Gravitational Lensing Statistics Research Articles

Detection of the significant impact of source clustering on higher order statistics with DES Year 3 weak gravitational lensing data

ABSTRACT We measure the impact of source galaxy clustering on higher order summary statistics of weak gravitational lensing data. By comparing simulated data with galaxies that either trace or do not trace the underlying density field, we show that this effect can exceed measurement uncertainties for common higher order statistics for certain analysis choices. We evaluate the impact on different weak lensing observables, finding that third moments and wavelet phase harmonics are more affected than peak count statistics. Using Dark Energy Survey (DES) Year 3 (Y3) data, we construct null tests for the source-clustering-free case, finding a p-value of p = 4 × 10−3 (2.6σ) using third-order map moments and p = 3 × 10−11 (6.5σ) using wavelet phase harmonics. The impact of source clustering on cosmological inference can be either included in the model or minimized through ad hoc procedures (e.g. scale cuts). We verify that the procedures adopted in existing DES Y3 cosmological analyses were sufficient to render this effect negligible. Failing to account for source clustering can significantly impact cosmological inference from higher order gravitational lensing statistics, e.g. higher order N-point functions, wavelet-moment observables, and deep learning or field-level summary statistics of weak lensing maps.

DISTORTION OF THE LUMINOSITY FUNCTION OF HIGH-REDSHIFT GALAXIES BY GRAVITATIONAL LENSING

The observed properties of high redshift galaxies depend on the underlying foreground distribution of large scale structure, which distorts their intrinsic properties via gravitational lensing. We focus on the regime where the dominant contribution originates from a single lens and examine the statistics of gravitational lensing by a population of virialized and non-virialized structures using sub-mm galaxies at z ~ 2.6 and Lyman-break galaxies at redshifts z ~ 6 - 15 as the background sources. We quantify the effect of lensing on the luminosity function of the high redshift sources, focusing on the intermediate and small magnifications, mu < 2, which affect the majority of the background galaxies, and comparing to the case of strong lensing. We show that, depending on the intrinsic properties of the background galaxies, gravitational lensing can significantly affect the observed luminosity function even when no obvious strong lenses are present. Finally, we find that in the case of the Lyman-break galaxies it is important to account for the surface brightness profiles of both the foreground and the background galaxies when computing the lensing statistics, which introduces a selection criterion for the background galaxies that can actually be observed. Not taking this criterion into account leads to an overestimation of the number densities of very bright galaxies by nearly two orders of magnitude.

Statistics of gravitational lensing of a remote source on a system of extended and point massesin presence of an external shear

Statistics of gravitational lensing of a remote source on a system of extended and point massesin presence of an external shear

Effects of galaxy-halo alignment and adiabatic contraction on gravitational lens statistics

We study the strong gravitational lens statistics of triaxial cold dark matter (CDM) halos occupied by central early-type galaxies. We calculate the image separation distribution for double, cusp and quad configurations. The ratios of image multiplicities at large separations are consistent with the triaxial NFW model, and at small separations are consistent with the singular isothermal ellipsoid (SIE) model. At all separations, the total lensing probability is enhanced by adiabatic contraction. If no adiabatic contraction is assumed, naked cusp configurations become dominant at approximately 2.5'', which is inconsistent with the data. We also show that at small-to-moderate separations, the image multiplicities depend sensitively on the alignment of the shapes of the luminous and dark matter projected density profiles. In constrast to other properties that affect these ratios, the degree of alignment does not have a significant effect on the total lensing probability. These correlations may therefore be constrained by comparing the theoretical image separation distribution to a sufficiently large lens sample from future wide and deep sky surveys such as Pan-Starrs, LSST and JDEM. Understanding the correlations in the shapes of galaxies and their dark matter halo is important for future weak lensing surveys.

