J. G. Buitrago

Time Delay of QSO 0957+561 and Cosmological Implications

We obtain the time delay between the arrival time of the A and B images of the QSO 0957+561. The results of applying two different methods (the discrete cross-correlation function and the dispersion estimation technique) to the observed light curves of the A and B images are presented. The adopted value (time delay) is of ΔτBA = 424 ± 3 days (1 σ). We have used this time delay as well as a recent measurement of the one-dimensional velocity dispersion of the main lensing galaxy (σgal) to estimate H0. Two H0 = H0(ΔτBA, σgal) relations based on different pictures of the lens galaxy, lead to H0 = 64+ 14−15 km s-1 Mpc-1 (2 σ) (softened power-law sphere) and H0 = 66+ 15−14 km s-1 Mpc-1 (2 σ) (King profile plus a point-mass at the center).

Two-dimensional Spectroscopy Reveals an Arc of Extended Emission in the Gravitational Lens System Q2237+0305

We present two-dimensional spectroscopy of the gravitational lens system Q2237+0305 (Einstein Cross) obtained with the INTEGRAL fiber system in subarcsecond seeing conditions. The four components of the system appear clearly separated in the continuum intensity maps. However, the intensity map of the C III] ?1909 line exhibits an arc of extended emission connecting the A, D, and B components. This result can be explained if, as is usually assumed, the continuum arises from a compact source 0.05 pc in extent in the nucleus of the object while the line emission comes from a much larger region. A lens model fitted to the positions of the four compact images also accounts for the arc morphology. In the framework of this model, the region generating the C III] ?1909 emission would have dimensions of about 400 h-1 pc across. We interpret the observed arc as a gravitational lens image of the extended narrow line region of the source.

The Influence of Microlensing on Time Delay Determinations in Double-imaged Quasars

The lag associated with the main peak of the cross-correlation function of the two light curves arriving from a double-imaged quasar is usually identified with the time delay between the components. However, short-timescale microlensing events can independently modify the light curve of each component, and when strong microlensing is present, the features of the cross-correlation function depend on both amplitude and shape of the microlensing events. This fact prevents a direct interpretation of the lag associated with the main peak as the true time delay. We present a new analysis of the light curves cross-correlation function including short-timescale microlensing. We discuss its application to the 1995/1996 optical photometry of Q0957+561, and determine the trend of a possible microlensing event taking place from JD 2,450,150 to 2,450,200.

Optical Photometry of Quasar 0957+561A, B

Observations of the gravitational lens system 0957+561A, B in the R band are presented in this Letter. The observations, taken with the 82 cm IAC-80 telescope, at Teide Observatory, Spain, were made from the beginning of 1996 February to June, as part of an on-going lens monitoring program to obtain the time delay between the two components of the system. By comparing our data with those previously published by Kundic et al., we infer that a large delay (>500 days) is inconsistent with both data sets.

Spectroscopy of the Lens Galaxy of Q0957+561A,B: Implications of a Possible Central Massive Dark Object

We present new long-slit William Herschel Telescope spectroscopic observations of the lens galaxy G1 associated with the double-imaged QSO 0957+561A,B. The central stellar velocity dispersion obtained, σl = 310 ± 20 km s-1, is in reasonable agreement with other measurements of this dynamical parameter. Using all updated measurements of the stellar velocity dispersion in the internal region of the galaxy (at angular separations <15) and a simple isotropic model, we discuss the mass of a possible central massive dark object. We find that the data of Falco et al. suggest the existence of an extremely massive object of (0.5-2.1) × 1010 h-1 M☉ (80% confidence level), whereas the inclusion of very recent data substantially changes the results: the compact central mass must be ≤6 × 109 h-1 M☉ at the 90% confidence level. We note that, taking into account all the available dynamical data, a compact nucleus with a mass of 109 h-1 M☉ (best fit) cannot be ruled out.

Analysis of the Difference Light Curve of the Gravitational Mirage QSO 0957+561

From optical data of Q0957+561 for 1995/1996 seasons (in the g band) and 1996/1997 seasons (in the R band) they are derived upper limits on the amplitude of the rapid microlensing fluctuations of 0.07 mag and 0.05 mag, respectively. The photometry in the R band (1996/1997 seasons) was taken at Teide Observatory (IAC-80 Telescope), Instituto de Astrofisica de Canarias, Spain. In this contribution, we also study the microlensing history (from 1981 to 1996) of the Twin QSO, which is a curious system with two optical images of similar brightness.

