标题： 一种从双星中反卷积质量比分布的方法 显示英文标题

标题： A method to deconvolve mass ratio distribution from binary stars

摘要： 为了更好地理解双星系统中恒星的演化以及限制双星的形成，了解双星质量比分布是很重要的。然而，在大多数情况下，即对于单线光谱双星，质量比不能直接测量，只能作为依赖于质量比和轨道在天球平面上的未知倾角的函数的卷积来推导。我们扩展了之前的方法来反卷积这个逆问题（Cure等，2014），即我们通过积分得到质量比分布的累积分布函数（CDF）。经过适当的变量变换后，发现这个问题与旋转速度$v \sin i$的问题相同，从而可以为CDF提供一个接近解析的公式。然后我们将该方法应用于两个真实数据集：Am型恒星双星系统样本和天鹅座OB2协会中的大质量光谱双星样本。\{我们能够再现Boffin（2010）对Am型恒星样本的先前结果，同时我们表明大质量恒星的质量比分布显示出小质量比系统的过剩，这与Kobulnicky等人（2014）的主张相反。我们的方法非常稳健，只需一步就能从样本中反卷积出分布。 显示英文摘要

摘要： To better understand the evolution of stars in binary systems as well as to constrain the formation of binary stars, it is important to know the binary mass-ratio distribution. However, in most cases, i.e. for single-lined spectroscopic binaries, the mass ratio cannot be measured directly but only derived as the convolution of a function that depends on the mass ratio and the unknown inclination angle of the orbit on the plane of the sky. We extend our previous method to deconvolve this inverse problem (Cure et al. 2014), i.e., we obtain as an integral the cumulative distribution function (CDF) for the mass ratio distribution. After a suitable transformation of variables it turns out that this problem is the same as the one for rotational velocities $v \sin i$, allowing a close analytic formulation for the CDF. We then apply our method to two real datasets: a sample of Am stars binary systems, and a sample of massive spectroscopic binaries in the Cyg OB2 Association.} {We are able to reproduce the previous results of Boffin (2010) for the sample of Am stars, while we show that the mass ratio distribution of massive stars shows an excess of small mass ratio systems, contrarily to what was claimed by Kobulnicky et al. (2014). Our method proves very robust and deconvolves the distribution from a sample in just a single step.