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Characterizing the surfaces of rocky exoplanets via the scattered light will be an essential challenge to investigate the existence of life on habitable exoplanets. We present a simple reconstruction method for fractional areas of different surface types from photometric variations, or colors, of a second Earth. We create mock light curves for Earth without clouds using empirical data. Then these light curves are fitted to the isotropic scattering model consisting of 4 surface types: ocean, soil, snow and vegetation. In an idealized situation where the photometric errors are only photon shot noise, we are able to reproduce the fractional areas of those components fairly well. We may be even able to detect a signature of vegetation from the distinct feature of photosynthesis on the Earth, known as the red edge. In our reconstruction method, Rayleigh scattering due to the atmosphere has an important effect, and for terrestrial exoplanets with atmosphere similar to our Earth, it is possible to estimate the presence of oceans and an atmosphere simultaneously., Comment: 39 pages, 18 figures, matches published version in ApJ

We monitored the Doppler shift of the G0V star TrES-2 throughout a transit of its giant planet. The anomalous Doppler shift due to stellar rotation (the Rossiter-McLaughlin effect) is discernible in the data, with a signal-to-noise ratio of 2.9, even though the star is a slow rotator. By modeling this effect we find that the planet's trajectory across the face of the star is tilted by -9 +/- 12 degrees relative to the projected stellar equator. With 98% confidence, the orbit is prograde., Comment: ApJ, in press [15 pages]

We present spectroscopy of a transit of the exoplanet HD 189733b. By modeling the Rossiter-McLaughlin effect (the anomalous Doppler shift due to the partial eclipse of the rotating stellar surface), we find the angle between the sky projections of the stellar spin axis and orbit normal to be lambda = -1.4 +/- 1.1 deg. This is the third case of a ``hot Jupiter'' for which lambda has been measured. In all three cases lambda is small, ruling out random orientations with 99.96% confidence, and suggesting that the inward migration of hot Jupiters generally preserves spin-orbit alignment., Comment: ApJ Letters, in press

著者人数: 18名, Accepted: 2006-04-25, 資料番号: SA1000374000

We address the following question: How does one reliably distinguish rapid microlensing events from atmospheric or instrumental effects on observed brightness fluctuations of distant objects? Our approach was to do a controlled, albeit limited, experiment, the first of its kind: observe Q0957+561A,B simultaneously through filters of the same characteristics with two telescopes with comparable fields of view but separated sufficiently for atmospheric fluctuations to be independent. Over the 1998-1999 viewing season, we succeeded in obtaining simultaneous data on 14 of the 55 nights scheduled. Analysis of these data led to the following: (1) after correction for "blending" of the A and B images, most rapid microlensing candidate outliers disappeared, and the agreement of the photometry from the two telescopes improved to an rms difference of about 15 mmag; (2) no microlensing events of amplitude greater than 0.1 mag were observed in either data set over the entire run, nearly ruling out ~10-5 M☉ MACHOs as composing more than about half the dark matter in the lens galaxy, if the source size is 3 × 1014 cm.

The distribution of differential time delays \Delta t between images produced by strong gravitational lensing contains information on the mass distributions in the lensing objects as well as on cosmological parameters such as H_0. We derive an explicit expression for the conditional probability distribution function of time delays P(\Delta t|\theta), given an image separation between multiple images \theta, and related statistics. We consider lensing halos described by the singular isothermal sphere (SIS) approximation and by its generalization as proposed by Navarro, Frenk, & White (NFW) which has a density profile \rho \propto r^{-\alpha} in the innermost region. The time delay distribution is very sensitive to these profiles; steeper inner slopes tend to produce larger time delays. For example, if H_0=70 km/s/Mpc, a \Lambda-dominated cosmology and a source redshift z_S=1.27 are assumed, lenses with \theta=5'' produce a time delay of \Delta t[yr]=1.5^{+1.7}_{-0.9}, 0.39^{+0.37}_{-0.22}, 0.15^{+0.11}_{-0.09}, and 0.071^{+0.054}_{-0.038} (50% confidence interval), for SIS, generalized NFW with \alpha=1.5, \alpha=1.0, and \alpha=0.5, respectively. At a fixed image separation, the time delay is determined by the difference in the lensing potential between the position of the two images, which typically occur at different impact parameters. Although the values of \Delta t are proportional to the inverse of H_0, P(\Delta t|\theta) is rather insensitive to all other cosmological model parameters, source redshifts, magnification biases and so on. A knowledge of P(\Delta t|\theta) will also be useful in designing the observing program of future large scale synoptic variability surveys and for evaluating possible selection biases operating against large splitting lens systems., Comment: 27 pages, 9 figures, accepted for publication in ApJ

