An increasing number of young circumstellar disks show strikingly ordered (sub)millimeter polarization orientations along the minor axis, which is strong evidence for polarization due to scattering by ~0.1 mm sized grains. To test this mechanism further, we model the dust continuum and polarization data of HD 163296, one of the best observed disks with prominent rings and gaps, using the RADMC-3D radiative transfer code. We find that scattering by grains with a maximum size of 90$\mu$m can simultaneously reproduce the polarization observed at 0.87 mm (ALMA Band 7) and the unusually low spectral index of $\alpha$ ~ 1.5 between 0.87 and 1.25 mm (ALMA Band 6) in the optically thick inner disk as a result of more efficient scattering at a shorter wavelength. The relatively low spectral index of $\alpha$ ~ 2.5 inferred for the optically thin gaps is also reproduced by the same (relatively small) grains, as a result of telescope beam averaging of the gaps (with an intrinsic $\alpha$ ~ 4) and their adjacent optically thick rings (where $\alpha$ << 2). In this case, the long-standing tension between the grain sizes inferred from polarization and spectral index disappears because the relatively low $\alpha$ values are illusory and do not require large mm-sized grains. In addition, the polarization fraction has a unique pattern of azimuthal variation: higher along the major axis than the minor axis in the gaps but higher along the minor axis than the major axis in the rings. We find a rapidly declining polarization spectrum (with the fraction $p \propto \lambda^{-3}$ approximately) in the gaps, which becomes flattened or even inverted towards short wavelengths in the optically thick rings. These contrasting behaviors in the rings and gaps provide further tests of scattering-induced polarization that can be tested via multi-wavelength observations that resolve the disk substructure.

中文翻译：

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通过光谱指数、波长相关偏振模式和偏振光谱验证散射引起的（亚）毫米圆盘偏振：以 HD 163296 为例

越来越多的年轻星周盘显示出沿短轴显着有序的（亚）毫米偏振方向，这是由于~0.1 毫米大小的颗粒散射引起的偏振的有力证据。为了进一步测试这种机制，我们使用 RADMC-3D 辐射传输代码对 HD 163296 的尘埃连续谱和偏振数据进行建模，HD 163296 是具有突出环和间隙的最佳观测盘之一。我们发现最大尺寸为 90$\mu$m 的颗粒散射可以同时再现在 0.87 mm（ALMA Band 7）处观察到的极化和在 0.87 和 1.25 mm 之间的 $\alpha$ ~ 1.5 的异常低光谱指数（ ALMA 波段 6) 在光学厚的内盘中，因为在更短的波长下更有效的散射。$\alpha$ ~ 2 的相对较低的光谱指数。由于间隙的望远镜光束平均（具有固有的 $\alpha$ ~ 4）及其相邻的光学厚环（其中 $\阿尔法$<<2）。在这种情况下，从偏振和光谱指数推断出的晶粒尺寸之间的长期张力消失了，因为相对较低的 $\alpha$ 值是虚幻的，不需要大的毫米尺寸的晶粒。此外，极化率具有独特的方位角变化模式：间隙中的长轴高于短轴，但环中的短轴高于长轴。我们在间隙中发现了一个快速下降的偏振光谱（大约有分数 $p \propto \lambda^{-3}$），在光学厚环中，它变得平坦甚至倒转为短波长。环和间隙中的这些对比行为提供了对散射引起的极化的进一步测试，可以通过解析盘子结构的多波长观测进行测试。