arXiv subjects

Donald R. Short

Publications and source records attributed to Donald R. Short.

15 recordsLinked to original sources

arXiv2021

Photodynamical Modeling of the Fascinating Eclipses in the Triple-Star System KOI-126

We explore the fascinating eclipses and dynamics of the compact hierarchical triple star system KOI-126 (KIC 5897826). This system is comprised of a pair of M-dwarf stars (KOI-126 B and C) in a 1.74 day orbit which revolve around an F-star (KOI-126 A) every 34 days. Complex eclipse shapes are created as the M stars transit the F star, due to two effects: (i) the duration of the eclipse is a significant fraction of the M-star orbital period, so the prograde or retrograde motion of the M stars in their orbit lead to unusually short or long duration eclipses; (ii) due to 3-body dynamics, the M-star orbit precesses with an astonishingly quick timescale of 1.74 years for the periastron (apsidal) precession, and 2.73 years for the inclination and nodal angle precession. Using the full Kepler data set, supplemented with ground-based photometry, plus 29 radial velocity measurements that span 6 years, our photodynamical modeling yields masses of $M_{A} = 1.2713 \pm 0.0047 M_{\odot}$ (0.37%), $M_{B} = 0.23529 \pm 0.00062 M_{\odot}$ (0.26%), and $M_{C} = 0.20739 \pm 0.00055 M_{\odot}$ (0.27%) and radii of $R_{A} = 1.9984 \pm 0.0027 R_{\odot}$ (0.14%), $R_{B}= 0.25504 \pm 0.00076 R_{\odot}$ (0.3%), and $R_{C} = 0.23196 \pm 0.00069 R_{\odot}$ (0.3%). We also estimate the apsidal motion constant of the M-dwarfs, a parameter that characterizes the internal mass distribution. While not particularly precise, we measure a mean apsidal motion constant, $\overline{k_{2}}$, of $ 0.046^{+0.046}_{-0.028}$, which is approximately 2-$σ$ lower than the theoretical model prediction of 0.150. We explore possible causes for this discrepancy.

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arXiv2020

Fast Transit Computation Using Tabulated Stellar Intensities

Limb darkening laws are convenient parameterizations of the stellar intensity center-to-limb variation, and their use is ubiquitous in eclipse and transit modeling. But they are not "laws" in any sense -- they are simple approximations of the real intensity variations, and their limitations are becoming more and more apparent as stellar atmosphere models improve and higher precision data become available. When fitting eclipses and transit light curves, one would ideally like to use model intensities that are based on fundamental stellar parameters such as the mass, radius, and effective temperature of the star, rather than a limb darkening law representation and its coefficients. This is especially true when attempting to detect higher-order effects such as planetary oblateness, rings, satellites, or atmospheres. However, using model intensities requires numerically integrating many small-area "tiles" on the model stellar surface(s) and this has traditionally been too computationally expensive for general use. Here we present a fast technique to compute light curves and the Rossiter-McLaughlin effect that uses tabulated stellar models intensities. This is a step in the development of tools that obviate the need for limb darkening laws.

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arXiv2020

TOI-1338: TESS' First Transiting Circumbinary Planet

We report the detection of the first circumbinary planet found by TESS. The target, a known eclipsing binary, was observed in sectors 1 through 12 at 30-minute cadence and in sectors 4 through 12 at two-minute cadence. It consists of two stars with masses of 1.1 MSun and 0.3 MSun on a slightly eccentric (0.16), 14.6-day orbit, producing prominent primary eclipses and shallow secondary eclipses. The planet has a radius of ~6.9 REarth and was observed to make three transits across the primary star of roughly equal depths (~0.2%) but different durations -- a common signature of transiting circumbinary planets. Its orbit is nearly circular (e ~ 0.09) with an orbital period of 95.2 days. The orbital planes of the binary and the planet are aligned to within ~1 degree. To obtain a complete solution for the system, we combined the TESS photometry with existing ground-based radial-velocity observations in a numerical photometric-dynamical model. The system demonstrates the discovery potential of TESS for circumbinary planets, and provides further understanding of the formation and evolution of planets orbiting close binary stars.

