E. Mediavilla

MICROLENSING-BASED ESTIMATE OF THE MASS FRACTION IN COMPACT OBJECTS IN LENS GALAXIES

We estimate the fraction of mass that is composed of compact objects in gravitational lens galaxies. This study is based on microlensing measurements (obtained from the literature) of a sample of 29 quasar image pairs seen through 20 lens galaxies. We determine the baseline for no microlensing magnification between two images from the ratios of emission line fluxes. Relative to this baseline, the ratio between the continua of the two images gives the difference in microlensing magnification. The histogram of observed microlensing events peaks close to no magnification and is concentrated below 0.6 mag, although two events of high magnification, DELTAm approx 1.5, are also present. We study the likelihood of the microlensing measurements using frequency distributions obtained from simulated microlensing magnification maps for different values of the fraction of mass in compact objects, alpha. The concentration of microlensing measurements close to DELTAm approx 0 can be explained only by simulations corresponding to very low values of alpha (10% or less). A maximum likelihood test yields alpha = 0.05{sup +0.09}{sub -0.03} (90% confidence interval) for a quasar continuum source of intrinsic size r{sub s{sub 0}}approx2.6x10{sup 15} cm. This estimate is valid in the 0.1-10 M {sub sun} range of microlensmorexa0» masses. We study the dependence of the estimate of alpha with r{sub s{sub 0}}, and find that alpha approx >2.6x10{sup 16} cm). Regarding the current controversy about Milky Way/LMC and M31 microlensing studies, our work supports the hypothesis of a very low content in MACHOS (Massive Compact Halo Objects). In fact, according to our study, quasar microlensing probably arises from the normal star populations of lens galaxies and there is no statistical evidence for MACHOS in the dark halos.«xa0less

MICROLENSING OF QUASAR BROAD EMISSION LINES: CONSTRAINTS ON BROAD LINE REGION SIZE

We measure the differential microlensing of the broad emission lines between 18 quasar image pairs in 16 gravitational lenses. We find that the broad emission lines are in general weakly microlensed. The results show, at a modest level of confidence (1.8σ), that high ionization lines such as C IV are more strongly microlensed than low ionization lines such as Hβ, indicating that the high ionization line emission regions are more compact. If we statistically model the distribution of microlensing magnifications, we obtain estimates for the broad line region size of rs = 24+22 –15 and rs = 55+150 –35 lt-day (90% confidence) for the high and low ionization lines, respectively. When the samples are divided into higher and lower luminosity quasars, we find that the line emission regions of more luminous quasars are larger, with a slope consistent with the expected scaling from photoionization models. Our estimates also agree well with the results from local reveberation mapping studies.

A ROBUST DETERMINATION OF THE SIZE OF QUASAR ACCRETION DISKS USING GRAVITATIONAL MICROLENSING

Using microlensing measurements for a sample of 27 image pairs of 19 lensed quasars we determine a maximum likelihood estimate for the accretion disk size of an average quasar of r{sub s} = 4.0{sup +2.4}{sub -3.1} lt-day at rest frame ({lambda}) = 1736 Angstrom-Sign for microlenses with a mean mass of (M) = 0.3 M{sub Sun }. This value, in good agreement with previous results from smaller samples, is roughly a factor of five greater than the predictions of the standard thin disk model. The individual size estimates for the 19 quasars in our sample are also in excellent agreement with the results of the joint maximum likelihood analysis.

A Study of Gravitational Lens Chromaticity Using Ground-based Narrowband Photometry

We present observations of wavelength-dependent flux ratios for four gravitational lens systems (SDSS J1650+4251, HE 0435–1223, FBQ 0951+2635, and Q 0142–100) obtained with the Nordic Optical Telescope. The use of narrowband photometry, as well as the excellent seeing conditions during the observations, allows us to study their chromatic behavior. For SDSS J1650+4251, we determine the extinction curve of the dust in the zL = 0.58 lens galaxy and find that the 2175 A feature is absent. In the case of HE 0435–1223, we clearly detect chromatic microlensing. This allows us to estimate the wavelength-dependent size of the accretion disk. We find an R-band disk size of rR s = 13 ± 5 light days for a linear prior on rR s and rR s = 7 ± 6 light days for a logarithmic prior. For a power-law size-wavelength scaling of rs λ p , we were able to constrain the value of the exponent to p = 1.3 ± 0.3 for both rR s priors, which is in agreement with the temperature profiles of simple thin disk models (p = 4/3).

