Analysis of the Q2237+0305 light-curve variability with regularization technique

The microlensing high-amplification events in the light curves of the gravitationally lensed quasar Q2237+0305 observed by the OGLE group and GLITP collaboration are analysed. The significant brightness amplification in the A and C components in 1999 observational season are considered under the assumption of the fold caustic crossing. Under this assumption we applied the model-independent method based on regularization technique for one-dimensional profile restoration of the quasar accretion disc brightness distribution. The recovered brightness distribution of the source seems to obey the standard model for the accretion disc. The estimated effective radius of the quasar emitting region is in agreement with the previous studies.     

Q2237+0305 source structure and dimensions from light-curve simulation

Assuming a two-component quasar structure model consisting of a central compact source and an extended outer feature, we produce microlensing simulations for a population of compact masses in the lensing galaxy of Q2237+0305. Such a model is a simplified version of that adopted to explain the brightness variations observed in Q0957. The microlensing light curves generated for a range of source parameters were compared to the light curves obtained in the framework of the Optical Gravitational Lensing Experiment program. With a large number of trials, we built, in the domain of the source structure parameters, probability distributions to find 'good' realizations of light curves. The values of the source parameters which provide the maximum of the joint probability distribution calculated for all the image components have been accepted as estimates for the source structure parameters. The results favour the two-component model of the quasar brightness structure over a single compact central source model, and in general the simulations confirm the Schild–Vakulik model that previously described successfully the microlensing and other properties of Q0957. Adopting 3300 km s⁻¹ for the transverse velocity of the source, the effective size of the central source was determined to be about  2 × 10¹⁵ cm  , and  ɛ≈ 2  was obtained for the ratio of the integral luminosity of the outer feature to that of the central source.     

VRI photometry of the Einstein Cross Q2237+0305 at Maidanak observatory

Observations of the gravitationally lensed quasar Q2237+0305 were made with the 1.5-meter AZT-22 telescope at Maidanak (Uzbekistan) on 17–19 September 1995. All four components of the quasar are clearly resolved. The results of photometric measurements of the components are presented. It is confirmed that the component A again became the brightest one in the system. A noticeable change of the mutual colours of the components A and B in comparison with previous observations is detected and discussed. We cannot decide, on the basis of existing observational data, whether varying extinction or “chromatic” microlensing is the cause. Stronger, correlated colour changes in the system are probably caused by quasar variability. The dominant time scale of the microlensing-governed brightness variations since the discovery is of the order of 10 years. A correlation between radio brightness and optical colour is found but cannot be explained.     

Microlensing-induced spectral variability in Q 2237+0305

We present both photometry and spectra of the individual images of the quadruple gravitational lens system Q 2237+0305. Comparison of spectra obtained at two epochs, separated by ∼3 yr, shows evidence for significant changes in the emission line-to-continuum ratio of the strong ultraviolet C  IV  λ1549, C  III ] λ1909 and Mg  II  λ2798 lines. The short, ∼1 day, light-travel time differences between the sight lines to the four individual quasar images rule out any explanation based on intrinsic variability of the source. The spectroscopic differences thus represent direct detection of microlensing-induced spectroscopic differences in a quasar. The observations allow constraints to be placed on the relative spatial scales in the nucleus of the quasar, with the ultraviolet continuum arising in a region of ≲0.05 pc in extent, while the broad emission-line material is distributed on scales much greater than this.     

Weighing a galaxy bar in the lens Q2237 +=0305

In the gravitational lens system Q2237+0305 the cruciform quasar image geometry is twisted by 10c by the lens effect of a bar in the lensing galaxy. This effect can be used to measure the mass of the bar. We construct a new lensing model for this system with a power-law elliptical bulge and a Ferrers bar. The observed ellipticity of the optical isophotes of the galaxy leads to a nearly isothermal elliptical profile for the bulge, with a total quasar magnification of 16⁺⁵₋₄. We measure a bar mass of (7.5 ∼ 1.5) −10⁸ h ⁻¹₇₅ M⊙ in the region inside the quasar images.     

A small source in Q2237+0305?

