ABSTRACT Characterization of transiting planets with transit timing variations (TTVs) requires understanding how to translate the observed TTVs into masses and orbital elements of the planets. This ...can be challenging in multi-planet transiting systems, but fortunately these systems tend to be nearly plane-parallel and low eccentricity. Here we present a novel derivation of analytic formulae for TTVs that are accurate to first order in the planet-star mass ratios and in the orbital eccentricities. These formulae are accurate in proximity to first-order resonances, as well as away from resonance, and compare well with more computationally expensive N-body integrations in the low-eccentricity, low mass-ratio regime when applied to simulated and to actual multi-transiting Kepler planet systems. We make code available for implementing these formulae.
EXOFAST: A Fast Exoplanetary Fitting Suite in IDL Eastman, Jason; Gaudi, B. Scott; Agol, Eric
Publications of the Astronomical Society of the Pacific,
01/2013, Volume:
125, Issue:
923
Journal Article
Peer reviewed
Open access
ABSTRACT We present EXOFAST, a fast, robust suite of routines written in IDL that is designed to fit exoplanetary transits and radial velocity variations simultaneously or separately and characterize ...the parameter uncertainties and covariances with a differential evolution Markov chain Monte Carlo method. We describe how our code incorporates both data sets to derive simultaneously stellar parameters along with the transit and RV parameters, resulting in more self-consistent results on an example fit of the discovery data of HAT-P-3b that is well-mixed in under 5 minutes on a standard desktop computer. We describe in detail how our code works and outline ways in which the code can be extended to include additional effects or generalized for the characterization of other data sets-including non-planetary data sets. We discuss the pros and cons of several common ways to parameterize eccentricity, highlight a subtle mistake in the implementation of MCMC that could bias the inferred eccentricity of intrinsically circular orbits to significantly non-zero results, discuss a problem with IDL's built-in random number generator in its application to large MCMC fits, and derive a method to analytically fit the linear and quadratic limb darkening coefficients of a planetary transit. Finally, we explain how we achieved improved accuracy and over a factor of 100 improvement in the execution time of the transit model calculation. Our entire source code, along with an easy-to-use online interface for several basic features of our transit and radial velocity fitting, are available online at http://astroutils.astronomy.ohio-state.edu/exofast.
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We derive analytic, closed form, numerically stable solutions for the total flux received from a spherical planet, moon, or star during an occultation if the specific intensity map of the body is ...expressed as a sum of spherical harmonics. Our expressions are valid to arbitrary degree and may be computed recursively for speed. The formalism we develop here applies to the computation of stellar transit light curves, planetary secondary eclipse light curves, and planet-planet/planet-moon occultation light curves, as well as thermal (rotational) phase curves. In this paper, we also introduce starry, an open-source package written in C++ and wrapped in Python that computes these light curves. The algorithm in starry is six orders of magnitude faster than direct numerical integration and several orders of magnitude more precise. starry also computes analytic derivatives of the light curves with respect to all input parameters for use in gradient-based optimization and inference, such as Hamiltonian Monte Carlo (HMC), allowing users to quickly and efficiently fit observed light curves to infer properties of a celestial body's surface map. (Please see https://github.com/rodluger/starry, https://rodluger.github.io/starry/, and https://doi.org/10.5281/zenodo.1312286).
We present an update to the EVEREST K2 pipeline that addresses various limitations in the previous version and improves the photometric precision of the light curves. We develop a fast regularization ...scheme for pixel-level decorrelation (PLD) and adapt the algorithm to include the PLD vectors of other stars to enhance the predictive power of the model and minimize overfitting, particularly for faint stars. We also modify PLD to work for saturated stars and improve its performance on variable stars, although some high-frequency variables may still suffer from overfitting. On average, EVEREST 2.0 light curves have 10-20% higher photometric precision than those in version 1, yielding the highest-precision light curves at all magnitudes of any publicly available K2 catalog. For most K2 campaigns, we recover the original Kepler precision to at least = 14, and to at least = 15 for campaigns 1, 5, 6, and 13. We also detrend most short-cadence targets observed by K2, obtaining even higher photometric precision for these stars. Like all aggressive, flexible models, EVEREST is prone to overfitting, and may cause a decrease in transit depths by ∼10%; we urge users to mask signals of interest using our open-source software, which we show removes this bias. Light curves for campaigns 0-8 and 10-13 are available online in the EVEREST catalog, which will be updated with future campaigns. EVEREST 2.0 is open source and is coded in a framework that can be adapted to other photometric surveys, including Kepler and the upcoming TESS mission.
