The Kuiper belt is a remnant of the primordial Solar System. Measurements of its size distribution constrain its accretion and collisional history, and the importance of material strength of Kuiper belt objects (KBOs)(1; 2; 3; 4). Small, sub-km sized, KBOs elude direct detection, but the signature of their occultations of background stars should be detectable (5; 6; 7; 8; 9). Observations at both optical(10) and Xray(11) wavelengths claim to have detected such occultations, but their implied KBO abundances are inconsistent with each other and far exceed theoretical expectations. Here, we report an analysis of archival data that reveals an occultation by a body with a ∼500 m radius at a distance of 45 AU. The probability of this event to occur due to random statistical fluctuations within our data set is about 2%. Our survey yields a surface density of KBOs with radii larger than 250 m of 2.1 +4.8 −1.7 × 10 7 deg −2 , ruling out inferred surface densities from previous claimed detections by more than 5 σ. The fact that we detected only one event, firmly shows a deficit of sub-km sized KBOs compared to a population extrapolated from objects with r > 50 km. This implies that sub-km-sized KBOs are undergoing collisional erosion, just like debris disks observed around other stars.A small KBO crossing the line of sight to a star will partially obscure the stellar light, an event which can be detected in the star's light curve. For visible light, the characteristic scale of diffraction effects, known as the Fresnel scale, is given by (λa/2) 1/2 ∼ 1.3 km, where a ∼ 40 AU is the distance to the Kuiper belt and λ ∼ 600 nm is the wavelength of our observations. Diffraction effects will be apparent in the star's light curve due to occulting KBOs provided that both star and the occulting object are smaller than the Fresnel scale (12; 13). Occultations by objects smaller than the Fresnel scale are in the Fraunhofer regime. In this regime the diffraction pattern is determined by the size of the KBO and its distance -2 -to the observer, the angular size of the star, the wavelength range of the observations and the impact parameter between the star and the KBO (see Supplementary Information for details). The duration of the occultation is approximately given by the ratio of the Fresnel scale to the relative velocity perpendicular to the line of sight between the observer and the KBO. Since the relative velocity is usually dominated by the Earth's velocity around the Sun, which is 30 km s −1 , typical occultations only last of order of a tenth of a second.Extensive ground based efforts have been conducted to look for optical occultations (10; 9; 14; 15). To date, these visible searches have announced no detections in the region of the Kuiper belt (30-60 AU), but one of these quests claims to have detected some events beyond 100 AU and at about 15 AU (10). Unfortunately, ground based surveys may suffer from a high rate of false-positives due to atmospheric scintillation, and lack the stability of space based platforms. The ground ...

We present here the analysis of about 19,500 new star hours of low ecliptic latitude observations (|b| ≤ 20 • ) obtained by the Hubble Space Telescope's Fine Guidance Sensors over a time span of more than nine years; which is an addition to the ∼ 12, 000 star hours previously analyzed by Schlichting et al. (2009). Our search for stellar occultations by small Kuiper belt objects (KBOs) yielded one new candidate event corresponding to a body with a 530 ± 70m radius at a distance of about 40 AU. Using bootstrap simulations, we estimate a probability of ≈ 5%, that this event is due to random statistical fluctuations within the new data set. Combining this new event with the single KBO occultation reported by Schlichting et al. (2009) we arrive at the following results: 1) The ecliptic latitudes of 6.6 • and 14.4 • of the two events are consistent with the observed inclination distribution of larger, 100 km-sized KBOs. 2) Assuming that small, sub-km sized KBOs have the same ecliptic latitude distribution as their larger counterparts, we find an ecliptic surface density of KBOs with radii larger than 250 m of N(r > 250 m) = 1.1 +1.5 −0.7 × 10 7 deg −2 ; if sub-km sized KBOs have instead a uniform ecliptic latitude distribution for −20 • < b < 20 • then N(r > 250 m) = 4.4 +5.8 −2.8 ×10 6 deg −2 . This is the best measurement of the surface density of sub-km sized KBOs to date. 3) Assuming the KBO size distribution can be well described by a single power law given by N(> r) ∝ r 1−q , where N(> r) is the number of KBOs with radii greater than r, and q is the power law index, we find q = 3.8±0.2 and q = 3.6±0.2 for a KBO ecliptic latitude distribution that follows the observed distribution for larger, 100-km sized KBOs and a uniform KBO ecliptic latitude distribution for −20 • < b < 20 • , respectively. 4) Regardless of the exact power law, our results suggest that small KBOs are numerous enough to satisfy the required supply rate for the Jupiter family comets. 5) We can rule out a single power law below the break with q > 4.0 at 2σ, confirming a strong deficit of sub-km sized KBOs compared to a population extrapolated from objects with r > 45 km. This suggests that small KBOs are undergoing collisional erosion and that the Kuiper belt is a true analogue to the dust producing debris disks observed around other stars.

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Data from the Hubble Space Telescope (HST) Fine Guidance Sensor (FGS) interferometers, covering 22 months of guide-star acquisition operations, have been analyzed for evidence of stellar duplicity. The data comprise a survey of observed guide stars, all of which are taken from the HST Guide Star Catalog, ranging in magnitude from 9 to 14. The survey results cover a parameter space for the newly found doubles, for the fainter stars, which are of smaller limiting angular separations than in any previous surveys. The normal HST engineering telemetry data from 13,979 acquisitions on 4882 stars have been processed. The FGS guidance data can reveal duplicity with separations ranging from approximately 30 mas, for the brighter stars, with small magnitude differences, up to the neighborhood of 500 mas, and in some cases to 1000 mas. The fraction of guide stars indicating duplicity is a function of the statistical criteria used but is over 5% at a very high level of confidence. It is possible that if some of the brighter and closer pairs could be identified as nearby, then their orbital motions would be rapid enough to allow a mass and distance determination on a timescale of a decade if followed with ground-based interferometric and spectroscopic instruments. A brief catalog of doubles is given, nearly all of which are of certain duplicity. Information for accessing on-line catalogs of large numbers of stars with lesser, but nevertheless strong, probabilities of duplicity and also for the solutions for duplicity from all acquisitions is provided.

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The social and economic impact of casino gambling has been a contentious issue in both the popular and academic press.  Prior academic research has focused largely on constructing piece-by-piece cost benefit accounting, but theoretical and measurement issues have prevented researchers from reaching a consensus as to the bottom line impact of casino gambling.  This paper uses a hedonic approach to estimate directly the implicit price and the welfare impacts of a casino on its local area.  The hedonic approach provides consistent estimates of the net change in social welfare without relying on a piecemeal approach to measuring costs and benefits.  Using data from the 1990 and 2000 U.S. Census of Population and Housing, the estimated net benefit of casino gambling at year 2000 levels was approximately 2% of household value, or about $2,000-$3,000 per household for households living near a casino.  Additionally, there are positive spillover effects to neighboring in-state regions and no significant costs to out-of-state border regions.  A particularly important finding for policymakers is that the benefits associated with a casino depend inversely on population density.  Casinos are more likely to create net benefits in areas where population density is low.

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