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arXiv · 1502.05628

Overshooting by differential heating

R. Andrássy·H. C. Spruit
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Abstract

On the long nuclear time scale of stellar main-sequence evolution, even weak mixing processes can become relevant for redistributing chemical species in a star. We investigate a process of "differential heating," which occurs when a temperature fluctuation propagates by radiative diffusion from the boundary of a convection zone into the adjacent radiative zone. The resulting perturbation of the hydrostatic equilibrium causes a flow that extends some distance from the convection zone. We study a simplified differential-heating problem with a static temperature fluctuation imposed on a solid boundary. The astrophysically relevant limit of a high Reynolds number and a low P\'eclet number (high thermal diffusivity) turns out to be interestingly non-intuitive. We derive a set of scaling relations for the stationary differential heating flow. A numerical method adapted to a high dynamic range in flow amplitude needed to detect weak flows is presented. Our two-dimensional simulations show that the flow reaches a stationary state and confirm the analytic scaling relations. These imply that the flow speed drops abruptly to a negligible value at a finite height above the source of heating. We approximate the mixing rate due to the differential heating flow in a star by a height-dependent diffusion coefficient and show that this mixing extends about $4\%$ of the pressure scale height above the convective core of a $10\,M_\odot$ zero-age main sequence star.

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R. Andrássy, H. C. Spruit. 2015-02-19. Overshooting by differential heating. https://doi.org/10.1051/0004-6361%2F201425125

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