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

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

Color Effects Associated with the 1999 Microlensing Brightness Peaks in Gravitationally Lensed Quasar Q2237+0305

Photometry of the Q2237+0305gravitational lens in VRI spectral bands with the 1.5-m telescope of the high-altitude Maidanak observatory in 1995-2000 is presented. Monitoring of Q2237+0305 in July-October 2000, made at nearly daily basis, did not reveal rapid (night-to-night and intranight) variations of brightness of the components during this time period. Rather slow changes of magnitudes of the components were observed, such as 0.08 mag fading of B and C components and 0.05 mag brightening of D in R band during July 23 - October 7, 2000. By good luck three nights in 1999 were almost at the time of the strong brightness peak of image C, and approximately in the middle of the ascending slope of the image A brightness peak. The C component was the most blue one in the system in 1998 and 1999, having changed its (V-I) color from 0.56 mag to 0.12 mag since August 1997, while its brightness increased almost 1.2 mag during this time period. The A component behaved similarly between August 1998 and August 2000, having become 0.47 mag brighter in R, and at the same time, 0.15 mag bluer. A correlation between the color variations and variations of magnitudes of the components is demonstrated to be significant and reaches 0.75, with a regression line slope of 0.33. A color (V-I) vrs color (V-R) plot shows the components settled in a cluster, stretched along a line with a slope of 1.31. Both slopes are noticeably smaller than those expected if a standard galactic interstellar reddening law were responsible for the differences between the colors of images and their variations over time. We attribute the brightness and color changes to microlensing of the quasar's structure, which we conclude is more compact at shorter wavelengths, as predicted by most quasar models featuring an energizing central source.Comment: 14 pages, 7 figures, LaTeX, submitted to A&

Direct Microlensing-Reverberation Observations of the Intrinsic magnetic Structure of AGN in Different Spectral States: A Tale of Two Quasars

We show how direct microlensing-reverberation analysis performed on two well-known Quasars (Q2237 - The Einstein Cross and Q0957 - The Twin) can be used to observe the inner structure of two quasars which are in significantly different spectral states. These observations allow us to measure the detailed internal structure of quasar Q2237 in a radio quiet high-soft state, and compare it to quasar Q0957 in a radio loud low-hard state. We find that the observed differences in the spectral states of these two quasars can be understood as being due to the location of the inner radii of their accretion disks relative to the co-rotation radii of rotating intrinsically magnetic supermassive compact objects in the centers of these quasars.Comment: 26 page manuscript with 2 tables and 2 figures, submitted to Astronomical Journa

Stars and dark matter in the spiral gravitational lens 2237+0305

We construct a mass model for the spiral lens galaxy 2237+0305, at redshift z_l=0.04, based on gravitational-lensing constraints, HI rotation, and new stellar-kinematic information, based on data taken with the ESI spectrograph on the 10m Keck-II Telescope. High resolution rotation curves and velocity dispersion profiles along two perpendicular directions, close to the major and minor axes of the lens galaxy, were obtained by fitting the Mgb-Fe absorption line region. The stellar rotation curve rises slowly and flattens at r~1.5" (~1.1 kpc). The velocity dispersion profile is approximately flat. A combination of photometric, kinematic and lensing information is used to construct a mass model for the four major mass components of the system -- the dark matter halo, disc, bulge, and bar. The best-fitting solution has a dark matter halo with a logarithmic inner density slope of gamma=0.9+/-0.3 for rho_DM propto r^-gamma, a bulge with M/L_B=6.6+/-0.3 Upsilon_odot, and a disc with M/L_B =1.2+/-0.3 Upsilon_odot, in agreement with measurements of late-type spirals. The bulge dominates support in the inner regions where the multiple images are located and is therefore tightly constrained by the observations. The disc is sub-maximal and contributes 45+/-11 per cent of the rotational support of the galaxy at 2.2r_d. The halo mass is (2.0+/-0.6) x 10^12 M_odot, and the stellar to virial mass ratio is 7.0+/-2.3 per cent, consistent with typical galaxies of the same mass.Comment: 14 pages, 6 figures, MNRAS, in pres