We present the first public code for the calculation of the astrometric centroid shift occurring during microlensing events. The computation is based on the contour integration scheme and covers single and binary lensing of finite sources with arbitrary limb darkening profiles. This allows for general detailed investigations of the impact of finite source size in astrometric binary microlensing. The new code is embedded in version 3.0 of VBBinaryLensing, which offers a powerful computational tool for extensive studies of microlensing data from current surveys and future space missions.
Context: Astrometric gravitational microlensing is an excellent tool to determine the mass of stellar objects. Using precise astrometric measurements of the lensed position of a background source in combination with accurate predictions of the positions of the lens and the unlensed source it is possible to determine the mass of the lens with an accuracy of a few percent. Aims: Making use of the recently published Gaia Data Release 2 (DR2) catalogue, we want to predict astrometric microlensing events caused by foreground stars with high proper motion passing a background source in the coming de…
A Fast Concentric-disk Contour Integration Method For Microlensing Limb-darkening Effect
The Kavli Institute for Astronomy and Astrophysics, Peking University（北京大学科维理天文与天体物理研究所）；Department of Astronomy, School of Physics, Peking University（北京大学物理学院天文学系）
Context. Astrometric microlensing is an excellent tool to determine the mass of a stellar object. By measuring the astrometric shift of a background source star in combination with precise predictions of its unlensed position and of the lens position, gravitational lensing allows to determine the mass of the lensing star with a precision of 1 percent, independent of any prior knowledge. Aims. Making use of the recently published Gaia Data Release 2 (Gaia DR2) we predict astrometric microlensing events by foreground stars of high proper motion passing by a background star in the coming years. M…
Astrometric microlensing can be used to make precise measurements of the masses of lens stars that are independent of their assumed internal physics. Such direct mass measurements, obtained purely by observing the gravitational effects of the stars on external objects, are crucial for validating theoretical stellar models. Specifically, astrometric microlensing provides a channel to direct mass measurements of single stars for which so few measurements exist. To use the astrometric solutions and photometric measurements of ~1.7 billion stars from Gaia Data Release 2 to predict microlensing eve…
Context. Astrometric gravitational microlensing can be used to determine the mass of a single star (the lens) with an accuracy of a few percent. To do so, precise measurements of the angular separations between lens and background star with an accuracy below 1 milli-arcsecond at different epochs are needed. Hence only the most accurate instruments can be used. However, since the timescale is in the order of months to years, the astrometric deflection might be detected by Gaia, even though each star is only observed on a low cadence. Aims. We want to show how accurately Gaia can determine the m…
We extend predictive microlensing event searches using the Vista Variables in the Via Lactea survey and the second Gaia data release. We identify two events with maxima in 2019 that require urgent follow-up. First, we predict that the nearby M2 dwarf L 338-152 will align with a background source with a closest approach of $35^{+35}_{-23}$ mas on 2019 November $16^{+28}_{-27}$ d. This will cause a peak astrometric shift and photometric amplification of the background source of $2.7^{+3.5}_{-1.5}$ mas and $5.6^{+143.2}_{-5.2}$ mmag respectively. This event should be astrometrically detectable by…
Using Gaia data release 2 (GDR2), we present an almanac of 2,509 predicted microlensing events, caused by 2,130 unique lens stars, that will peak between 25th July 2026 and the end of the century. This work extends and completes a thorough search for future microlensing events initiated by Bramich (2018) and Nielsen & Bramich (2018) using GDR2. The almanac includes 161 lenses that will cause at least two microlensing events each. A few highlights are presented and discussed, including: (i) an astrometric microlensing event with a peak amplitude of ~9.7 mas, (ii) an event that will probe the pl…
Testing General Relativity with Binary Lens Microlensing Events
Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University（北京师范大学前沿天文与天体物理研究所）；School of Physics and Astronomy, Beijing Normal University（北京师范大学物理学院）
Extracting Microlensing Signals from K2 Campaign 9
减少\emph{K2}的战役9（K 2 C 9）微透镜数据是具有挑战性的，主要是因为非常拥挤的场和航天器的不稳定指向。在这项工作中，我们提出了第一种方法，可以从这个K2 C9数据产品中提取微透镜信号。首先利用Soares-Furtado等人和Huang等人的\emph{K2}密场测光技术导出原始光变曲线和天体测量解。然后，我们通过与微透镜信号同时进行建模来最小化和去除系统效应。我们还推导出精确的$(K_p-I)$与$(V-I)$的颜色-颜色关系，可以预测微透镜源通量的\emph{Kepler}带通。通过在光变曲线建模中实现颜色-颜色关系，我们表明可以更好地约束微透镜参数。最后，我们使用两个示例微透镜事件OGLE-2016-BLG-0980和OGLE-2016-BLG-0940来测试我们的方法。
The computation of microlensing light curves represents a bottleneck for the modeling of planetary events, making broad searches in the vast parameter space of microlensing extremely time-consuming. The release of the first version of VBBinaryLensing (based on the advanced contour integration method presented in Bozza(2010)) has represented a considerable advance in the field, with the birth of several analysis platforms running on this code. Here we present the version 2.0 of VBBinaryLensing, which contains several upgrades with respect to the first version, including new decision trees that …
Towards sub-milliarcsecond astrometric precision using seeing-limited imaging
Weizmann Institute of Science（魏茨曼科学研究所）；Korea Astronomy and Space Science Institute（韩国天体宇宙科学研究所）；Center for Astrophysics — Harvard & Smithsonian（哈佛-史密森天体物理中心）；University of Canterbury（坎特伯雷大学）；Ohio State University（俄亥俄州立大学）
We present a method to compute the magnification of a finite source star lensed by a triple lens system based on the image boundary (contour integration) method. We describe a new procedure to obtain continuous image boundaries from solutions of the tenth-order polynomial obtained from the lens equation. Contour integration is then applied to calculate the image areas within the image boundaries, which yields the magnification of a source with uniform brightness. We extend the magnification calculation to limb-darkened stars approximated with a linear profile. In principle, this method works f…
Modeling Binary Lenses and Sources with the BAGLE Python Package
University of Maryland（马里兰大学）；NASA Goddard Space Flight Center（NASA戈达德太空飞行中心）；University of California, Berkeley（加州大学伯克利分校）；Observatories of the Carnegie Institution for Science（卡内基科学研究所天文台）
Gaia DR2 published positions, parallaxes and proper motions for an unprecedented 1,331,909,727 sources, revolutionising the field of Galactic dynamics. We complement this data with the Astrometry Spread Function (ASF), the expected uncertainty in the measured positions, proper motions and parallax for a non-accelerating point source. The ASF is a Gaussian function for which we construct the 5D astrometric covariance matrix as a function of position on the sky and apparent magnitude using the Gaia DR2 scanning law and demonstrate excellent agreement with the observed data. This can be used to a…
Gaia16aye was a binary microlensing event discovered in the direction towards the northern Galactic disc and was one of the first microlensing events detected and alerted to by the Gaia space mission. Its light curve exhibited five distinct brightening episodes, reaching up to I=12 mag, and it was covered in great detail with almost 25,000 data points gathered by a network of telescopes. We present the photometric and spectroscopic follow-up covering 500 days of the event evolution. We employed a full Keplerian binary orbit microlensing model combined with the motion of Earth and Gaia around t…
