SDSS J1004 Research Articles

Microlensing analysis of 14.5-year light curves in SDSS J1004+4112: Quasar accretion disk size and intracluster stellar mass fraction

Context. The gravitational lens system SDSS J1004+4112 was the first known example of a quasar lensed by a galaxy cluster. The interest in this system has been renewed following the publication of r-band light curves spanning 14.5 years and the determination of the time delays between the four brightest quasar images. Aims. We constrained the quasar accretion disk size and the fraction of the lens mass in stars using the signature of microlensing in the quasar image light curves. Methods. We built the six possible histograms of microlensing magnitude differences between the four quasar images and compared them with simulated model histograms, using a χ2 test to infer the model parameters. Results. We infer a quasar disk half-light radius of R1/2 = (0.70 ± 0.04)RE = (6.4 ± 0.4) √M/0.3M⊙ light-days at 2407 Å in the rest frame and stellar mass fractions at the quasar image positions of αA > 0.059, αB = 0.056+0.021-0.027, αC = 0.030+0.031-0.021, and αD = 0.072+0.034-0.016. Conclusions. The inferred disk size is broadly compatible with most previous estimates, and the stellar mass fractions are within the expected ranges for galaxy clusters. In the region where image C lies, the stellar mass fraction is compatible with a stellar contribution from the brightest cluster galaxy, galaxy cluster members, and intracluster light, but the values at images B, D, and especially A are slightly larger, possibly suggesting the presence of extra stellar components.

SDSS J102915.14+172927.9: Revisiting the chemical pattern

The small- to intermediate-mass ($ M<0.8 M_ most metal-poor stars that formed in the infancy of the Universe are still shining today in the sky. They are very rare, but their discovery and investigation brings new knowledge on the formation of the first stellar generations. SDSS J102915.14+172927.9 is one of the most metal-poor star known to date. Since no carbon can be detected in its spectrum, a careful upper limit is important, both to classify this star and to distinguish it from the carbon-enhanced stars that represent the majority at these metallicities. We undertook a new observational campaign to acquire high-resolution UVES spectra. The new spectra were combined with archival spectra in order to increase the signal-to-noise ratio. From the combined spectrum, we derived abundances for seven elements (Mg, Si, Ca, Ti, Fe, Ni, and a tentative Li) and five significant upper limits (C, Na, Al, Sr, and Ba). The star has a carbon abundance $ A(C)<4.68$ and therefore is not enhanced in carbon, at variance with the majority of the stars at this Fe regime, which typically show $ A(C)>6.0$. A feature compatible with the Li doublet at 670.7\,nm is tentatively detected. The upper limit on carbon implies $ Z<1.915 $, more than 20 times lower than the most iron-poor star known. Therefore, the gas cloud out of which the star was formed did not cool via atomic lines but probably through dust. Fragmentation of the primordial cloud is another possibility for the formation of a star with a metallicity this low.

First Direct Evidence for Keplerian Rotation in Quasar Inner Broad-line Regions

We introduce a novel method to derive rotation curves with light-day spatial resolution of the inner regions of lensed quasars. We aim to probe the kinematics of the inner part of the broad-line region by resolving the microlensing response—a proxy for the size of the emitting region—in the wings of the broad emission lines. Specifically, we assess the strength of the microlensing effects in the wings of the high-ionization lines Si iv and C iv across various velocity bins in five gravitationally lensed quasars: SDSS J1001+5027, SDSS J1004+4112, HE 1104−1805, SDSS J1206+4332, and SDSS J1339+1310. Using Bayesian methods to estimate the dimensions of the corresponding emission regions and adopting a Keplerian model as our baseline, we examine the consistency of the hypothesis of disklike rotation. Our results reveal a monotonic, smooth increase in microlensing magnification with velocity. The deduced velocity–size relationships inferred for the various quasars and emission lines closely conform to the Keplerian model of an inclined disk. This study provides the first direct evidence of Keplerian rotation in the innermost region of quasars across a range of radial distances spanning from ∼5 to 20 lt-days.

