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تسجيل مستخدم جديدA two-dimensional mixing length theory of convective transport
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The helioseismic observations of the internal rotation profile of the Sun raise questions about the two-dimensional (2D) nature of the transport of angular momentum in stars. Here we derive a convective prescription for axisymmetric (2D) stellar evolution models. We describe the small scale motions by a spectrum of unstable linear modes in a Boussinesq fluid. Our saturation prescription makes use of the angular dependence of the linear dispersion relation to estimate the anisotropy of convective velocities. We are then able to provide closed form expressions for the thermal and angular momentum fluxes with only one free parameter, the mixing length. We illustrate our prescription for slow rotation, to first order in the rotation rate. In this limit, the thermodynamical variables are spherically symetric, while the angular momentum depends both on radius and latitude. We obtain a closed set of equations for stellar evolution, with a self-consistent description for the transport of angular momentum in convective regions. We derive the linear coefficients which link the angular momentum flux to the rotation rate ($Lambda$- effect) and its gradient ($alpha$-effect). We compare our results to former relevant numerical work.
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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.
Turbulent convection is certainly one of the most important and thorny issues in stellar physics. Our deficient knowledge of this crucial physical process introduces a fairly large uncertainty concerning the internal structure and evolution of stars.
A striking example is overshoot at the edge of convective cores. Indeed, nearly all stellar evolutionary codes treat the overshooting zones in a very approximative way that considers both its extent and the profile of the temperature gradient as free parameters. There are only a few sophisticated theories of stellar convection such as Reynolds stress approaches, but they also require the adjustment of a non-negligible number of free parameters. We present here a theory, based on the plume theory as well as on the mean-field equations, but without relying on the usual Taylors closure hypothesis. It leads us to a set of eight differential equations plus a few algebraic ones. Our theory is essentially a non-mixing length theory. It enables us to compute the temperature gradient in a shrinking convective core and its overshooting zone. The case of an expanding convective core is also discussed, though more briefly. Numerical simulations have quickly improved during recent years and enabling us to foresee that they will probably soon provide a model of convection adapted to the computation of 1D stellar models.
Classical novae are thermonuclear explosions that take place in the envelopes of accreting white dwarfs in binary systems. The material piles up under degenerate conditions, driving a thermonuclear runaway. The energy released by the suite of nuclear
processes operating at the envelope heats the material up to peak temperatures about 100 - 400 MK. During these events, about 10-3 - 10-7 Msun, enriched in CNO and, sometimes, other intermediate-mass elements (e.g., Ne, Na, Mg, Al) are ejected into the interstellar medium. To account for the gross observational properties of classical novae (in particular, the large concentrations of metals spectroscopically inferred in the ejecta), models require mixing between the (solar-like) material transferred from the secondary and the outermost layers (CO- or ONe-rich) of the underlying white dwarf. Recent multidimensional simulations have demonstrated that Kelvin-Helmholtz instabilities can naturally produce self-enrichment of the accreted envelope with material from the underlying white dwarf at levels that agree with observations. However, the feasibility of this mechanism has been explored in the framework of CO white dwarfs, while mixing with different substrates still needs to be properly addressed. Three-dimensional simulations of mixing at the core-envelope interface during nova outbursts have been performed with the multidimensional code FLASH, for two types of substrates: CO- and ONe-rich. We show that the presence of an ONe-rich substrate, as in neon novae, yields larger metallicity enhancements in the ejecta, compared to CO,rich substrates (i.e., non-neon novae). A number of requirements and constraints for such 3-D simulations (e.g., minimum resolution, size of the computational domain) are also outlined.
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