THE STRUCTURE OF THE ACCRETION DISK IN THE LENSED QUASAR SBS 0909+532

We derive the size and temperature profile of the accretion disk of the lensed quasar SBS 0909+532 by measuring the wavelength dependence (chromaticity) of the microlensing magnification produced by the stars in the lens galaxy. After correcting for extinction using the flux ratios of 14 emission lines, we observe a marked change in the B-A flux ratio with wavelength, varying from –0.67 ± 0.05 mag at (rest frame) ~1460 A to –0.24 ± 0.07 mag at ~6560 A. For λ 7000 A both effects, extinction and microlensing, look minimal. Simulations indicate that image B rather than A is strongly microlensed. If we model the change in disk size from 1460 A to 6560 A using a Gaussian source (I ∝ exp(–R 2/2r 2 s )) with a disk size scaling with wavelength as rs ∝ λ p , we find rs = 7+5 –3 light-days at 1460 A and p = 0.9+0.6 –0.3 for uniform priors on rs and p, and rs = 4+3 –3 light-days and p = 1.0+0.6 –0.4 for a logarithmic prior on rs . The disk temperature profile T ∝ R –1/p is consistent with thin disk theory (T ∝ R –3/4), given the uncertainties. The estimates of rs are also in agreement with the size inferred from thin disk theory using the estimated black hole mass (M BH 2 × 109 M ☉) but not with the smaller size estimated from thin disk theory and the optical flux. We also use the flux ratios of the unmicrolensed emission lines to determine the extinction curve of the dust in the lens galaxy, finding that it is similar to that of the LMC2 Supershell.

THE AVERAGE SIZE AND TEMPERATURE PROFILE OF QUASAR ACCRETION DISKS

We use multi-wavelength microlensing measurements of a sample of 10 image pairs from 8 lensed quasars to study the structure of their accretion disks. By using spectroscopy or narrowband photometry, we have been able to remove contamination from the weakly microlensed broad emission lines, extinction, and any uncertainties in the large-scale macro magnification of the lens model. We determine a maximum likelihood estimate for the exponent of the size versus wavelength scaling (rs ∝λ p , corresponding to a disk temperature profile of T∝r –1/p ) of and a Bayesian estimate of p = 0.8 ± 0.2, which are significantly smaller than the prediction of the thin disk theory (p = 4/3). We have also obtained a maximum likelihood estimate for the average quasar accretion disk size of lt-day at a rest frame wavelength of λ = 1026 A for microlenses with a mean mass of M = 1 M ☉, in agreement with previous results, and larger than expected from thin disk theory.

NEW DEVELOPMENTS ON INVERSE POLYGON MAPPING TO CALCULATE GRAVITATIONAL LENSING MAGNIFICATION MAPS: OPTIMIZED COMPUTATIONS