Single-epoch and Differential Astrometric Microlensing of Quasars

We propose and discuss a new experimental approach to measure the centroid shift induced by gravitational microlensing in the images of lensed quasars (astrometric microlensing). Our strategy is based on taking the photocenter of a region in the quasar large enough as to be insensitive to microlensing as reference to measure the centroid displacement of the continuum. In this way, single-epoch measurements of astrometric microlensing can be performed. Using numerical simulations, we show that, indeed, the centroid shift monotonically decreases as the size of the emitting region increases, and only for relatively large regions, like the broad line region (BLR), does the centroid shift become negligible. This opens interesting possibilities to study the stratification of the different emitters in the accretion disk and the BLR. We estimate the amplitude of the centroid shifts for 79 gravitationally lensed images and study more thoroughly the special cases Q2237+030 A, RXJ1131-1231 A, PG1115+080 A2, and SDSS J1004+4112 A. We propose to use spectro-astrometry to simultaneously obtain the photocenters of the continuum and of different emission line regions since, with the precision of forthcoming instruments, astrometric microlensing by ∼1 M ⊙ mass microlenses may be detected in many quasar lensed images. When we consider more massive micro/millilenses, M ≳ 10 M ⊙, often proposed as the constituents of dark matter, the BLR becomes sensitive to microlensing and can no longer be used as a positional reference to measure centroid shifts. Differential microlensing between the images of a lensed quasar along several epochs should be used instead.

Light Curves of Lensed Components and Time Delay Measurements in the Binary Gravtationally Lensed Quasars SDSS J2124$$+$$1632 and SDSS J0806$$+$$2006

Light Curves of Lensed Components and Time Delay Measurements in the Binary Gravtationally Lensed Quasars SDSS J2124$$+$$1632 and SDSS J0806$$+$$2006

Extrapolating the projected potential of gravitational lens models: property-preserving degeneracies

ABSTRACT While gravitational lens inversion holds great promise to reveal the structure of the light-deflecting mass distribution, both light and dark, the existence of various kinds of degeneracies implies that care must be taken when interpreting the resulting lens models. This article illustrates how thinking in terms of the projected potential helps to gain insight into these matters. Additionally it is shown explicitly how, when starting from a discretized version of the projected potential of one particular lens model, the technique of quadratic programming can be used to create a multitude of equivalent lens models that preserve all or a subset of lens properties. This method is applied to a number of scenarios, showing the lack of grasp on the mass outside the strong lensing region, revisiting mass redistribution in between images, and applying this to a recent model of the SDSS J1004+4112 cluster, as well as illustrating the generalized mass sheet degeneracy and source-position transformation. In the case of J1004, we show that this mass redistribution did not succeed at completely eliminating a dark mass clump recovered by grale near one of the quasar images.

Probing the structure of the lensed quasar SDSS J1004+4112 through microlensing analysis of spectroscopic data

Aims. We aim to reveal the sizes of the continuum and broad emission line (BEL) emitting regions in the gravitationally lensed quasar SDSS J1004+4112 by analyzing the unique signatures of microlensing in this system. Through a comprehensive analysis of 20 spectroscopic observations acquired between 2003 and 2018, we studied the striking deformations of various BEL profiles and determined the sizes of their respective emitting regions. Methods. Our approach involves a detailed analysis of the magnitude differences in the BEL wings and their adjacent continua, and the implementation of a statistical model to quantify the distribution and impact of microlensing magnifications. To ensure a reliable baseline for no microlensing, we used the emission line cores as a reference. We then applied a Bayesian estimate to derive the size lower limits of the Lyα, Si IV, C IV, C III], and Mg II emitting regions, as well as the sizes of the underlying continuum-emitting sources. Results. We analyzed the outstanding microlensing-induced distortions in the line profiles of various BELs in the quasar image A, characterized by a prominent magnification of the blue part and a strong demagnification of the red part. From the statistics of microlensing magnifications and using Bayesian methods, we estimate the lower limit to the overall size of the regions emitting the BELs to be a few light-days across, which is significantly smaller than in typically lensed quasars. The asymmetric deformations in the BELs indicate that the broad-line region is generally not spherically symmetric, and is likely confined to a plane and following the motions of the accretion disk. Additionally, the inferred continuum-emitting region sizes are larger than predictions based on standard thin-disk theory by a factor of ∼3.6 on average. The size-wavelength relation is consistent with that of a geometrically thin and optically thick accretion disk.

