How empty is an empty loss cone
How empty is an empty loss cone
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空的损失锥有多空
DOI：
10.1093/mnras/stx485
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发表时间：
2017
影响因子：
4.8
通讯作者：
R. Sari
中科院分区：
文献类型：
--
作者：
A. Weissbein;R. Sari
考虑具有损失锥的球面系统中的两体弛豫。考虑二维角动量空间，我们将重点放在“空损失锥”系统上，其中在动态时间内的典型散射$j_{d}$小于损失锥的大小$j_{\rm lc}$。因此，损耗锥内的占用数明显小于外部。该区域的经典扩散处理预测了损耗锥深处的指数级小占位数。我们重新审视这个经典的推导占用分布的对象在空损失锥制度。我们强调了罕见的大散射的作用，并表明占用率在损失锥内不会呈指数衰减，但它相当平坦，与圆形角动量的占用相比具有典型值$\sim [(j_d/j_{\rm lc})]^2\ln^{-2}(j_{\rm lc}/j_{\min})$（其中$j_{\min}$是最小的可能散射）。这意味着，虽然巨星或双星潮汐破裂的损失锥通常是空的，但在损失锥内显著发生的潮汐事件（$\beta\gtrsim 2$）几乎与$\beta\cong 1$的潮汐事件一样常见，其中$\beta$是潮汐半径与近视点之间的比率。具有穿透因子$>\beta$的事件概率仅以$\beta^{-1}$而不是指数形式减小。这种效应对以完全损失锥为特征的事件没有影响，例如$\sim 1m_\odot$主序星的潮汐破坏事件。
We consider two body relaxation in a spherical system with a loss cone. Considering two-dimensional angular momentum space, we focus on "empty loss cone" systems, where the typical scattering during a dynamical time $j_{d}$ is smaller than the size of the loss cone $j_{\rm lc}$. As a result, the occupation number within the loss cone is significantly smaller than outside. Classical diffusive treatment of this regime predict exponentially small occupation number deep in the loss cone. We revisit this classical derivation of occupancy distribution of objects in the empty loss cone regime. We emphasize the role of the rare large scatterings and show that the occupancy does not decay exponentially within the loss cone, but it is rather flat, with a typical value $\sim [(j_d/j_{\rm lc})]^2\ln^{-2}(j_{\rm lc}/j_{\min})$ compared to the occupation in circular angular momentum (where $j_{\min}$ is the smallest possible scattering). Implication are that although the loss cone for tidal break of Giants or binaries is typically empty, tidal events which occurs significantly inside the loss cone ($\beta\gtrsim 2$), are almost as common as those with $\beta\cong 1$ where $\beta$ is the ratio between the tidal radius and the periastron. The probability for event with penetration factor $>\beta$ decreases only as $\beta^{-1}$ rather than exponentially. This effect has no influence on events characterized by full loss cone, such as tidal disruption event of $\sim 1m_\odot$ main sequence star.