Probing The Gravity Induced Bias with Weak Lensing: Test of Analytical results Against Simulations

Future weak lensing surveys will directly probe the density fluctuation in the universe. Recent studies have shown how the statistics of the weak lensing convergence field is related to the statistics of collapsed objects. Extending earlier analytical results on the probability distribution function of the convergence field we show that the bias associated with the convergence field can directly be related to the bias associated with the statistics of underlying over-dense objects. This will provide us a direct method to study the gravity induced bias in galaxy clustering. Based on our analytical results which use the hierarchical {\em ansatz} for non-linear clustering, we study how such a bias depends on the smoothing angle and the source red-shift. We compare our analytical results against ray tracing experiments through N-body simulations of four different realistic cosmological scenarios and found a very good match. Our study shows that the bias in the convergence map strongly depends on the background geometry and hence can help us in distinguishing different cosmological models in addition to improving our understanding of the gravity induced bias in galaxy clustering.Comment: 17 pages including 8 figures and 1 table, MNRAS, submitte

Parameter degeneracy in models of the quadruple lens system Q2237+0305

The geometry of the quadruple lens system Q2237+0305 is modeled with a simple astigmatic lens: a power-law mass distribution: m \propto r^\beta with an external shear \gamma. The image positions can be reproduced with an accuracy better than 0.01 arcsec for any 0.0 < \beta < 1.85 and the corresponding value of \gamma = 0.1385 - 0.0689 \beta. This is a factor of about 4 more precise than what can be achieved by the best constant M/L lens models. The image intensity ratios and the time delay ratios are almost constant along our one parameter family of models, but the total magnification varies from 8 to > 1000, and the maximum time delay (between leading image B and trailing image C) for H_0 of 75 km/sec/Mpc varies from more than 20 hours to about 1.5 hours, while \beta increases from 0.0 to 1.85.Comment: 15 pages uuencoded compressed postscript text plus 4 postscript figures; MPI Astrophysik report MPA-821; to appear in Astronomical Journa

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

Detectability of extrasolar moons as gravitational microlenses

We evaluate gravitational lensing as a technique for the detection of extrasolar moons. Since 2004 gravitational microlensing has been successfully applied as a detection method for extrasolar planets. In principle, the method is sensitive to masses as low as an Earth mass or even a fraction of it. Hence it seems natural to investigate the microlensing effects of moons around extrasolar planets. We explore the simplest conceivable triple lens system, containing one star, one planet and one moon. From a microlensing point of view, this system can be modelled as a particular triple with hierarchical mass ratios very different from unity. Since the moon orbits the planet, the planet-moon separation will be small compared to the distance between planet and star. Such a configuration can lead to a complex interference of caustics. We present detectability and detection limits by comparing triple-lens light curves to best-fit binary light curves as caused by a double-lens system consisting of host star and planet -- without moon. We simulate magnification patterns covering a range of mass and separation values using the inverse ray shooting technique. These patterns are processed by analysing a large number of light curves and fitting a binary case to each of them. A chi-squared criterion is used to quantify the detectability of the moon in a number of selected triple-lens scenarios. The results of our simulations indicate that it is feasible to discover extrasolar moons via gravitational microlensing through frequent and highly precise monitoring of anomalous Galactic microlensing events with dwarf source stars.Comment: 14 pages, 11 figures. Updated to A&A published version: updated references, 1 additional illustration (Fig. 10), further analogies to solar system and extended discussio

Error Estimates for Measurements of Cosmic Shear

In the very near future, weak lensing surveys will map the projected density of the universe in an unbiased way over large regions of the sky. In order to interpret the results of studies it is helpful to develop an understanding of the errors associated with quantities extracted from the observations. In a generalization of one of our earlier works, we present estimators of the cumulants and cumulant correlators of the weak lensing convergence field, and compute the variance associated with these estimators. By restricting ourselves to so-called compensated filters we are able to derive quite simple expressions for the errors on these estimates. We also separate contributions from cosmic variance, shot noise and intrinsic ellipticity of the source galaxies.Comment: 12 pages, including 5 figures, uses mn.sty. Substantially revised version accepted by MNRA

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