Parameter-free Hubble constant from the quadruply lensed quasar SDSS J1004+4112

We present a free-form lens model for the multiply lensed quasar in the galaxy cluster SDSS J1004+4112. Our lens model draws minimal assumptions on the distribution of mass in the lens plane. We have paid particular attention to the model uncertainties on the predicted time delay originating from the particular configuration of model variables. Taking into account this uncertainty, we obtained a value of the Hubble constant of H0 = 74−13+9 km s−1 Mpc−1, which is consistent with recent independent estimates. The predicted time delay between the central image E and image C (the first to arrive) is ΔTE−C = 3200 ± 200 days for the estimated Hubble constant. Future measurements of ΔTE−C will allow for a tighter constraint to be imposed on H0 in this cluster-QSO system.

Hubble Constant Measurement from Three Large-separation Quasars Strongly Lensed by Galaxy Clusters

Tension between cosmic microwave background–based and distance ladder–based determinations of the Hubble constant H 0 motivates the pursuit of independent methods that are not subject to the same systematic effects. A promising alternative, proposed by Refsdal in 1964, relies on the inverse scaling of H 0 with the delay between the arrival times of at least two images of a strongly lensed variable source such as a quasar. To date, Refsdal’s method has mostly been applied to quasars lensed by individual galaxies rather than by galaxy clusters. Using the three quasars strongly lensed by galaxy clusters (SDSS J1004+4112, SDSS J1029+2623, and SDSS J2222+2745) that have both multiband Hubble Space Telescope data and published time delay measurements, we derive H 0, accounting for the systematic and statistical sources of uncertainty. While a single time delay measurement does not yield a well-constrained H 0 value, analyzing the systems together tightens the constraint. Combining the six time delays measured in the three cluster-lensed quasars gives H 0 = 74.1 ± 8.0 km s−1 Mpc−1. To reach 1% uncertainty in H 0, we estimate that a sample size of order of 620 time delay measurements of similar quality as those from SDSS J1004+4112, SDSS J1029+2623, and SDSS J2222+2745 would be needed. Improving the lens modeling uncertainties by a factor of two and a half may reduce the needed sample size to 100 time delays, potentially reachable in the next decade.

Free-form and hybrid lens models for SDSS J1004+4112: substructure and central image time delay constraints

ABSTRACT SDSS J1004+4112 is a well-studied gravitational lens with a recently measured time delay between its first and fourth arriving quasar images. Using this new constraint, we present updated free-form lens reconstructions using the lens inversion method grale, which only uses multiple image and time delay data as inputs. In addition, we obtain hybrid lens reconstructions by including a model of the brightest cluster galaxy as a Sersic lens. For both reconstructions, we use two sets of images as input: one with all identified images, and the other a revised set leaving out images that have been potentially misidentified. We also develop a source position optimization Markov chain Monte Carlo (MCMC) routine, performed on completed grale runs, that allows each model to better match observed image positions and time delays. All the reconstructions produce similar mass distributions, with the hybrid models finding a steeper profile in the centre. Similarly, all the mass distributions are fitted by the Navarro–Frenk–White profile, finding results consistent with previous parametric reconstructions and those derived from Chandra X-ray observations. We identify an ∼5 × 1011 M⊙ substructure apparently unaffiliated with any cluster member galaxy and present in all our models, and study its reality. Using our free-form and hybrid models, we predict a central quasar image time delay of ∼2980 ± 270 and ∼3280 ± 215 d, respectively. A potential future measurement of this time delay will, while being an observational challenge, further constrain the steepness of the central density profile.

