Source Size Limitation from Variabilities of a Lensed Quasar

In the case of gravitationally-lensed quasars, it is well-known that there is a time delay between occurrence of the intrinsic variabilities in each split image. Generally, the source of variabilities has a finite size, and there are time delays even in one image. If the origin of variabilities is widely distributed, say over \gsim 100 pc as whole, variabilities between split images will not show a good correlation even though their origin is identical. Using this fact, we are able to limit the whole source size of variabilities in a quasar below the limit of direct resolution by today's observational instruments.Comment: 15 pages LaTeX, 3 figures, accepted to ApJ Letter. e-mail: [email protected]

Distances and Cosmology From Galaxy Cluster CMB Data

The measurement of angular diameter distance to galaxy clusters, through combined Sunyaev-Zel'dovich (SZ) effect data with X-ray emission observations, is now a well-known probe of cosmology. Using a combination of SZ data and a map of the lensed CMB anisotropies by the galaxy cluster potential, we propose an alternative geometric technique to measure distance information primarily through cluster related multi-frequency CMB measurements. We discuss necessary requirements to implement this measurement, potential errors including systematic biases, and the extent to which cosmological parameters can be extracted. While individual cluster distances are not likely to be precise, with upcoming subarcminute resolution wide-area CMB observations, useful information on certain cosmological parameters, such as the equation of state of dark energy, can be obtained from a large sample of galaxy clusters.Comment: 4 pages, 2 figure

New Modeling of the Lensing Galaxy and Cluster of Q0957+561: Implications for the Global Value of the Hubble Constant

The gravitational lens 0957+561 is modeled utilizing recent observations of the galaxy and the cluster as well as previous VLBI radio data which have been re-analyzed recently. The galaxy is modeled by a power-law elliptical mass density with a small core while the cluster is modeled by a non-singular power-law sphere as indicated by recent observations. Using all of the current available data, the best-fit model has a reduced chi-squared of approximately 6 where the chi-squared value is dominated by a small portion of the observational constraints used; this value of the reduced chi-squared is similar to that of the recent FGSE best-fit model by Barkana et al. However, the derived value of the Hubble constant is significantly different from the value derived from the FGSE model. We find that the value of the Hubble constant is given by H_0 = 69 +18/-12 (1-K) and 74 +18/-17 (1-K) km/s/Mpc with and without a constraint on the cluster's mass, respectively, where K is the convergence of the cluster at the position of the galaxy and the range for each value is defined by Delta chi-squared = reduced chi-squared. Presently, the best achievable fit for this system is not as good as for PG 1115+080, which also has recently been used to constrain the Hubble constant, and the degeneracy is large. Possibilities for improving the fit and reducing the degeneracy are discussed.Comment: 22 pages in aaspp style including 6 tables and 5 figures, ApJ in press (Nov. 1st issue

A determination of H_0 with the CLASS gravitational lens B1608+656: II. Mass models and the Hubble constant from lensing

EDITED FROM PAPER: We present mass models of the four-image gravitational lens system B1608+656. A mass model for the lens galaxies has been determined that reproduces the image positions, two out of three flux-density ratios and the model time delays. Using the time delays determined by Fassnacht et al. (1999a), we find that the best isothermal mass model gives H_0=59^{+7}_{-6} km/s/Mpc for Omega_m=1 and Omega_l=0.0, or H_0=(65-63)^{+7}_{-6} km/s/Mpc for Omega_m=0.3 and Omega_l = 0.0-0.7 (95.4% statistical confidence). A systematic error of +/-15 km/s/Mpc is estimated. This cosmological determination of H_0 agrees well with determinations from three other gravitational lens systems (i.e. B0218+357, Q0957+561 and PKS1830-211), SNe Ia, the S-Z effect and local determinations. The current agreement on H_0 from four out of five gravitational lens systems (i) emphasizes the reliability of its determination from isolated gravitational lens systems and (ii) suggests that a close-to-isothermal mass profile can describe disk galaxies, ellipticals and central cluster ellipticals. The average of H_0 from B0218+357, Q0957+561, B1608+656 and PKS1830-211, gives H_0(GL)=69 +/-7 km/s/Mpc for a flat universe with Omega_m=1 or H_0(GL)=74 +/-8 km/s/Mpc for Omega_m=0.3 and Omega_l=0.0-0.7. When including PG1115+080, these values decrease to 64 +/-11 km/s/Mpc and 68 +/-13 km/s/Mpc (2-sigma errors), respectively.Comment: Accepted for publication in ApJ. 34 pages, 4 figure

Constraining H0 from Chandra Observations of Q0957+561

We report the detection of the lens cluster of the gravitational lens (GL) system Q0957+561 from a deep observation with the Advanced CCD Imaging Spectrometer on-board the Chandra X-ray Observatory. Intracluster X-ray emission is found to be centered 4.3 +/- 1.3 arcsec east and 3.5(-0.6,+1.3) arcsec north of image B, nearer than previous estimates. Its spectrum can be modeled well with a thermal plasma model consistent with the emission originating from a cluster at a redshift of 0.36. Our best-fit estimates of the cluster temperature of T_e = 2.09(-0.54,+0.83) keV (90 percent confidence) and mass distribution of the cluster are used to derive the convergence parameter kappa, the ratio of the cluster surface mass density to the critical density required for lensing. We estimate the convergence parameter at the location of the lensed images A and B to be kappa_A = 0.22(+0.14,-0.07) and kappa_B = 0.21(+0.12,-0.07), respectively (90 percent confidence levels). The observed cluster center, mass distribution and convergence parameter kappa provide additional constraints to lens models of this system. Our new results break a mass-sheet degeneracy in GL models of this system and provide better constraints of ~ 29 percent (90 percent confidence levels) on the Hubble constant. We also present results from the detection of the most distant X-ray jet (z = 1.41) detected to date. The jet extends approximately 8 arcsec NE of image A and three knots are resolved along the X-ray jet with flux densities decreasing with distance from the core. The observed radio and optical flux densities of the knots are fitted well with a synchrotron model and the X-ray emission is modeled well with inverse Compton scattering of Cosmic Microwave Background photons by synchrotron-emitting electrons in the jet.Comment: 18 pages, includes 7 figures, Accepted for publication in Ap

