4,685 research outputs found
KOI 1224, a Fourth Bloated Hot White Dwarf Companion Found With Kepler
We present an analysis and interpretation of the Kepler binary system KOI
1224. This is the fourth binary found with Kepler that consists of a thermally
bloated, hot white dwarf in a close orbit with a more or less normal star of
spectral class A or F. As we show, KOI 1224 contains a white dwarf with Teff =
14400 +/- 1100 K, mass = 0.20 +/- 0.02 Msun, and radius = 0.103 +/- 0.004 Rsun,
and an F-star companion of mass = 1.59 +/- 0.07 Msun that is somewhat beyond
its terminal-age main sequence. The orbital period is quite short at 2.69802
days. The ingredients that are used in the analysis are the Kepler binary light
curve, including the detection of the Doppler boosting effect; the NUV and FUV
fluxes from the Galex images of this object; an estimate of the spectral type
of the F-star companion; and evolutionary models of the companion designed to
match its effective temperature and mean density. The light curve is modelled
with a new code named Icarus which we describe in detail. Its features include
the full treatment of orbital phase-resolved spectroscopy, Doppler boosting,
irradiation effects and transits/eclipses, which are particularly suited to
irradiated eclipsing binaries. We interpret the KOI 1224 system in terms of its
likely evolutionary history. We infer that this type of system, containing a
bloated hot white dwarf, is the direct descendant of an Algol-type binary. In
spite of this basic understanding of the origin of KOI 1224, we discuss a
number of problems associated with producing this type of system with this
short of an short orbital period.Comment: 14 pages, 8 figures, 2 tables, submitted to Ap
Infrared Variability of the Gliese 569B System
Gliese 569B is a multiple brown dwarf system whose exact nature has been the
subject of several investigations over the past few years. Interpretation has
partially relied on infra-red photometry and spectroscopy of the resolved
components of the system. We present seeing limited Ks photometry over four
nights, searching for variability in this young low mass substellar system. Our
photometry is consistent with other reported photometry, and we report the
tentative detection of several periodic signals consistent with rotational
modulation due to spots on their surfaces. The five significant periods range
from 2.90 hours to 12.8 hours with peak to peak variabilities from 28 mmag to
62 mmag in the Ks band.
If both components are rotating with the shortest periods, then their
rotation axes are not parallel with each other, and the rotation axis of the Bb
component is not perpendicular to the Ba-Bb orbital plane. If Bb has one of the
longer rotational periods, then the Bb rotation axis is consistent with being
parallel to the orbital axis of the Ba-Bb system.Comment: 22 pages, 7 figures, accepted for publication in the Astrophysical
Journa
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Skeleton Structures and Origami Design
In this dissertation we study problems related to polygonal skeleton structures that have applications to computational origami. The two main structures studied are the straight skeleton of a simple polygon (and its generalizations to planar straight line graphs) and the universal molecule of a Lang polygon. This work builds on results completed jointly with my advisor Ileana Streinu.
Skeleton structures are used in many computational geometry algorithms. Examples include the medial axis, which has applications including shape analysis, optical character recognition, and surface reconstruction; and the Voronoi diagram, which has a wide array of applications including geographic information systems (GIS), point location data structures, motion planning, etc.
The straight skeleton, studied in this work, has applications in origami design, polygon interpolation, biomedical imaging, and terrain modeling, to name just a few. Though the straight skeleton has been well studied in the computational geometry literature for over 20 years, there still exists a significant gap between the fastest algorithms for constructing it and the known lower bounds.
One contribution of this thesis is an efficient algorithm for computing the straight skeleton of a polygon, polygon with holes, or a planar straight-line graph given a secondary structure called the induced motorcycle graph.
