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arXiv 0905.0433astro-ph.EP
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轨道拟合中的可探测性和误差估计

Detectability and Error Estimation in Orbital Fits

C. A. Giuppone, M. Tadeu dos Santos, C. Beaugé, S. Ferraz-Mello, T. A. Michtchenko

摘要:

我们估计的条件,两颗行星在2/1平均运动共振径向速度数据,作为其质量,观测次数和信噪比的函数。即使对于100次观测的数据集和每秒几米的标准偏差,我们发现,如果行星的质量相差大于$\sim 4$的系数,木星大小的共振行星是很难检测到的。这与2/1可探测性中的真实外系统的当前人口是一致的,其中大多数具有类似最小质量的共振对,并且可能表明存在许多其他共振系统,但目前超出了可探测性极限。此外,我们分析了质量和轨道根数的轨道拟合从合成数据集的共振行星在2/1可测量性的误差分布。对于不同的质量比和数据点的数量,我们发现外行星的偏心率被系统地高估了,尽管内行星的偏心率受到的影响要小得多。如果初始条件对应于稳定拱共转共振(ACR)周围的小振幅振荡,从轨道拟合估计的振幅偏向较大的振幅,根据在真正的太阳系外共振系统中发现的结果。

英文摘要:

We estimate the conditions for detectability of two planets in a 2/1 mean-motion resonance from radial velocity data, as a function of their masses, number of observations and the signal-to-noise ratio. Even for a data set of the order of 100 observations and standard deviations of the order of a few meters per second, we find that Jovian-size resonant planets are difficult to detect if the masses of the planets differ by a factor larger than $\sim 4$. This is consistent with the present population of real exosystems in the 2/1 commensurability, most of which have resonant pairs with similar minimum masses, and could indicate that many other resonant systems exist, but are presently beyond the detectability limit. Furthermore, we analyze the error distribution in masses and orbital elements of orbital fits from synthetic data sets for resonant planets in the 2/1 commensurability. For various mass ratios and number of data points we find that the eccentricity of the outer planet is systematically over estimated, although the inner planet's eccentricity suffers a much smaller effect. If the initial conditions correspond to small amplitude oscillations around stable apsidal corotation resonances (ACR), the amplitudes estimated from the orbital fits are biased toward larger amplitudes, in accordance to results found in real resonant extrasolar systems.

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