Which Radial Velocity Exoplanets Have Undetected Outer Companions?

(Abridged) The observed radial velocity (RV) eccentricity distribution for extrasolar planets in single-planet systems shows that a significant fraction of planets are eccentric ($e > 0.1$). Here we investigate the effects on an RV planet's eccentricity produced by undetected outer companions. We have carried out Monte Carlo simulations of mock RV data to understand this effect and predict its impact on the observed distribution. We first quantify the statistical effect of undetected outer companions and show that this alone cannot explain the observed distribution. We then modify the simulations to consist of two populations, one of zero-eccentricity planets in double-planet systems and the other of single planets drawn from an eccentric distribution. Our simulations show that a good fit to the observed distribution is obtained with 45% zero-eccentricity double-planets and 55% single eccentric planets. Matching the observed distribution allows us to determine the probability that a known RV planet's orbital eccentricity has been biased by an undetected wide-separation companion. Our simulations show that moderately-eccentric planets, with $0.1 < e < 0.3$ and $0.1 < e < 0.2$, have a $\sim 13$ and $\sim 19$ probability, respectively, of having an undetected outer companion. We encourage both high-contrast direct imaging and RV follow-up surveys of known RV planets with moderate eccentricities to test our predictions and look for previously undetected outer companions.Comment: 23 pages (12 text, 2 tables, 9 figures). Accepted to the Astrophysical Journal 30 June 200

LSST: Comprehensive NEO Detection, Characterization, and Orbits

(Abridged) The Large Synoptic Survey Telescope (LSST) is currently by far the most ambitious proposed ground-based optical survey. Solar System mapping is one of the four key scientific design drivers, with emphasis on efficient Near-Earth Object (NEO) and Potentially Hazardous Asteroid (PHA) detection, orbit determination, and characterization. In a continuous observing campaign of pairs of 15 second exposures of its 3,200 megapixel camera, LSST will cover the entire available sky every three nights in two photometric bands to a depth of V=25 per visit (two exposures), with exquisitely accurate astrometry and photometry. Over the proposed survey lifetime of 10 years, each sky location would be visited about 1000 times. The baseline design satisfies strong constraints on the cadence of observations mandated by PHAs such as closely spaced pairs of observations to link different detections and short exposures to avoid trailing losses. Equally important, due to frequent repeat visits LSST will effectively provide its own follow-up to derive orbits for detected moving objects. Detailed modeling of LSST operations, incorporating real historical weather and seeing data from LSST site at Cerro Pachon, shows that LSST using its baseline design cadence could find 90% of the PHAs with diameters larger than 250 m, and 75% of those greater than 140 m within ten years. However, by optimizing sky coverage, the ongoing simulations suggest that the LSST system, with its first light in 2013, can reach the Congressional mandate of cataloging 90% of PHAs larger than 140m by 2020.Comment: 10 pages, color figures, presented at IAU Symposium 23

The Blue Tip of the Stellar Locus: Measuring Reddening with the SDSS

We present measurements of reddening due to dust using the colors of stars in the Sloan Digital Sky Survey (SDSS). We measure the color of main sequence turn-off stars by finding the "blue tip" of the stellar locus: the prominent blue edge in the distribution of stellar colors. The method is sensitive to color changes of order 18, 12, 7, and 8 mmag of reddening in the colors u-g, g-r, r-i, and i-z, respectively, in regions measuring 90' by 14'. We present maps of the blue tip colors in each of these bands over the entire SDSS footprint, including the new dusty southern Galactic cap data provided by the SDSS-III. The results disfavor the best fit O'Donnell (1994) and Cardelli et al. (1989) reddening laws, but are well described by a Fitzpatrick (1999) reddening law with R_V = 3.1. The SFD dust map is found to trace the dust well, but overestimates reddening by factors of 1.4, 1.0, 1.2, and 1.4 in u-g, g-r, r-i, and i-z, largely due to the adopted reddening law. In select dusty regions of the sky, we find evidence for problems in the SFD temperature correction. A dust map normalization difference of 15% between the Galactic north and south sky may be due to these dust temperature errors.Comment: 18 pages, 22 figure

Differential algebras on kappa-Minkowski space and action of the Lorentz algebra

We propose two families of differential algebras of classical dimension on kappa-Minkowski space. The algebras are constructed using realizations of the generators as formal power series in a Weyl super-algebra. We also propose a novel realization of the Lorentz algebra so(1,n-1) in terms of Grassmann-type variables. Using this realization we construct an action of so(1,n-1) on the two families of algebras. Restriction of the action to kappa-Minkowski space is covariant. In contrast to the standard approach the action is not Lorentz covariant except on constant one-forms, but it does not require an extra cotangent direction.Comment: 16 page

Differential structure on kappa-Minkowski space, and kappa-Poincare algebra

We construct realizations of the generators of the $\kappa$-Minkowski space and $\kappa$-Poincar\'{e} algebra as formal power series in the $h$-adic extension of the Weyl algebra. The Hopf algebra structure of the $\kappa$-Poincar\'{e} algebra related to different realizations is given. We construct realizations of the exterior derivative and one-forms, and define a differential calculus on $\kappa$-Minkowski space which is compatible with the action of the Lorentz algebra. In contrast to the conventional bicovariant calculus, the space of one-forms has the same dimension as the $\kappa$-Minkowski space.Comment: 20 pages. Accepted for publication in International Journal of Modern Physics