Lensing Probability Research Articles

New Limits on a Cosmological Constant from Statistics of Gravitational Lensing

We present new limits on cosmological parameters from the statistics of gravitational lensing, based on the recently revised knowledge of the luminosity function and internal dynamics of E/S0 galaxies that are essential in lensing high-redshift QSOs. We find that the lens models using updated Schechter parameters for such galaxies, derived from the recent redshift surveys combined with morphological classification, are found to give smaller lensing probabilities than were calculated earlier. Inconsistent adoption of these parameters from a mixture of various galaxy surveys gives rise to systematic biases in the results. We also show that less compact dwarf-type galaxies that largely dominate the faint part of the Schechter form luminosity function contribute little to lensing probabilities, so that earlier lens models overestimate incidents of small separation lenses. Applications of the lens models to the existing lens surveys indicate that reproduction of both the lensing probability of optical sources and the image separations of optical and radio lenses is significantly improved in the revised lens models. The likelihood analyses allow us to conclude that a flat universe with ?0=0.3 and ?0+?0=1 is preferable, and a matter-dominated flat universe with ?0=0 is ruled out at the 98% confidence level. These new limits are unaffected by the inclusion of uncertainties in the lens properties.

Do Lensing Statistics Rule out a Cosmological Constant?

We present new calculations of the gravitational lensing statistics following recent revised knowledge of the luminosity function and internal velocity dispersion of E/S0 galaxies which work as effective lenses for background high-redshift QSOs. We show that the theoretical prediction of the lensing statistics is much smaller than previously expected. In sharp contrast with the earlier statistics supporting an Ω0 = 1 universe, the reported small lensing probability from the Hubble Space Telescope (HST) snapshot lens survey is in best agreement with a low-density, flat universe with Ω0 ≃ 0.2 and Ω0 + λ0 = 1. The age of this universe, combined with the HST measurement of a high value of the Hubble constant H0, can be reconciled with the age of the oldest globular clusters in the Milky Way (ApJ, 1997, Vol. 489, in press).

Do Lensing Statistics Rule Out a Cosmological Constant?

We present new calculations of gravitational lensing statistics in view of recent revisions in our knowledge of the luminosity function and internal velocity dispersion of E/S0 galaxies that work as effective lenses for background high-redshift QSOs. We show that the theoretical prediction of the lensing statistics is much smaller than previously expected. In sharp contrast to earlier statistics supporting an Ω0 = 1 universe, the small lensing probability reported from the Hubble Space Telescope (HST) Snapshot Lens Survey is in best agreement with a low-density, flat universe with Ω0 0.2 and Ω0 + λ0 = 1. The age of this universe, combined with the HST measurement of a high value for the Hubble constant H0, can be reconciled with the age of the oldest globular clusters in the Milky Way.

Strong Gravitational Lensing and Velocity Function as Tools to Probe Cosmological Parameters: Current Constraints and Future Predictions

Constraints on cosmological models from strong gravitational lensing statistics are investigated. We pay particular attention to the role of the velocity function in the calculation of the lensing probability. The velocity function derived from the observed galaxy luminosity function, which is used in most previous work, is unable to predict the large separation lensing events. In this paper, we also use the Press-Schechter theory to construct a velocity function theoretically. Model predictions are compared with the observed velocity function and the HST snapshot survey. Comparison with the latter observation shows that the predictions based on the theoretical velocity function are consistent with the observed large separation events in COBE normalized low-density models, especially with a non-vanishing cosmological constant. Adopting the COBE normalization, however, we could find no model which simultaneously satisfies both the observed velocity function and the HST snapshot survey. We systematically investigate various uncertainties in the gravitational lensing statistics including finite core radius, the distance formula, magnification bias, and dust obscuration. The results are very sensitive to these effects as well as theoretical models for the velocity function, implying that current limits on the cosmological parameters should be interpreted with caution. Predictions for future surveys are also presented.

