Self-similar Accretion Flows with Convection
Self-similar Accretion Flows with Convection
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DOI：
10.1086/309268
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发表时间：
1999-12
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影响因子：
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通讯作者：
R. Narayan;I. Igumenshchev;M. Abramowicz
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文献类型：
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作者：
R. Narayan;I. Igumenshchev;M. Abramowicz
本文考虑对流占优吸积流（ADAF）的高度积分方程，假定没有质量外流。我们包括对流通过混合长度的形式主义。我们寻求自相似的解决方案，其中的旋转速度和声速的比例为R-1/2，其中R是半径，并考虑两个限制处方的对流角动量的运输。在一个极限中，输运沿着角速度梯度发生，因此对流将角动量向外移动。在另一种情况下，输运是沿着特定的角动量梯度，因此对流将角动量向内移动。我们还考虑了介于这两个极限之间的一般处方。当对流将角动量向外移动时，我们恢复了ADAF的通常自相似解，其中质量密度标度为ρ <$R-3/2。当对流将角动量向内移动时，结果取决于粘性系数α。如果α > α crit 1 ~ 0.05，我们再次找到标准ADAF解。但当α < α crit 2 ~ α crit 1时，我们找到了一个非增生解，其中ρ <$R-1/2.我们称之为“对流包络”解或“对流主导的吸积流”。“几位作者已经报道了α = 0.03的ADAF的二维数值模拟。模拟的ADAF表现出对流。由于它们的轴对称性，在这些模拟中的对流将角动量向内移动，正如我们通过计算雷诺应力所证实的那样。模拟结果表明，ρ_∞ R ~（-1/2）与对流包络线解符合得很好。R-1/2密度剖面不是质量外流的结果。这些轴对称低α模拟与真实的吸积流的相关性是不确定的。
We consider height-integrated equations of an advection-dominated accretion flow (ADAF), assuming that there is no mass outflow. We include convection through a mixing-length formalism. We seek self-similar solutions in which the rotational velocity and sound speed scale as R-1/2, where R is the radius, and consider two limiting prescriptions for the transport of angular momentum by convection. In one limit, the transport occurs down the angular velocity gradient, so convection moves angular momentum outward. In the other, the transport is down the specific angular momentum gradient, so convection moves angular momentum inward. We also consider general prescriptions that lie in between the two limits. When convection moves angular momentum outward, we recover the usual self-similar solution for ADAFs in which the mass density scales as ρ ∝ R-3/2. When convection moves angular momentum inward, the result depends on the viscosity coefficient α. If α > αcrit1 ~ 0.05, we once again find the standard ADAF solution. For α < αcrit2 ~ αcrit1, however, we find a nonaccreting solution in which ρ ∝ R-1/2. We refer to this as a "convective envelope" solution or a "convection-dominated accretion flow." Two-dimensional numerical simulations of ADAFs with values of α ≲ 0.03 have been reported by several authors. The simulated ADAFs exhibit convection. By virtue of their axisymmetry, convection in these simulations moves angular momentum inward, as we confirm by computing the Reynolds stress. The simulations give ρ ∝ R-1/2, in good agreement with the convective envelope solution. The R-1/2 density profile is not a consequence of mass outflow. The relevance of these axisymmetric low-α simulations to real accretion flows is uncertain.