Expectations on the mass determination using astrometric microlensing by Gaia

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 mass of the lensing star. Methods. Using conservative assumptions based on the results of the second Gaia Data release, we simulated the individual Gaia measurements for 501 predicted astrometric microlensing events during the Gaia era (2014.5 - 2026.5). For this purpose we use the astrometric parameters of Gaia DR2, as well as an approximative mass based on the absolute G magnitude. By fitting the motion of lens and source simultaneously we then reconstruct the 11 parameters of the lensing event. For lenses passing by multiple background sources, we also fit the motion of all background sources and the lens simultaneously. Using a Monte-Carlo simulation we determine the achievable precision of the mass determination. Results. We find that Gaia can detect the astrometric deflection for 114 events. Further, for 13 events Gaia can determine the mass of the lens with a precision better than 15% and for 13 + 21 = 34 events with a precision of 30% or better.Comment: 13 pages; 10 figures; 3 tables; accepted by A&A (April. 28th 2020) The Python-based code for our simulation is made publicly available https://github.com/jkluter/ML

Ongoing Astrometric Microlensing Events of Two Nearby Stars

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. Methods. We compile a list of ~148.000 high-proper-motion stars within Gaia DR2 with $\mu_{tot}$ > 150 mas/yr. We then search for background stars close to their paths and calculate the dates and separations of the closest approaches. Using color and absolute magnitude, we determine approximate masses of the lenses. Finally, we calculate the expected astrometric shifts and magnifications of the predicted events. Results . We detect two ongoing microlensing events by the high proper motion stars Luyten 143-23 and Ross 322 and predict closest separations of (108.5 $\pm$ 1.4) mas in July 2018 and (125.3 $\pm$ 3.4) mas in August 2018, respectively. The respective expected astrometric shifts are (1.74 $\pm$ 0.12) mas and (0.76 $\pm$ 0.06) mas. Furthermore, Luyten 143-23 will pass by another star in March 2021 with a closest separation of (280.1 $\pm$ 1.1) mas, which results in an expected shift of (0.69 $\pm$ 0.05) mas.Comment: Submitted to A&A, accepted June 14, 2018. 4 pages, 3 figures, 2 table

Gravitational lensing in astronomy

Deflection of light by gravity was predicted by General Relativity and observationally confirmed in 1919. In the following decades, various aspects of the gravitational lens effect were explored theoretically. Among them were: the possibility of multiple or ring-like images of background sources, the use of lensing as a gravitational telescope on very faint and distant objects, and the possibility of determining Hubble's constant with lensing. It is only relatively recently, (after the discovery of the first doubly imaged quasar in 1979), that gravitational lensing has became an observational science. Today lensing is a booming part of astrophysics. In addition to multiply-imaged quasars, a number of other aspects of lensing have been discovered: For example, giant luminous arcs, quasar microlensing, Einstein rings, galactic microlensing events, arclets, and weak gravitational lensing. At present, literally hundreds of individual gravitational lens phenomena are known. Although still in its childhood, lensing has established itself as a very useful astrophysical tool with some remarkable successes. It has contributed significant new results in areas as different as the cosmological distance scale, the large scale matter distribution in the universe, mass and mass distribution of galaxy clusters, the physics of quasars, dark matter in galaxy halos, and galaxy structure. Looking at these successes in the recent past we predict an even more luminous future for gravitational lensing

The multiple quasar Q2237+0305 under a microlensing caustic

We use the high magnification event seen in the 1999 OGLE campaign light curve of image C of the quadruply imaged gravitational lens Q2237+0305 to study the structure of the quasar engine. We have obtained g'- and r'-band photometry at the Apache Point Observatory 3.5m telescope where we find that the event has a smaller amplitude in the r'-band than in the g'- and OGLE V-bands. By comparing the light curves with microlensing simulations we obtain constraints on the sizes of the quasar regions contributing to the g'- and r'-band flux. Assuming that most of the surface mass density in the central kiloparsec of the lensing galaxy is due to stars and by modeling the source with a Gaussian profile, we obtain for the Gaussian width 1.20 x 10^15 sqrt(M/0.1M_sun)cm < sigma_g' < 7.96 x 10^15 sqrt(M/0.1Msun) cm, where M is the mean microlensing mass, and a ratio sigma_r'/sigma_g'=1.25^{+0.45}_{-0.15}. With the limits on the velocity of the lensing galaxy from Gil-Merino et al. (2005) as our only prior, we obtain 0.60 x 10^15 sqrt(M/0.1Msun) cm < sigma_g' < 1.57 x 10^15 sqrt(M/0.1Msun) cm and a ratio sigma_r'/sigma_g'=1.45^{+0.90}_{-0.25} (all values at 68 percent confidence). Additionally, from our microlensing simulations we find that, during the chromatic microlensing event observed, the continuum emitting region of the quasar crossed a caustic at >72 percent confidence.Comment: Accepted for publication in A&A, 8 pages, 4 figures. Slightly modified compared to the original version: qualitative results unchanged, constraints on the r'/g' source size ratio now tighter due to correction of an error in the numerical treatment of the simulated light curve