We report on a wide-area (48' x 9') imaging survey of faint galaxies in R and I bands toward the 1338+27 field where an unusual concentration of five QSOs at z\sim1.1, embedded in a larger-scale clustering of 23 QSOs, is known to exist. Using a quite homogeneous galaxy catalog with a detection completeness limit of I~23.5, we detect a significant clustering signature of faint red galaxies with I > 21 and R-I > 1.2 over a scale extending to ~20h^{-1}_{50} Mpc. Close examination of the color-magnitude diagram, the luminosity function, and the angular correlation function indeed suggests that those galaxies are located at z~1.1 and trace the underlying large-scale structure at that epoch, together with the group of 5 QSOs. Since the whole extent of the cluster of 23 QSOs (~70h^{-1}_{50} Mpc) is roughly similar to the local ``Great Wall'', the area may contain a high-redshift counterpart of superclusters in the local universe., 21 pages including 7 EPS color figures; accepted for publication for the Astrophysical Journal (2001)

We present an R- and J-band photometry of an optical transient that is likely to be associated with the gamma-ray burst event GRB 971214. Our first measurement took place 13 hr after the gamma-ray event. The brightness decayed with a power-law exponent α=-1.20±0.02, which is similar to those of GRB 970228 andGRB 970508, which had exponents of α=-1.10±0.04 and α=-1.141±0.014, respectively. The transient decayed monotonically during the first 4 days following the gamma-ray event in contrast with the optical transient associated with GRB 970508, which increased in brightness, peaking 2 days after the burst, before settling to a power-law decay.

Low amplitude (linear regime) cosmic density fluctuations lead to spatial variations in the locally measurable value of $H_0$ (denoted as $H_L$), $\delta_H \equiv (H_L-H_0)/H_0$, which are of order 3-6% (95% confidence interval) in a sphere of 200$ h^{-1}$Mpc in diameter, and of order 1-2% in a sphere of 400$ h^{-1}$Mpc in diameter, for three currently viable structure formation models (tilted CDM, $\Lambda$CDM, and open CDM) as normalized by the 4 year COBE DMR data. However, the true matter distribution power spectrum may differ from any of the currently viable models. For example, it may contain sharp features which have escaped detection so far. The measured CMB dipole velocity (the Galaxy's peculiar velocity with respect to the CMB rest frame) provides additional constraints on the probability distribution of $\delta_H$ that supplement our limited knowledge of the power spectrum. For a matter power spectrum which consists of the smooth power spectrum of a viable cosmological model plus a delta-function bump, we find that given the CMB dipole velocity, the 95% CL upper limit of $|\delta_H|$ increases approximately by a factor of two, but the probability distribution of $\delta_H$ is non-Gaussian, with increased probability at small $\delta_H$ compared to Gaussian. Abandoning model power spectra entirely, we find that the observed CMB dipole velocity alone provides a very robust limit, $\sqrt{< \delta_H^2 >_R}, Comment: Final version with very minor changes in wording. To appear in ApJ on May 1, 1998

We examine the possibility that a population of relic massive black holes, perhaps constituting an important component of the dark matter, might be indirectly detected via their occasional very strong gravitational lensing of individual luminous stars in distant external galaxies. For plausible, and in some respects conservative, values of the relevant physical parameters, we show that such events might be detected either in wide area surveys reaching routine CCD magnitude limits (such as the Sloan Digital Sky Survey) or in small field, very deep images (such as the Hubble Deep Field). Thus, it would be a challenging but not impossible task to detect or place limits on a cosmic population of relic massive black holes.