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arXiv2019

Stellar Properties of KIC 8736245: An Eclipsing Binary with a Solar-type Star Leaving the Main Sequence

There is a well-known stellar parameter discrepancy for late K and M dwarfs, in that the observed radii and temperatures are often respectively larger and cooler than predicted by theory by several percent. In an on-going effort to elucidate this issue, we examine the double-lined Kepler eclipsing binary star system KIC 8736245. We supplement the near-continuous 4-year Kepler light curve with ground-based multicolor photometry from Mount Laguna Observatory and spectroscopy from the Hobby-Eberly Telescope. The binary has an edge-on, circular 5.07 day orbit with stellar masses equal to $0.987\pm0.009$ and $0.782\pm0.009\,\text{M}_\odot$ and radii of $1.311 \pm 0.006$ and $0.804 \pm 0.004\,\text{R}_\odot$, respectively, and an estimated age of 7-9 Gyr. We find that the stellar radii are consistent with theoretical models within the uncertainties, whereas the temperature of the secondary star is $\sim$6% cooler than predicted. An important aspect of this work is that the uncertainties derived from a single epoch (individual night of observations) underestimates the overall system parameter uncertainties due to the effect of the 1-4% fluctuations caused by stellar activity. Our error estimates come from the spread in parameters measured at 8 epochs. From the periodicities in the light curve and from the eclipse times, we measure candidate spin periods to be approximately 4.98 and 5.87 days for the primary and secondary star. Surprisingly, these imply super- and sub-synchronous rotation compared to the orbital period. Thus KIC 8736245 serves as an interesting case study for the exchange of angular momentum and general stellar astrophysics as stars in binaries evolve off the main sequence.

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arXiv2019

Note on the Power-2 Limb Darkening Law

Recently there has been a renewed interest in the power-2 limb darkening law for modeling exoplanet transits. This law provides a better match to the intensities generated by spherical stellar atmosphere models than other 2-parameter laws. To help facilitate a wider use of the power-2 law we correct a minor error and, expanding on previous work, suggest a parametrization that can improve the sampling required by some numerical methods such as MCMC.

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arXiv2019

Discovery of a Third Transiting Planet in the Kepler-47 Circumbinary System

Of the nine confirmed transiting circumbinary planet systems, only Kepler-47 is known to contain more than one planet. Kepler-47 b (the "inner planet") has an orbital period of 49.5 days and a radius of about $3\,R_{\oplus}$. Kepler-47 c (the "outer planet") has an orbital period of 303.2 days and a radius of about $4.7\,R_{\oplus}$. Here we report the discovery of a third planet, Kepler-47 d (the "middle planet"), which has an orbital period of 187.4 days and a radius of about $7\,R_{\oplus}$. The presence of the middle planet allows us to place much better constraints on the masses of all three planets, where the $1σ$ ranges are less than $26\,M_{\oplus}$, between $7-43\,M_{\oplus}$, and between $2-5\,M_{\oplus}$ for the inner, middle, and outer planets, respectively. The middle and outer planets have low bulk densities, with $ρ_{\rm middle} < 0.68$ g cm$^{-3}$ and $ρ_{\rm outer} < 0.26$ g cm$^{-3}$ at the $1σ$ level. The two outer planets are "tightly packed," assuming the nominal masses, meaning no other planet could stably orbit between them. All of the orbits have low eccentricities and are nearly coplanar, disfavoring violent scattering scenarios and suggesting gentle migration in the protoplanetary disk.

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arXiv2016

Kepler-1647b: the largest and longest-period Kepler transiting circumbinary planet

We report the discovery of a new Kepler transiting circumbinary planet (CBP). This latest addition to the still-small family of CBPs defies the current trend of known short-period planets orbiting near the stability limit of binary stars. Unlike the previous discoveries, the planet revolving around the eclipsing binary system Kepler-1647 has a very long orbital period (~1100 days) and was at conjunction only twice during the Kepler mission lifetime. Due to the singular configuration of the system, Kepler-1647b is not only the longest-period transiting CBP at the time of writing, but also one of the longest-period transiting planets. With a radius of 1.06+/-0.01 RJup it is also the largest CBP to date. The planet produced three transits in the light-curve of Kepler-1647 (one of them during an eclipse, creating a syzygy) and measurably perturbed the times of the stellar eclipses, allowing us to measure its mass to be 1.52+/-0.65 MJup. The planet revolves around an 11-day period eclipsing binary consisting of two Solar-mass stars on a slightly inclined, mildly eccentric (e_bin = 0.16), spin-synchronized orbit. Despite having an orbital period three times longer than Earth's, Kepler-1647b is in the conservative habitable zone of the binary star throughout its orbit.

