A Posteriori Transit Probabilities
A Posteriori Transit Probabilities
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后验运输概率
DOI：
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发表时间：
2013
期刊：
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通讯作者：
B. Gaudi
中科院分区：
文献类型：
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作者：
D. Stevens;B. Gaudi
鉴于对看不见的伴星的径向速度（RV）检测，估计伴星也经过主星的概率通常很有趣。通常，我们假设伴星轨道倾角 i 的余弦分布均匀。给定主半径 R* 和轨道半长轴 a，并假设小伴星和圆形轨道，这产生了对 ∼R*/a 的先验概率的熟悉估计。然而，后验传输概率不仅取决于 i 的先验概率分布，还取决于伴星质量 Mc 的先验概率分布，前提是从 RV 信号测量两者的乘积（最小质量 Mc sin i）。一般来说，后验概率可以大于或小于先验概率。我们推导了后验传输概率的解析表达式，假设真实质量分布采用幂律形式 d Γ / d M c ∝ M c α ，整数值 -3 ≤ α ≤ 3。我们表明，对于低传输概率，这些概率减少到相应先验传输概率的常数乘法因子 fα ，其中 fα 通常取决于 α 和假设的真实质量上限。当 α = -1 时，先验概率和后验概率相等。对于 α = -3，后验过境概率比先验概率大 ∼1.5 倍；对于 α = -2，后验过境概率大 ∼4/π 倍；但对于 α≥0，后验过境概率小于先验概率；对于 α > 1，后验过境概率可以任意小。我们还计算了类太阳恒星周围伴星的两种物理驱动质量分布在不同质量状态下的后验过境概率。我们发现，对于木星质量的行星，后验概率大致等于先验概率，而超级地球和海王星 (10 M⊕ - 30 M⊕) 和超级木星 (3 MJup - 10 MJup) 的后验概率可能更高，因为预测这些区域中质量函数会急剧上升到较小质量。因此，我们建议，在这些政权中质量最小的伴星可能是凌日跟踪的好于预期的目标，并且我们在文献中从 RV 探测到的行星中确定了有希望的目标。最后，我们考虑由输入参数的不确定性引起的传输概率的不确定性，以及忽略传输概率对 i 的真实半长轴的依赖性的影响。
Given the radial velocity (RV) detection of an unseen companion, it is often of interest to estimate the probability that the companion also transits the primary star. Typically, one assumes a uniform distribution for the cosine of the inclination angle i of the companion’s orbit. This yields the familiar estimate for the prior transit probability of ∼R∗/a, given the primary radius R∗ and orbital semimajor axis a, and assuming small companions and a circular orbit. However, the posterior transit probability depends not only on the prior probability distribution of i but also on the prior probability distribution of the companion mass Mc, given a measurement of the product of the two (the minimum mass Mc sin i) from an RV signal. In general, the posterior can be larger or smaller than the prior transit probability. We derive analytic expressions for the posterior transit probability assuming a power-law form for the distribution of true masses, d Γ / d M c ∝ M c α , for integer values -3 ≤ α ≤ 3. We show that for low transit probabilities, these probabilities reduce to a constant multiplicative factor fα of the corresponding prior transit probability, where fα in general depends on α and an assumed upper limit on the true mass. The prior and posterior probabilities are equal for α = -1. The posterior transit probability is ∼1.5 times larger than the prior for α = -3 and is ∼4/π times larger for α = -2, but is less than the prior for α≥0, and can be arbitrarily small for α > 1. We also calculate the posterior transit probability in different mass regimes for two physically-motivated mass distributions of companions around Sun-like stars. We find that for Jupiter-mass planets, the posterior transit probability is roughly equal to the prior probability, whereas the posterior is likely higher for Super-Earths and Neptunes (10 M⊕ - 30 M⊕) and Super-Jupiters (3 MJup - 10 MJup), owing to the predicted steep rise in the mass function toward smaller masses in these regimes. We therefore suggest that companions with minimum masses in these regimes might be better-than-expected targets for transit follow-up, and we identify promising targets from RV-detected planets in the literature. Finally, we consider the uncertainty in the transit probability arising from uncertainties in the input parameters, and the effect of ignoring the dependence of the transit probability on the true semimajor axis on i.