Microlensing in Q2237+0305 between 1985 and 1995 has been interpreted in two different ways. First, the observed variations can be explained through microlensing by stellar mass objects of a continuum source with dimensions significantly smaller than the microlens Einstein Radius ( ₀), but consistent with that expected for thermal accretion discs . However, other studies have shown that models having sources as large as 5 ₀ can reproduce the observed variation . In this paper we present evidence in favour of a small source. Our approach uses the distribution of microlensed light-curve derivatives to place statistical limits (as a function of source size) on the number of microlens Einstein radii crossed by the source during the monitoring period. In contrast with previous analyses, our results are therefore not dependent on an assumed time-scale. Limits on the source size are obtained from two separate light-curve features. First, recently published monitoring data show large variations (0.81.5 mag) between image brightnesses over a period of 700 d or 15 per cent of the monitoring period. Secondly, the 1988 peak in the image A light curve had a duration that is a small fraction (0.02) of the monitoring period. Such rapid microlensing rises and short microlensing peaks only occur for small sources. We find that the observed large, rapid variation limits the source size to be <0.2 ₀ (95 per cent confidence). The width of the light-curve peak provides a stronger constraint of <0.025 ₀ (99 per cent confidence). The Einstein radius (projected into the source plane) of the average microlens mass m in Q2237+0305 is The interpretation that stars are responsible for microlensing in Q2237+0305 therefore results in limits on the continuum source size that are consistent with current accretion disc theory.     

Probing subparsec structure in the Lyman α forest with gravitational microlensing

We present the results of microlens ray-tracing simulations showing the effect of absorbing material between a source quasar and a lensing galaxy in a gravitational lens system. We find that, in addition to brightness fluctuations due to microlensing, the strength of the absorption line relative to the continuum varies with time, with the properties of the variations depending on the structure of the absorbing material. We conclude that such variations will be measurable via ultraviolet spectroscopy of image A of the gravitationally lensed quasar Q2237+0305 if the Lyman α clouds between the quasar and the lensing galaxy possess structure on scales smaller than ∼0.1 pc. The time-scale for the variations is on the order of years to decades, although very short-term variability can occur. While the Lyman α lines may not be accessible at all wavelengths, this approach is applicable to any absorption system, including metal lines.     

Caustic crossing in the gravitational lens Q2237+0305

The monitoring of the gravitational lens Q2237+0305 carried out by the OGLE group during 1997–2000 is analyzed. The significant light amplifications in the C and A quasar components with maxima in mid-and late 1999, respectively, are interpreted as the crossing of microlens caustics by the source. A constraint on the emitting-region size R≤10¹⁵ cm has been obtained from the light-curve shape by assuming a power-law quasar brightness distribution (r ²+R ²)^?p . To estimate the exponent p～1.2 requires refining the standard model for the quasar continuum formation in an optically thick accretion disk with p=1.5.     

Degeneracies and scaling relations in general power-law models for gravitational lenses

The time-delay in gravitational lenses can be used to derive the Hubble constant in a relatively simple way. The results of this method are less dependent on astrophysical assumptions than in many other methods. For systems with accurately measured positions and time-delays, the most important uncertainty is related to the mass model used. Simple parametric models like isothermal ellipsoidal mass distributions seem to provide consistent results with a reasonably small scatter when applied to several lens systems. We discuss a family of models with a separable radial power law and an arbitrary angular dependence for the potential   ψ = r ^β F ( θ )  . Isothermal potentials are a special case of these models with   β =1  . An additional external shear is used to take into account perturbations from other galaxies. Using a simple linear formalism for quadruple lenses, we can derive H ₀ as a function of the observables and the shear. If the latter is fixed, the result depends on the assumed power-law exponent according to   H ₀∝(2- β )/ β   . The effect of external shear is quantified by introducing a 'critical shear' γ _c as a measure for the amount of shear that changes the result significantly. The analysis shows that in the general case H ₀ and γ _c do not depend on the position of the lens galaxy. Spherical lens models with images close to the Einstein radius with fitted external shear differ by a factor of   β /2  from shearless models, leading to   H ₀∝2- β   in this case. We discuss these results and compare them with numerical models for a number of real lens systems.     

The distribution of microlensed light-curve derivatives: the relationship between stellar proper motions and transverse velocity

We present a method for computing the probability distribution of microlensed light-curve derivatives both in the case of a static lens with a transverse velocity, and in the case of microlensing that is produced through stellar proper motions. The distributions are closely related in form, and can be considered equivalent after appropriate scaling of the input transverse velocity. The comparison of the distributions in this manner provides a consistent way to consider the relative contribution to microlensing (both large and small fluctuations) of the two classes of motion, a problem that is otherwise an extremely expensive computational exercise. We find that the relative contribution of stellar proper motions to the microlensing rate is independent of the mass function assumed for the microlenses, but is a function of optical depth and shear. We find that stellar proper motions produce a higher overall microlensing rate than a transverse velocity of the same magnitude. This effect becomes more pronounced at higher optical depth. With the introduction of shear, the relative rates of microlensing become dependent on the direction of the transverse velocity. This may have important consequences in the case of quadruply lensed quasars such as Q2237+0305, where the alignment of the shear vector with the source trajectory varies between images.