TDCOSMO

Context. Time-delay cosmography uses strong gravitational lensing of a time-variable source to infer the Hubble constant. The measurement is independent from both traditional distance ladder and CMB measurements. An accurate measurement with this technique requires considering the effects of objects along the line of sight outside the primary lens, which is quantified by the external convergence (κext). In absence of such corrections, H0 will be biased towards higher values in overdense fields and lower values in underdense fields. Aims. We discuss the current state of the methods used to account for environment effects. We present a new software package built for this kind of analysis and others that can leverage large astronomical survey datasets. We apply these techniques to the SDSS J0924+0219 strong lens field. Methods. We infer the relative density of the SDSS J0924+0219 field by computing weighted number counts for all galaxies in the field, and comparing to weighted number counts computed for a large number of fields in a reference survey. We then compute weighted number counts in the Millennium Simulation and compare these results to infer the external convergence of the lens field. Results. Our results show the SDSS J0924+0219 field is a fairly typical line of sight, with median κext = −0.012 and standard deviation σκ = 0.028.

X-ray properties and obscured fraction of AGN in the J1030 Chandra field

The 500ks Chandra ACIS-I observation of the field around the z = 6.31 quasar SDSS J1030+0524 is currently the fifth deepest extragalactic X-ray survey. The rich multi-band coverage of the field allowed an effective identification and redshift determination of the X-ray source counterparts; to date, a catalog of 243 extragalactic X-ray sources with either a spectroscopic or photometric redshift estimate in the range z ≈ 0 − 6 is available over an area of 355 arcmin2. Given its depth and the multi-band information, this catalog is an excellent resource to investigate X-ray spectral properties of distant active galactic nuclei (AGN) and derive the redshift evolution of their obscuration. We performed a thorough X-ray spectral analysis for each object in the sample, and measured its nuclear column density NH and intrinsic (de-absorbed) 2–10 keV rest-frame luminosity, L2 − 10. Whenever possible, we also used the presence of the Fe Kα emission line to improve the photometric redshift estimates. We measured the fractions of AGN hidden by column densities in excess of 1022 and 1023 cm−2 (f22 and f23, respectively) as a function of L2 − 10 and redshift, and corrected for selection effects to recover the intrinsic obscured fractions. At z ∼ 1.2, we found f22 ∼ 0.7 − 0.8 and f23 ∼ 0.5 − 0.6, respectively, in broad agreement with the results from other X-ray surveys. No significant variations in X-ray luminosity were found within the limited luminosity range probed by our sample (log L2 − 10 ∼ 42.8 − 44.3). When focusing on luminous AGN with log L2 − 10 ∼ 44 to maximize the sample completeness up to large cosmological distances, we did not observe any significant change in f22 or f23 over the redshift range z ∼ 0.8 − 3. Nonetheless, the obscured fractions we measure are significantly higher than is seen in the local Universe for objects of comparable intrinsic luminosity, pointing toward an increase in the average AGN obscuration toward early cosmic epochs, as also observed in other X-ray surveys. We finally compared our results with recent analytic models that ascribe the greater obscuration observed in AGN at high redshifts to the dense interstellar medium (ISM) of their hosts. When combined with literature measurements, our results favor a scenario in which the total column density of the ISM and the characteristic surface density of its individual clouds both increase toward early cosmic epochs as NH, ISM∝(1 + z)δ, with δ ∼ 3.3 − 4 and Σc, * ∝ (1 + z)2, respectively.

