We present synthetic dust polarization maps of simulated molecular clouds (MCs) with the goal to systematically explore the origin of the relative orientation of the magnetic field ($\bf{B}$) with respect to the MC sub-structures identified in density ($n$; 3D) and column density ($N$; 2D). The polarization maps are generated with the radiative transfer code POLARIS, including self-consistently calculated efficiencies for radiative torque alignment. The MCs are formed in two sets of 3D MHD simulations: in (i) colliding flows (CF), and (ii) the SILCC-Zoom simulations. In 3D, for the CF simulations with an initial field strength below $\sim$5 $\mu$G, $\bf{B}$ is oriented parallel or randomly with respect to the $n$-structures. For CF runs with stronger initial fields and all SILCC-Zoom simulations, which have an initial field strength of 3 $\mu$G, a flip from parallel to perpendicular orientation occurs at high densities of $n_\text{trans}$ $\simeq$ 10$^2$ - 10$^3$ cm$^{-3}$. We suggest that this flip happens if the MC's mass-to-flux ratio, $\mu$, is close to or below the critical value of 1. This corresponds to a field strength around 3 - 5 $\mu$G. In 2D, we use the Projected Rayleigh Statistics (PRS) to study the orientation of $\bf{B}$. If present, the flip in orientation occurs at $N_\text{trans}$ $\simeq$ 10$^{21 - 21.5}$ cm$^{-2}$, similar to the observed transition value from sub- to supercritical magnetic fields in the ISM. However, projection effects can reduce the power of the PRS method: Depending on the MC or LOS, the projected maps of the SILCC-Zoom simulations do not always show the flip, although expected from the 3D morphology. Such projection effects can explain the variety of recently observed field configurations, in particular within a single MC. Finally, we do not find a correlation between the observed orientation of $\bf{B}$ and the $N$-PDF.

中文翻译：

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从平行到垂直——论分子云中磁场的方向

我们展示了模拟分子云 (MCs) 的合成尘埃极化图，目的是系统地探索磁场 ($\bf{B}$) 相对于密度确定的 MC 子结构的相对方向的起源（ $n$；3D）和列密度（$N$；2D）。极化图是使用辐射传输代码 POLARIS 生成的，包括用于辐射扭矩对准的自洽计算效率。MC 在两组 3D MHD 模拟中形成：在 (i) 碰撞流 (CF) 和 (ii) SILCC-Zoom 模拟中。在 3D 中，对于初始场强低于 $\sim$5 $\mu$G 的 CF 模拟，$\bf{B}$ 相对于 $n$ 结构平行或随机定向。对于具有更强初始场的 CF 运行和所有 SILCC-Zoom 模拟，其初始场强为 3 $\mu$G，从平行方向到垂直方向的翻转发生在 $n_\text{trans}$ $\simeq$ 10$^2$ - 10$^3$ cm$^{-3}$ 的高密度下。我们建议，如果 MC 的质量通量比 $\mu$ 接近或低于临界值 1，就会发生这种翻转。这对应于大约 3 - 5 $\mu$G 的场强。在 2D 中，我们使用投影瑞利统计 (PRS) 来研究 $\bf{B}$ 的方向。如果存在，方向翻转发生在 $N_\text{trans}$ $\simeq$ 10$^{21 - 21.5}$ cm$^{-2}$，类似于观察到的从亚临界到超临界的转变值ISM 中的磁场。然而，投影效果会降低 PRS 方法的功效：根据 MC 或 LOS，SILCC-Zoom 模拟的投影图并不总是显示翻转，尽管从 3D 形态学中可以预期到。这种投影效应可以解释最近观察到的各种场配置，特别是在单个 MC 内。最后，我们没有发现观察到的 $\bf{B}$ 方向和 $N$-PDF 之间的相关性。