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arXiv 2403.05883astro-ph.IM
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精度溢价变换——一种基于精度溢价曲线的高精度天体测量解决方案

Precision premium transformation -- a high-precision astrometric solution based on the precision premium curve

Z. J. Zheng, Q. Y. Peng, F. R. Lin, D. Li, Y. Zheng

AI总结:

针对大气湍流限制地基光学天体测量精度的问题,提出基于精度溢价曲线的精度溢价变换方法,利用小区域湍流误差相似性和密集Gaia参考星加权求解,有效提升了高恒星密度区的测量精度与适用性。

摘要:

研究背景与问题:在盖亚(Gaia)时代,导致恒星图像随机漂移的大气湍流是地基光学成像天体测量精度的根本限制因素。不过,由于相距仅几十角秒范围内的目标与参考天体(恒星或快速移动目标)会受到相似的湍流误差影响,通过相对于该参考天体测量目标位置,可有效降低湍流导致的位置偏差(本文称为湍流误差)。这一现象被称为精度溢价,已被有效应用于太阳系天体测量。对精度溢价的进一步研究表明,对于两个特定天体,精度溢价在约100角秒以内生效,且相对位置精度随角间距的变化可被称为精度溢价曲线(PPC)的S型函数很好地拟合。研究目标:若地基观测中目标位于高恒星密度区域,我们希望利用更多Gaia参考恒星降低目标的湍流误差。研究方法:本文基于PPC提出了一种名为精度溢价变换(PPT)的高精度天体测量解决方案,该方案利用小区域内湍流误差的高度相似性,以及区域内密集的Gaia参考恒星,通过加权求解降低观测中的湍流误差。实验设置与结果:通过系统分析,当目标位于高恒星密度区域时,PPT方法不仅在精度上,还在适用性上展现出显著优势。我们还将PPT方法应用于疏散星团自行的测定,结果证明并量化了PPT方法为地基天体测量带来的增益。结论与意义:该方法充分利用小视场内湍流误差的相关性与密集参考星资源,有效突破了大气湍流对地基天体测量精度的限制,拓展了高精度地基天体测量的应用场景。

英文摘要:

Context. In Gaia era, atmospheric turbulence, which causes stochastic wander of a star image, is a fundamental limitation to the astrometric accuracy of ground-based optical imaging. However, the positional bias caused by turbulence (called turbulence error here) can be effectively reduced by measuring a target relative to another reference (a star or a fast-moving target) which locates in the range of only several tens of arcsec, since they suffer from similar turbulence errors. This phenomenon is called the precision premium and has been effectively applied to the astrometry of solar system. Further investigation for the precision premium shows that, the precision premium works at less than about 100 arcsec for two specific objects and the relative positional precision as a function of their angular seperation can be well fitted by a sigmoidal function, called the precision premium curve (PPC). Aims. We want to reduce the turbulence error of a target if it is imaged in an area of high stellar density of a ground-based observation by taking advantage of more Gaia reference stars. Methods. Based on the PPC, we proposed a high-precision astrometric solution called precision premium transformation (PPT) in this paper, which takes advantage of high similarity of turbulence errors in a small region and the dense Gaia reference stars in the region to reduce the turbulence errors on the observation, through a weighted solution. Results. Through systematic analysis, the PPT method exhibits significant advantages in terms of not only precision but also applicability when a target is imaged in an area of high stellar density. The PPT method is also applied to the determination of the proper motion of an open cluster, and the results demonstrate and quantify benefits that the PPT method bestows on ground-based astrometry.

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