TD-CARMA: Painless, Accurate, and Scalable Estimates of Gravitational Lens Time Delays with Flexible CARMA Processes

Cosmological parameters encoding our understanding of the expansion history of the universe can be constrained by the accurate estimation of time delays arising in gravitationally lensed systems. We propose TD-CARMA, a Bayesian method to estimate cosmological time delays by modeling observed and irregularly sampled light curves as realizations of a continuous auto-regressive moving average (CARMA) process. Our model accounts for heteroskedastic measurement errors and microlensing, an additional source of independent extrinsic long-term variability in the source brightness. The semiseparable structure of the CARMA covariance matrix allows for fast and scalable likelihood computation using Gaussian process modeling. We obtain a sample from the joint posterior distribution of the model parameters using a nested sampling approach. This allows for “painless” Bayesian computation, dealing with the expected multimodality of the posterior distribution in a straightforward manner and not requiring the specification of starting values or an initial guess for the time delay, unlike existing methods. In addition, the proposed sampling procedure automatically evaluates the Bayesian evidence, allowing us to perform principled Bayesian model selection. TD-CARMA is parsimonious, and typically includes no more than a dozen unknown parameters. We apply TD-CARMA to six doubly lensed quasars HS2209+1914, SDSS J1001+5027, SDSS J1206+4332, SDSS J1515+1511, SDSS J1455+1447, and SDSS J1349+1227, estimating their time delays as −21.96 ± 1.448, 120.93 ± 1.015, 111.51 ± 1.452, 210.80 ± 2.18, 45.36 ± 1.93, and 432.05 ± 1.950, respectively. These estimates are consistent with those derived in the relevant literature, but are typically two to four times more precise.

Raising the observed metallicity floor with a 3D non-LTE analysis of SDSS J102915.14+172927.9

Context. The first stars marked the end of the cosmic dark ages, produced the first heavy elements, and set the stage for the formation of the first galaxies. Accurate chemical abundances of ultra metal-poor stars ([Fe/H] < −4) can be used to infer the properties of the first stars and thus the formation mechanism for low-mass second-generation stars in the early Universe. Spectroscopic studies have shown that most second-generation stars are carbon enhanced. A notable exception is SDSS J102915.14+172927.9, which is the most metal-poor star known to date, largely by virtue of the low upper limits of the carbon abundance reported in earlier studies. Aims. We re-analysed the composition of SDSS J102915.14+172927.9 with the aim of providing improved observational constraints on the lowest metallicity possible for low-mass star formation and constraining the properties of its Population III progenitor star. Methods. We developed a tailored three-dimensional model atmosphere for SDSS J102915.14+172927.9 with the Stagger code, making use of an improved surface gravity estimate based on the Gaia DR3 parallax. Snapshots from the model were used as input in the radiative transfer code Balder to compute 3D non-local thermodynamic equilibrium (non-LTE) synthetic spectra. These spectra were then used to infer abundances for Mg, Si, Ca, Fe, and Ni as well as upper limits on Li, Na, and Al. Synthetic 3D LTE spectra were computed with Scate to infer the abundance of Ti and upper limits on C and N. Results. In contrast to earlier works based on 1D non-LTE corrections applied to 3D LTE results, we are able to achieve ionisation balance for Ca I and Ca II when employing our consistent 3D non-LTE treatment. The elemental abundances are systematically higher than those found in earlier works. In particular, [Fe/H] is increased by 0.57 dex, and the upper limits of C and N are larger by 0.90 dex and 1.82 dex, respectively. Conclusions. We find that Population III progenitors with masses 10–20 M⊙ exploding with energy E ⪅ 3 × 1051 erg can reproduce our 3D non-LTE abundance pattern. Our 3D non-LTE abundances are able to better constrain the progenitor mass and explosion energy as compared to our 1D LTE abundances. Contrary to previous work, we obtain higher upper limits on the carbon abundance that are ‘marginally consistent’ with star formation through atomic line cooling, and consequently, these results prevent us from drawing strong conclusions about the formation mechanism of this low-mass star.

