Q2237+0305 source structure and dimensions from light curves 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 star-like objects in the lens galaxy. Such a model is a simplified version of that adopted to explain the brightness variations observed in Q0957 (Schild & Vakulik 2003). The microlensing light curves generated for a range of source parameters were compared to the light curves obtained in the framework of the OGLE 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 for the transverse velocity of the source, the effective size of the central source was determined to be about 2x10^15 cm, and Epsilon =2 was obtained for the ratio of the integral luminosity of the outer feature to that of the central source.Comment: 7 pages, 4 figures, LaTe

Gravitational potential of a homogeneous circular torus: new approach

The integral expression for gravitational potential of a homogeneous circular torus composed of infinitely thin rings is obtained. Approximate expressions for torus potential in the outer and inner regions are found. In the outer region a torus potential is shown to be approximately equal to that of an infinitely thin ring of the same mass; it is valid up to the surface of the torus. It is shown in a first approximation, that the inner potential of the torus (inside a torus body) is a quadratic function of coordinates. The method of sewing together the inner and outer potentials is proposed. This method provided a continuous approximate solution for the potential and its derivatives, working throughout the region.Comment: 10 pages, 9 figures, 1 table; some misprints in formulae were correcte

Time delays in PG1115+080: new estimates

We report new estimates of the time delays in the quadruple gravitationally lensed quasar PG1115+080, obtained from the monitoring data in filter R with the 1.5-m telescope at the Maidanak Mountain (Uzbekistan, Central Asia) in 2004-2006. The time delays are 16.4 days between images C and B, and 12 days between C and A1+A2, with image C being leading for both pairs. The only known estimates of the time delays in PG1115 are those based on observations by Schechter et al. (1997) -- 23.7 and 9.4 days between images C and B, C and A1+A2, respectively, as calculated by Schechter et al., and 25 and 13.3 days as revised by Barkana (1997) for the same image components with the use of another method. The new values of time delays in PG 1115+080 may be expected to provide larger estimates of the Hubble constant thus decreasing a diversity between the H_0 estimates taken from gravitationally lensed quasars and with other methods.Comment: 5 pages, 2 figures, Accepted for publication in MNRAS Letter

Asymptotic Expansions and Amplification of a Gravitational Lens Near a Fold Caustic

We propose two methods that enable us to obtain approximate solutions of the lens equation near a fold caustic with an arbitrary degree of accuracy. We obtain "post-linear" corrections to the well-known formula in the linear caustic approximation for the total amplification of two critical images of a point source. In this case, in order to obtain the nontrivial corrections we had to go beyond the approximation orders earlier used by Keeton et al. and to take into account the Taylor expansion of the lens equation near caustic up to the fourth order. Corresponding analytical expressions are derived for the amplification in cases of the Gaussian and power-law extended source models; the amplifications depend on three additional fitting parameters. Conditions of neglecting the correction terms are analysed. The modified formula for the amplification is applied to the fitting of light curves of the Q2237+0305 gravitational lens system in a vicinity of the high amplification events (HAEs). We show that the introduction of some "post-linear" corrections reduces chi^2 by 30% in the case of known HAE on the light curve of image C (1999). These corrections can be important for a precise comparison of different source models with regard for observational data. Key words: gravitational lensing: micro - quasars: individual (Q2237+0305) - gravitational lensing: strong - methods: analyticalComment: 16 pages, 3 figure

Q2237+0305 in X-rays: spectra and variability with XMM-Newton

X-ray observations of gravitationally lensed quasars may allow us to probe the inner structure of the central engine of a quasar. Observations of Q2237+0305 (Einstein Cross) in X-rays may be used to constrain the inner structure of the X-ray emitting source. Here we analyze the XMM-Newton observation of the quasar in the gravitational lens system Q2237+0305 taken during 2002. Combined spectra of the four images of the quasar in this system were extracted and modelled with a power-law model. Statistical analysis was used to test the variability of the total flux. The total X-ray flux from all the images of this quadruple gravitational lens system is 6 x 10^{-13} erg/cm2/s in the range 0.2-10 keV, showing no significant X-ray spectral variability during almost 42 ks of the observation time. Fitting of the cleaned source spectrum yields a photon power-law index of Gamma=1.82+0.07/-0.08. The X-ray lightcurves obtained after background subtraction are compatible with the hypothesis of a stationary flux from the source.Comment: 6 pages, 7 figures, 4 tables, accepted by A&

PG 1115+080: variations of the A2/A1 flux ratio and new values of the time delays

We report the results of our multicolor observations of PG 1115+080 with the 1.5-m telescope of the Maidanak Observatory (Uzbekistan, Central Asia) in 2001-2006. Monitoring data in filter R spanning the 2004, 2005 and 2006 seasons (76 data points) demonstrate distinct brightness variations of the source quasar with the total amplitude of almost 0.4 mag. Our R light curves have shown image C leading B by 16.4d and image (A1+A2) by 12d that is inconsistent with the previous estimates obtained by Schechter et al. in 1997 - 24.7d between B and C and 9.4d between (A1+A2) and C. The new values of time delays in PG 1115+080 must result in larger values for the Hubble constant, thus reducing difference between its estimates taken from the gravitational lenses and with other methods. Also, we analyzed variability of the A2/A1 flux ratio, as well as color changes in the archetypal "fold" lens PG 1115+080. We found the A1/A2 flux ratio to grow during 2001-2006 and to be larger at longer wavelengths. In particular, the A2/A1 flux ratio reached 0.85 in filter I in 2006. We also present evidence that both the A1 and A2 images might have undergone microlensing during 2001-2006, with the descending phase for A1 and initial phase for A2. We find that the A2/A1 flux ratio anomaly in PG 1115 can be well explained both by microlensing and by finite distance of the source quasar from the caustic fold.Comment: 14 pages, 7 figures, 8 tables, Accepted for publication in MNRA

The multiple quasar Q2237+0305 under a microlensing caustic

We use the high magnification event seen in the 1999 OGLE campaign light curve of image C of the quadruply imaged gravitational lens Q2237+0305 to study the structure of the quasar engine. We have obtained g'- and r'-band photometry at the Apache Point Observatory 3.5m telescope where we find that the event has a smaller amplitude in the r'-band than in the g'- and OGLE V-bands. By comparing the light curves with microlensing simulations we obtain constraints on the sizes of the quasar regions contributing to the g'- and r'-band flux. Assuming that most of the surface mass density in the central kiloparsec of the lensing galaxy is due to stars and by modeling the source with a Gaussian profile, we obtain for the Gaussian width 1.20 x 10^15 sqrt(M/0.1M_sun)cm < sigma_g' < 7.96 x 10^15 sqrt(M/0.1Msun) cm, where M is the mean microlensing mass, and a ratio sigma_r'/sigma_g'=1.25^{+0.45}_{-0.15}. With the limits on the velocity of the lensing galaxy from Gil-Merino et al. (2005) as our only prior, we obtain 0.60 x 10^15 sqrt(M/0.1Msun) cm < sigma_g' < 1.57 x 10^15 sqrt(M/0.1Msun) cm and a ratio sigma_r'/sigma_g'=1.45^{+0.90}_{-0.25} (all values at 68 percent confidence). Additionally, from our microlensing simulations we find that, during the chromatic microlensing event observed, the continuum emitting region of the quasar crossed a caustic at >72 percent confidence.Comment: Accepted for publication in A&A, 8 pages, 4 figures. Slightly modified compared to the original version: qualitative results unchanged, constraints on the r'/g' source size ratio now tighter due to correction of an error in the numerical treatment of the simulated light curve