Testing the DGP model with gravitational lensing statistics

The self-accelerating braneworld model (DGP) seems to provide a simple alternative to the the standard $\Lambda$CDM cosmology to explain the current cosmic acceleration, which is strongly indicated by measurements of Type Ia supernovae, as well as other concordant observations. In this work, we investigate observational constraints on this scenario from gravitational lensing statistics using the Cosmic Lens All-Sky Survey (CLASS) lensing sample. We show that a large parameter space of the DGP model is in good agreement with this radio source gravitational lensing sample. In the flat case, $\Omega_\mathrm{K}=0$, the likelihood is maximized, ${\cal L}={\cal L_\mathrm{max}}$, for $\1 = 0.30_{-0.11}^{+0.19}$. If we relax the prior on $\Omega_\mathrm{K}$, the likelihood peaks at $\{\1,\2 \} \simeq \{0.29, 0.12\}$, just slightly in the region of open models. However the confidence contours are pretty elongated so that we can not discard either close or flat or open models

Is modified gravity required by observations? An empirical consistency test of dark energy models

We apply the technique of parameter splitting to existing cosmological data sets, to check for a generic failure of dark energy models. Given a dark energy parameter, such as the energy density ${\ensuremath{\Omega}}_{\ensuremath{\Lambda}}$ or equation of state $w$, we split it into two meta-parameters with one controlling geometrical distances, and the other controlling the growth of structure. Observational data spanning Type Ia Supernovae, the cosmic microwave background (CMB), galaxy clustering, and weak gravitational lensing statistics are fit without requiring the two meta-parameters to be equal. This technique checks for inconsistency between different data sets, as well as for internal inconsistency within any one data set (e.g., CMB or lensing statistics) that is sensitive to both geometry and growth. We find that the cosmological constant model is consistent with current data. Theories of modified gravity generally predict a relation between growth and geometry that is different from that of general relativity. Parameter splitting can be viewed as a crude way to parametrize the space of such theories. Our analysis of current data already appears to put sharp limits on these theories: assuming a flat universe, current data constrain the difference $\ensuremath{\Delta}{\ensuremath{\Omega}}_{\ensuremath{\Lambda}}={\ensuremath{\Omega}}_{\ensuremath{\Lambda}}(\mathrm{geom})\ensuremath{-}{\ensuremath{\Omega}}_{\ensuremath{\Lambda}}(\mathrm{grow})$ to be $\ensuremath{-}{0.0044}_{\ensuremath{-}0.0057\ensuremath{-}0.0119}^{+0.0058+0.0108}$ (68% and 95% C.L. respectively); allowing the equation of state $w$ to vary, the difference $\ensuremath{\Delta}w=w(\mathrm{geom})\ensuremath{-}w(\mathrm{grow})$ is constrained to be ${0.37}_{\ensuremath{-}0.36\ensuremath{-}0.53}^{+0.37+1.09}$. Interestingly, the region $w(\mathrm{grow})&gt;w(\mathrm{geom})$, which should be generically favored by theories that slow structure formation relative to general relativity, is quite restricted by data already. We find $w(\mathrm{grow})&lt;\ensuremath{-}0.80$ at $2\ensuremath{\sigma}$. As an example, the best-fit flat Dvali-Gabadadze-Porrati model approximated by our parametrization lies beyond the $3\ensuremath{\sigma}$ contour for constraints from all the data sets.

The Cosmic Lens All-Sky Survey parent population - I. Sample selection and number counts

We present the selection of the Jodrell Bank Flat-spectrum (JBF) radio source sample, which is designed to reduce the uncertainties in the Cosmic Lens All-Sky Survey (CLASS) gravitational lensing statistics arising from the lack of knowledge about the parent population luminosity function. From observations at 4.86 GHz with the Very Large Array, we have selected a sample of 117 flat-spectrum radio sources with flux densities greater than 5 mJy. These sources were selected in a similar manner to the CLASS complete sample and are therefore representative of the parent population at low flux densities. The vast majority (~90 per cent) of the JBF sample are found to be compact on the arcsecond scales probed here and show little evidence of any extended radio jet emission. Using the JBF and CLASS complete samples we find the differential number counts slope of the parent population above and below the CLASS 30 mJy flux density limit to be -2.07+/-0.02 and -1.96+/-0.12, respectively.

