Using gravitational lenses to detect gravitational waves

Gravitational lenses could be used to detect gravitational waves, because a gravitational wave affects the travel-time of a light ray. In a gravitational lens, this effect produces time-delays between the different images. Thus the bending of light, which was the first experimental confirmation of Einstein's theory, can be used to search for gravitational waves, which are the most poorly confirmed aspect of that same theory. Applying this method to the gravitational lens 0957+561 gives new upper bounds on the amplitude of low-frequency gravitational waves in the universe, and new limits on the energy-density during an early ldquoinflationaryrdquo phase

Values of H_0 from Models of the Gravitational Lens 0957+561

The lensed double QSO 0957+561 has a well-measured time delay and hence is useful for a global determination of H0. Uncertainty in the mass distribution of the lens is the largest source of uncertainty in the derived H0. We investigate the range of \hn produced by a set of lens models intended to mimic the full range of astrophysically plausible mass distributions, using as constraints the numerous multiply-imaged sources which have been detected. We obtain the first adequate fit to all the observations, but only if we include effects from the galaxy cluster beyond a constant local magnification and shear. Both the lens galaxy and the surrounding cluster must depart from circular symmetry as well. Lens models which are consistent with observations to 95% CL indicate H0=104^{+31}_{-23}(1-\kthirty) km/s/Mpc. Previous weak lensing measurements constrain the mean mass density within 30" of G1 to be kthirty=0.26+/-0.16 (95% CL), implying H0=77^{+29}_{-24}km/s/Mpc (95% CL). The best-fitting models span the range 65--80 km/s/Mpc. Further observations will shrink the confidence interval for both the mass model and \kthirty. The range of H0 allowed by the full gamut of our lens models is substantially larger than that implied by limiting consideration to simple power law density profiles. We therefore caution against use of simple isothermal or power-law mass models in the derivation of H0 from other time-delay systems. High-S/N imaging of multiple or extended lensed features will greatly reduce the H0 uncertainties when fitting complex models to time-delay lenses.Comment: AASTEX, 48 pages 4 figures, 2 tables. Also available at: http://www.astro.lsa.umich.edu:80/users/philf/www/papers/list.htm

Magnification Ratio of the Fluctuating Light in Gravitational Lens 0957+561

Radio observations establish the B/A magnification ratio of gravitational lens 0957+561 at about 0.75. Yet, for more than 15 years, the optical magnfication ratio has been between 0.9 and 1.12. The accepted explanation is microlensing of the optical source. However, this explanation is mildly discordant with (i) the relative constancy of the optical ratio, and (ii) recent data indicating possible non-achromaticity in the ratio. To study these issues, we develop a statistical formalism for separately measuring, in a unified manner, the magnification ratio of the fluctuating and constant parts of the light curve. Applying the formalism to the published data of Kundi\'c et al. (1997), we find that the magnification ratios of fluctuating parts in both the g and r colors agrees with the magnification ratio of the constant part in g-band, and tends to disagree with the r-band value. One explanation could be about 0.1 mag of consistently unsubtracted r light from the lensing galaxy G1, which seems unlikely. Another could be that 0957+561 is approaching a caustic in the microlensing pattern.Comment: 12 pages including 1 PostScript figur

Improved Parameters and New Lensed Features for Q0957+561 from WFPC2 Imaging

New HST WFPC2 observations of the lensed double QSO 0957+561 will allow improved constraints on the lens mass distribution and hence will improve the derived value of H$_0$. We first present improved optical positions and photometry for the known components of this lens. The optical separation between the A and B quasar images agrees with VLBI data at the 10 mas level, and the optical center of the primary lensing galaxy G1 coincides with the VLBI source G' to within 10 mas. The best previous model for this lens (Grogin and Narayan 1996) is excluded by these data and must be reevaluated. Several new resolved features are found within 10\arcsec of G1, including an apparent fold arc with two bright knots. Several other small galaxies are detected, including two which may be multiple images of each other. We present positions and crude photometry of these objects.Comment: 7 pages including 2 postscript figures, LaTeX, emulateapj style. Also available at http://www.astro.lsa.umich.edu:80/users/philf/www/papers/list.htm

Analytic Time Delays and H_0 Estimates for Gravitational Lenses

We study gravitational lens time delays for a general family of lensing potentials, which includes the popular singular isothermal elliptical potential and singular isothermal elliptical density distribution but allows general angular structure. Using a novel approach, we show that the time delay can be cast in a very simple form, depending only on the observed image positions. Including an external shear changes the time delay proportional to the shear strength, and varying the radial profile of the potential changes the time delay approximately linearly. These analytic results can be used to obtain simple estimates of the time delay and the Hubble constant in observed gravitational lenses. The naive estimates for four of five time delay lenses show surprising agreement with each other and with local measurements of H_0; the complicated Q 0957+561 system is the only outlier. The agreement suggests that it is reasonable to use simple isothermal lens models to infer H_0, although it is still important to check this conclusion by examining detailed models and by measuring more lensing time delays.Comment: 16 pages with 2 embedded figures; submitted to Ap

The Mass distribution of the Cluster 0957+561 from Gravitational Lensing

Multiply gravitationally lensed objects with known time delays can lead to direct determinations of H$_0$ independent of the distance ladder if the mass distribution of the lens is known. Currently, the double QSO 0957+561 is the only lensed object with a precisely known time delay. The largest remaining source of systematic error in the H$_0$ determination results from uncertainty in the mass distribution of the lens which is comprised of a massive galaxy (G1) and the cluster in which it resides. We have obtained V-band CCD images from CFHT in order to measure the mass distribution in the cluster from its gravitional distorting effect on the appearance of background galaxes. We use this data to constuct a two-dimensional mass map of the field. A mass peak is detected at the $4.5\sigma$ level, offset from, but consistent with, the position of G1. Simple tests reveal no significant substructure and the mass distribution is consistent with a spherical cluster. The peak in the number density map of bright galaxies is offset from G1 similarly to the mass peak. We constructed an azimuthally averaged mass profile centered on G1 out to 2 \arcmin ($400 h^{-1}$ kpc). It is consistent with an isothermal mass distribution with a small core (r_c \approx 5 \arcsec = 17 h^{-1} kpc). The inferred mass within 1 Mpc is consistent with the dynamical mass estimate but $2\sigma$ higher than the upper limits from a ROSAT X-ray study. We discuss implications for H$_0$ in a future paper.Comment: LaTeX, aas version 4 macros. Calibration error in original led to overestimate of cluster mass. Seven out of twelve figures included. Complete paper is available at: http://www.astro.lsa.umich.edu:80/users/philf