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

Microlens Parallaxes with SIRTF

The Space Infrared Telescope Facility (SIRTF) will drift away from the Earth at about 0.1 AU/yr. Microlensing events will therefore have different characteristics as seen from the satellite and the Earth. From the difference, it is possible in principle to measure v-tilde, the transverse velocity of the lens projected onto the observer plane. Since v-tilde has very different values for different populations (disk, halo, Large Magellanic Cloud), such measurements could help identify the location, and hence the nature, of the lenses. I show that the method previously developed by Gould for measuring such satellite parallaxes fails completely in the case of SIRTF: it is overwhelmed by degeneracies which arise from fact that the Earth and satellite observations are in different band passes. I develop a new method which allows for observations in different band passes and yet removes all degeneracies. The method combines a purely ground-based measurement of the "parallax asymmetry" with a measurement of the delay between the time the event peaks at the Earth and satellite. In effect, the parallax asymmetry determines the component of v-tilde in the Earth-Sun direction, while the delay time measures the component of v-tilde in the direction of the Earth's orbit.Comment: 21 pages plus 3 figure

Probing For Machos of Mass 10−15M⊙10^{-15}M_\odot-10−7M⊙10^{-7}M_\odot with Gamma-Ray Burst Parallax Spacecraft

Two spacecraft separated by \sim 1\,\au and equipped with gamma-ray burst (GRB) detectors could detect or rule out a cosmological density of Massive Compact Halo Objects (MACHOs) in the mass range 10^{-15} M_{\odot}\lsim M \lsim 10^{-7} M_{\odot} provided that GRBs prove to be cosmological. Previously devised methods for detecting MACHOs have spanned the mass range 10^{-16} M_{\odot}\lsim M \lsim 10^{7} M_{\odot}, but with a gap of several orders of magnitude near $10^{-9} M_{\odot}$. For MACHOs and sources both at a cosmological distance, the Einstein radius is \sim 1\,\au\,(M/10^{-7} M_\odot)^{1/2}. Hence, if a GRB lies within the Einstein ring of a MACHO of mass M\lsim 10^{-7}M_\odot as seen by one detector, it will not lie in the Einstein ring as seen by a second detector \sim 1\,\au away. This implies that if GRBs are measured to have significantly different fluxes by the two detectors, this would signal the presence of a MACHO \lsim 10^{-7}M_\odot. By the same token, if the two detectors measured similar fluxes for several hundred events a cosmological abundance of such low-mass MACHOs would be ruled out. The lower limit of sensitivity, M\lsim 10^{-15}M_\odot is set by the finite size of the source. If low-mass MACHOs are detected, there are tests which can discriminate among events generated by MACHOs in the three mass ranges M\lsim 10^{-12}\,M_\odot, 10^{-12}\,M_\odot\lsim M\lsim 10^{-7}\,M_\odot, and M\gsim 10^{-7}\ M_\odot. Further experiments would then be required to make more accurate mass measurements.Comment: 8 pages, uuencoded postscript, no figure

Small-Angle Scattering of X-Rays from Extragalactic Sources by Dust in Intervening Galaxies

Gamma-ray bursts are now known to be a cosmological population of objects, which are often accompanied by X-ray and optical afterglows. The total energy emitted in the afterglow can be similar to the energy radiated in the gamma-ray burst itself. If a galaxy containing a large column density of dust is near the line of sight to a gamma-ray burst, small-angle scattering of the X-rays due to diffraction by the dust grains will give rise to an X-ray echo of the afterglow. A measurement of the angular size of the echo at a certain time after the afterglow is observed yields a combination of the angular diameter distances to the scattering galaxy and the gamma-ray burst that can be used to constrain cosmological models in the same way as a time delay in a gravitational lens. The scattering galaxy will generally cause gravitational lensing as well, and this should modify the shape of the X-ray echo from a circular ring. The main difficulty in detecting this phenomenon is the very low flux expected for the echo. The flux can be increased when the gamma-ray burst is highly magnified by gravitational lensing, or when the deflecting galaxy is at low redshift. X-ray echos of continuous (but variable) sources, such as quasars, may also be detectable with high-resolution instruments and would allow similar measurements.Comment: To be published in Ap

A comparison of approximate gravitational lens equations and a proposal for an improved new one

Keeping the exact general relativistic treatment of light bending as a reference, we compare the accuracy of commonly used approximate lens equations. We conclude that the best approximate lens equation is the Ohanian lens equation, for which we present a new expression in terms of distances between observer, lens and source planes. We also examine a realistic gravitational lensing case, showing that the precision of the Ohanian lens equation might be required for a reliable treatment of gravitational lensing and a correct extraction of the full information about gravitational physics.Comment: 11 pages, 6 figures, to appear on Physical Review