Constraints on the Velocity Dispersion Function of Early‐Type Galaxies from the Statistics of Strong Gravitational Lensing

We use the distribution of gravitationally lensed image separations observed in the Cosmic Lens All-Sky Survey (CLASS) and the PMN-NVSS Extragalactic Lens Survey (PANELS), which are (nearly) complete for the image separation range 03 ≤ Δθ ≤ 6'', to constrain a model velocity dispersion function (VF) of early-type galaxies. Assuming a current concordance cosmological model and adopting a singular isothermal ellipsoid (SIE) model for galactic potentials, we consider constraining both a characteristic velocity dispersion (parameter σ*) and the shape of the function (parameters α and β; from Sheth et al.) for 0.3 z 1. If all three parameters are allowed to vary, then none of the parameters can be tightly constrained by the lensing data because of the small size of the sample. If we fix the shape of the function by either the SDSS local stellar VF or an inferred local stellar VF based on the SSRS2 galaxy sample, then the constrained values of σ* are nearly equal to the corresponding stellar values; we have fSIE/center(≡ σ*,SIE/σ*,center) = 0.90 ± 0.18 (SDSS) or 1.04 ± 0.19 (SSRS2), assuming nonevolution of the function between the present epoch and z ~ 0.6. Finally, using only the CLASS statistical sample (from Browne et al.), and thus including an absolute multiple-imaging probability, we find that the SDSS stellar VF may have significantly underestimated the abundance of morphologically early-type galaxies.

Nonsingular Density Profiles of Dark Matter Halos and Strong Gravitational Lensing

We use the statistics of strong gravitational lenses to investigate whether mass profiles with a flat density core are supported. The probability for lensing by halos modeled by a nonsingular truncated isothermal sphere (NTIS) with image separations greater than a certain value (ranging from zero to ten arcseconds) is calculated. NTIS is an analytical model for the postcollapse equilibrium structure of virialized objects derived by Shapiro, Iliev & Raga. This profile has a soft core and matches quite well with the mass profiles of dark matter-dominated dwarf galaxies deduced from their observed rotation curves. It also agrees well with the NFW (Navarro-Frenk-White) profile at all radii outside of a few NTIS core radii. Unfortunately, comparing the results with those for singular lensing halos (NFW and SIS+NFW) and strong lensing observations, the probabilities for lensing by NTIS halos are far too low. As this result is valid for any other nonsingular density profiles (with a large core radius), we conclude that nonsingular density profiles (with a large core radius) for CDM halos are ruled out by statistics of strong gravitational lenses.

Improved Cosmological Constraints from Gravitational Lens Statistics

We combine the Cosmic Lens All-Sky Survey (CLASS) with new Sloan Digital Sky Survey (SDSS) data on the local velocity dispersion distribution function of E/S0 galaxies, $\phi(\sigma)$, to derive lens statistics constraints on $\Omega_\Lambda$ and $\Omega_m$. Previous studies of this kind relied on a combination of the E/S0 galaxy luminosity function and the Faber-Jackson relation to characterize the lens galaxy population. However, ignoring dispersion in the Faber-Jackson relation leads to a biased estimate of $\phi(\sigma)$ and therefore biased and overconfident constraints on the cosmological parameters. The measured velocity dispersion function from a large sample of E/S0 galaxies provides a more reliable method for probing cosmology with strong lens statistics. Our new constraints are in good agreement with recent results from the redshift-magnitude relation of Type Ia supernovae. Adopting the traditional assumption that the E/S0 velocity function is constant in comoving units, we find a maximum likelihood estimate of $\Omega_\Lambda = 0.74$--0.78 for a spatially flat unvierse (where the range reflects uncertainty in the number of E/S0 lenses in the CLASS sample), and a 95% confidence upper bound of $\Omega_\Lambda<0.86$. If $\phi(\sigma)$ instead evolves in accord with extended Press-Schechter theory, then the maximum likelihood estimate for $\Omega_\Lambda$ becomes 0.72--0.78, with the 95% confidence upper bound $\Omega_\Lambda<0.89$. Even without assuming flatness, lensing provides independent confirmation of the evidence from Type Ia supernovae for a nonzero dark energy component in the universe.

