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An X-Ray Study of Gravitational Lenses

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An X-Ray Study of Gravitational Lenses The Pennsylvania State University The Graduate School Department of Astronomy and Astrophysics AN X-RAY STUDY OF GRAVITATIONAL LENSES A Thesis in Astronomy and Astrophysics by Xinyu Dai c 2004 Xinyu Dai Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy December 2004 The thesis of Xinyu Dai was reviewed and approved* by the following: Gordon P. Garmire Evan Pugh Professor of Astronomy and Astrophysics Thesis Co-Adviser Co-Chair of Committee George Chartas Sr. Research Associate of Astronomy and Astrophysics Thesis Co-Adviser Co-Chair of Committee Michael Eracleous Associate Professor of Astronomy and Astrophysics Robin Ciardullo Professor of Astronomy and Astrophysics L. Samuel Finn Professor of Physics Lawrence W. Ramsey Professor of Astronomy and Astrophysics Head of the Department of Astronomy and Astrophysics *Signatures are on file in the Graduate School. iii Abstract Gravitational lensing of distant quasars by intervening galaxies is a spectacular phenomenon in the universe. With the advent of Chandra, it is possible to resolve for the first time in the X-ray band lensed quasar images with separations greater than about 0.35 arcsec. We use lensing as a tool to study AGN and Cosmology with Chandra and XMM-Newton. First, we present results from a mini-survey of relatively high redshift (1:7 < z < 4) gravitationally lensed radio-quiet quasars observed with the Chandra X-ray Observa- tory and with XMM-Newton. The lensing magnification effect allows us to search for changes in quasar spectroscopic and flux variability properties with redshift over three orders of magnitude in intrinsic X-ray luminosity. It extends the study of quasar proper- ties to unlensed X-ray flux levels as low as a few times 10−15erg cm−2 s−1 in the observed 0.4{8 keV band. For the first time, these observations of lensed quasars have provided medium to high signal-to-noise ratio X-ray spectra of a sample of relatively high-redshift and low X-ray luminosity quasars. We find a possible correlation between the X-ray pow- erlaw photon index and X-ray luminosity of the gravitationally lensed radio-quiet quasar sample. The X-ray spectral slope steepens as the X-ray luminosity increases. This cor- relation is still significant when we combine our data with other samples of radio-quiet quasars with z > 1:5, especially in the low luminosity range between 1043{1045:5 erg s−1. This result is surprising considering that such a correlation is not found for quasars with redshifts below 1.5. We suggest that this correlation can be understood in the context of the hot-corona model for X-ray emission from quasar accretion disks, under the hy- pothesis that the quasars in our sample accrete very close to their Eddington limits and the observed luminosity range is set by the range of black hole masses (this hypothesis is consistent with recent predictions of semi-analytic models for quasar evolution). The upper limits of X-ray variability of our relatively high redshift sample of lensed quasars are consistent with the known correlation between variability and luminosity observed in Seyfert 1s when this correlation is extrapolated to the larger luminosities of our sample. Second, we present the observations of the gravitationally lensed system Q 2237+0305 (Einstein Cross) performed with the Advanced CCD Imaging Spectrometer (ACIS) on- board the Chandra X-ray Observatory on 2000 September 6, and on 2001 December 8 for 30.3 ks and 9.5 ks, respectively. Imaging analysis resolves the four X-ray images of the Einstein Cross. A possible fifth image is detected; however, the poor signal-to-noise ratio of this image combined with contamination produced by a nearby brighter image make this detection less certain. We investigate possible origins of the additional image. Fits to the combined spectrum of all images of the Einstein Cross assuming a simple power law with Galactic and intervening absorption at the lensing galaxy yields a photon index, +0:05 Γ, of 1:90−0:05 consistent with the range of Γ measured for large samples of radio-quiet quasars. For the first Chandra observation of the Einstein Cross this spectral model yields a 0.4{8.0 keV X-ray flux of 4:6 × 10−13erg cm−2 s−1 and a 0.4{8.0 keV lensed luminosity of 1:0 × 1046erg s−1. The source exhibits variability both over long and short time scales. The X-ray flux has dropped by 20% between the two observations, and the iv Kolmogorov-Smirnov test showed that image A is variable at the 97% confidence level within the first observation. The