The SEDs of some nearby stars show mid-infrared excesses from warm habitable zone dust, known as exozodiacal dust. This dust may originate in collisions in a planetesimal belt before being dragged inwards. This paper presents an analytical model for the size distribution of particles at different radial locations in such a scenario, considering evolution due to destructive collisions and Poynting-Robertson (P-R) drag. Results from more accurate but computationally expensive numerical simulations of this process are used to validate the model and fit its free parameters. The model predicts 11 $\mu$m excesses ($R_{11}$) for discs with a range of dust masses and planetesimal belt radii using realistic grain properties. We show that P-R drag should produce exozodiacal dust levels detectable with the Large Binocular Telescope Interferometer (LBTI) ($R_{11} > 0.1\%$) in systems with known outer belts; non-detection may indicate dust depletion, e.g. by an intervening planet. We also find that LBTI could detect exozodiacal dust dragged in from a belt too faint to detect at far-infrared wavelengths, with fractional luminosity $f\sim 10^{-7}$ and radius $\sim 10-80$ au. Application to systems observed with LBTI shows that P-R drag can likely explain most (5/9) of the exozodiacal dust detections in systems with known outer belts; two systems ($\beta$ Uma and $\eta$ Corvi) with bright exozodi may be due to exocomets. We suggest that the three systems with exozodiacal dust detections but no known belt may have cold planetesimal belts too faint to be detectable in the far-infrared. Even systems without outer belt detections could have exozodiacal dust levels $R_{11} > 0.04\%$ which are problematic for exo-Earth imaging.

中文翻译：

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碎片盘中的尘埃大小和空间分布：对从外柯伊伯带拖入的外生代尘埃的预测

一些附近恒星的 SED 显示出来自温暖宜居带尘埃（称为外生代尘埃）的中红外过剩。这些尘埃可能起源于行星带中的碰撞，然后被拖向内部。本文介绍了这种情况下不同径向位置的粒子尺寸分布的分析模型，考虑了由于破坏性碰撞和波印廷-罗伯逊 (PR) 阻力引起的演化。该过程的更准确但计算成本高的数值模拟结果用于验证模型并拟合其自由参数。该模型使用真实的颗粒特性预测了具有一系列尘埃质量和行星带半径的圆盘的 11 $\mu$m 过量 ($R_{11}$)。我们表明，在已知外带的系统中，PR 阻力应该产生可通过大型双筒望远镜干涉仪 (LBTI) ($R_{11} > 0.1\%$) 检测到的外生代尘埃水平；未检测到可能表明灰尘耗尽，例如由干预行星造成的。我们还发现，LBTI 可以检测到从太微弱而无法在远红外波长检测到的带拖入的外生代尘埃，其分数光度为 $f\sim 10^{-7}$，半径为 $\sim 10-80$ au。LBTI 观察到的系统的应用表明，PR 阻力可能可以解释已知外带系统中的大多数（5/9）外生代尘埃检测；两个系统（$\beta$ Uma 和 $\eta$ Corvi）具有明亮的 exozodi 可能是由于系外彗星。我们认为这三个具有外生肖尘埃探测但没有已知带的系统可能有冷星子带太暗而无法在远红外探测到。即使没有外带检测的系统也可能具有外生肖尘埃水平 $R_{11} > 0.04\%$，这对于外地球成像来说是有问题的。