饱和克尔玻色子云的相对论潮汐跃迁
Relativistic Tidal Transitions of Saturated Kerr Boson Clouds
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- State Key Laboratory of Radio Astronomy and Technology, Xinjiang Astronomical Observatory, CAS（中国科学院新疆天文台射电天文技术国家重点实验室）
- College of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）
- Xinjiang Key Laboratory of Radio Astrophysics（新疆射电天体物理重点实验室）
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中文总结 AI 辅助
研究旋转黑洞束缚超轻玻色子云团的潮汐跃迁，通过结合克尔准束缚模等方法计算矩阵元，发现相对论矩阵元与氢原子值有差异，对云团损耗预测有影响，凸显相对论云团结构在双星历史中的定量重要性。
中文摘要 AI 辅助
旋转黑洞可在宏观云团中束缚超轻玻色子，其能级结构会被伴星的潮汐场改变。现有的共振跃迁估计大多使用氢原子波函数，而本文计算了$|211\rangle$、$|322\rangle$和$|433\rangle$云团在数值确定的饱和分支上的潮汐跃迁矩阵元。计算结合了克尔准束缚模、相对论双线性归一化和克尔度规的绝热四极扰动。结果表明，相对论矩阵元与氢原子值的差异高达$21.67\%$，且对云团损耗预测有显著影响，说明相对论云团结构对交叉饱和云共振的双星历史具有重要定量意义。
英文摘要
Rotating black holes can bind ultralight bosons in macroscopic clouds whose level structure is swept by the tidal field of a binary companion. Existing estimates of the resulting resonant transitions have largely used hydrogenic wave functions, even where the cloud grows most efficiently and the Kerr geometry appreciably deforms its quasibound states. I compute tidal transition matrix elements on the numerically determined saturation branches of the $|211\rangle$, $|322\rangle$, and $|433\rangle$ clouds. The calculation combines Kerr quasibound modes, their relativistic bilinear normalization, and an adiabatic uadrupolar perturbation of the Kerr metric. Across five $Δm=-2$ channels, the relativistic matrix element differs from its hydrogenic value by as much as $21.67\%$. Corrections above $10\%$ persist when $99\%$ of the cloud lies within $7\%$ of the orbital separation. A component-resolved comparison attributes $78.7-82.5\%$ of the logarithmic change to the radial mode profile and $13.3-16.2\%$ to the bilinear normalization; the relativistic tidal geometry supplies a smaller additional correction. Exact Newtonian multipoles and an independent complex-contour construction confirm the quadrupole matrix elements. For resonances with intermediate Landau--Zener adiabaticity, the corrected matrix elements change the predicted cloud depletion by up to $13.7\%$. Relativistic cloud structure is therefore quantitatively important for binary histories that cross saturated-cloud resonances.
