Astrometry for Determining the MACHO Mass and Trajectory

Miyamoto, M.; Yoshii, Yuzuru

doi:10.1086/117616

Cited by 158 publications

(125 citation statements)

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“…Even if the images cannot be resolved, it may be possible to measure the deflection of the image centroid (Hog, Novikov, & Polnarev 1995;Miyamoto & Yoshi 1995;Walker 1995), which is given by…”

Section: Follow-up Observationsmentioning

confidence: 99%

Gravitational Microlensing Events Due to Stellar‐Mass Black Holes

Bennett

Becker

Quinn

et al. 2002

ApJ

135

134

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We present an analysis of the longest timescale microlensing events discovered by the MACHO Collaboration during a 7 year survey of the Galactic bulge. We find six events that exhibit very strong microlensing parallax signals due, in part, to accurate photometric data from the GMAN and MPS collaborations. The microlensing parallax fit parameters are used in a likelihood analysis, which is able to estimate the distances and masses of the lens objects based on a standard model of the Galactic velocity distribution. This analysis indicates that the most likely masses of five of the six lenses are greater than 1 M , which suggests that a substantial fraction of the Galactic lenses may be massive stellar remnants. This could explain the observed excess of long-timescale microlensing events. The lenses for events MACHO-96-BLG-5 and MACHO-98-BLG-6 are the most massive, with mass estimates of M=M ¼ 6 þ10 À3 and M=M ¼ 6 þ7 À3 , respectively. The observed upper limits on the absolute brightness of main-sequence stars for these lenses are less than 1 L , so both lenses are black hole candidates. The black hole interpretation is also favored by a likelihood analysis with a Bayesian prior using a conventional model for the lens mass function. We consider the possibility that the source stars for some of these six events may lie in the foreground Galactic disk or in the Sagittarius (Sgr) dwarf galaxy behind the bulge, but we find that bulge sources are likely to dominate our microlensing parallax event sample. Future Hubble Space Telescope observations of these events can either confirm the black hole lens hypothesis or detect the lens stars and provide a direct measurement of their masses. Future observations of similar events by the Space Interferometry Mission or the Keck or VLT interferometers, as explained by Delplancke, Gó rski, & Richichi, will allow direct measurements of the lens masses for stellar remnant lenses as well.

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Section: Follow-up Observationsmentioning

confidence: 99%

Gravitational Microlensing Events Due to Stellar‐Mass Black Holes

Bennett

Becker

Quinn

et al. 2002

ApJ

135

134

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“…The half-brightness radius of LD and AD models was fixed: R 1/2 = 0.2R E (this choice was determined by the AD1 model, see comments after formula (47)) and that of the Gaussian source was varied to get better fitting; here P = 3/2 for PL model and q = 1 for LD model. One example of the relative light curve differences η(T) according to (62) between LD, AD1 and the best fitted Gaussian models is shown in Figure 4. As we see from this figure, usage of an optimal size of the Gaussian model can diminish η m as compared to the average estimate from Table 2 dealing with the same R 1/2 for all the models.…”

Section: Gaussian Fittings Of Accretion Disk and Limb Darkeningmentioning

confidence: 99%

Analytical Methods in Gravitational Microlensing

Жданов

Alexandrov

Fedorova

et al. 2012

ISRN Astronomy and Astrophysics

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We discuss analytical results dealing with photometric and astrometric gravitational microlensing. The first two sections concern approximation methods that allow us to get solutions of the general lens equation near fold caustics and cusp points up to any prescribed accuracy. Two methods of finding approximate solutions near the fold are worked out. The results are applied to derive new corrections to total amplifications of critical source images. Analytic expressions are obtained in case of the Gaussian, power-law, and limb-darkening extended source models; here we present the first nonzero corrections to the well-known linear caustic approximation. Possibilities to distinguish different source models in observations are discussed on the basis of statistical simulations of microlensed light curves. In the next section, we discuss astrometric microlensing effects in various cases of extended sources and extended lenses, including a simple model of weak statistical microlensing by extended dark matter clumps. Random walks of a distant source image microlensed by stochastic masses are estimated. We note that the bulk motion of foreground stars induces a small apparent rotation of the extragalactic reference frame. Compact analytical relations describing the statistics of such motions are presented.

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“…Parameters of the lensing object can be derived from an analysis of the light curve, but unfortunately there are degeneracies between lens mass, relative proper motion, and relative parallax. These degeneracies can be broken by astrometric observations, determining the position of the center of light as a function of time during the encounter (Miyamoto & Yoshii 1995).…”

Section: A Quirrenbachmentioning

confidence: 99%

Optical interferometry from the Earth

Quirrenbach

2009

Proc. IAU

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Abstract. Ground-based optical interferometers can perform astrometric measurements with a precision approaching 10 μas between pairs of stars separated by ∼ 10 on the sky. These narrow-angle measurements can be used to search for extrasolar planets and to determine their orbital parameters, to characterize microlensing events, and to measure the orbits of stars around the black hole at the center of our Galaxy.

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Astrometry for Determining the MACHO Mass and Trajectory

Cited by 158 publications

References 0 publications

Gravitational Microlensing Events Due to Stellar‐Mass Black Holes

Gravitational Microlensing Events Due to Stellar‐Mass Black Holes

Analytical Methods in Gravitational Microlensing

Optical interferometry from the Earth

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