The Ray Bundle method for calculating weak magnification by gravitational lenses

We present here an alternative method for calculating magnifications in gravitational lensing calculations -- the Ray Bundle method. We provide a detailed comparison between the distribution of magnifications obtained compared with analytic results and conventional ray-shooting methods. The Ray Bundle method provides high accuracy in the weak lensing limit, and is computationally much faster than (non-hierarchical) ray shooting methods to a comparable accuracy. The Ray Bundle method is a powerful and efficient technique with which to study gravitational lensing within realistic cosmological models, particularly in the weak lensing limit.Comment: 9 pages Latex, 8 figures, submitted to MNRA

Limits on the Transverse Velocity of the Lensing Galaxy in Q2237+0305 from the Lack of Strong Microlensing Variability

We present a method for the determination of upper limits on the transverse velocity of the lensing galaxy in the quadruple quasar system Q2237+0305, based on the lack of strong microlensing signatures in the quasar lightcurves. The limits we derive here are based on four months of high quality monitoring data, by comparing the low amplitudes of the lightcurves of the four components with extensive numerical simulations. We make use of the absence of strong variability of the components (especially components B and D) to infer that a "flat" time interval of such a length is only compatible with an effective transverse velocity of the lensing galaxy of v_bulk <=630 km/s for typical microlenses masses of M_microlens=0.1 M_solar (or v_bulk <=2160 km/s for M_microlens=1.0 M_solar) at the 90% confidence level. This method may be applicable in the future to other systems.Comment: 7 pages, 5 figures, accepted for publication in Astronomy & Astrophysic

Quasar Microlensing at High Magnification and the Role of Dark Matter: Enhanced Fluctuations and Suppressed Saddlepoints

Contrary to naive expectation, diluting the stellar component of the lensing galaxy in a highly magnified system with smoothly distributed ``dark'' matter increases rather than decreases the microlensing fluctuations caused by the remaining stars. For a bright pair of images straddling a critical curve, the saddlepoint (of the arrival time surface) is much more strongly affected than the associated minimum. With a mass ratio of smooth matter to microlensing matter of 4:1, a saddlepoint with a macro-magnification of mu = 9.5 will spend half of its time more than a magnitude fainter than predicted. The anomalous flux ratio observed for the close pair of images in MG0414+0534 is a factor of five more likely than computed by Witt, Mao and Schechter if the smooth matter fraction is as high as 93%. The magnification probability histograms for macro-images exhibit distinctly different structure that varies with the smooth matter content, providing a handle on the smooth matter fraction. Enhanced fluctuations can manifest themselves either in the temporal variations of a lightcurve or as flux ratio anomalies in a single epoch snapshot of a multiply imaged system. While the millilensing simulations of Metcalf and Madau also give larger anomalies for saddlepoints than for minima, the effect appears to be less dramatic for extended subhalos than for point masses. Morever, microlensing is distinguishable from millilensing because it will produce noticeable changes in the magnification on a time scale of a decade or less.Comment: As accepted for publication in ApJ. 17 pages. Substantial revisions include a discussion of constant M/L models and the calculation of a "photometric" dark matter fraction for MG0414+053

Microlensing of the broad line region in 17 lensed quasars

When an image of a strongly lensed quasar is microlensed, the different components of its spectrum are expected to be differentially magnified owing to the different sizes of the corresponding emitting region. Chromatic changes are expected to be observed in the continuum while the emission lines should be deformed as a function of the size, geometry and kinematics of the regions from which they originate. Microlensing of the emission lines has been reported only in a handful of systems so far. In this paper we search for microlensing deformations of the optical spectra of pairs of images in 17 lensed quasars. This sample is composed of 13 pairs of previously unpublished spectra and four pairs of spectra from literature. Our analysis is based on a spectral decomposition technique which allows us to isolate the microlensed fraction of the flux independently of a detailed modeling of the quasar emission lines. Using this technique, we detect microlensing of the continuum in 85% of the systems. Among them, 80% show microlensing of the broad emission lines. Focusing on the most common lines in our spectra (CIII] and MgII) we detect microlensing of either the blue or the red wing, or of both wings with the same amplitude. This observation implies that the broad line region is not in general spherically symmetric. In addition, the frequent detection of microlensing of the blue and red wings independently but not simultaneously with a different amplitude, does not support existing microlensing simulations of a biconical outflow. Our analysis also provides the intrinsic flux ratio between the lensed images and the magnitude of the microlensing affecting the continuum. These two quantities are particularly relevant for the determination of the fraction of matter in clumpy form in galaxies and for the detection of dark matter substructures via the identification of flux ratio anomalies.Comment: Accepted for publication in Astronomy and Astrophysics. Main data set available via the German virtual observatory http://dc.g-vo.org/mlqso/q/web/form and soon via CDS. Additional material available on reques

Probing the inner structure of distant AGNs with gravitational lensing

Microlensing is a powerful technique which can be used to study the continuum and the broad line emitting regions in distant AGNs. After a brief description of the methods and required data, we present recent applications of this technique. We show that microlensing allows one to measure the temperature profile of the accretion disc, estimate the size and study the geometry of the region emitting the broad emission lines.Comment: 6 pages, Proceedings of the Seyfert 2012 conferenc