A New Application of the Astrometric Method to Break Severe Degeneracies in Binary Microlensing Events
📝 Abstract
When a source star is microlensed by one stellar component of a widely separated binary stellar components, after finishing the lensing event, the event induced by the other binary star can be additionally detected. In this paper, we investigate whether the close/wide degeneracies in binary lensing events can be resolved by detecting the additional centroid shift of the source images induced by the secondary binary star in wide binary lensing events. From this investigation, we find that if the source star passes close to the Einstein ring of the secondary companion, the degeneracy can be easily resolved by using future astrometric follow-up observations with high astrometric precision. We determine the probability of detecting the additional centroid shift in binary lensing events with high magnification. From this, we find that the degeneracy of binary lensing events with a separation of $\lesssim 20.0$ AU can be resolved with a significant efficiency. We also estimate the waiting time for the detection of the additional centroid shift in wide binary lensing events. We find that for typical Galactic lensing events with a separation of $\lesssim 20.0$ AU, the additional centroid shift can be detected within 100 days, and thus the degeneracy of those events can be sufficiently broken within a year.
💡 Analysis
When a source star is microlensed by one stellar component of a widely separated binary stellar components, after finishing the lensing event, the event induced by the other binary star can be additionally detected. In this paper, we investigate whether the close/wide degeneracies in binary lensing events can be resolved by detecting the additional centroid shift of the source images induced by the secondary binary star in wide binary lensing events. From this investigation, we find that if the source star passes close to the Einstein ring of the secondary companion, the degeneracy can be easily resolved by using future astrometric follow-up observations with high astrometric precision. We determine the probability of detecting the additional centroid shift in binary lensing events with high magnification. From this, we find that the degeneracy of binary lensing events with a separation of $\lesssim 20.0$ AU can be resolved with a significant efficiency. We also estimate the waiting time for the detection of the additional centroid shift in wide binary lensing events. We find that for typical Galactic lensing events with a separation of $\lesssim 20.0$ AU, the additional centroid shift can be detected within 100 days, and thus the degeneracy of those events can be sufficiently broken within a year.
📄 Content
arXiv:0901.4411v2 [astro-ph.SR] 29 Jan 2009 A New Application of the Astrometric Method to Break Severe Degeneracies in Binary Microlensing Events Sun-Ju Chung1, Byeong-Gon Park1, Yoon-Hyun Ryu2, and Andrew Humphrey1 ABSTRACT When a source star is microlensed by one stellar component of a widely separated binary stellar components, after finishing the lensing event, the event induced by the other binary star can be additionally detected. In this paper, we investigate whether the close/wide degeneracies in binary lensing events can be resolved by detecting the additional centroid shift of the source images induced by the secondary binary star in wide binary lensing events. From this investigation, we find that if the source star passes close to the Einstein ring of the secondary companion, the degeneracy can be easily resolved by using future astrometric follow-up observations with high astrometric precision. We determine the probability of detecting the additional centroid shift in binary lensing events with high magnification. From this, we find that the degeneracy of binary lensing events with a separation of ≲20.0 AU can be resolved with a significant efficiency. We also estimate the waiting time for the detection of the additional centroid shift in wide binary lensing events. We find that for typical Galactic lensing events with a separation of ≲20.0 AU, the additional centroid shift can be detected within 100 days, and thus the degeneracy of those events can be sufficiently broken within a year. Subject headings: astrometry — binaries: general — gravitational lensing 1. INTRODUCTION Observations are currently being undertaken for the detection of microlensing events, with survey observations being carried out by the OGLE (Udalski 2003) and MOA (Bond et al. 2002) groups, and with follow-up observations being performed by the PLANET (Albrow et al. 2001) and MicroFun (Dong et al. 2006) groups. The follow-up observations are focusing on high magnification events toward the Galactic bulge, so that they are efficient for detecting events with the character- istic features of binary lens systems, such as the caustic-crossing appearing in high magnification events. Moreover, if future space missions such as Microlensing Planet Finder (MPF (Bennett et al. 1Korea Astronomy and Space Science Institute, Hwaam-Dong, Yuseong-Gu, Daejeon 305-348, Korea; sjchung;bgpark;ajh@kasi.re.kr 2Department of Astronomy and Atmospheric Science, Kyungpook National University, Daegu 702-701, Korea; yhryu@knu.ac.kr – 2 – 2004)) with high photometric precision and monitoring cadence are carried out, the efficiency will significantly increase, and thus many more binary lensing events with the characteristic features will be found. Detection of binary microlensing events is important for providing various information about the lensing parameters. First, the binary mass ratio and projected separation are obtained. If many binary lensing events are detected, these parameters can help to infer statistical properties of binaries in the lens population (Gaudi & Sackett 2000). Second, the special case of caustic-crossing events provides the caustic-crossing time, ∆tcc, which is given by ∆tcc = ρ⋆ | sin φ|tE = θ⋆ µ| sin φ| , (1) where ρ⋆is the source radius normalized to the Einstein ring radius, corresponding to the total mass of the binary, tE is the Einstein timescale of the binary lens, θ⋆is the angular source radius, φ is the caustic-crossing angle, and µ is the lens-source proper motion. The angular source radius can be measured from its color and apparent magnitude. The Einstein timescale and caustic- crossing angle can be determined from fitting of the observed light curve. Third, we can obtain the information of the lens-source proper motion and the normalized source radius from equation (1). Fourth, because µ = θE/tE, if the proper motion is determined, the angular Einstein ring radius, θE, can be measured. The Einstein ring radius is related to the total mass of the binary lens, M, which is expressed as θE = s 4GM c2 1 DL −1 DS , (2) where DL and DS are the distances to the lens and the source from the observer, respectively. Therefore, measuring the proper motion is very important to determine the lens mass and distance to the lens. Dominik (1999a) first reported that there exist multiple solutions to a photometrically ob- served binary lensing event. Han, Chun, & Chang (1999) investigated the pattern of the centroid shift of the source images selecting four of the multiple solutions in the paper of Dominik (1999a). As a result, all four cases showed different centroid shift patterns, and thus they demonstrated that the photometric degeneracy could be astrometrically resolved. Gould & Han (2000), however, showed that for the MACHO 98-SMC-1 event (Afonso et al. 2000), both of the light curves and centroid shift patterns of the close and wide binary solutions are extremely similar. The degeneracy of the close and wide binaries is rooted in the si
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