Effects of Ellipticity and Shear on Gravitational Lens Statistics

We study the effects of ellipticity in lens galaxies and external tidal shear from neighboring objects on the statistics of strong gravitational lenses. For isothermal lens galaxies normalized so that the Einstein radius is independent of ellipticity and shear, ellipticity reduces the lensing cross section slightly, and shear leaves it unchanged. Ellipticity and shear can significantly enhance the magnification bias, but only if the luminosity function of background sources is steep. Realistic distributions of ellipticity and shear lower the total optical depth by a few percent for most source luminosity functions, and increase the optical depth only for steep luminosity functions. The boost in the optical depth is noticeable (5%) only for surveys limited to the brightest quasars (L/L* 10). Ellipticity and shear broaden the distribution of lens image separations but do not affect the mean. Ellipticity and shear naturally increase the abundance of quadruple lenses relative to double lenses, especially for steep source luminosity functions, but the effect is not enough (by itself) to explain the observed quadruple-to-double ratio. With such small changes to the optical depth and image separation distribution, ellipticity and shear have a small effect on cosmological constraints from lens statistics: neglecting the two leads to biases of just ??M = 0.00 ? 0.01 and ??? = -0.02 ? 0.01 (where the error bars represent statistical uncertainties in our calculations).

The statistics of gravitational lenses in a clumpy Universe

We evaluate the effect of small-scale inhomogeneities on large-scale observations within the statistics of gravitationally lensed quasars. To this end, we consider a cosmological model whose large-scale properties (dynamics, matter distribution) are the same as in Friedmann–Lemaître models, but whose matter distribution is locally inhomogeneous. We use the well-known Dyer–Roder distances to allow a simple analytical expression of the optical depth τ, and pay particular attention to the different roles played by the different notions of distance (filled beam angular diameter distance and Dyer–Roder distances) when calculating this quantity, following the 1986 prescription of Ehlers & Schneider for a coherent formalism. We find that the expected number of gravitationally lensed quasars is a decreasing function of the clumpiness parameter α.

Constraints on the Cardassian Expansion from the Cosmic Lens All‐Sky Survey Gravitational Lens Statistics

The existence of a dark energy component has usually been invoked as the most plausible way to explain the recent observational results. However, it is also well known that effects arising from new physics (e.g., extra dimensions) can mimic the gravitational effects of a dark energy through a modification of the Friedmann equation. In this paper we investigate some observational consequences of a flat, matter-dominated, and accelerating/decelerating scenario in which this modification is given by H2 = g(ρm,n,q), where g(ρm,n,q) is a new function of the energy density ρm, the so-called generalized Cardassian models. We mainly focus our attention on the constraints from the recent Cosmic All-Sky Survey (CLASS) lensing sample on the parameters n and q that fully characterize the models. We show that, for a large interval of the q-n parametric space, these models are in agreement with the current gravitational lenses data. The influence of these parameters on the acceleration redshift, i.e., the redshift at which the universe begins to accelerate, and on the age of the universe at high-redshift is also discussed.

Gravitational Lensing as Probe of Large Scale Structure of the Universe

We apply gravitational lensing statistics to: (1) place a limit on the cosmological constant (ΩΛ); (2) place a limit on the average red-shift (&lt; z &gt;) of gamma-ray bursters (GRBs); (3) investigate models of galaxy evolution to see how compatible these models are with lensing statistics. We also point out the sources of uncertainty in lensing statistics, leading to uncertainty in the results.

Constraints on a quintessence model from gravitational lensing statistics

Constraints on an exact quintessence scalar-field model with an exponential potential are derived from gravitational lens statistics. An exponential potential can account for data from both optical quasar surveys and radio-selected sources. Based on the Cosmic Lens All-Sky Survey (CLASS) sample, lensing statistics provides, for the pressureless matter density parameter, an estimate of Ω M0 = 0.31 +0.12 -0.14 .