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arXiv2014

KIC 9632895 - The 10th Kepler Transiting Circumbinary Planet

We present the discovery of KIC 9632895b, a 6.2 Earth-radius planet in a low-eccentricity, 240.5-day orbit about an eclipsing binary. The binary itself consists of a 0.93 and 0.194 solar mass pair of stars with an orbital period of 27.3 days. The plane of the planet's orbit is rapidly precessing, and its inclination only becomes sufficiently aligned with the primary star in the latter portion of the Kepler data. Thus three transits are present in the latter half of the light curve, but none of the three conjunctions that occurred during the first half of the light curve produced transits. The precession period is ~103 years, and during that cycle, transits are visible only ~8% of the time. This has the important implication that for every system like KIC 9632895 that we detect, there are ~12 circumbinary systems that exist but are not currently exhibiting transits. The planet's mass is too small to noticeably perturb the binary, consequently its mass is not measurable with these data; but our photodynamical model places a 1-sigma upper limit of 16 Earth masses. With a period 8.8 times that of the binary, the planet is well outside the dynamical instability zone. It does, however, lie within the habitable zone of the binary, and making it the third of ten Kepler circumbinary planets to do so.

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arXiv2013

All Six Planets Known to Orbit Kepler-11 Have Low Densities

The Kepler-11 planetary system contains six transiting planets ranging in size from 1.8 to 4.2 times the radius of Earth. Five of these planets orbit in a tightly-packed configuration with periods between 10 and 47 days. We perform a dynamical analysis of the system based upon transit timing variations observed in more than three years of \ik photometric data. Stellar parameters are derived using a combination of spectral classification and constraints on the star's density derived from transit profiles together with planetary eccentricity vectors provided by our dynamical study. Combining masses of the planets relative to the star from our dynamical study and radii of the planets relative to the star from transit depths together with deduced stellar properties yields measurements of the radii of all six planets, masses of the five inner planets, and an upper bound to the mass of the outermost planet, whose orbital period is 118 days. We find mass-radius combinations for all six planets that imply that substantial fractions of their volumes are occupied by constituents that are less dense than rock. The Kepler-11 system contains the lowest mass exoplanets for which both mass and radius have been measured.

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arXiv2012

Kepler-47: A Transiting Circumbinary Multi-Planet System

We report the detection of Kepler-47, a system consisting of two planets orbiting around an eclipsing pair of stars. The inner and outer planets have radii 3.0 and 4.6 times that of the Earth, respectively. The binary star consists of a Sun-like star and a companion roughly one-third its size, orbiting each other every 7.45 days. With an orbital period of 49.5 days, eighteen transits of the inner planet have been observed, allowing a detailed characterization of its orbit and those of the stars. The outer planet's orbital period is 303.2 days, and although the planet is not Earth-like, it resides within the classical "habitable zone", where liquid water could exist on an Earth-like planet. With its two known planets, Kepler-47 establishes that close binary stars can host complete planetary systems.

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arXiv2012

The Neptune-Sized Circumbinary Planet Kepler-38b

We discuss the discovery and characterization of the circumbinary planet Kepler-38b. The stellar binary is single-lined, with a period of 18.8 days, and consists of a moderately evolved main-sequence star (M_A = 0.949 +/- 0.059 solar masses and R_A = 1.757 +/- 0.034 solar radii) paired with a low-mass star (M_B = 0.249 +/- 0.010 solar masses and R_B = 0.2724 +/- 0.0053 solar radii) in a mildly eccentric (e=0.103) orbit. A total of eight transits due to a circumbinary planet crossing the primary star were identified in the Kepler light curve (using Kepler Quarters 1 through 11), from which a planetary period of 105.595 +/- 0.053 days can be established. A photometric dynamical model fit to the radial velocity curve and Kepler light curve yields a planetary radius of 4.35 +/- 0.11 Earth radii, or 1.12 +/- 0.03 Neptune radii. Since the planet is not sufficiently massive to observably alter the orbit of the binary from Keplerian motion, we can only place an upper limit on the mass of the planet of 122 Earth masses (7.11 Neptune masses or 0.384 Jupiter masses) at 95% confidence. This upper limit should decrease as more Kepler data become available.

