Revealing the Structure of an Accretion Disk Through Energy Dependent X-ray Microlensing

We present results from monitoring observations of the gravitationally lensed quasar RX J1131-1231 performed with the Chandra X-ray Observatory. The X-ray observations were planned with relatively long exposures that allowed a search for energy-dependent microlensing in the soft (0.2-2 keV) and hard (2-10 keV) light curves of the images of RX J1131-1231. We detect significant microlensing in the X-ray light-curves of images A and D, and energy-dependent microlensing of image D. The magnification of the soft band appears to be larger than that in the hard band by a factor of ~ 1.3 when image D becomes more magnified. This can be explained by the difference between a compact, softer-spectrum corona that is producing a more extended, harder spectrum reflection component off the disk. This is supported by the evolution of the fluorescent iron line in image D over three consecutive time-averaged phases of the light curve. In the first period, a Fe line at E = 6.36(-0.16,+0.13) keV is detected (at > 99% confidence). In the second period, two Fe lines are detected, one at E = 5.47(-0.08,+0.06) keV (detected at > 99% confidence) and another at E = 6.02(-0.07,+0.09) keV (marginally detected at > 90% confidence), and in the third period, a broadened Fe line at 6.42(-0.15,+0.19) keV is detected (at > 99% confidence). This evolution of the Fe line profile during the microlensing event is consistent with the line distortion expected when a caustic passes over the inner disk where the shape of the fluorescent Fe line is distorted by General Relativistic and Doppler effects.Comment: 20 pages, includes 10 figures, submitted to Ap

A Robust Determination of the size of quasar accretion disks using gravitational microlensing

Using microlensing measurements from a sample of 27 image-pairs of 19 lensed quasars we determine a maximum likelihood estimate for the accretion disk size of an {{\em}average} quasar of $r_s=4.0^{+2.4}_{-3.1}$ light days at rest frame $=1736$\AA\ for microlenses with a mean mass of $=0.3M_\odot$. This value, in good agreement with previous results from smaller samples, is roughly a factor of 5 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.Comment: 6 pages, 3 figures, submitted to Ap

X-Ray and Optical Flux Anomalies in the Quadruply Lensed QSO 1RXS J1131-1231

Optical and X-ray observations of the quadruply imaged quasar 1RXS J1131-1231 show flux ratio anomalies among the images factors of ~2 in the optical and \~3-9 in X-rays. Temporal variability of the quasar seems an unlikely explanation for the discrepancies between the X-ray and optical flux ratio anomalies. The negative parity of the most affected image and the decreasing trend of the anomalies with wavelength suggest microlensing as a possible explanation; this would imply that the source of optical radiation in RXS J1131 is ~10^4 R_g in size for a black hole mass of ~10^8 M_sun. We also present evidence for different X-ray spectral hardness ratios among the four images.Comment: 5 pages, 1 color figure, replaced with version accepted to Ap

Information flows among rivals and corporate investment

Using a novel pairwise measure of firms' acquisitions of rivals' disclosures, we show that investment opportunities drive interfirm information flows. We find that these flows predict subsequent mergers and acquisitions as well as how and how much firms invest, relative to rivals. Moreover, firms' use of rivals' information often hinges on the similarities of their products. Our results suggest that rivals' public information, far from being unusable, helps facilitate investment and product decisions, including acquisitions and product differentiation strategies. The findings also support a learning mechanism that could partly underlie the emerging literature on peer investment effects

I. Flux and color variations of the quadruply imaged quasar HE 0435-1223

aims: We present VRi photometric observations of the quadruply imaged quasar HE 0435-1223, carried out with the Danish 1.54m telescope at the La Silla Observatory. Our aim was to monitor and study the magnitudes and colors of each lensed component as a function of time. methods: We monitored the object during two seasons (2008 and 2009) in the VRi spectral bands, and reduced the data with two independent techniques: difference imaging and PSF (Point Spread Function) fitting.results: Between these two seasons, our results show an evident decrease in flux by ~0.2-0.4 magnitudes of the four lensed components in the three filters. We also found a significant increase (~0.05-0.015) in their V-R and R-i color indices. conclusions: These flux and color variations are very likely caused by intrinsic variations of the quasar between the observed epochs. Microlensing effects probably also affect the brightest "A" lensed component.Comment: 10 pages, 8 figure

