Engineering topics

Katherine M Deck

Publications and source records attributed to Katherine M Deck.

3 records

NASA NTRS2016

Transit Timing Variations for Planets Near Eccentricity-Type Mean Motion Resonances

We derive the transit timing variations (TTVs) of two planets near a second-order mean motion resonance (MMR) on nearly circular orbits. We show that the TTVs of each planet are given by sinusoids with a frequency of jn(sub 2) - ( j - 2)n(sub 1), where j ≽ 3 is an integer characterizing the resonance and n(sub 2) and n(sub 1) are the mean motions of the outer and inner planets, respectively. The amplitude of the TTV depends on the mass of the perturbing planet, relative to the mass of the star, and on both the eccentricities and longitudes of pericenter of each planet. The TTVs of the two planets are approximated anti-correlated, with phases of ϕ and ≈ϕ + π, where the phase ϕ also depends on the eccentricities and longitudes of pericenter. Therefore, the TTVs caused by proximity to a second-order MMR do not in general uniquely determine both planet masses, eccentricities, and pericenters. This is completely analogous to the case of TTVs induced by two planets near a first-order MMR. We explore how other TTV signals, such as the short-period synodic TTV or a first-order resonant TTV, in combination with the second-order resonant TTV, can break degeneracies. Finally, we derive approximate formulae for the TTVs of planets near any order eccentricity-type MMR; this shows that the same basic sinusoidal TTV structure holds for all eccentricity-type resonances. Our general formula reduces to previously derived results near first-order MMRs.

Celestial mechanics↗

NASA NTRS2016

Secure Mass Measurements From Transit Timing: 10 Kepler Exoplanets Between 3 and 8M⊕ with Diverse Densities and Incident Fluxes

We infer dynamical masses in eight multiplanet systems using transit times measured from Keplerʼs complete dataset, including short-cadence data where available. Of the 18 dynamical masses that we infer, 10 pass multiple tests for robustness. These are in systems Kepler-26 (KOI-250), Kepler-29 (KOI-738), Kepler-60 (KOI-2086), Kepler-105 (KOI-115), and Kepler-307 (KOI-1576). Kepler -105 c has a radius of 1.3R⊕ and a density consistent with an Earth-like composition. Strong transit timing variation (TTV) signals were detected from additional planets, but their inferred masses were sensitive to outliers or consistent solutions could not be found with independently measured transit times, including planets orbiting Kepler-49 (KOI-248), Kepler-57 (KOI-1270), Kepler-105 (KOI-115), and Kepler-177 (KOI-523). Nonetheless, strong upper limits on the mass of Kepler-177 cimply an extremely low density of 0.1 g cm−3. In most cases, individual orbital eccentricities were poorly constrained owing to degeneracies in TTV inversion. For five planet pairs in our sample, strong secular interactions imply a moderate to high likelihood of apsidal alignment over a wide range of possible eccentricities. We also find solutions for the three planets known to orbit Kepler-60 in a Laplace-like resonance chain. However, nonlibrating solutions also match the transit timing data. For six systems, we calculate more precise stellar parameters than previously known, enabling useful constraints on planetary densities where we have secure mass measurements. Placing these exoplanets on the mass–radius diagram, we find that a wide range of densities is observed among sub-Neptune-mass planets and that the range in observed densities is anticorrelated with incident flux.

Stars individual↗

NASA NTRS2016

Secure Mass Measurements From Transit Timing: 10 Kepler Exoplanets Between 3 and 8 M⊕ With Diverse Densities and Incident Fluxes

We infer dynamical masses in eight multiplanet systems using transit times measured from Keplerʼs complete data set, including short-cadence data where available. Of the 18 dynamical masses that we infer, 10 pass multiple tests for robustness. These are in systems Kepler-26 (KOI-250), Kepler-29 (KOI-738), Kepler-60 (KOI-2086), Kepler-105 (KOI-115), and Kepler-307 (KOI-1576). Kepler-105 c has a radius of 1.3 R(sub ⨁) and a density consistent with an Earth-like composition. Strong transit timing variation (TTV) signals were detected from additional planets, but their inferred masses were sensitive to outliers or consistent solutions could not be found with independently measured transit times, including planets orbiting Kepler-49 (KOI-248), Kepler-57 (KOI-1270), Kepler-105 (KOI-115), and Kepler-177 (KOI-523). Nonetheless, strong upper limits on the mass of Kepler-177 c imply an extremely low density of ∽0.1 g cm(exp −3). In most cases, individual orbital eccentricities were poorly constrained owing to degeneracies in TTV inversion. For five planet pairs in our sample, strong secular interactions imply a moderate to high likelihood of apsidal alignment over a wide range of possible eccentricities. We also find solutions for the three planets known to orbit Kepler-60 in a Laplace-like resonance chain. However, nonlibrating solutions also match the transit timing data. For six systems, we calculate more precise stellar parameters than previously known, enabling useful constraints on planetary densities where we have secure mass measurements. Placing these exoplanets on the mass–radius diagram, we find that a wide range of densities is observed among sub-Neptune-mass planets and that the range in observed densities is anticorrelated with incident flux.

Individual stars↗