Constraints on Scalar-Field Dark Energy from the Cosmic Lens All-Sky Survey Gravitational Lens Statistics

We use the statistics of strong gravitational lensing based on Cosmic Lens All-Sky Survey (CLASS) data to constrain cosmological parameters in a spatially flat, inverse power-law potential energy density scalar-field dark energy cosmological model. The lensing-based constraints are consistent with, but weaker than, those derived from Type Ia supernova redshift-magnitude data, and mildly favor the Einstein cosmological constant limit of this dark energy model.

Constraints on Chaplygin quartessence from the CLASS gravitational lens statistics and supernova data

The nature of the dark components (dark matter and dark energy) that dominate the current cosmic evolution is a completely open question at present. In reality, we do not even know if they really constitute two separated substances. In this paper we use the recent Cosmic All Sky Survey (CLASS) lensing sample to test the predictions of one of the candidates for a unified dark matter/energy scenario, the so-called generalized Chaplygin gas (Cg) which is parametrized by an equation of state $p = -A/\rho_{Cg}^{\alpha}$ where $A$ and $\alpha$ are arbitrary constants. We show that, although the model is in good agreement with this radio source gravitational lensing sample, the limits obtained from CLASS statistics are only marginally compatible with the ones obtained from other cosmological tests. We also investigate the constraints on the free parameters of the model from a joint analysis between CLASS and supernova data.

The Effects of Massive Substructures on Image Multiplicities in Gravitational Lenses

Surveys for gravitational lens systems have typically found a significantly larger fraction of lenses with four (or more) images than are predicted by standard ellipsoidal lens models (50% versus 25%-30%). We show that including the effects of smaller satellite galaxies, with an abundance normalized by the observations, significantly increases the expected number of systems with more than two images and largely explains the discrepancy. The effect is dominated by satellites with ~20% the luminosity of the primary lens, in rough agreement with the typical luminosities of the observed satellites. We find that the lens systems with satellites cannot be dropped from estimates of the cosmological model based on gravitational lens statistics without significantly biasing the results.

Gravitational Lensing by Dark Matter Halos with Nonuniversal Density Profiles

The statistics of gravitational lensing can provide us with a very powerful probe of the mass distribution of matter in the universe. By comparing predicted strong lensing probabilities with observations, we can test the mass distribution of dark matter halos, in particular, the inner density slope. In this Letter, unlike previous work that directly models the density profiles of dark matter halos semianalytically, we generalize the density profiles of dark matter halos from high-resolution N-body simulations by means of generalized Navarro-Frenk-White (GNFW) models of three populations with slopes, α, of about -1.5, -1.3, and -1.1 for galaxies, groups, and clusters, respectively. This approach is an alternative and independent way to examine the slopes of mass-density profiles of halos. We present calculations of lensing probabilities using these GNFW profiles for three populations in various spatially flat cosmological models with a cosmological constant Λ. We show that the compound model of density profiles does not match well with the observed lensing probabilities derived from the Jodrell-Bank VLA Astrometric Survey data in combination with the Cosmic Lens All-Sky Survey data. Together with the previous work on lensing probability, our results suggest that a singular isothermal sphere mass model of less than about 1013 h-1 M☉ can predict strong lensing probabilities that are consistent with observations of small splitting angles.

Gravitational Lens Statistics as a Probe of Halo Profiles

Recent development of the structure formation theory based on the cold dark matter scenario implies that a number of larger separation lensed quasars, for which a confirmed detection has not yet been achieved, will be observed in the ongoing large-scale surveys such as the 2dF survey and SDSS. We show that statistics of such large separation lenses can be a powerful probe of the density profile of dark halos. After we summarize the current status of the lens surveys in the 2dF and SDSS, we focus our discussion on what information can be extracted from these lens surveys. in addition, we also propose statistics of differential time delays between multiple images as an alternative probe of the density profile of dark halos.