On the Eulerian Approach to the Evolution of Large-Scale Structures

Within the classical Eulerian theory of gravitational instability, and in an Ω = 1 universe, we introduce a method for obtaining iterative solutions for the density contrast and peculiar velocity that can be extended to any order of approximation in the quasilinear regime. We compute the solution up to the fourth order (E4) and establish a standard criterion on the validity of Eulerian perturbative studies. The accuracy of E1-E4 is analyzed by using a power-law spherical initial profile for the average density contrast. Within the standard validity range, predictions of E4 generally have an accuracy of 95% or better. Concordance between perturbative predictions and the exact values depends on the index of the initial profile, the nature of the structure (cluster or void), and the magnitude under study (density contrast, δ, or relative deviation from the Hubble flow, β). From a global point of view, the E2 approximation describes the final status of clusters quite well (with a relative error of under 10%), while it is poorer in studying the inner parts of voids. So E2 may be considered as a sufficiently good approximation for the study of the evolution of the halo of overdense regions. We also compare the Eulerian approximation with the two main Lagrangian approximations (L1 = Zeldovich and L2) and show that, in a quasilinear regime (| δ | 1) and within the standard validity range, E2 is better than L2. There is one exception to this general behavior, for instance, the contrast density for clusters with a steep initial density profile or voids with a smooth one. The Zeldovich approximation is particularly inefficient at tracing the evolution of peculiar motions (E1 is clearly better). This L1 approximation leads to an artificial behavior of the inner regions of voids, in disagreement with previous work based on a homogeneous void (top-hat spherical underdensity). Our results warn of the risks of a systematic and indiscriminate use of Lagrangian approximations in the study of the large-scale structures evolution.

THIRD-ORDER PERTURBATIVE APPROACH TO GRAVITATIONAL INSTABILITY: EVOLUTION OF ISOLATED STRUCTURES AND ENVIRONMENTAL EFFECTS

In an Ω0 = 1 universe, within the classical Eulerian theory of gravitational instability, the redshift evolution of a peculiar velocity field in a region with arbitrary initial density contrast is derived, for the first time, in real space and third-order perturbation theory. A vector proportional to the gravitational acceleration can also be expanded in terms of the redshift and the initial density contrast. The results are applied to isolated (spherically symmetric) superclusters and voids. Using reasonable models and the exact solution, we tested the accuracy of three (linear, second order, and third order) approaches. A numerical example showed that the relative error of the third-order solutions (average density contrast and peculiar velocity) is less than 5% when 0 < δ 1. In another example, a relative error was derived (at -1 < δ < 0) of less than 10% (average density contrast) to 2% (peculiar velocity). On the other hand, second-order environmental dynamical terms (supercluster-supercluster, supercluster-void, and void-void complexes) have been also obtained. In the complexes (which contain two large-scale structures with spherical symmetry at recombination), the global peculiar flow can be described as a natural (but not trivial) superposition of two effective peculiar flows. Given a member of a complex, its effective peculiar velocity field is the sum of a spherically symmetric radial field (which is equal to the peculiar velocity field obtained from an isolated evolution) and an environmental (due to the interaction with the companion) field. In general, the external tides can be comparable to the internal ones. The imprint of the environment fields in the mean radial effective peculiar flows is also studied.

Eulerian Perturbative Approximations in Planar Symmetry

In planar symmetry (one-dimensional peculiar motions), using the Eulerian perturbative framework and an arbitrary initial profile, we compute the analytical evolution of the peculiar velocity and the density contrast up to the fourth order (E1-E4 approximations). From these results and the exact (Lagrangian) solutions, the accuracy of the Ej (j ≤ 4) approaches in describing the quasi-linear evolution of some particular initial profiles (overdense and underdense planar halos) are studied. For the peculiar velocity, E2 works well. On the contrary, only E3 and E4 are good descriptors of the quasi-linear regime of the density contrast in underdensities, and the situation is worse for the density contrast in overdensities. We have also analyzed the true power of the Eulerian theory in general planar problems. In spite of the apparent weakness of the Eulerian scheme in planar problems (in relation to the Lagrangian formalism, which leads to the exact solution even in the first-order approximation), we showed that this formalism is capable of yielding the exact solution to some plane-symmetric gravitational instability problems. For the E1-E4 approximations, the local relation agrees with the exact one. Moreover, for the evolution of planar cores (a top-hat initial profile or the central shell of an arbitrary inhomogeneity), it is possible to make, in a relatively simple way, a superapproach E∞, which leads to the exact solution (peculiar velocity and density contrast). We observe finally that the Eulerian formalism may, however, be a poor tracer for the evolution of planar halos. Only when a superapproach is viable does the Eulerian theory rival the Lagrangian one.

Gravitational Lenses and the Hubble Constant: Present and Future

For a multiple QSO, the propagation time from the source to the observer varies from the image i to the image j, and this difference (▵τij) can be measured when the source is variable. In general, assuming a flat universe without cosmological constant, the parameter ▵τij x 0 (H0 is the Hubble constant) depends on the redshifts of the lens and the source, as well as the positions of the individual images and the source (2, j), and the scaled surface potential Ψa at i and j (see, e.g., Blandford and Kundic 1996, Williams and Schechter 1997). The observations of multiple images of the same source are used to infer and the adjustable parameters α ≡ (α1,...,αp) that appear in the picture of the deflector, i.e., a lens model. From the lens model corresponding to the lens picture, ▵τij, i, j and the redshifts, one obtains H0.