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Register a new userThe Rewards of Patience: An 822 Day Time Delay in the Gravitational Lens SDSS J1004+4112
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We present 107 new epochs of optical monitoring data for the four brightest images of the gravitational lens SDSS J1004+4112 observed between October 2006 and June 2007. Combining this data with the previously obtained light curves, we determine the time delays between images A, B and C. We confirm our previous measurement finding that A leads B by dt_BA=40.6+-1.8 days, and find that image C leads image A by dt_CA=821.6+-2.1 days. The lower limit on the remaining delay is that image D lags image A by dt_AD>1250 days. Based on the microlensing of images A and B we estimate that the accretion disk size at a rest wavelength of 2300 angstrom is 10^{14.8+-0.3} cm for a disk inclination of cos{i}=1/2, which is consistent with the microlensing disk size-black hole mass correlation function given our estimate of the black hole mass from the MgII line width of logM_BH/M_sun=8.44+-0.14. The long delays allow us to fill in the seasonal gaps and assemble a continuous, densely sampled light curve spanning 5.7 years whose variability implies a structure function with a logarithmic slope of gamma = 0.35+-0.02. As C is the leading image, sharp features in the C light curve can be intensively studied 2.3 years later in the A/B pair, potentially allowing detailed reverberation mapping studies of a quasar at minimal cost.
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We present 426 epochs of optical monitoring data spanning 1000 days from December 2003 to June 2006 for the gravitationally lensed quasar SDSS J1004+4112. The time delay between the A and B images is 38.4+/-2.0 days in the expected sense that B leads A and the overall time ordering is C-B-A-D-E. The measured delay invalidates all published models. The models failed because they neglected the perturbations from cluster member galaxies. Models including the galaxies can fit the data well, but strong conclusions about the cluster mass distribution should await the measurement of the longer, and less substructure sensitive, delays of the C and D images. For these images, a CB delay of 681+/-15 days is plausible but requires confirmation, while CB and AD delays of >560 days and > 800 days are required. We clearly detect microlensing of the A/B images, with the delay-corrected flux ratios changing from B-A=0.44+/-0.01 mag in the first season to 0.29+/-0.01 mag in the second season and 0.32+/-0.01 mag in the third season.
In this article we study the well-known strong lensing system SDSS J1004+4112. Not only does it host a large-separation lensed quasar with measured time-delay information, but several other lensed galaxies have been identified as well. A previously developed strong lens inversion procedure that is designed to handle a wide variety of constraints, is applied to this lensing system and compared to results reported in other works. Without the inclusion of a tentative central image of one of the galaxies as a constraint, we find that the model recovered by the other constraints indeed predicts an image at that location. An inversion which includes the central image provides tighter constraints on the shape of the central part of the mass map. The resulting model also predicts a central image of a second galaxy where indeed an object is visible in the available ACS images. We find masses of 2.5x10^13 M_O and 6.1x10^13 M_O within a radius of 60 kpc and 110 kpc respectively, confirming the results from other authors. The resulting mass map is compatible with an elliptical generalization of a projected NFW profile, with r_s = 58_{-13}^{+21} arcsec and c_vir = 3.91 +/- 0.74. The orientation of the elliptical NFW profile follows closely the orientation of the central cluster galaxy and the overall distribution of cluster members.
We study the recently discovered gravitational lens SDSS J1004+4112, the first quasar lensed by a cluster of galaxies. It consists of four images with a maximum separation of 14.62. The system has been confirmed as a lensed quasar at z=1.734 on the basis of deep imaging and spectroscopic follow-up observations. We present color-magnitude relations for galaxies near the lens plus spectroscopy of three central cluster members, which unambiguously confirm that a cluster at z=0.68 is responsible for the large image separation. We find a wide range of lens models consistent with the data, but they suggest four general conclusions: (1) the brightest cluster galaxy and the center of the cluster potential well appear to be offset by several kpc; (2) the cluster mass distribution must be elongated in the North--South direction, which is consistent with the observed distribution of cluster galaxies; (3) the inference of a large tidal shear (~0.2) suggests significant substructure in the cluster; and (4) enormous uncertainty in the predicted time delays between the images means that measuring the delays would greatly improve constraints on the models. We also compute the probability of such large separation lensing in the SDSS quasar sample, on the basis of the CDM model. The lack of large separation lenses in previous surveys and the discovery of one in SDSS together imply a mass fluctuation normalization sigma_8=1.0^{+0.4}_{-0.2} (95% CL), if cluster dark matter halos have an inner slope -1.5. Shallower profiles would require higher values of sigma_8. Although the statistical conclusion might be somewhat dependent on the degree of the complexity of the lens potential, the discovery is consistent with the predictions of the abundance of cluster-scale halos in the CDM scenario. (Abridged)
We have identified three multiply imaged galaxies in Hubble Space Telescope images of the redshift z=0.68 cluster responsible for the large-separation quadruply lensed quasar, SDSS J1004+4112. Spectroscopic redshifts have been secured for two of these systems using the Keck I 10m telescope. The most distant lensed galaxy, at z=3.332, forms at least four images, and an Einstein ring encompassing 3.1 times more area than the Einstein ring of the lensed QSO images at z=1.74, due to the greater source distance. For a second multiply imaged galaxy, we identify Ly_alpha emission at a redshift of z=2.74. The cluster mass profile can be constrained from near the center of the brightest cluster galaxy, where we observe both a radial arc and the fifth image of the lensed quasar, to the Einstein radius of the highest redshift galaxy, ~110 kpc. Our preliminary modeling indicates that the mass approximates an elliptical body, with an average projected logarithmic gradient of ~-0.5. The system is potentially useful for a direct measurement of world models in a previously untested redshift range.
We investigate the dependence of the time delays for the large-separation gravitationally lensed quasar SDSS J1004+4112 on the inner mass profile of the lensing cluster. Adopting the mass model whose innermost density profile is parameterized as rho propto r^{-alpha}, we derive a series of mass models which can fit observational data and then compute the probability distribution functions of time delays. We find that larger alpha has longer time delays, longer tails at the higher end of the probability distribution, and larger model uncertainties. The ratios of time delays slightly depend on the slope alpha. Among others, time delays between images C and A (or B) have little dependence on the inner slope, particularly when the time delays are short. The dependence of time delays on alpha is well fitted by a linear form, which reflects well-known degeneracy between the mass profile and time delays. We perform a Monte-Carlo simulation to illustrate how well the inner slope can be constrained from measurements of time delays. We find that measurements of more than one time delays result in reasonably tight constraints on the inner slope (sigma_{alpha} lesssim 0.25), while only one time delay cannot determine the inner slope very well. Our result indicates that time delays indeed serve as a powerful tool to determine the mass profile, despite the complexity of the lensing cluster.
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