In a galactic halo like the Milky Way, bosonic dark matter particles lighter than about $100$ eV have a de Broglie wavelength larger than the average inter-particle separation and are therefore well described as a set of classical waves. This applies to, for instance, the QCD axion as well as to lighter axion-like particles such as fuzzy dark matter. We show that the interference of waves inside a halo inevitably leads to vortices, locations where chance destructive interference takes the density to zero. The phase of the wavefunction has non-trivial winding around these points. This can be interpreted as a non-zero velocity circulation, so that vortices are sites where the fluid velocity has a non-vanishing curl. Using analytic arguments and numerical simulations, we study the properties of vortices and show they have a number of universal features: (1) In three spatial dimensions, the generic defects take the form of vortex rings. (2) On average there is about one vortex ring per de Broglie volume and (3) generically only single winding ($\pm 1$) vortices are found in a realistic halo. (4) The density near a vortex scales as $r^2$ while the velocity goes as $1/r$, where $r$ is the distance to vortex. (5) A vortex segment moves at a velocity inversely proportional to its curvature scale so that smaller vortex rings move faster, allowing momentary motion exceeding escape velocity. We discuss observational/experimental signatures from vortices and, more broadly, wave interference. In the ultra-light regime, gravitational lensing by interference substructures leads to flux anomalies of $5-10 \%$ in strongly lensed systems. For QCD axions, vortices lead to a diminished signal in some detection experiments but not in others. We advocate the measurement of correlation functions by axion detection experiments as a way to probe and capitalize on the expected interference substructures.

中文翻译：

---

光暗物质中的涡旋和波

在像银河系这样的星系晕中，比约 100 美元 eV 轻的玻色暗物质粒子的德布罗意波长大于平均粒子间间隔，因此被很好地描述为一组经典波。例如，这适用于 QCD 轴子以及较轻的类轴子粒子，例如模糊暗物质。我们表明，光晕内波的干扰不可避免地会导致涡旋，在这些位置，偶然的破坏性干扰使密度为零。波函数的相位围绕这些点具有非平凡的缠绕。这可以解释为非零速度循环，因此涡流是流体速度具有非零旋度的位置。使用解析论证和数值模拟，我们研究了涡流的特性并表明它们具有许多普遍特征：（1）在三个空间维度中，一般缺陷采用涡环的形式。(2) 平均每个德布罗意体积大约有一个涡环，并且 (3) 在现实光环中通常只发现单绕组 ($\pm 1$) 涡旋。(4) 涡旋附近的密度按 $r^2$ 缩放，而速度按 $1/r$ 缩放，其中 $r$ 是到涡旋的距离。(5) 涡流段以与其曲率尺度成反比的速度移动，因此较小的涡环移动得更快，允许瞬时运动超过逃逸速度。我们讨论了来自涡旋的观察/实验特征，更广泛地说，是波干扰。在超轻状态下，在强透镜系统中，干涉子结构的引力透镜导致 $5-10 \%$ 的通量异常。对于 QCD 轴子，涡流会在某些检测实验中导致信号减弱，但在其他实验中不会。我们提倡通过轴子检测实验测量相关函数，作为探测和利用预期干扰子结构的一种方式。