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arXiv 1003.4738astro-ph.EP
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由径向速度数据确定M_Tsin(i)系外行星sin(i)值的后验分布

The Posterior Distribution of sin(i) Values For Exoplanets With M_T sin(i) Determined From Radial Velocity Data

Shirley Ho, Edwin L. Turner

摘要:

外行星系统的径向速度(RV)观测给出了M_T sin(i)条件的值(即不仅给出了行星的真实质量M_T的信息,而且给出了sin(i)的值(其中i是轨道倾角))。因此,对于具有任何特定观测值的系统,不能假设sin(i)的值是从零和1之间的均匀分布(对应于各向同性i分布)中随机抽取的。它的实际分布取决于所研究的系外行星种群M_T的内在分布。我们给出了一个简单的贝叶斯推导这种关系,并将其应用到几个“玩具模型”的(目前未知的)内在分布的M_T。结果表明,这种影响可能是一个重要的影响。例如,即使对于M_T的简单幂律分布,对于幂律指数在-2和-0.5之间的合理范围内,观察到的RV样本中sin(i)的中值可以分别在0.25和0.71之间变化(与各向同性i分布的0.5值相比)。在相同的指标范围内,由于sin(i)的不确定性,M_T的95%置信上限范围分别为M_T sin(i)的4.5至400倍。M_T的分布更复杂,但仍然简单和合理,产生更复杂和更不直观的$sin(i)$分布。特别地,如果M_T分布包含任何特征质量尺度M_c,则sin(i)分布将取决于M_T sin(i)与$M_c$的比率,通常以非平凡的方式。我们的定性结论是,RV研究的系外行星,无论是个人的对象和统计样本,应该把sin(i)的因素比一个简单的和很好理解的统计特性的“数字常数的顺序单位”。(节略)

英文摘要:

Radial velocity (RV) observations of an exoplanet system giving a value of M_T sin(i) condition (i.e. give information about) not only the planet's true mass M_T but also the value of sin(i) (where i is the orbital inclination angle). Thus the value of sin(i) for a system with any particular observed value of M_T sin(i) cannot be assumed to be drawn randomly from a uniform distribution between zero and unity (corresponding to an isotropic i distribution). The actual distribution from which it is drawn depends on the intrinsic distribution of M_T for the exoplanet population being studied. We give a simple Bayesian derivation of this relationship and apply it to several "toy models" for the (currently unknown) intrinsic distribution of M_T. The results show that the effect can be an important one. For example, even for simple power-law distributions of M_T, the median value of sin(i) in an observed RV sample can vary between 0.25 and 0.71 (as compared to the 0.5 value for an isotropic i distribution) for indices of the power-law in the quite plausible range between -2 and -0.5, respectively. Over the same range of indicies, the 95% confidence upper bound on M_T ranges from 4.5 to 400 times larger than M_T sin(i), respectively, due to sin(i) uncertainty alone. More complex, but still simple and plausible, distributions of M_T yield still more complicated and less intuitive $sin(i)$ distributions. In particular, if the M_T distribution contains any characteristic mass scale M_c, the sin(i) distribution will depend on the ratio of M_T sin(i) to $M_c$, often in a non-trivial way. Our qualitative conclusion is that RV studies of exoplanets, both individual objects and statistical samples, should regard the sin(i) factor as more than a "numerical constant of order unity" with simple and well understood statistical properties. (abridged)

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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