Relativistic radiative transfer problems require the calculation of photon trajectories in curved spacetime. We present a novel technique for rapid and accurate calculation of null geodesics in the ...Kerr metric. The equations of motion from the Hamilton-Jacobi equation are reduced directly to Carlson's elliptic integrals, simplifying algebraic manipulations and allowing all coordinates to be computed semianalytically for the first time. We discuss the method, its implementation in a freely available FORTRAN code, and its application to toy problems from the literature.
KOI-3278: A Self-Lensing Binary Star System Kruse, Ethan; Agol, Eric
Science (American Association for the Advancement of Science),
04/2014, Volume:
344, Issue:
6181
Journal Article
Peer reviewed
Over 40% of Sun-like stars are bound in binary or multistar systems. Stellar remnants in edge-on binary systems can gravitationally magnify their companions, as predicted 40 years ago. By using data ...from the Kepler spacecraft, we report the detection of such a "self-lensing" system, in which a 5-hour pulse of 0.1% amplitude occurs every orbital period. The white dwarf stellar remnant and its Sun-like companion orbit one another every 88.18 days, a long period for a white dwarf–eclipsing binary. By modeling the pulse as gravitational magnification (microlensing) along with Kepler's laws and stellar models, we constrain the mass of the white dwarf to be ∼63% of the mass of our Sun. Further study of this system, and any others discovered like it, will help to constrain the physics of white dwarfs and binary star evolution.
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ABSTRACT We present EPIC Variability Extraction and Removal for Exoplanet Science Targets (EVEREST), an open-source pipeline for removing instrumental noise from K2 light curves. EVEREST employs a ...variant of pixel level decorrelation to remove systematics introduced by the spacecraft's pointing error and a Gaussian process to capture astrophysical variability. We apply EVEREST to all K2 targets in campaigns 0-7, yielding light curves with precision comparable to that of the original Kepler mission for stars brighter than , and within a factor of two of the Kepler precision for fainter targets. We perform cross-validation and transit injection and recovery tests to validate the pipeline, and compare our light curves to the other de-trended light curves available for download at the MAST High Level Science Products archive. We find that EVEREST achieves the highest average precision of any of these pipelines for unsaturated K2 stars. The improved precision of these light curves will aid in exoplanet detection and characterization, investigations of stellar variability, asteroseismology, and other photometric studies. The EVEREST pipeline can also easily be applied to future surveys, such as the TESS mission, to correct for instrumental systematics and enable the detection of low signal-to-noise transiting exoplanets. The EVEREST light curves and the source code used to generate them are freely available online.
ABSTRACT The Kepler mission has discovered thousands of exoplanets and revolutionized our understanding of their population. This large, homogeneous catalog of discoveries has enabled rigorous ...studies of the occurrence rate of exoplanets and planetary systems as a function of their physical properties. However, transit surveys such as Kepler are most sensitive to planets with orbital periods much shorter than the orbital periods of Jupiter and Saturn, the most massive planets in our solar system. To address this deficiency, we perform a fully automated search for long-period exoplanets with only one or two transits in the archival Kepler light curves. When applied to the ∼40,000 brightest Sun-like target stars, this search produces 16 long-period exoplanet candidates. Of these candidates, six are novel discoveries and five are in systems with inner short-period transiting planets. Since our method involves no human intervention, we empirically characterize the detection efficiency of our search. Based on these results, we measure the average occurrence rate of exoplanets smaller than Jupiter with orbital periods in the range 2-25 years to be 2.0 0.7 planets per Sun-like star.
The size of the jet launching region in M87 Dexter, Jason; McKinney, Jonathan C; Agol, Eric
Monthly Notices of the Royal Astronomical Society,
April 2012, Volume:
421, Issue:
2
Journal Article
Peer reviewed
Open access
The supermassive black hole candidate at the centre of M87 drives an ultra-relativistic jet visible on kiloparsec scales, and its large mass and relative proximity allow for event horizon scale ...imaging with very long baseline interferometry at millimetre wavelengths (mm-VLBI). Recently, relativistic magnetohydrodynamic simulations of black hole accretion flows have proven capable of launching magnetically dominated jets. We construct time-dependent disc/jet models of the innermost portion of the M87 nucleus by performing relativistic radiative transfer calculations from one such simulation. We identify two types of models, jet-dominated or disc/jet, that can explain the spectral properties of M87, and use them to make predictions for current and future mm-VLBI observations. The Gaussian source size for the favoured sky orientation and inclination from observations of the large-scale jet is
as (≃4-6 Schwarzschild radii) on current mm-VLBI telescopes, very similar to existing observations of Sgr A*. The black hole shadow, direct evidence for an event horizon, should be visible in future measurements using baselines between Hawaii and Mexico. Both models exhibit variability at millimetre wavelengths with factor of ≃2 amplitudes on year time-scales. For the low inclination of M87, the counter-jet dominates the event horizon scale millimetre wavelength emission from the jet-forming region.
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