ON THE STRUCTURE OF COMETARY DUST TAILS
ON THE STRUCTURE OF COMETARY DUST TAILS
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论彗星尘埃尾的结构
DOI：
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发表时间：
1975
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通讯作者：
C. Iu
中科院分区：
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作者：
C. Iu
本文在力学理论的框架内研究了彗星尘埃尾的结构，特别是对问题的三维处理。我们开始重新研究彗星粒子的轨道力学，导出一组便于以后讨论和计算的公式。例如，利用汉密尔顿积分B，我们得到了关于力参数μ的推广的矢量形式的轨道方程（第二部分）。在第二部分的基础上，我们考虑了下列问题：初始条件和μ与轨道特性的关系;粒子运动的计算机计算算法、电子空间分布的一些有趣特征、相对于彗星轨道平面的垂直运动及其对尾部结构的影响。§2.5中的论证得出两个重要结果，一个是检验FP（Finson和Probstein）方法适用性的判据，另一个是关于彗星通过近日点后尘埃尾中出现的有点特殊的结构，可称之为《颈线结构（NLS）》。在第三部分中，我们用NLS的概念对反常尾作了新的解释。讨论了NLS的发展，指出NLS的产生和发展可以为C/Arend-Roland，1957 Ⅲ的反常尾的行为提供一个充分的解释。最后，对反常向日尾的可见性作了统计上的考虑。结果还表明，NLS解释似乎与1801年以来的数据是一致的。在第四部分中，我们发展了一种新的数值分析方法。这种方法的基本思想是将联合收割机对大量样本粒子运动的精确处理和计数技术结合起来，考虑到彗星尘埃发射特性，即发射率N_d（t）、修正的粒子尺寸分布f（γ;t）和速度分布（γ（v;r，t）γ=1-μ）三个源函数。这样得到的尾亮度分布基本上给出了指定源函数的精确解，在这个意义上它不受任何辅助近似的影响。此外，在处理源函数时也没有困难，因为所需的过程可以简化为有关参数值的抽样，因此本方法同样适用于各向异性发射的情况。在C/Arend-Roland方法的一个应用中，我们假定辐射率随日心距N_d（t）的平方反比变化<$[rc（t）]~（-2）），速度分布为各向同性分布，速度v_o（t，γ）是唯一的，函数f（γ;t）留待与观测比较确定。图16给出了C/Arend-Roland的函数f（r），忽略了它的时间依赖性，并将相应的亮度概率分别与图14和15中4月28日和4月30日的观测值进行了比较。值得注意的是，主尾和异常尾都被统一处理，即在发射特征上没有任何时间异常。结果表明：（1）两个函数N_d（t）和f（v;γ，t）的简单形式可以作为一级近似;（2）导出的函数f（γ）在γ=0.10~0.12附近有一个宽峰，在γ~0.015附近可能有一个次峰;（3）亮度分析定量地支持了NLS对异常尾的解释;（4）然而，要确定彗星的尘埃排放特征还需要更多的观测数据和仔细的分析，希望本文所述的方法和观点可以作为今后研究的基础。
The structure of cometary dust tails is studied in the frame of mechanical theory with special regards to threedimensional treatment of the problem. We begin with the reexamination of orbit mechanics of cometary particles to derive a set of formulae convenient to subsequent discussions and calculations.Mak- ing use of Hamilton's integral b,we have obtained,for example,the equation of orbit in a vectorial form with generalization respecting to force parameter μ(Part 2).On the basis of Part 2,we consider such problems as follows:the relation between initial conditions together with μ and the orbit characteristics;the algorithm for computer-calculation of the motion of particles some interesting features of ele- mentary space distributions vertical motion relative to the comet orbit plane and its implications to the tail structure. Arguments given in §2.5 yield two important results.One is a criterion to check the applicability of the FP(Finson and Probstein)-method.The other con- cerns with the somewhat peculiar structure to appears in the dust tail of comet after perihelion passage,which might be termed as《Neck-line structure(henceforce ab- breviated to NLS)》. In Part 3,we present a new interpretation of the anomalous tails refered to the concept of NLS.A discussion of the development of NLS is given,and it is shown that the emergence and development of NLS can provide an adequate expla- nation for the behaviour of the anomalous tail of C/Arend-Roland,1957 Ⅲ.Fur- thermore,statistical consideration on the visibility of anomalous sunward tail is at- tempted,the result of which also shows that the NLS-interpretation seems to be compatible with the data since 1801. In Part4,we develop a new method for numerical analysis of tail brightness. The basic idea of this method is to combine exact treatment of the motion of a large number of sample particles and counting-technique to estimate the surface brightness integral,taking account of the dust emission characteristics of comets which may be expressed by three source functions,namely,the emission rate N_d(t),the modified size-distribution f(γ;t),and the velocity distribution where Ψ(v;r,t)γ=1-μ). Distribution of tail brightness thus obtained gives essentially the exact solution for the assigned source funtions,in the sense that it is not affected by any auxiliary approximations.Moreover,no difficulties arise in the handling of source functions, because the requisite procedure can be reduced to the sampling of values of relevant parameters;thus the present method is applicable equally well for the case of ani- sotropic emission. In an application of the method for C/Arend-RolandPart4),we suppose that the emission rate varies as the inverse-square of heliocentric distanceN_d(t)∝[rc(t)]~(-2)), and that the velocity distribution is characterized as the isotropic one with a unique speed vo(t,γ).The function f(γ;t)is left as one to be determined through the comparison with observation. The function f(r)for C/Arend-Roland,derived by neglecting its time-dependency, is shown in Fig.16.The corresponding brightness probiles are compared with observed ones in Figs.14 and 15,for Apr.28 and Apr.30,respectively,it is worth noting that both main and anomalous tails have been treated in a unified manner, that is,without any temporal anomalies in emission characteristics. With these results,we conclude:(1)The simple forms presupposed for two functionsN_d(t)and Ψ(v;γ,t))may be well accepted as first approximations;(2) The derived function f(γ)shows its broad peak around γ=0.10～0.12 and possibly a secondary peak around γ～0.015;(3)The present brightness analysis adds support, in a quantitative way,to the NLS-interpretation of the.anomalous tails;(4)More observational data and careful analyses are needed,however,to establish the dust emission characteristics of comets.It is hoped that methods and viewpoints described in the present article may serve as the basis for future investigations.