We present new analysis of multi-epoch, H-band, scattered light images of the AB Aur system. We used a Monte Carlo, radiative transfer code to simultaneously model the system's SED and H-band polarized intensity imagery. We find that a disk-dominated model, as opposed to one that is envelope dominated, can plausibly reproduce AB Aur's SED and near-IR imagery. This is consistent with previous modeling attempts presented in the literature and supports the idea that at least a subset of AB Aur's spirals originate within the disk. In light of this, we also analyzed the movement of spiral structures in multi-epoch H-band total light and polarized intensity imagery of the disk. We detect no significant rotation or change in spatial location of the spiral structures in these data, which span a 5.8 year baseline. If such structures are caused by disk-planet interactions, the lack of observed rotation constrains the location of the orbit of planetary perturbers to be >47 AU., 8 pages, 3 figures, 1 table, Accepted to ApJ

We present a new Subaru/HiCIAO high-contrast H-band polarized intensity (PI) image of a nearby transitional disk associated with TW Hydrae. The scattered light from the disk was detected from 0.2" to 1.5" (11 - 81 AU) and the PI image shows a clear axisymmetric depression in polarized intensity at ~ 0.4" (~ 20 AU) from the central star, similar to the ~ 80 AU gap previously reported from HST images. Azimuthal polarized intensity profile also shows the disk beyond 0.2" is almost axisymmetric. We discuss two possible scenarios explaining the origin of the polarized intensity depression: 1) a gap structure may exist at ~ 20 AU from the central star because of shallow slope seen in the polarized intensity profile, and 2) grain growth may be occurring in the inner region of the disk. Multi-band observations at NIR and millimeter/sub-millimeter wavelengths play a complementary role in investigating dust opacity and may help reveal the origin of the gap more precisely., 8 pages, 2 figures, ApJL accepted for publication

Debris disks around young main-sequence stars often have gaps and cavities which for a long time have been interpreted as possibly being caused by planets. In recent years, several giant planet discoveries have been made in systems hosting disks of precisely this nature, further implying that interactions with planets could be a common cause of such disk structures. As part of the SEEDS high-contrast imaging survey, we are surveying a population of debris disk-hosting stars with gaps and cavities implied by their spectral energy distributions, in order to attempt to spatially resolve the disk as well as to detect any planets that may be responsible for the disk structure. Here we report on intermediate results from this survey. Five debris disks have been spatially resolved, and a number of faint point sources have been discovered, most of which have been tested for common proper motion, which in each case has excluded physical companionship with the target stars. From the detection limits of the 50 targets that have been observed, we find that beta Pic b-like planets (~10 Mjup planets around G--A-type stars) near the gap edges are less frequent than 15--30%, implying that if giant planets are the dominant cause of these wide (27 AU on average) gaps, they are generally less massive than beta Pic b., 17 pages, 9 figures, accepted for publication in ApJ

We study the variability of major atmospheric absorption features in the disk-integrated spectra of the Earth with future application to Earth-analogs in mind, concentrating on the diurnal timescale. We first analyze observations of the Earth provided by the EPOXI mission, and find 5-20% fractional variation of the absorption depths of H2O and O2 bands, two molecules that have major signatures in the observed range. From a correlation analysis with the cloud map data from the Earth Observing Satellite (EOS), we find that their variation pattern is primarily due to the uneven cloud cover distribution. In order to account for the observed variation quantitatively, we consider a simple opaque cloud model, which assumes that the clouds totally block the spectral influence of the atmosphere below the cloud layer, equivalent to assuming that the incident light is completely scattered at the cloud top level. The model is reasonably successful, and reproduces the EPOXI data from the pixel-level EOS cloud/water vapor data. A difference in the diurnal variability patterns of H2O and O2 bands is ascribed to the differing vertical and horizontal distribution of those molecular species in the atmosphere. On the Earth, the inhomogeneous distribution of atmospheric water vapor is due to the existence of its exchange with liquid and solid phases of H2O on the planet's surface on a timescale short compared to atmospheric mixing times. If such differences in variability patterns were detected in spectra of Earth-analogs, it would provide the information on the inhomogeneous composition of their atmospheres., 10 pages, 8 figures, 4 tables, accepted for publication in ApJ

We present Subaru/HiCIAO H-band high-contrast images of the debris disk around HIP 79977, whose pres- ence was recently inferred from an infrared excess. Our images resolve the disk for the first time, allowing characterization of its shape, size, and dust grain properties. We use angular differential imaging (ADI) to reveal the disk geometry in unpolarized light out to a radius of ~2", as well as polarized differential imaging (PDI) to measure the degree of scattering polarization out to ~1.5". In order to strike a favorable balance between suppression of the stellar halo and conservation of disk flux, we explore the application of principal component analysis (PCA) to both ADI and reference star subtraction. This allows accurate forward modeling of the effects of data reduction on simulated disk images, and thus direct comparison with the imaged disk. The resulting best-fit values and well-fitting intervals for the model parameters are a surface brightness power-law slope of S_out = -3.2 [-3.6,-2.9], an inclination of i = 84{\deg} [81{\deg},86{\deg}], a high Henyey-Greenstein forward-scattering parameter of g = 0.45 [0.35, 0.60], and a non-significant disk-star offset of u = 3.0 [-1.5, 7.5] AU = 24 [-13, 61] mas along the line of nodes. Furthermore, the tangential linear polarization along the disk rises from ~10% at 0.5" to ~45% at 1.5". These measurements paint a consistent picture of a disk of dust grains produced by collisional cascades and blown out to larger radii by stellar radiation pressure., Comment: 6 pages, 4 figures, 1 table. Accepted for publication in ApJ Letters