Stellar mass fraction and quasar accretion disk size in SDSS J1004+4112 from photometric follow-up

AbstractThe gravitational lens SDSS J1004+4112 was the first discovered system where a background quasar is lensed by a galaxy cluster instead of a single galaxy. We use the 14.5-year r-band light curves together with the recently measured time delay of the fourth brightest quasar image (Munõz et al. (2022)) and the mass model from Forés-Toribio et al. (2022) to study the microlensing effect in this system. We constrain the quasar accretion disk size to light-days at 2407Å in the restframe which is compatible with most previous estimates. We also infer the fraction of mass in stars at the positions of the quasar images: $${\alpha _A} = 0.058_{ - 0.032}^{ + 0.024},{\alpha _B} = 0.048_{ - 0.014}^{ + 0.032},{\alpha _C} = 0.018_{ - 0.018}^{ + 0.015}$$ and $${\alpha _D} = 0.008_{ - 0.008}^{ + 0.033}$$ . The stellar fraction estimates are reasonable for intracluster medium although the stellar fractions at images A and B are slightly larger, suggesting the presence of a near undetected galaxy.

Probing the Structure of SDSS J1004+4112 through Microlensing Analysis of Spectroscopic Data

AbstractWe aim to uncover the structure of the continuum and broad emission line (BEL) emitting regions in the gravitationally lensed quasar SDSS J1004+4112 through unique microlensing signatures. Analyzing 20 spectroscopic observations from 2003 to 2018, we study the striking deformations of various BEL profiles and determine the sizes of their respective emitting regions. We use the emission line cores as a baseline for no microlensing and then apply Bayesian methods to derive the sizes of the Lyα, Si IV, C IV, C III], and Mg II emitting regions, as well as of the underlying continuum-emitting sources. We find that the sizes of the emitting regions for the BELs are a few light-days across, notably smaller than in typical lensed quasars. The asymmetric distortions observed in the BELs suggest that the broad-line region lacks spherical symmetry and is likely confined to a plane. The inferred continuum emitting region sizes are larger than predictions based on standard thin-disk theory by a factor of ∼ 4. We find that the size-wavelength relation is in agreement with that of a geometrically thin and optically thick accretion disk.

The interstellar medium distribution, gas kinematics, and system dynamics of the far-infrared luminous quasar SDSS J2310+1855 atz= 6.0

We present Atacama Large Millimeter/submillimeter Array (ALMA) sub-kiloparsec- to kiloparsec-scale resolution observations of the [C II], CO (9–8), and OH+(11–01) lines along with their dust continuum emission toward the far-infrared (FIR) luminous quasar SDSS J231038.88+185519.7 atz = 6.0031, to study the interstellar medium distribution, the gas kinematics, and the quasar-host system dynamics. We decompose the intensity maps of the [C II] and CO (9–8) lines and the dust continuum with two-dimensional elliptical Sérsic models. The [C II] brightness follows a flat distribution with a Sérsic index of 0.59. The CO (9–8) line and the dust continuum can be fit with an unresolved nuclear component and an extended Sérsic component with a Sérsic index of ∼1, which may correspond to the emission from an active galactic nucleus dusty molecular torus and a quasar host galaxy, respectively. The different [C II] spatial distribution may be due to the effect of the high dust opacity, which increases the FIR background radiation on the [C II] line, especially in the galaxy center, significantly suppressing the [C II] emission profile. The dust temperature drops with distance from the center. The effective radius of the dust continuum is smaller than that of the line emission and the dust mass surface density, but is consistent with that of the star formation rate surface density. This may indicate that the dust emission is a less robust tracer of the dust and gas distribution but is a decent tracer of the obscured star formation activity. The OH+(11–01) line shows a P-Cygni profile with an absorption at ∼–400 km s−1, which may indicate an outflow with a neutral gas mass of (6.2 ± 1.2)×108 M⊙along the line of sight. We employed a three-dimensional tilted ring model to fit the [C II] and CO (9–8) data cubes. The two lines are both rotation dominated and trace identical disk geometries and gas motions. This suggest that the [C II] and CO (9–8) gas are coplanar and corotating in this quasar host galaxy. The consistent circular velocities measured with [C II] and CO (9–8) lines indicate that these two lines trace a similar gravitational potential. We decompose the circular rotation curve measured from the kinematic model fit to the [C II] line into four matter components (black hole, stars, gas, and dark matter). The quasar-starburst system is dominated by baryonic matter inside the central few kiloparsecs. We constrain the black hole mass to be 2.97+0.51-0.77 × 109M⊙; this is the first time that the dynamical mass of a black hole has been measured atz ∼ 6. This mass is consistent with that determined using the scaling relations from quasar emission lines. A massive stellar component (on the order of 109 M⊙) may have already existed when the Universe was only ∼0.93 Gyr old. The relations between the black hole mass and the baryonic mass of this quasar indicate that the central supermassive black hole may have formed before its host galaxy.