Cosmological Applications of Gravitational Lensing

It was recognized very early that the gravitational lens effect can be used as an efficient cosmological tool. Of the many researchers who foresaw the use of lensing, F. Zwicky and S. Refsdal should be explicitly mentioned. The perhaps most accurate predictions and foresights by these two authors are as follows: Zwicky estimated the probability that a distant object is multiply imaged to be about 1/400, and thus that the observation of this effect is “a certainty” [73] – his value, which was obtained by a very crude reasoning, is in fact very close to current estimates of the lensing probability of high-redshift QSOs. He predicted that the magnification caused by gravitational light deflection will allow a “deeper look” into the universe –in fact, the spectroscopy of very faint galaxies which are imaged into giant luminous arcs have yielded spectral information which would be very difficult to obtain without these ‘natural telescopes’. And third, Zwicky saw that gravitational lenses may be used to determine the mass of distant extragalactic objects[72] – in fact, the mass determination of clusters masses from giant luminous arcs is as least as accurate as other methods, but does not rely on special assumptions (like spherical symmetry, virial or thermal equilibrium) inherent in other methods, and the determination of the mass within the inner 0.9 arcseconds of the lensing galaxy in the quadruple QSO 2237+0305 to within 2% [52] is the most accurate extragalactic mass determination known. Refsdal predicted the use of gravitational lenses for determining cosmological parameters and for testing cosmological theories [48][49] – we shall return to these issues below.

Statistics of cosmological gamma-ray bursts: Source evolution, cosmological geometry, and relativistic beaming

view Abstract Citations (16) References (47) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Statistics of Cosmological Gamma-Ray Bursts: Source Evolution, Cosmological Geometry, and Relativistic Beaming Yi, Insu Abstract We calculate effects of source evolution, cosmological geometry, and luminosity distribution on statistics of gamma-ray bursts in the cosmological scenario. Nonstandard cosmological models affect the burst statistics in such a way that effects of source evolution or luminosity distribution may not be easily distinguishable from those of the cosmological geometry. The probability of gravitational lensing of gamma-ray bursts depends sensitively on source evolution, which suggests that detection of lensed bursts could not only confirm the cosmological origin itself but also give some constraints on source evolution. If gamma rays are emitted from sources in relativistic bulk motion such as collimated jets, observed gamma rays are strongly beamed. The apparent observed luminosity of the burst is a function of an angle between the observer's line of sight and the direction of bulk motion. We consider effects of apparent luminosity distributions (due to beaming) on the burst statistics. The predicted distributions of durations and the flux-duration relation differ greatly from those of the simplest cosmological model without beaming. Source evolution, luminosity distribution, and cosmological geometry are virtually indistinguishable from one another within the simplest statistical measures. More detailed statistical measures such as the distribution of durations or the peak-flux-duration relation may provide further information. Publication: The Astrophysical Journal Pub Date: August 1994 DOI: 10.1086/174506 Bibcode: 1994ApJ...431..543Y Keywords: Cosmology; Galactic Evolution; Galactic Structure; Gamma Ray Bursts; Gravitational Lenses; Luminosity; Radiation Sources; Astronomical Models; Relativistic Effects; Statistical Analysis; Astrophysics; COSMOLOGY: THEORY; GAMMA RAYS: BURSTS; METHODS: STATISTICAL full text sources ADS |

Gravitational microlensing of gamma-ray bursts

A Monte Carlo code is developed to calculate gravitational microlensing in three dimensions when the lensing optical depth is low or moderate (<= 0.25). The code calculates positions of microimages and time delays between the microimages. Assuming the gamma-ray bursters are cosmological, and adopting {OMEGA}_0_ = 0.15 in massive black holes (~10^6.5^ M_sun_), as proposed by Gnedin & Ostriker, we find that the lensing probability is 5% for those gamma-ray bursts for which the brightest (primary) microimages will be detectable by the BATSE experiment on board the Compton Gamma-Ray Observatory, and for which at least one secondary image is brighter than 25% of the primary image. The majority (90%) of lensed gamma-ray bursts should show a simple double- burst structure, as predicted by a single point mass lens model. A small fraction (~10%) should show complicated multiple events due to the collective effects of several point masses (black holes). Cosmological models with a significant fraction of mass density in massive compact objects (M > 10^6^ M_sun_) can be tested by searching for microlensing events in the current BATSE data. Our catalog generated by 10,000 Monte Carlo models is accessible through the computer network. The catalog can be used to take realistic selection effects into account.

