. This behavior should exist in the ratios of stars with a large convective core. The characteristic of the ratios at high frequencies provides a strict constraint on stellar models and aids in determining the size of the convective core and the extent of overshooting. Observational constraints point to a star with $M=1.28\pm0.01 M_{\odot}$, $R=1.458\pm0.005 R_{\odot}$, $t=1.83\pm0.1$ Gyr, $r_{cc}=0.16\pm0.02 R_{\odot}$, $\alpha=1.85\pm0.05$, and $\delta_{ov}=0.6\pm0.2$ for HD 49933.

Turbulence in Stars. III. Unified Treatment of Diffusion, Convection, Semiconvection, Salt Fingers, and Differential Rotation

The goal of this paper is to propose a unified treatment of diffusion, convection, semiconvection, salt fingers, overshooting, and rotational mixing. The detection of SN 1987A has served, among other things, to highlight the incompleteness of our understanding of such phenomena. Moreover, the variety of solutions proposed thus far to deal with each phenomenon separately, the uncertainty about the Ledoux-Schwarzschild criteria, the extent of overshooting, the effect of a μ gradient, the role of differential rotational mixing, etc., have added further urgency to the need of a unified, rather than a case-by-case, treatment of these processes. Since at the root of these difficulties lies the fact that we are dealing with a highly nonlinear, turbulent regime under the action of three gradients T (temperature), C (concentration), and (mean flow), it is not surprising that such difficulties have arisen. In this paper we propose a unified treatment based on a turbulence model. A key difference with previous models is that we do not employ heuristic arguments to determine the five basic timescales that enter the problem and that entail a corresponding number of adjustable constants. These timescales are computed using renormalization group (RNG) techniques. The model comes in three flavors: (a) all the turbulent variables are treated nonlocally; (b) the turbulent kinetic energy K and its rate of dissipation are nonlocal, while the remaining turbulence variables (fluxes, Reynolds stresses, etc.) are treated locally; and (c) all turbulence variables are local. In the latter case, one must specify a mixing length. Some of the results are as follows: 1. The local model entails the solution of two algebraic equations, one being the flux conservation law. By solving them, we obtain the desired - ad versus μ relations for semiconvection and salt fingers. We also derive other variables of interest, turbulent diffusivities, Peclet number, turbulent velocity, etc. 2. Schwarzschild and Ledoux criteria for instability are replaced by a new criterion that is physically equivalent to the requirement that turbulent mixing can exist only so long as the turbulent kinetic energy is positive. In addition to , ad, and μ, the new criterion depends on the turbulent diffusivities for temperature and concentration that only a turbulence model can provide. 3. We derive the dynamic equations necessary to quantify the extent of overshooting OV in the presence of a μ barrier. 4. We prove that OV(μ) < OV(μ = const.). Although this result is physically understandable, no direct proof has been available as yet. 5. We derive the turbulent diffusivity for a passive scalar, one that does not affect a preexisting turbulence, e.g., a sedimentation of He. We show that it differs from that of an active scalar, e.g., a μ field causing semiconvection and/or salt fingers. Such diffusivity is a function of the temperature gradient (stable/unstable) and shear (rotational mixing). 6. We show that the turbulent diffusivities of momentum (entering the angular momentum equation), of heat (entering the model of convection), and concentration (entering the diffusion equation and/or semiconvection and salt fingers) are different from one another and should not be taken to be the same, as has been done thus far. 7. We consider the effect of shear. We solve the local turbulence problem analytically and derive the turbulent diffusivities for momentum, heat, and concentration in terms of the three gradients of the mean fields, T, C, and . Since shear is itself a source of turbulent mixing, one could expect it to enhance the diffusivities. However, its interaction with salt fingers and semiconvection is a subtle one, and the opposite may occur, a phenomenon for which we offer a physical interpretation and a validation with laboratory data. 8. A comparison is made with previous models.

Overshooting and the μ-Barrier

Using general arguments and without numerical calculations, we present three complementary proofs that the extent of overshooting (OV) outside a convective region is decreased by a gradient of the mean molecular weight.

Integral Constraints on Convective Overshooting Two-Dimensional Numerical Studies

AbstractThe integral constraint on convective overshooting (Roxburgh 1976, 1978, 1989) is re-derived for for statistically stationary two-dimensional convection between stress-free horizontal boundaries maintained at constant temperatures, the vertical boundaries being periodic. We report on numerical simulations of such two-dimensional compressible convection in a fluid where the central regions are convectively unstable and the surrounding layers are stable. The results support the conclusion by Roxburgh (1989) that the contribution from the radiative flux is well approximated by the flux carried by the mean temperature gradient, but demonstrate that viscous dissipation is important, reducing the extent of overshooting.

Present problems of the solar interior

The standard model of solar evolution is reviewed and a number of problems highlighted. A fundamental question is whether there is any mixing of matter in the central regions, since such mixing could radically alter the model of the present Sun and modify our understanding of the evolution of other stars. Standard models of solar evolution become unstable to 3He driven global oscillations at an age of 3 × 108 years and this may drive some mixing, even if this is not the case the finite amptitude limit of these oscillations is likely to produce modifications in the standard model. Convective overshooting at the bottom of the outer convective zone leads to an increased depth of this zone and small changes in the interior. It is pointed out that the young Sun had a 12C driven convective core whose extent and duration depends on the extent of overshooting. Such a core is likely to produce a magnetic field which will affect the internal dynamics. The internal rotation of the Sun remains an enigma and absence of knowledge of any internal magnetic field makes it difficult to study the problem. Rotationally driven instabilities are ineffective in the central chemically inhomogenous regions but may contribute to the inward diffusion of lithium from the convective zone. These and other problems are considered, but few solutions are proposed.

TRANSIENT COOLING OF CONDUCTION HEATING PRODUCTS DURING STERILIZATION: TEMPERATURE HISTORIES

Temperature histories at the geometric center of containers filled with conduction heating products exhibit a rise after steamoff under certain conditions. This temperature rise (called overshooting), is quantified for cylindrical containers subjected to air and water cooling. Results of computer simulations using the Finite Element method suggest that the extent of overshooting is greater during air cooling than during water cooling. Heat penetration tests in laboratory and industrial retorts indicate that the overshooting phenomenon during water cooling is especially pronounced when conduction heating products are packaged in large metal containers and glass jars (e.g., a temperature rise of 2.5°C for 30 min was measured in a No. 10 can).

Dynamics of thunderstorms

The development of a thunderstorm which is essentially a convective phenomenon needs a cause for initial convection and then conditions for its maintenance once started. The possibility of the inherent instability due to potentially colder air superposed on potentially warmer air or the analogous case of extra injection of moisture in the lower layers in shown to be not applicable in nature and that causes for initial convection must be found elsewhere than in the potential density distribution. Some of the causes are non-horizontality of surfaces of equal temperature and equal humidity; and gradient of wind velocity. It is shown that upward rise of air produced by unequal heating of the ground, does not stop where the rising mass of air attains a density equal to that of the environment (hydrostatic equilibrium), but continues to rise higher till the momentum developed is reduced to zero. The extent of over-shooting is nearly of the same order as the height between the initial level and the level of hydrostatic equilibrium. Once the condensation level is reached, it is well known that the convection will become regenerative due to the evolution of the latent heat of condensation. In the usual treatment of the problem, the ascending parcel of air is expected to condense at or before it reaches the level of hydrostatic equilibrium if it is to develop into a thunderstorm. The dynamical treatment outlined in this paper takes into consideration the overshooting of the parcel of air and thereby allows much drier air to reach condensation and thereafter maintain convection: and can thus account for a larger number of thunderstorms.