X-ray flux ratios of the images are consistent with the optical flux ratios which are affected by microlensing suggesting that the X-ray emission is also microlensed. A comparison between our measured column densities and those inferred from extinction measurements suggests a higher dust-to-gas ratio in the lensing galaxy than the average value of our Galaxy. We report the detection at the 99.99% confidence level of a broad emission feature near the redshifted energy of the Fe Kα line in only the spectrum of image A. The rest frame energy, width, and equivalent width +0:2 +0:30 +300 of this feature are Eline = 5:7−0:3 keV, σline = 0:87−0:15 keV, and EW = 1200−200 eV, respectively. The enhancement of the emission line in image A is possibly caused by microlensing since the combined spectrum of the other three images does not show such a significant feature. The redshift and broadening of the line may be the result of the Doppler effect and special and general relativistic effects. It is likely that the broad iron line region that is affected by the GR and SR effects is smaller than the X-ray continuum region. Finally, we present results from time-delay searches in our sample of gravitational lenses observed with Chandra and XMM-Newton. We applied cross correlation and auto correlation techniques to the X-ray light-curves of the gravitational lenses. The time-delays between some of the short separation systems are predicted to be of the order of several hours. We have measured two time-delays and one lower limit on a time-delay. In RX J0911.4+0551, we have detected a flare only in image A2 and not in image A1 constraining the time-delay between the two images to be greater than 23 ks. Although, we did not measure the time-delay in this system it was realized for the first time that short time-delays can be measured in single X-ray observations. In a Chandra +0:5 observation of Q 2237+0305, we detected a tentative time-delay of 2:7−0:9 hours between images A and B with image A leading. This time-delay is important in constraining the mass profile of the lensing galaxy and the amount of dark matter substructure in the lensing galaxy. In a Chandra observation of PG 1115+080, we detected a time-delay +0:02 of ∆τA1A2 = 0:162−0:01 days with image A1 leading. Furthermore, the analysis of an XMM-Newton observation of PG 1115+080 also yields a time-delay of 0.149 0.006 days, which is consistent with the time-delay between images A1 and A2 measured from the Chandra observation. Combining this time delay with other constraints in the +13 −1 −1 system, a Hubble constant of H0 = 67−8 3 km s Mpc is obtained. v Table of Contents List of Tables : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : vii List of Figures : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : viii Acknowledgments : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : xi Chapter 1. Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 1.1 Gravitational Lenses . 1 1.1.1 Lens Equations . 2 1.1.2 Strategy for Solving the Lens Equation . 3 1.1.3 Lens Potentials . 3 1.1.4 Applications of Gravitational Lensing . 4 1.1.4.1 Placing Constraints on the Hubble Constant . 4 1.1.4.2 Constraining the Cosmological Constant ΩΛ . 5 1.1.4.3 Determining the Mass Profiles of the Lensing Galaxies 5 1.1.4.4 Studying the Properties of the Sources with the Aid of Lensing Magnification . 5 1.1.4.5 Micro-lensing and Milli-lensing Events . 6 1.2 X-ray Properties of Active Galactic Nuclei . 6 1.2.1 X-ray Continuum . 7 1.2.2 X-ray Reflection Component and the Fe Kα line . 7 1.3 Motivation of the Thesis . 7 1.4 Outline of the Thesis . 8 1.4.1 Chapter 1: A Study of Quasar Evolution with the Aid of Lensing 8 1.4.2 Chapter 2: An X-ray Microlensing Event in Q 2237+0305 . 9 1.4.3 Chapter 3: X-ray Time-delay Measurements of Gravitational Lensing Systems . 9 1.4.4 Chapter 4: Conclusions . 10 Chapter 2. A Study of Quasar Evolution in the X-ray Band with the Aid of Grav- itational Lensing : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 11 2.1 Introduction . 11 2.2 Observations and Data Reduction . 12 2.3 Spectral Analysis . 13 2.3.1 Power-law Continuum . 13 2.3.2 αox . 15 2.4 Magnification and Intrinsic X-ray Luminosities . 15 2.5 Variability Analysis . 16 2.6 Results and Discussion . 17 2.6.1 Luminosity and Spectral Index . 17 vi 2.6.2 Possible Interpretations of the Correlation Between the X-Ray Luminosity and Spectral Index . 19 2.6.3 The Optical-to-X-Ray Index, αox . 21 2.6.4 Short Time Scale Variability . 21 2.7 Conclusions . 22 Chapter 3. Chandra Observations of Q 2237+0305 : : : : : : : : : : : : : : : : : 37 3.1 Introduction .
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