分子云厚度的估计

Estimates of the Thickness of Molecular Clouds

分子云是星际介质的一种形态。分子云的主要成分包括分子氢、氦、原子氢、其他分子、尘埃以及磁场和宇宙线等。分子云的形态多种多样，除了看起来像一团云的分子云，还有丝状、片状的分子云。分子云可能是分形结构的。距离较近的著名分子云包括金牛座分子云、猎户座分子云、蛇夫座分子云、英仙座分子云等。

Molecular clouds are a form of interstellar medium. The primary contents of molecular clouds include molecular hydrogen, helium, atom hydrogen, other molecules, dust, magnetic field and cosmic rays. Molecular clouds have various morphology (shape), besides the cloud-like ones, there are also filamentary and sheet-like molecular clouds. Molecular clouds may be fractal. The famous nearby molecular clouds include Taurus, Orion, Ophiuchus, Perseus etc.

这是金牛座分子云的图像，看起来像一团云。细节上也有一些其他形态的结构。

This is the image of Taurus molecular cloud. It looks like a cloud. But looking in detail, there are also some structures of other morphology.

和天文中普遍遇到的问题一样，分子云在天球面上的大小容易测量，但在视线方向的厚度不容易测量。估计分子云视线方向厚度的方法主要有以下几种。其中测量分子云中年轻恒星、脉泽点的距离是容易想到的方法，但实施起来并不容易。分子云的平均厚度还可以通过测量柱密度和体密度估计。分子云中的气泡形态也可以用于限制分子云的厚度。通过类似地震波探测地球内部结构的方法，也可以用磁振荡探测分子云的“隐藏维度”。使用线宽-投影尺度关系也可以测量分子云在视线方向的厚度。此外还可以通过形态区别丝状结构和侧视的片状结构。

Like ubiquitous problems in astronomy, the size of molecular clouds projected onto the celestial sphere is easy to measure. However, it is difficult to measure the line of sight thickness. There are several methods to estimates of the line of sight thickness of molecular clouds. It is easy to conceiver that measuring the distance to the young stars and maser points in molecular clouds can estimate the thickness. In practice, it is not easy to do. The average thickness of molecular clouds can also be obtained by measuring the column density and volume density. The bubbles in the clouds can also be used to constrain the thickness. With similar technique used to profile the inner structure of the Earth, we can use magnetoseismology to detect the hidden dimension of molecular clouds. Linewidth-projected size relation can also be used to measure the thickness along the line of sight. Additionally, we can distinguish filaments and edge-on sheets with morphology.

根据定义，柱密度是体密度在视线方向的积分。所以视线方向的平均厚度等于柱密度除以体密度。

By definition, the column density is the integral of the volume density along the line of sight. So the average thickness along the line of sight is the column density divided by the volume density.

以金牛座分子云中的B213为例。柱密度可以通过HC₃N（2-1）谱线的强度计算，体密度可以HC₃N（10-9）和HC₃N（2-1）的线强比得到。由此得到B213视线方向的尺度大约是0.12 pc。这表明B213确实是丝状的。从另外一方面，这也暗示金牛座可能是一块比较薄的云。

As an example, for B213 in Taurus molecular cloud, the column density can be obtained by the strength of HC₃N (2-1) line. The volume density can be obtained by the line ratio of HC₃N (10-9) and HC₃N (2-1) lines. The obtained size along the line of sight of B213 is about 0.12 pc, which means that B213 is indeed a filament. On the other hand, it indicates that Taurus molecular cloud is thin.

想象一块分子云中有一个气泡，如果气泡比较大，尺度超过了分子云的厚度，气泡就会破裂，只留下一个圆环。中心部分几乎没有分子气体，所以没有谱线辐射。

Imaging there is a bubble in a cloud. If the bubble is large, with the size larger than the thickness of the cloud, the bubble will break and leave a ring. There is little gas in the central part, and no line radiation.

这是一个例子。在所有通道图（也就是不同频率的图）上，中心部分都没有辐射。从强度的径向分布来看，这也更像一个圆环而非完整的气泡。由此可以对这块分子云的厚度给出限制。

This is an example. On all the channel maps, there is little radiation at the center. From the radial distribution of the intensity, this looks like a ring rather than an integral bubble. The thickness of the cloud can thus be constrained.

我们知道，通过分析地震波，可以探测地球的内部。探测分子云中的波也可以达到类似的效果。通过分析特征频率，可以得到苍蝇座分子云的视线方向尺度和最大的横向尺度相当。这意味着这块分子云是侧视的片状云。

We know that we can detect the inner structure of the Earth by analyzing seismic waves. Similar goals can be achieved by analyzing waves in molecular clouds. With analyzing the characteristic frequencies, one can conclude that the line-of-sight size of the Musca molecular cloud is comparable with the larger transverse scale. This means that this molecular cloud is an edge-one sheet.

比较一下真正的丝状云B213和侧视的片状云苍蝇座分子云。真正的丝状云更容易扭曲。这符合直觉。所以如果要寻找侧视的片状云，应该从扭曲较少的“丝状云”里去找。

Let’s look at the true filament, B213 and the edge-on sheet, Musca molecular cloud. The true filaments tend to be distorted. This is not hard to understand when you look at a thread. We should search for edge-one sheet in the “filament” with less distortion.

除此之外，分子云中的线宽尺度关系也可以用来限制分子云厚度。观测发现，分子云谱线的平均轮廓的宽度和三维尺度的1/2次方成正比。

Additionally, the linewidth-size relation can be used to constrain the thickness of molecular clouds. Observationally, the width of the average line profile of molecular clouds is proportional to the square root of the 3-dimension scale.

对于金牛座这样大面积的分子云，可以在分子云中取不同的点，每个点取一系列半径的区域测量平均轮廓的宽度。

For large cloud like Taurus, we can sample at different points in the cloud, use series of area with different radii for each point to measure the with of the average line profile.

注意到，由于分子云有厚度，线宽和尺度的关系可以用投影尺度和厚度表示。通过线宽和投影尺度的关系可以得出分子云的厚度下限的一个估计。

Notice the linewidth-size relation can be expressed with projected size and the thickness. We can get a lower limit of the molecular cloud with linewidth-size relation.

总结起来，我们可以通过线宽-投影尺度关系、气泡形态和磁振荡估计分子云厚度。我们也可以通过寻找扭曲较少的“丝状云”寻找更多的侧视的片状云。

To sum up, we can estimate the thickness of molecular clouds with linewidth-size relation, bubble morphology and megnetoseismology. We can search for edge-on sheets in straight “filaments”.