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arXiv2012

The Transiting Circumbinary Planets Kepler-34 and Kepler-35

Most Sun-like stars in the Galaxy reside in gravitationally-bound pairs of stars called "binary stars". While long anticipated, the existence of a "circumbinary planet" orbiting such a pair of normal stars was not definitively established until the discovery of Kepler-16. Incontrovertible evidence was provided by the miniature eclipses ("transits") of the stars by the planet. However, questions remain about the prevalence of circumbinary planets and their range of orbital and physical properties. Here we present two additional transiting circumbinary planets, Kepler-34 and Kepler-35. Each is a low-density gas giant planet on an orbit closely aligned with that of its parent stars. Kepler-34 orbits two Sun-like stars every 289 days, while Kepler-35 orbits a pair of smaller stars (89% and 81% of the Sun's mass) every 131 days. Due to the orbital motion of the stars, the planets experience large multi-periodic variations in incident stellar radiation. The observed rate of circumbinary planets implies > ~1% of close binary stars have giant planets in nearly coplanar orbits, yielding a Galactic population of at least several million.

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arXiv2011

Kepler-16: A Transiting Circumbinary Planet

We report the detection of a planet whose orbit surrounds a pair of low-mass stars. Data from the Kepler spacecraft reveal transits of the planet across both stars, in addition to the mutual eclipses of the stars, giving precise constraints on the absolute dimensions of all three bodies. The planet is comparable to Saturn in mass and size, and is on a nearly circular 229-day orbit around its two parent stars. The eclipsing stars are 20% and 69% as massive as the sun, and have an eccentric 41-day orbit. The motions of all three bodies are confined to within 0.5 degree of a single plane, suggesting that the planet formed within a circumbinary disk.

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arXiv2011

Kepler Eclipsing Binary Stars. II. 2165 Eclipsing Binaries in the Second Data Release

The Kepler Mission provides nearly continuous monitoring of ~156 000 objects with unprecedented photometric precision. Coincident with the first data release, we presented a catalog of 1879 eclipsing binary systems identified within the 115 square degree Kepler FOV. Here, we provide an updated catalog augmented with the second Kepler data release which increases the baseline nearly 4-fold to 125 days. 386 new systems have been added, ephemerides and principle parameters have been recomputed. We have removed 42 previously cataloged systems that are now clearly recognized as short-period pulsating variables and another 58 blended systems where we have determined that the Kepler target object is not itself the eclipsing binary. A number of interesting objects are identified. We present several exemplary cases: 4 EBs that exhibit extra (tertiary) eclipse events; and 8 systems that show clear eclipse timing variations indicative of the presence of additional bodies bound in the system. We have updated the period and galactic latitude distribution diagrams. With these changes, the total number of identified eclipsing binary systems in the Kepler field-of-view has increased to 2165, 1.4% of the Kepler target stars.

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arXiv2011

A Closely-Packed System of Low-Mass, Low-Density Planets Transiting Kepler-11

When an extrasolar planet passes in front of its star (transits), its radius can be measured from the decrease in starlight and its orbital period from the time between transits. Multiple planets transiting the same star reveal more: period ratios determine stability and dynamics, mutual gravitational interactions reflect planet masses and orbital shapes, and the fraction of transiting planets observed as multiples has implications for the planarity of planetary systems. But few stars have more than one known transiting planet, and none has more than three. Here we report Kepler spacecraft observations of a single Sun-like star that reveal six transiting planets, five with orbital periods between 10 and 47 days plus a sixth one with a longer period. The five inner planets are among the smallest whose masses and sizes have both been measured, and these measurements imply substantial envelopes of light gases. The degree of coplanarity and proximity of the planetary orbits imply energy dissipation near the end of planet formation.

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