The universal molecule is a generalization of the straight skeleton to certain convex polygons that have a particular relationship to a metric tree. It is used in Robert Lang\u27s seminal TreeMaker method for origami design. Informally, the universal molecule is a subdivision of a polygon (or polygonal sheet of paper) that allows the polygon to be ``folded\u27\u27 into a particular 3D shape with certain tree-like properties. One open problem is whether the universal molecule can be rigidly folded: given the initial flat state and a particular desired final ``folded\u27\u27 state, is there a continuous motion between the two states that maintains the faces of the subdivision as rigid panels? A partial characterization is known: for a certain measure zero class of universal molecules there always exists such a folding motion. Another open problem is to remove the restriction of the universal molecule to convex polygons. This is of practical importance since the TreeMaker method sometimes fails to produce an output on valid input due the convexity restriction and extending the universal molecule to non-convex polygons would allow TreeMaker to work on all valid inputs. One further interesting problem is the development of faster algorithms for computing the universal molecule. In this thesis we make the following contributions to the study of the universal molecule. We first characterize the tree-like family of surfaces that are foldable from universal molecules. In order to do this we define a new family of surfaces we call Lang surfaces and prove that a restricted class of these surfaces are equivalent to the universal molecules. Next, we develop and compare efficient implementations for computing the universal molecule. Then, by investigating properties of broader classes of Lang surfaces, we arrive at a generalization of the universal molecule from convex polygons in the plane to non-convex polygons in arbitrary flat surfaces. This is of both practical and theoretical interest. The practical interest is that this work removes the case from Lang\u27s TreeMaker method that causes TreeMaker to fail to produce output in the presence of non-convex polygons. The theoretical interest comes from the fact that our generalization encompasses more than just those surfaces that can be cut out of a sheet of paper, and pertains to polygons that cannot be lied flat in the plane without self-intersections. Finally, we identify a large class of universal molecules that are not foldable by rigid folding motions. This makes progress towards a complete characterization of the foldability of the universal molecule
Geodesic Universal Molecules
The first phase of TreeMaker, a well-known method for origami design, decomposes a planar polygon (the “paper”) into regions. If some region is not convex, TreeMaker indicates it with an error message and stops. Otherwise, a second phases is invoked which computes a crease pattern called a “universal molecule”. In this paper we introduce and study geodesic universal molecules, which also work with non-convex polygons and thus extend the applicability of the TreeMaker method. We characterize the family of disk-like surfaces, crease patterns and folded states produced by our generalized algorithm. They include non-convex polygons drawn on the surface of an intrinsically flat piecewise-linear surface which have self-overlap when laid open flat, as well as surfaces with negative curvature at a boundary vertex
Stellar Variability: A Broad and Narrow Perspective
A broad near-infrared photometric survey is conducted of 1678 stars in the direction of the Ophiuchi ( Oph) star forming region using data from the 2MASS Calibration Database. The survey involves up to 1584 photometric measurements in the \emph{J}, \emph{H} and \emph{K} bands with an 1 day cadence spanning 2.5 years. Identified are 101 variable stars with \emph{K} band amplitudes from 0.044 to 2.31 mag and (\emph{J}-\emph{K}) color amplitudes ranging from 0.053 to 1.47 mag. Of the 72 Oph star cluster members, 79 are variable; in addition, 22 variable stars are identified as candidate members. The variability is categorized as periodic, long timescale, or irregular based on the \emph{K} time series morphology. The dominant variability mechanisms are assigned based on the correlation between the stellar color and single band variability. Periodic signals are found in 32 variable stars with periods between 0.49 to 92 days. The most common variability mechanism among these stars is rotational modulation of cool starspots. Periodic eclipse-like variability is identified in 6 stars with periods ranging from 3 to 8 days; in these cases the variability mechanism may be warped circumstellar material driven by a hot proto-Jupiter. Aperiodic, long time scale variability is identified in 31 stars with time series ranging from 64 to 790 days. The variability mechanism is split evenly between either variable extinction or mass accretion. The remaining 40 stars exhibit sporadic, aperiodic variability with no discernible time scale or variability mechanism.
Interferometric images of the active giant Andromedae ( And) were obtained for 27 epochs spanning November. 2007 to September, 2011. The \emph{H} band angular diameter and limb darkening coefficient of And are 2.777 0.027 mas and 0.241 0.014, respectively. Starspot properties are extracted via a parametric model and an image reconstruction program. High fidelity images are obtained from the 2009, 2010, and 2011 data sets. Stellar rotation, consistent with the photometrically determined period, is traced via starspot motion in 2010 and 2011. The orientation of And is fully characterized with a sky position angle and inclination angle of 23 and 78, respectively
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A First Order Analysis of Lighting, Shading, and Shadows
The shading in a scene depends on a combination of many factors---how the lighting varies spatially across a surface, how it varies along different directions, the geometric curvature and reflectance properties of objects, and the locations of soft shadows. In this paper, we conduct a complete first order or gradient analysis of lighting, shading and shadows, showing how each factor separately contributes to scene appearance, and when it is important. Gradients are well suited for analyzing the intricate combination of appearance effects, since each gradient term corresponds directly to variation in a specific factor. First, we show how the spatial {\em and} directional gradients of the light field change, as light interacts with curved objects. This extends the recent frequency analysis of Durand et al.\ to gradients, and has many advantages for operations, like bump-mapping, that are difficult to analyze in the Fourier domain. Second, we consider the individual terms responsible for shading gradients, such as lighting variation, convolution with the surface BRDF, and the object's curvature. This analysis indicates the relative importance of various terms, and shows precisely how they combine in shading. As one practical application, our theoretical framework can be used to adaptively sample images in high-gradient regions for efficient rendering. Third, we understand the effects of soft shadows, computing accurate visibility gradients. We generalize previous work to arbitrary curved occluders, and develop a local framework that is easy to integrate with conventional ray-tracing methods. Our visibility gradients can be directly used in practical gradient interpolation methods for efficient rendering
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