A Comparative L-dwarf Sample Exploring the Interplay between Atmospheric Assumptions and Data Properties

Comparisons of atmospheric retrievals can reveal powerful insights on the strengths and limitations of our data and modeling tools. In this paper, we examine a sample of five L dwarfs of similar effective temperature (T eff) or spectral type to compare their pressure–temperature (P-T) profiles. Additionally, we explore the impact of an object’s metallicity and the signal-to-noise ratio (S/N) of the observations on the parameters we can retrieve. We present the first atmospheric retrievals: 2MASS J15261405+2043414, 2MASS J05395200−0059019, 2MASS J15394189−0520428, and GD 165B increasing the small but growing number of L dwarfs retrieved. When compared to the atmospheric retrievals of SDSS J141624.08+134826.7, a low-metallicity d/sdL7 primary in a wide L+T binary, we find that similar T eff sources have similar P-T profiles with metallicity differences impacting the relative offset between their P-T profiles in the photosphere. We also find that for near-infrared spectra, when the S/N is ≳80 we are in a regime where model uncertainties dominate over data measurement uncertainties. As such, S/N does not play a role in the retrieval’s ability to distinguish between a cloud-free and cloudless model, but may impact the confidence of the retrieved parameters. Lastly, we also discuss how to break cloud model degeneracies and the impact of extraneous gases in a retrieval model.

A Mass Model for the Lensing Cluster SDSS J1004+4112: Constraints from the Third Time Delay

We have built a new model for the lens system SDSS J1004+4112 including the recently measured time delay of the fourth quasar image. This time delay has a strong influence on the inner mass distribution of the lensing cluster (ρ ∝ r −α ) allowing us to determine at the 68% (95%) confidence level in agreement with hydrodynamical simulations of massive galaxy clusters. We find an offset between the brightest cluster galaxy and the dark matter halo of kpc at 68% (95%) confidence which is compatible with other galaxy cluster measurements. As an observational challenge, the estimated time delay between the leading image C and the faint (I = 24.7) fifth image E is roughly 8 yr.

The Longest Delay: A 14.5 yr Campaign to Determine the Third Time Delay in the Lensing Cluster SDSS J1004+4112

We present new light curves for the four bright images of the five image cluster-lensed quasar gravitational lens system SDSS J1004+4112. The light curves span 14.5 yr and allow the measurement of the time delay between the trailing bright quasar image D and the leading image C. When we fit all four light curves simultaneously and combine the models using the Bayesian information criterion, we find a time delay of Δt DC = 2458.47 ± 1.02 days (6.73 yr), the longest ever measured for a gravitational lens. For the other two independent time delays we obtain Δt BC = 782.20 ± 0.43 days (2.14 yr) and Δt AC = 825.23 ± 0.46 days (2.26 yr), in agreement with previous results. The information criterion is needed to weight the results for light curve models with different polynomial orders for the intrinsic variability and the effects of differential microlensing. The results using the Akaike information criterion are slightly different, but, in practice, the absolute delay errors are all dominated by the ∼4% cosmic variance in the delays rather than the statistical or systematic measurement uncertainties. Despite the lens being a cluster, the quasar images show slow differential variability due to microlensing at the level of a few tenths of a magnitude.