CCD photometry of the gravitational lens system 0957+561A,B in the g and r bands was obtained on alternate nights, weather permitting, from December 1994 through May 1995 using the Double Imaging Spectrograph (DIS) on the Apache Point Observatory (APO) 3.5-meter telescope. The remote observing and fast instrument change capabilities of this facility allowed accumulation of light curves sampled frequently and consistently. The Honeycutt ensemble photometry algorithm was applied to the data set and yielded typical relative photometric errors of approximately 0.01 magnitudes. Image A exhibited a sharp drop of about 0.1 magnitudes in late December 1994; no other strong features were recorded in either image. This event displays none of the expected generic features of a microlensing-induced flux variation and is likely to be intrinsic to the quasar; if so, it should also be seen in the B image with the lensing differential time delay. We give the expected 1996 image B light curves based on two values of the time delay and brightness ratio which have been proposed and debated in the literature. Continued monitoring of the system in the first half of 1996 should easily detect the image B event and thus resolve the time-delay controversy.

We present high-contrast images of HR 4796 A taken with Subaru/HiCIAO in H-band, resolving the debris disk in scattered light. The application of specialized angular differential imaging methods (ADI) allows us to trace the inner edge of the disk with high precision, and reveals a pair of "streamers" extending radially outwards from the ansae. Using a simple disk model with a power-law surface brightness profile, we demonstrate that the observed streamers can be understood as part of the smoothly tapered outer boundary of the debris disk, which is most visible at the ansae. Our observations are consistent with the expected result of a narrow planetesimal ring being ground up in a collisional cascade, yielding dust with a wide range of grain sizes. Radiation forces leave large grains in the ring and push smaller grains onto elliptical, or even hyperbolic trajectories. We measure and characterize the disk's surface brightness profile, and confirm the previously suspected offset of the disk's center from the star's position along the ring's major axis. Furthermore, we present first evidence for an offset along the minor axis. Such offsets are commonly viewed as signposts for the presence of unseen planets within a disk's cavity. Our images also offer new constraints on the presence of companions down to the planetary mass regime (~9 Jupiter masses at 0.5", ~3 Jupiter masses at 1")., Comment: 6 pages, 4 figures, 1 table; accepted for publication in ApJ Letters

Radial velocity (RV) observations of an exoplanet system giving a value of MT sin(i) condition (i.e., give information about) not only the planet's true mass MT but also the value of sin(i) for that system (where i is the orbital inclination angle). Thus, the value of sin(i) for a system with any particular observed value of MT sin(i) cannot be assumed to be drawn randomly from a distribution corresponding to an isotropic i distribution, i.e., the presumptive prior distribution. Rather, the posterior distribution from which it is drawn depends on the intrinsic distribution of MT for the exoplanet population being studied. We give a simple Bayesian derivation of this relationship and apply it to several "toy models" for the intrinsic distribution of MT , on which we have significant information from available RV data in some mass ranges but little or none in others. The results show that the effect can be an important one. For example, even for simple power-law distributions of MT , the median value of sin(i) in an observed RV sample can vary between 0.860 and 0.023 (as compared to the 0.866 value for an isotropic i distribution) for indices of the power law in the range between –2 and +1, respectively. Over the same range of indices, the 95% confidence interval on MT varies from 1.0001-2.405 (α = –2) to 1.13-94.34 (α = +2) times larger than MT sin(i) due to sin(i) uncertainty alone. More complex, but still simple and plausible, distributions of MT yield more complicated and somewhat unintuitive posterior sin(i) distributions. In particular, if the MT distribution contains any characteristic mass scale Mc , the posterior sin(i) distribution will depend on the ratio of MT sin(i) to Mc , often in a non-trivial way. Our qualitative conclusion is that RV studies of exoplanets, both individual objects and statistical samples, should regard the sin(i) factor as more than a "numerical constant of order unity" with simple and well-understood statistical properties. We argue that reports of MT sin(i) determinations should be accompanied by a statement of the corresponding confidence bounds on MT at, say, the 95% level based on an explicitly stated assumed form of the true MT distribution in order to reflect more accurately the mass uncertainties associated with RV studies.

