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.     

A measurement of the transverse velocity of Q2237+0305

Determination of microlensing parameters in the gravitationally lensed quasar Q2237+0305 from the statistics of high-magnification events will require monitoring for more than 100 years (Wambsganss, Paczynski & Schneider). However, we show that the effective transverse velocity of the lensing galaxy can be determined on a more realistic time-scale through consideration of the distribution of light-curve derivatives. The 10 years of existing monitoring data for Q2237+0305 are analysed. These data display strong evidence for microlensing that is not associated with a high-magnification event. An upper limit of v _t<500 km s⁻¹ is obtained for the galactic transverse velocity, which is smaller than previously assumed values. The analysis suggests that the observed microlensing variation may be predominantly due to stellar proper motions. The statistical significance of the results obtained from our method will be increased by the addition of data points from current and future monitoring campaigns. However, reduced photometric errors will be more valuable than an increased sampling rate.     

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.     

GLITP optical monitoring of QSO 0957+561: VR light curves and variability

The Gravitational Lenses International Time Project (GLITP) collaboration observed the first gravitational lens system (QSO 0957+561) from 2000 February 3 to March 31. The daily VR observations were made with the 2.56-m Nordic Optical Telescope at Roque de los Muchachos Observatory, La Palma, Spain. We have derived detailed and robust VR light curves of the two components Q0957+561A and Q0957+561B. In spite of the excellent sampling rate, we have not found evidence in favour of true daily variability. With respect to variability on time-scales of several weeks, we measure VR gradients of about −0.8 mmag d⁻¹ in Q0957+561A and +0.3 mmag d⁻¹ in Q0957+561B. The gradients are very probably originated in the far source. Thus, adopting this reasonable hypothesis (intrinsic variability), we compare them to the expected gradients during the evolution of a compact supernova remnant at the redshift of the source quasar. The starburst scenario is roughly consistent with some former events, but the new gradients do not seem to be caused by supernova remnant activity.     

Evidence for accretion disc reprocessing in QSO 0957+561

We use archival g - and r -band photometry of the gravitational lens system QSO 0957+561A, B to estimate the intrinsic variability of the quasar during 1996 February–June. The light curves span 234 d with temporal resolutions of about 2.5 d. Both light curves display a single large-amplitude event, of ∼0.1 mag (max-to-min) in about 100 d, followed by small-amplitude variations of ∼0.02 mag on time-scales of tens of days. We find the r -band variations lag those at g by 3.4_−1.4^+1.5 d for the large-amplitude event. This lag is greater than zero at no less than 98 per cent confidence. The delayed coupling of the rest-frame UV intrinsic variations strongly suggests the existence of a stratified reprocessing region extending ∼light-days from the putative central black hole source. The observed lag is consistent with that expected from a reverberation within an irradiated accretion disc structure. However, any definitive statement requires further detailed theoretical modelling and high-quality, signal-to-noise ratio of about 100, optical/IR simultaneous monitoring with about 3-d resolution for approximately 6 months.     

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.