BYU Physics and Astronomy

We use numerical simulations to measure the sensitivity of the tidal spin-down rate of a homogeneous triaxial ellipsoid to its axis ratios by comparing the drift rate in orbital semimajor axis to that of a spherical body with the same mass, volume and simulated rheology. We use a mass-spring model approximating a viscoelastic body spinning around its shortest body axis, with spin aligned with orbital spin axis, and in circular orbit about a point mass. The torque or drift rate can be estimated from that predicted for a sphere with equivalent volume if multiplied by $0.5 (1 + b^4/a^4)(b/a)^{-4/3} (c/a)^{-\alpha _c}$ where b/a and c/a are the body axis ratios and index αc ≈ 1.05 is consistent with the random lattice mass-spring model simulations but αc = 4/3 suggested by scaling estimates. A homogeneous body with axis ratios 0.5 and 0.8, like Haumea, has orbital semimajor axis drift rate about twice as fast as a spherical body with the same mass, volume and material properties. A simulation approximating a mostly rocky body but with 20 per cent of its mass as ice concentrated at its ends has a drift rate 10 times faster than the equivalent homogeneous rocky sphere. However, this increase in drift rate is not enough to allow Haumea's satellite, Hi'iaka, to have tidally drifted away from Haumea to its current orbital semimajor axis.

Hi’iaka is the larger outer satellite of the dwarf planet Haumea. Using relative photometry from the Hubble Space Telescope and Magellan and a phase dispersion minimization analysis, we have identified the rotation period of Hi’iaka to be ∼9.8 hr (double peaked). This is ∼120 times faster than its orbital period, creating new questions about the formation of this system and possible tidal evolution. The rapid rotation suggests that Hi’iaka could have a significant obliquity and spin precession that could be visible in light curves within a few years. We then turn to an investigation of what we learn about the (currently unclear) formation of the Haumea system and family based on this unexpectedly rapid rotation rate. We explore the importance of the initial semimajor axis and rotation period in tidal evolution theory and find that they strongly influence the time required to despin to synchronous rotation, relevant to understanding a wide variety of satellite and binary systems. We find that despinning tides do not necessarily lead to synchronous spin periods for Hi’iaka, even if it formed near the Roche limit. Therefore, the short rotation period of Hi’iaka does not rule out significant tidal evolution. Hi’iaka’s spin period is also consistent with formation near its current location and spin-up due to Haumea-centric impactors.

During the planet formation process, billions of comets are created and ejected into interstellar space. The detection and characterization of such interstellar comets (ICs) (also known as extra-solar planetesimals or extra-solar comets) would give us in situ information about the efficiency and properties of planet formation throughout the galaxy. However, no ICs have ever been detected, despite the fact that their hyperbolic orbits would make them readily identifiable as unrelated to the solar system. Moro-Martín et al. have made a detailed and reasonable estimate of the properties of the IC population. We extend their estimates of detectability with a numerical model that allows us to consider “close” ICs, e.g., those that come within the orbit of Jupiter. We include several constraints on a “detectable” object that allow for realistic estimates of the frequency of detections expected from the Large Synoptic Survey Telescope (LSST) and other surveys. The influence of several of the assumed model parameters on the frequency of detections is explored in detail. Based on the expectation from Moro-Martín et al., we expect that LSST will detect 0.001–10 ICs during its nominal 10 year lifetime, with most of the uncertainty from the unknown number density of small (nuclei of ∼0.1–1 km) ICs. Both asteroid and comet cases are considered, where the latter includes various empirical prescriptions of brightening. Using simulated LSST-like astrometric data, we study the problem of orbit determination for these bodies, finding that LSST could identify their orbits as hyperbolic and determine an ephemeris sufficiently accurate for follow-up in about 4–7 days. We give the hyperbolic orbital parameters of the most detectable ICs. Taking the results into consideration, we give recommendations to future searches for ICs.

NASA's Kepler Space Telescope has successfully discovered thousands of exoplanet candidates using the transit method, including hundreds of stars with multiple transiting planets. In order to estimate the frequency of these valuable systems, it is essential to account for the unique geometric probabilities of detecting multiple transiting extrasolar planets around the same parent star. In order to improve on previous studies that used numerical methods, we have constructed an efficient, semi-analytical algorithm called the Computed Occurrence of Revolving Bodies for the Investigation of Transiting Systems (CORBITS), which, given a collection of conjectured exoplanets orbiting a star, computes the probability that any particular group of exoplanets can be observed to transit. The algorithm applies theorems of elementary differential geometry to compute the areas bounded by circular curves on the surface of a sphere. The implemented algorithm is more accurate and orders of magnitude faster than previous algorithms, based on comparisons with Monte Carlo simulations. We use CORBITS to show that the present solar system would only show a maximum of three transiting planets, but that this varies over time due to dynamical evolution. We also used CORBITS to geometrically debias the period ratio and mutual Hill sphere distributions of Kepler's multi-transiting planet candidates, which results in shifting these distributions toward slightly larger values. In an Appendix, we present additional semi-analytical methods for determining the frequency of exoplanet mutual events, i.e., the geometric probability that two planets will transit each other (planet-planet occultation, relevant to transiting circumbinary planets) and the probability that this transit occurs simultaneously as they transit their star. The CORBITS algorithms and several worked examples are publicly available.

The primary Kepler Mission provided nearly continuous monitoring of similar to 200,000 objects with unprecedented photometric precision. We present the final catalog of eclipsing binary systems within the 105 deg(2) Kepler field of view. This release incorporates the full extent of the data from the primary mission (Q0-Q17 Data Release). As a result, new systems have been added, additional false positives have been removed, ephemerides and principal parameters have been recomputed, classifications have been revised to rely on analytical models, and eclipse timing variations have been computed for each system. We identify several classes of systems including those that exhibit tertiary eclipse events, systems that show clear evidence of additional bodies, heartbeat systems, systems with changing eclipse depths, and systems exhibiting only one eclipse event over the duration of the mission. We have updated the period and galactic latitude distribution diagrams and included a catalog completeness evaluation. The total number of identified eclipsing and ellipsoidal binary systems in the Kepler field of view has increased to 2878, 1.3% of all observed Kepler targets. An online version of this catalog with downloadable content and visualization tools is maintained at http://keplerEBs.villanova.edu.