We investigate the impact of hierarchical galaxy merging on the statistics of gravitational lensing of distant sources. Since no definite theoretical predictions for the merging history of luminous galaxies exist, we adopt a parametrized prescription, which allows us to adjust the expected number of pieces comprising a typical present galaxy at z=0.65. The existence of global parameter relations for elliptical galaxies and constraints on the evolution of the phase space density in dissipationless mergers, allow us to limit the possible evolution of galaxy lens properties under merging. We draw two lessons from implementing this lens evolution into statistical lens calculations: (1) The total optical depth to multiple imaging (e.g. of quasars) is quite insensitive to merging. (2) Merging leads to a smaller mean separation of observed multiple images. Because merging does not reduce drastically the expected lensing frequency it cannot make $\lambda$-dominated cosmologies compatible with the existing lensing observations. A comparison with the data from the HST Snapshot Survey shows that models with little or no evolution of the lens population are statistically favored over strong merging scenarios. The specific merging scenario proposed by Toomre (1977) can be rejected (95\% level) by such a comparison. Some versions of the scenario proposed by Broadhurst, Ellis \& Glazebrook (1992), are statistically acceptable., Comment: uuencoded postscript file with figures

Gravitational lensing statistics can provide a direct and powerful test of cosmic structure formation theories. Since lensing tests, directly, the magnitude of the nonlinear mass density fluctuations on lines of sight to distant objects, no issues of 'bias' (of mass fluctuations with respect to galaxy density fluctuations) exist here, although lensing observations provide their own ambiguities of interpretation. We develop numerical techniques for generating model density distributions with the very large spatial dynamic range required by lensing considerations and for identifying regions of the simulations capable of multiple image lensing in a conservative and computationally efficient way that should be accurate for splittings significantly larger than 3 seconds. Applying these techniques to existing standard Cold dark matter (CDM) (Omega = 1) and Primeval Baryon Isocurvature (PBI) (Omega = 0.2) simulations (normalized to the Cosmic Background Explorer Satellite (COBE) amplitude), we find that the CDM model predicts large splitting (greater than 8 seconds) lensing events roughly an order-of-magnitude more frequently than the PBI model. Under the reasonable but idealized assumption that lensing structrues can be modeled as singular isothermal spheres (SIS), the predictions can be directly compared to observations of lensing events in quasar samples. Several large splitting (Delta Theta is greater than 8 seconds) cases are predicted in the standard CDM model (the exact number being dependent on the treatment of amplification bias), whereas none is observed. In a formal sense, the comparison excludes the CDM model at high confidence (essentially for the same reason that CDM predicts excessive small-scale cosmic velocity dispersions.) A very rough assessment of low-density but flat CDM model (Omega = 0.3, Lambda/3H(sup 2 sub 0) = 0.7) indicates a far lower and probably acceptable level of lensing. The PBI model is consistent with, but not strongly tested by, the available lensing data, and other open models would presumably do as well as PBI. These preliminary conclusions and the assumptions on which they are based can be tested and the analysis can be applied to other cosmogonic models by straightforward extension of the work presented here.

The evolution of nonlinear density fluctuations around the Jeans mass shortly after cosmological recombination is analyzed using a 3D hydrodynamics/dark--matter code. The Cosmic Background Radiation (CBR) exerts Compton friction on free electrons due to peculiar velocities. The dynamics therefore depends strongly on the gas ionization history. Under a variety of ionization conditions and in systems with or without non-baryonic components, the baryons lose angular momentum efficiently and collapse to form a compact optically--thick object which would probably quickly evolve into a massive black hole. Attention is concentrated on elucidating some of the novel physical effects in early cosmological collapses, but ways in which more realistic calculations might be made and in which the scenario could be incorporated into a more complete cosmogonic model are discussed., Comment: LaTeX file, figures not included. For hardcopy of figures contact BEST@IASSNS.BITNET. Institute for Advanced Study number AST 93/11-2

The presence of substructure in clusters of galaxies indicates that they have recently formed or accreted a significant fraction of their mass. The cosmic time at which this occurs is set in large part by the density of that region of space at very large redshift. If the distribution of density perturbations at high redshift is Gaussian, then the frequency of subclustering now is set by the mean density at recombination. Thus, the observed frequency of subclustering can be used to constrain. Surprisingly, plausible values of Lambda have little effect on this result. Unless three independent evaluations of the incidence of subclustering are all overestimates, or substructure lasts significantly longer than a crossing time in clusters, or perturbations at high redshift are not Gaussian, the universe is fairly dense (Omega sub 0 greater than about 0.5). The same line of argument suggests that direct observations (e.g., with Rosat) of evolution of the cluster population with shifts will provide a complementary direct measure of Omega sub 0.