A high-resolution gravitational lens survey

We have conducted a search for gravitationally lensed QSOs using the Canada-France-Hawaii telescope under very good seeing conditions (median 0″70 full width at half maximum). A sample of 104 bright (V<18.5 mag), high redshift (z≥1.5) QSOs was chosen to maximize the probability of lensing. At least two r band CCD exposures were obtained of almost every QSO, with a subsequent exposure in B if there was evidence of a close neighbor. Each QSO was carefully examined by visually comparing its contour plot with that of at least one reference star from the same field. Simulations were used to determine upper limits of detectability of a close companion

Statistics of gravitational lenses - The uncertainties

The assumptions in the analysis of gravitational lensing statistics are examined. Special emphasis is given to the uncertainties in the theoretical predictions. It is shown that a simple redshift cutoff model, which may result from galaxy evolution, can significantly reduce the lensing probability and explain the large mean separation of images in observed gravitational lenses. This effect may affect the constraint on the contribution of the cosmological constant to producing a flat universe from the number counts of the observed lenses. For the Omega(0) = 1 (filled beam) model, the lensing probability of early-type galaxies with finite core radii is reduced roughly by a factor of 2 for high-redshift quasars as compared with the corresponding singular isothermal sphere model. The finite core radius effect is about 20 percent for a lambda-dominated flat universe. It is also shown that the most recent galaxy luminosity function gives lensing probabilities that are smaller than previously estimated roughly by a factor of 3.

The probability of arc lensing by clusters of galaxies

view Abstract Citations (15) References (19) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Probability of Arc Lensing by Clusters of Galaxies Nemiroff, Robert J. ; Dekel, Avishai Abstract We examine the probability that clusters of galaxies act as gravitational lenses and create extended detectable arcs, or unusually elongated images, from distant sources. It is assumed that the clusters are isothermal spheres, and the sources are galaxies modeled as exponential disks. We consider detection thresholds in image shape (axial ratio, A, and angular extent θ), and in brightness (apparent surface brightness, s, or apparent magnitude, m). For galaxies of a given size, these thresholds define an axisymmetric source volume behind the cluster extending to a maximum redshift z_m_, within which a galaxy must fall to be lensed by the cluster into an arc. The number of detectable sources is then determined by integration over the number density of visible galaxies in this volume. We find that for a cluster like Abell 370 (σ ~ 1500 km s^-1^ and z_l_ ~ 0.37), the probability of observing giant arcs like those already found (A >= 15, θ >= 90^deg^) is about 1 in 200 for z_m_ = 0.72, and approaches 1 in 10 if the cluster is inspected down to a B_j_ surface brightness of 26.5 mag arcsec^-2^. Many more clusters should show distorted galaxy images which are unusually elongated perpendicular to the radius vector to the cluster center. For example, if nearby clusters of σ >= 1000 are inspected to a limiting B_j_ magnitude of 26.5, roughly 1 in 3 (1 in 16) should show a distorted galaxy with axial ratio >= 5 (>=10). Publication: The Astrophysical Journal Pub Date: September 1989 DOI: 10.1086/167776 Bibcode: 1989ApJ...344...51N Keywords: Computational Astrophysics; Galactic Clusters; Gravitational Lenses; Brightness Distribution; Red Shift; Velocity Distribution; Astrophysics; GALAXIES: CLUSTERING; GRAVITATIONAL LENSES full text sources ADS | data products SIMBAD (1) NED (1)

Random gravitational lensing

A simple three-dimensional approach to calculate the probability of observing gravitational lensing, caused by a chance superposition of lens and source, is presented. The formalism is then used to estimate the lensing probabilities in a number of astrophysical situations. As indicated in earlier works, we find that the chance of random gravitational lensing being detected locally is small, and the chance at extra-galactic distances is large.