We derive an exact solution (in the form of a series expansion) to compute gravitational lensing magnification maps. It is based on the backward gravitational lens mapping of a partition of the image plane in polygonal cells (inverse polygon mapping, IPM), not including critical points (except perhaps at the cell boundaries). The zeroth-order term of the series expansion leads to the method described by Mediavilla etxa0al. The first-order term is used to study the error induced by the truncation of the series at zeroth order, explaining the high accuracy of the IPM even at this low order of approximation. Interpreting the Inverse Ray Shooting (IRS) method in terms of IPM, we explain the previously reported N –3/4 dependence of the IRS error with the number of collected rays per pixel. Cells intersected by critical curves (critical cells) transform to non-simply connected regions with topological pathologies like auto-overlapping or non-preservation of the boundary under the transformation. To define a non-critical partition, we use a linear approximation of the critical curve to divide each critical cell into two non-critical subcells. The optimal choice of the cell size depends basically on the curvature of the critical curves. For typical applications in which the pixel of the magnification map is a small fraction of the Einstein radius, a one-to-one relationship between the cell and pixel sizes in the absence of lensing guarantees both the consistence of the method and a very high accuracy. This prescription is simple but very conservative. We show that substantially larger cells can be used to obtain magnification maps with huge savings in computation time.

MEASURING MICROLENSING USING SPECTRA OF MULTIPLY LENSED QUASARS

We report on a program of spectroscopic observations of gravitationally lensed QSOs with multiple images. We seek to establish whether microlensing is occurring in each QSO image using only single-epoch observations. We calculate flux ratios for the cores of emission lines in image pairs to set a baseline for no microlensing. The offset of the continuum flux ratios relative to this baseline yields the microlensing magnification free from extinction, as extinction affects the continuum and the lines equally. When we find chromatic microlensing, we attempt to constrain the size of the QSO accretion disk. SDSSJ1004+4112 and HE1104-1805 show chromatic microlensing with amplitudes 0.2 < |{Delta}m| < 0.6 and 0.2 < |{Delta}m| < 0.4 mag, respectively. Modeling the accretion disk with a Gaussian source (I{proportional_to}exp (- R{sup 2}/2r{sup 2}{sub s})) of size r{sub s} {proportional_to}{lambda}{sup p} and using magnification maps to simulate microlensing, we find r{sub s} ({lambda}3363) = 7 {+-} 3 lt-day(18.1 {+-} 7.8 Multiplication-Sign 10{sup 15} cm) and p = 1.1 {+-} 0.4 for SDSS1004+4112, and r{sub s} ({lambda}3363) = 6 {+-} 2 lt-day(15.5 {+-} 5.2 Multiplication-Sign 10{sup 15} cm) and p = 0.7 {+-} 0.1 for HE1104-1805. For SDSSJ1029+2623, we find strong chromaticity of {approx}0.4 mag in the morexa0» continuum flux ratio, which probably arises from microlensing, although not all the available data fit within this explanation. For Q0957+561, we measure B - A magnitude differences of 0.4 mag, much greater than the {approx}0.05 mag amplitude usually inferred from light-curve variability. It may substantially modify the current interpretations of microlensing in this system, likely favoring the hypothesis of smaller sources and/or larger microdeflectors. For HS0818+1227, our data yield possible evidence of microlensing. «xa0less

Dark Matter Mass Fraction in Lens Galaxies: New Estimates from Microlensing

We present a joint estimate of the stellar/dark matter mass fraction in lens galaxies and the average size of the accretion disk of lensed quasars based on microlensing measurements of 27 quasar image pairs seen through 19 lens galaxies. The Bayesian estimate for the fraction of the surface mass density in the form of stars is α = 0.21 ± 0.14 near the Einstein radius of the lenses (~1-2 effective radii). The estimate for the average accretion disk size is light days. The fraction of mass in stars at these radii is significantly larger than previous estimates from microlensing studies assuming quasars were point-like. The corresponding local dark matter fraction of 79% is in good agreement with other estimates based on strong lensing or kinematics. The size of the accretion disk inferred in the present study is slightly larger than previous estimates.

Probing the Dark Matter Radial Profile in Lens Galaxies and the Size of X-Ray Emitting Region in Quasars with Microlensing

We use X-ray and optical microlensing measurements to study the shape of the dark matter density profile in the lens galaxies and the size of the (soft) X-ray emission region. We show that single epoch X-ray microlensing is sensitive to the source size. Our results, in good agreement with previous estimates, show that the size of the X-ray emission region scales roughly linearly with the black hole mass, with a half light radius of