論單線光譜雙星系統之質量比分佈

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陳韋達(Wei-Da Chen) 查詢紙本館藏

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天文研究所

論文名稱

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)

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摘要(中)

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。

摘要(英)

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.

關鍵字(中)

★ 雙星系統
★ 質量比

關鍵字(英)

★ binary systems
★ mass ratio

論文目次

Abstract i
Acknowledge iii
Contents iv
Contents for Figures vi
Contents for Tables viii
1 Introduction 1
2 The Statistical Model 3
2.1 The Mass Function for Binary Systems 3
2.2 The Statistical Basis 5
2.3 The Model 7
2.4 The Solutions to the Problem 8
3 The Methods of Analysis 10
3.1 The Stellar Masses 10
3.2 The Probability Density Function of the Reduced Mass Function 11
3.2.1 The Kolmogorov-Smirnov Test 11
3.2.2 Finding the Probability Density Function of the Reduced Mass Function 13
3.3 The Algorithm 14
3.4 The Test of the Algorithm 15
4 Data Reduction 17
4.1 The Ninth Catalogue of Spectroscopic Binary Orbits 17
4.2 The Data Selection 18
4.3 The Period Distribution 18
4.4 The Eccentricity Distribution 22
5 The Results and Discussions 25
5.1 Result for the B Sample 25
5.2 Result for the A Sample 28
5.3 Result for the F Sample 32
5.4 Result for the G Sample 37
5.5 Discussion 42
6 Conclusion 44
Reference 46
Appendix 1 Orbital Parameters for the Binary Systems Used in This Study 47
Appendix 2 The Fortran90 code used to carry out the K-S test 57
Appendix 3 The Fortran90 code used to carry out the analytic solution 60
Appendix 4 The Fortran90 code used to carry out the Richardson-Lucy solution 63

參考文獻

Aitken, R. G. 1935, in The Binary Stars (New York: McGraw-Hill), 218
Batten, A. H., Fletcher, J. M., & McCarthy D. G., 1989, Publ. Dom. Ap. Obs., 17, 1
Goldberg, D., Mazeh, T., & Latham, D. W., 2003, ApJ, 591,397
Habets, & Heintze, 1981, A&AS, 46, 193
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
Levato, H., Malaroda, S., Morrell, N., & Solivella, G., 1987, ApJS, 64, 487
Mazeh, T., & Goldberg, D. 1992, ApJ, 394, 592
Mazeh, T., Simon, M., Prato, L., Markus, B., & Zucker, S., 2003, 599, 1344
Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P., 1992, in Numerical Recipies in FORTRAN: The Art of Scientific Computing, 2nd Edition (Cambridge University Press, New Yor)
Pourbaix, D., Tokovinin, A. A., Batten, A. H., Fekel, F. C., Hartkopf, W. I., Levato, H., Morrell, N. I., Torres, G., & Udry, S., 2004, A&A, 424, 727
Richardson, W. H., 1972, J. Opt. Soc. Am., 62, 55
Slettebak, A., 1968, ApJ, 151, 1043
Trimble, V., 1974, AJ, 79, 967
Trimble, V., 1990, MNRAS, 242, 79

指導教授

江瑛貴(Ing-Guey Jiang)

審核日期

2006-7-17

推文