J. A. Muñoz

MOA-2011-BLG-293Lb: A TEST OF PURE SURVEY MICROLENSING PLANET DETECTIONS

Mathematical and Physical Sciences: 1st Place (The Ohio State University Edward F. Hayes Graduate Research Forum)

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.

The Extinction Law in High-Redshift Galaxies*

We estimate the dust extinction laws in two intermediate-redshift galaxies. The dust in the lens galaxy of LBQS 1009-0252, which has an estimated lens redshift of zl 0.88, appears to be similar to that of the SMC, with no significant feature at 2175 A. Only if the lens galaxy is at a redshift of zl 0.3, which is completely inconsistent with the galaxy colors, luminosity, and location on the fundamental plane, can the data be fitted with a normal Galactic extinction curve. The dust in the zl = 0.68 lens galaxy for B028+357, whose reddened image lies behind a molecular cloud, requires a very flat ultraviolet extinction curve with (formally) RV = 12 ± 2. Both lens systems seem to have unusual extinction curves by Galactic standards.

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).

A Study of the Correlation between the Amplification of the Fe Kα Line and the X-Ray Continuum of Quasars due to Microlensing

The observed enhancement of the Fe Kα line in three gravitationally lensed QSOs (MG J0414+0534, QSO 2237+0305, and H1413+117) is interpreted in terms of microlensing, even when equivalent X-ray continuum amplification is not observed. In order to interpret these observations, first we studied the effects of microlensing on quasar spectra produced by a straight fold caustic crossing over a standard relativistic accretion disk. The disk emission was analyzed using the ray-tracing method, considering Schwarzschild and Kerr metrics. When the emission is separated into two regions (an inner disk corresponding to the Fe Kα line and an outer annulus corresponding to the continuum, or vice versa), we find microlensing events that enhance the Fe Kα line without noticeable amplification of the X-ray continuum, but only during a limited time interval. Continuum amplification is expected if a complete microlensing event is monitored. Second, we studied a more realistic case of amplification by a caustic magnification pattern. In this case we could satisfactorily explain the observations if the Fe Kα line is emitted from the innermost part of the accretion disk while the continuum is emitted from a larger region. We also studied the chromatic effects of microlensing, finding that the radial distribution of temperature in the accretion disk, combined with microlensing itself, can induce wavelength-dependent variability of ~30% for microlenses with very small masses. All these results show that X-ray monitoring of gravitational lenses is a method well suited for studying the innermost structure of active galactic nucleus accretion disks.

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.

DETECTION OF CHROMATIC MICROLENSING IN Q 2237 + 0305 A

We present narrowband images of the gravitational lens system Q 2237 + 0305 made with the Nordic Optical Telescope in eight different filters covering the wavelength interval 3510-8130 A. Using point-spread function photometry fitting we have derived the difference in magnitude versus wavelength between the four images of Q 2237 + 0305. At λ = 4110 A, the wavelength range covered by the Stromgren-v filter coincides with the position and width of the C IV emission line. This allows us to determine the existence of microlensing in the continuum and not in the emission lines for two images of the quasar. Moreover, the brightness of image A shows a significant variation with wavelength which can only be explained as a consequence of chromatic microlensing. To perform a complete analysis of this chromatic event, our observations were used together with Optical Gravitational Lensing Experiment light curves. Both data sets cannot be reproduced by the simple phenomenology described under the caustic crossing approximation; using more realistic representations of microlensing at high optical depth, we found solutions consistent with simple thin disk models (rs ∝ λ4/3); however, other accretion disk size-wavelength relationships also lead to good solutions. New chromatic events from the ongoing narrowband photometric monitoring of Q 2237 + 0305 are needed to accurately constrain the physical properties of the accretion disk for this system.

A Fast and Very Accurate Approach to the Computation of Microlensing Magnification Patterns Based on Inverse Polygon Mapping

A new method of calculating microlensing magnification patterns is proposed that is based on the properties of the backward gravitational lens mapping of a lattice of polygonal cells defined at the image plane. To a first-order approximation, the local linearity of the transformation allows us to compute the contribution of each image-plane cell to the magnification by apportioning the area of the inverse image of the cell (transformed cell) among the source-plane pixels covered by it. Numerical studies in the κ = 0.1-0.8 range of mass surface densities demonstrate that this method (provided with an exact algorithm for distributing the area of the transformed cells among the source-plane pixels) is more efficient than the inverse ray-shooting technique (IRS). Magnification patterns with relative errors of ~5 × 10-4 are obtained with an image-plane lattice of only 1 ray per unlensed pixel. This accuracy is, in practice, beyond the reach of IRS performance (more than 10,000 rays should be collected per pixel to achieve this result with the IRS) and is obtained in a small fraction (less than 4%) of the computing time that is used by the IRS technique to achieve an error more than an order of magnitude larger. The computing time for the new method is reduced to below 1% of the IRS computing time when the same accuracy is required of both methods. We have also studied the second-order approximation to control departures from linearity that could induce variations in the magnification within the boundaries of a transformed cell. This approximation is used to identify and control the cells enclosing a critical curve.

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.