論單線光譜雙星系統之質量比分佈

On the mass ratio distribution of single-lined spectroscopic binary systems

陳韋達(Wei-Da Chen)

指導教授 ： 江瑛貴

國立中央大學/理學院/天文研究所/碩士(2006年)

摘要

雙星系統之真實的質量比分佈（mass ratio distribution）可為雙星系統的性質與形成過程提供一些條件限制。然而，多數的光譜雙星系統都是單線的（single-lined），只有主星的光譜線能被偵測到，以致吾人無法獲悉雙星系統的質量比（mass ratio）。儘管如此，吾人仍舊可以透過統計模型的建立，依據系統的質量函數（mass function）而從中導出質量比。

根據統計模型，從觀測得來的質量函數推導出質量比分佈的過程，在數學上可表示為一個積分方程式，此積分方程式同時兼具解析解（analytic solution）與數值解（numerical solution）（Heacox 1995）。

在本篇研究中，我們同時採用了解析解與數值解，從觀測到的質量函數分佈來推測質量比的分佈。我們發現，對於主星的光譜型（spectral type）早於G的雙星系統來說，擁有低質量比的系統所佔的比例高於擁有相同質量的雙星系統。然而，對於主星的光譜型為G的雙星系統，情況卻完全相反。

關鍵字

雙星系統 ； 質量比

並列摘要

The actual mass-ratio distributions can be used to constrain the properties and formation processes of binary systems. However, most spectroscopic binaries are single-lined (SB1) so that only the mass of the primary star can be derived, leaving unknown the mass ratio of the binary system. Nevertheless, some statistical models have been established, according to which the mass-ratio distribution can be deduced from the mass functions of binary systems.

Based on the statistical model, the problem of deducing the mass ratio distribution from the observed mass functions can be stated mathematically as an inverse problem, which can be solved both analytically and numerically (Heacox 1995). The numerical method, which is the Richardson-Lucy method in inverse problems, is of iterative nature.

In this work, we use both the analytic and the Richardson-Lucy method to deduce the mass-ratio distributions from observed mass functions. We found that it is more probable to have small mass-ratio systems than to have systems with equal-mass components for the binary systems with primary stars whose spectral types are earlier than G. However, for binaries with G dwarf as the primary, the situation is reversed.

並列關鍵字

binary systems ； mass ratio

參考文獻

Aitken, R. G. 1935, in The Binary Stars (New York: McGraw-Hill), 218

Heacox, W. D. 1995, AJ, 109, 2670

Kuiper, G. P., 1935. Publs astr. Soc. Pacif., 47, 38

Kholopov, P. N., Samus, N. N., Frolov, M. S., et al. 1998, Combined general catalogue of variable stars, 4th ed.

Lucy, L. B., 1974, AJ, 79, 745