Possible connections between the inhomogeneities responsible for the Lyman-alpha forest in quasar spectra and gravitational lensing effects are investigated. For most models of the Lyman-alpha forest, no significant lensing is expected. For some versions of the CDM model-based minihalo hypothesis, gravitational lensings on scales less than abour 0.1 arcsec would occur with a frequency approaching that with which ordinary galaxies cause arcsecond scale lensing.

Inflationary cosmological theories predict, and some more general aesthetic criteria suggest, that the large-scale spatial curvature of the universe k should be accurately zero (i.e., flat), a condition which is satisfied when the universe's present mean density and the value of the cosmological constant Lambda have certain pairs of values. Available data on the frequency of multiple image-lensing of high-redshift quasars by galaxies suggest that the cosmological constant cannot make a dominant contribution to producing a flat universe. In particular, if the mean density of the universe is as small as the baryon density inferred from standard cosmic nucleosynthesis calculations or as determined from typical dynamical studies of galaxies and galaxy clusters, then a value of Lambda large enough to produce a k = 0 universe would result in a substantially higher frequency of multiple-image lensing of quasars than has been observed so far. Shortcomings of the available lens data and uncertainties concerning galaxy properties allow some possibility of escaping this conclusion, but systematic searches for a gravitational lenses and continuing investigations of galaxy mass distributions should soon provide decisive information. It is also noted that nonzero-curvature cosmological models can account for the observed frequency of galaxy-quasar lens systems and for a variety of other constraints.

New optical and radio observations of the gravitational lens system 2016 + 112 are presented. Deep optical images reveal the presence of an extremely red galaxy located in the midst of the three radio positions. There is no evidence for a cluster of galaxies in the region; the lensing appears to be dominated by the new galaxy and the galaxy associated with the third radio source. The A image has remained constant in brightness since its discovery nearly a year ago, but B has faded by about 0.3 mag. A new spectrum of B shows that the equivalent widths of its emission lines have increased by roughly a factor of 2. A wide-field radio map shows that the postulated third image must either be more than 100 times fainter than A and B, or else lie close to one of the detected radio sources. The discovery of the new lensing mass makes the geometry of this lens system somewhat easier to understand, but no model based only on idealized mass distributions at the locations of the two known galaxies can explain all the observed properties. 18 references.

The Shane-Wirtanen galaxy count catalog gives the strong visual impression of large-scale linear or filamentary features in the galaxy distribution. Computer simulations of hierarchical galaxy clustering constructed to have two-, three-, and four-point autocorrelation functions like those observed do not have such an appearance. A simple and well-defined algorithm which maps and quantifies filamentary structure is developed. It appears to be successful in identifying those (and only those) filaments which the eye picks out in the Shane-Wirtanen catalog and thus provides an objective tool for studying these structures. A catalog and map of the most prominent Shane-Wirtanen filaments is given. Application of the algorithm to a computer simulation of hierarchical galaxy clustering reveals a set of visually less conspicuous filaments with statistical properties strikingly similar to those of the Shane-Wirtanen filaments in many respects. Long (> or approx. =10/sup 0/) filaments do occur significantly more frequently in the data than in the simulations and the real filaments do occur at slightly higher relative contrast than the simulation filaments. These facts may explain their greater visual impact. It is not yet clear whether the Shane-Wirtanen filaments can be understood in terms of simple hierarchical galaxy clustering models.

An analytical calculation is presented which determines the probability that the light from a distant quasar can be lensed by objects in a different redshift range. Three types of information are used to make the calculation: (1) the physical properties of the intervening scattering lenses; (2) the intrinsic properties of the quasars and (3) the selection procedures by which the quasar samples are acquired. A series of differential equations is given in which the probability is derived, and a number of recommendations are offered with respect to VLA and Space Telescope observations of quasars lensed in this way.