A GPU-Enabled, High-Resolution Cosmological Microlensing Parameter Survey

In the era of synoptic surveys, the number of known gravitationally lensed quasars is set to increase by over an order of magnitude. These new discoveries will enable a move from single-quasar studies to investigations of statistical samples, presenting new opportunities to test theoretical models for the structure of quasar accretion discs and broad emission line regions (BELRs). As one crucial step in preparing for this influx of new lensed systems, a large-scale exploration of microlensing convergence-shear parameter space is warranted, requiring the computation of O(10^5) high resolution magnification maps. Based on properties of known lensed quasars, and expectations from accretion disc/BELR modelling, we identify regions of convergence-shear parameter space, map sizes, smooth matter fractions, and pixel resolutions that should be covered. We describe how the computationally time-consuming task of producing ~290000 magnification maps with sufficient resolution (10000^2 pixel/map) to probe scales from the inner edge of the accretion disc to the BELR can be achieved in ~400 days on a 100 teraflop/s high performance computing facility, where the processing performance is achieved with graphics processing units. We illustrate a use-case for the parameter survey by investigating the effects of varying the lens macro-model on accretion disc constraints in the lensed quasar Q2237+0305. We find that although all constraints are consistent within their current error bars, models with more densely packed microlenses tend to predict shallower accretion disc radial temperature profiles. With a large parameter survey such as the one described here, such systematics on microlensing measurements could be fully explored.Comment: 30 pages, 3 figures, accepted for publication in Ap

Gravitational Microlensing as a probe of the Electron Scattering Region in Q2237+0305

Recent observations have provided strong evidence for the presence of an Electron Scattering Region (ESR) within the central regions of AGNs. This is responsible for reprocessing emission from the accretion disk into polarised radiation. The geometry of this scattering region is, however, poorly constrained. In this paper, we consider the influence of gravitational microlensing on polarised emission from the ESR in the quadruply imaged quasar, Q2237+0305, demonstrating how correlated features in the resultant light curve variations can determine both the size and orientation of the scattering region. This signal is due to differential magnification between perpendicularly polarised views of the ESR, and is clearest for a small ESR width and a large ESR radius. Cross- and auto-correlation measures appear to be independent of lens image shear and convergence parameters, making it ideal to investigate ESR features. As with many microlensing experiments, the time-scale for variability, being of order decades to centuries, is impractically long. However, with a polarization filter oriented appropriately with respect to the path that the quasar takes across the caustic structure, the ESR diameter and radius can be estimated from the auto- and cross-correlation of polarized light curves on much shorter time-scales.Comment: 11 pages, 12 figures, 1 table, accepted for MNRA

The accretion disc in the quasar SDSS J0924+0219

We present single-epoch multi-wavelength optical-NIR observations of the "anomalous" lensed quasar SDSS J0924+0219, made using the Magellan 6.5-metre Baade telescope at Las Campanas Observatory, Chile. The data clearly resolve the anomalous bright image pair in the lensed system, and exhibit a strong decrease in the anomalous flux ratio with decreasing wavelength. This is interpreted as a result of microlensing of a source of decreasing size in the core of the lensed quasar. We model the radius of the continuum emission region, sigma, as a power-law in wavelength, sigma lambda^zeta. We place an upper limit on the Gaussian radius of the u'-band emission region of 3.04E16 h70^{-1/2} (/M_sun)^{1/2} cm, and constrain the size-wavelength power-law index to zeta<1.34 at 95% confidence. These observations rule out an alpha-disc prescription for the accretion disc in SDSS J0924+0219 with 94% confidence.Comment: 8 pages, 5 figures. Accepted for publication in MNRA

A New Microlensing Event in the Doubly-Imaged Quasar Q0957+561

We present evidence for ultraviolet/optical microlensing in the gravitationally lensed quasar Q0957+561. We combine new measurements from our optical monitoring campaign at the United States Naval Observatory, Flagstaff (USNO) with measurements from the literature and find that the time-delay-corrected r-band flux ratio m_A - m_B has increased by ~0.1 magnitudes over a period of five years beginning in the fall of 2005. We apply our Monte Carlo microlensing analysis procedure to the composite light curves, obtaining a measurement of the optical accretion disk size, log {(r_s/cm)[cos(i)/0.5]^{1/2}} = 16.2^{+0.5}_{-0.6}, that is consistent with the quasar accretion disk size - black hole mass relation.Comment: Replaced with accepted version. Minor adjustments to text but conclusions unchanged. Data in Table 2 have been updated and table now includes additional observation

Further Evidence that Quasar X-Ray Emitting Regions Are Compact: X-Ray and Optical Microlensing in the Lensed Quasar Q J0158-4325

We present four new seasons of optical monitoring data and six epochs of X-ray photometry for the doubly-imaged lensed quasar Q J0158-4325. The high-amplitude, short-period microlensing variability for which this system is known has historically precluded a time delay measurement by conventional methods. We attempt to circumvent this limitation by application of a Monte Carlo microlensing analysis technique, but we are only able to prove that the delay must have the expected sign (image A leads image B). Despite our failure to robustly measure the time delay, we successfully model the microlensing at optical and X-ray wavelengths to find a half light radius for soft X-ray emission log(r_{1/2,X,soft}/cm) = 14.3^{+0.4}_{-0.5}, an upper limit on the half-light radius for hard X-ray emission log(r_{1/2,X,hard}/cm) <= 14.6 and a refined estimate of the inclination-corrected scale radius of the optical R-band (rest frame 3100 Angstrom) continuum emission region of log(r_s/cm) = 15.6+-0.3.Comment: 9 pages, 6 figures, submitted to Ap