用稀疏采样径向速度数据表征银河系白矮星双星星族
Characterizing the Galactic White Dwarf Binary Population with Sparsely Sampled Radial Velocity Data
摘要：
我们提出了一种方法来统计特征的参数分离的二进制样本-二进制分数，分离分布，质量比分布-使用嘈杂的径向速度数据与少至两个，随机间隔，历元每个对象。为此，我们分析了DRVmax的分布，DRVmax是同一物体任何两个时期之间的最大径向速度差。在低值时，该分布的核心由测量误差主导，但对于足够大的样本，存在可以有效约束二进制总体参数的高速尾部。我们讨论了我们的方法的情况下，人口的分离白矮星（WD）的二进制分离，通过引力波发射衰减。我们推导出解析表达式的分离，集成在银河系的恒星形成的历史，参数化的初始WD分离分布在年底的共同信封阶段。我们使用Monte Carlo技术产生网格的模拟DRVmax分布与特定的二进制人口参数，和相同的采样节奏和径向速度误差的观察，我们比较他们的真实DRVmax分布，以约束二进制人口的属性。我们说明了模型和观测参数的方法的灵敏度。在双白矮星的特殊情况下，每一个模型群体预测的每颗恒星的合并率可以很容易地与Ia型超新星的比率进行比较。在一篇配套的论文中，我们将该方法应用于斯隆数字巡天的约4000个WD样本，我们发现合并率与银河系中Ia型超新星的合并率非常相似。
英文摘要：
We present a method to characterize statistically the parameters of a detached binary sample - binary fraction, separation distribution, and mass ratio distribution - using noisy radial-velocity data with as few as two, randomly spaced, epochs per object. To do this, we analyze the distribution of DRVmax, the maximum radial-velocity difference between any two epochs for the same object. At low values, the core of this distribution is dominated by measurement errors, but for large enough samples there is a high-velocity tail that can effectively constrain the parameters of the binary population. We discuss our approach for the case of a population of detached white-dwarf (WD) binaries with separations that are decaying via gravitational wave emission. We derive analytic expressions for the present-day distribution of separations, integrated over the star-formation history of the Galaxy, for parametrized initial WD separation distributions at the end of the common-envelope phase. We use Monte Carlo techniques to produce grids of simulated DRVmax distributions with specific binary population parameters, and the same sampling cadences and radial velocity errors as the observations, and we compare them to the real DRVmax distribution to constrain the properties of the binary population. We illustrate the sensitivity of the method to both the model and the observational parameters. In the particular case of binary white dwarfs, every model population predicts a merger rate per star which can easily be compared to type-Ia supernova rates. In a companion paper, we apply the method to a sample of about 4000 WDs from the Sloan Digital Sky Survey, and we find a merger rate remarkably similar to the rate of Type-Ia supernovae in Milky-Way-like galaxies.
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