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arXiv 1502.05628astro-ph.SRphysics.flu-dyn
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差热过冲

Overshooting by differential heating

R. Andrássy, H. C. Spruit

摘要:

在恒星主序星演化的长核时间尺度上,即使是微弱的混合过程也可能与恒星中化学物质的重新分布有关。我们调查的“差热”的过程中,发生时,温度波动传播的辐射扩散从边界的对流区到相邻的辐射区。由此产生的流体静力平衡的扰动导致从对流区延伸一定距离的流动。本文研究了一个简化的固体边界上有静态温度波动的微分加热问题。天体物理学上与高雷诺数和低佩克莱数(高热扩散率)相关的极限被证明是有趣的非直观的。我们推导出一组定常微分热流的标度关系。提出了一种适用于检测弱流所需的高动态范围的数值方法。我们的二维模拟表明,流动达到一个稳定的状态,并确认解析标度关系。这意味着在热源上方的有限高度处,流速突然下降到可忽略的值。我们近似的混合率,由于差分加热流在一个明星的高度依赖的扩散系数,并表明,这种混合延伸约$4\%$的压力标度高度以上的对流核心的$10\,M_\odot$零年龄主序星。

英文摘要:

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 Péclet 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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