arXiv subjects

Daniel Foreman-Mackey

Publications and source records attributed to Daniel Foreman-Mackey.

At least 73 records · Page 4Linked to original sources

arXiv2019

emcee v3: A Python ensemble sampling toolkit for affine-invariant MCMC

emcee is a Python library implementing a class of affine-invariant ensemble samplers for Markov chain Monte Carlo (MCMC). This package has been widely applied to probabilistic modeling problems in astrophysics where it was originally published, with some applications in other fields. When it was first released in 2012, the interface implemented in emcee was fundamentally different from the MCMC libraries that were popular at the time, such as PyMC, because it was specifically designed to work with "black box" models instead of structured graphical models. This has been a popular interface for applications in astrophysics because it is often non-trivial to implement realistic physics within the modeling frameworks required by other libraries. Since emcee's release, other libraries have been developed with similar interfaces, such as dynesty (Speagle 2019). The version 3.0 release of emcee is the first major release of the library in about 6 years and it includes a full re-write of the computational backend, several commonly requested features, and a set of new "move" implementations.

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arXiv2019

Analytic Planetary Transit Light Curves and Derivatives for Stars with Polynomial Limb Darkening

We derive analytic, closed-form solutions for the light curve of a planet transiting a star with a limb darkening profile which is a polynomial function of the stellar elevation, up to arbitrary integer order. We provide improved analytic expressions for the uniform, linear, and quadratic limb-darkened cases, as well as novel expressions for higher order integer powers of limb darkening. The formulae are crafted to be numerically stable over the expected range of usage. We additionally present analytic formulae for the partial derivatives of instantaneous flux with respect to the radius ratio, impact parameter, and limb darkening coefficients. These expressions are rapid to evaluate, and compare quite favorably in speed and accuracy to existing transit light curve codes. We also use these expressions to numerically compute the first partial derivatives of exposure-time averaged transit light curves with respect to all model parameters. An additional application is modeling eclipsing binary or eclipsing multiple star systems in cases where the stars may be treated as spherically symmetric. We provide code which implements these formulae in C++, Python, IDL, and Julia, with tests and examples of usage.

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arXiv2019

Four newborn planets transiting the young solar analog V1298 Tau

Exoplanets orbiting pre-main sequence stars are laboratories for studying planet evolution processes, including atmospheric loss, orbital migration, and radiative cooling. V1298 Tau, a young solar analog with an age of 23 $\pm$ 4 Myr, is one such laboratory. The star is already known to host a Jupiter-sized planet on a 24 day orbit. Here, we report the discovery of three additional planets --- all between the size of Neptune and Saturn --- based on our analysis of K2 Campaign 4 photometry. Planets c and d have sizes of 5.6 and 6.4 $R_\oplus$, respectively and with orbital periods of 8.25 and 12.40 days reside 0.25% outside of the nominal 3:2 mean-motion resonance. Planet e is 8.7 $R_\oplus$ in size but only transited once in the K2 time series and thus has a period longer than 36 days, but likely shorter than 223 days. The V1298 Tau system may be a precursor to the compact multiplanet systems found to be common by the Kepler mission. However, the large planet sizes stand in sharp contrast to the vast majority of Kepler multis which have planets smaller than 3 $R_\oplus$. Simple dynamical arguments suggest total masses of $<$28 $M_\oplus$ and $<$120 $M_\oplus$ for the c-d and d-b planet pairs, respectively. The implied low masses suggest that the planets may still be radiatively cooling and contracting, and perhaps losing atmosphere. The V1298 Tau system offers rich prospects for further follow-up including atmospheric characterization by transmission or eclipse spectroscopy, dynamical characterization through transit-timing variations, and measurements of planet masses and obliquities by radial velocities.

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arXiv2019

Wobble: A Data-driven Analysis Technique for Time-series Stellar Spectra

In recent years, dedicated extreme-precision radial velocity (EPRV) spectrographs have produced vast quantities of high-resolution, high-signal-to-noise time-series spectra for bright stars. These data contain valuable information for the dual purposes of planet detection via the measured RVs and stellar characterization via the co-added spectra. However, considerable data analysis challenges exist in extracting these data products from the observed spectra at the highest possible precision, including the issue of poorly-characterized telluric absorption features and the common use of an assumed stellar spectral template. In both of these examples, precision-limiting reliance on external information can be sidestepped using the data directly. Here we propose a data-driven method to simultaneously extract precise RVs and infer the underlying stellar and telluric spectra using a linear model (in the log of flux). The model employs a convex objective and convex regularization to keep the optimization of the spectral components fast. We implement this method in wobble, an open-source python package which uses TensorFlow in one of its first non-neural-network applications to astronomical data. In this work, we demonstrate the performance of wobble on archival HARPS spectra. We recover the canonical exoplanet 51 Pegasi b, detect the secular RV evolution of the M dwarf Barnard's Star, and retrieve the Rossiter-McLaughlin effect for the Hot Jupiter HD 189733b. The method additionally produces extremely high-S/N composite stellar spectra and detailed time-variable telluric spectra, which we also present here.

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arXiv2019

Detection of Hundreds of New Planet Candidates and Eclipsing Binaries in K2 Campaigns 0-8

We implement a search for exoplanets in campaigns zero through eight (C0-8) of the K2 extension of the Kepler spacecraft. We apply a modified version of the QATS planet search algorithm to K2 light curves produced by the EVEREST pipeline, carrying out the C0-8 search on $1.5 \times 10^5$ target stars with magnitudes in the range of Kp = 9-15. We detect 818 transiting planet candidates, of which 374 were undiscovered by prior searches, with {64,15,5,2,1} in {2,3,4,5,6}-planet multi-planet candidate systems, respectively. Of the new planets detected, 100 orbit M dwarfs, including one which is potentially rocky and in the habitable zone. 154 of our candidates reciprocally transit with our Solar System: they are geometrically aligned to see at least one Solar System planet transit. We find candidates which display transit timing variations and dozens of candidates on both period extremes with single transits or ultra-short periods. We point to evidence that our candidates display similar patterns in frequency and size-period relation as confirmed planets, such as tentative evidence for the radius gap. Confirmation of these planet candidates with follow-up studies will increase the number of K2 planets by up to 50%, and characterization of their host stars will improve statistical studies of planet properties. Our sample includes many planets orbiting bright stars amenable for radial velocity follow-up and future characterization with JWST. We also list the 579 eclipsing binary systems detected as part of this search.

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arXiv2019

Towards precise stellar ages: combining isochrone fitting with empirical gyrochronology

We present a new age-dating technique that combines gyrochronology with isochrone fitting to infer ages for FGKM main-sequence and subgiant field stars. Gyrochronology and isochrone fitting are each capable of providing relatively precise ages for field stars in certain areas of the Hertzsprung-Russell diagram: gyrochronology works optimally for cool main-sequence stars, and isochrone fitting can provide precise ages for stars near the main-sequence turnoff. Combined, these two age-dating techniques can provide precise and accurate ages for a broader range of stellar masses and evolutionary stages than either method used in isolation. We demonstrate that the position of a star on the Hertzsprung- Russell or color-magnitude diagram can be combined with its rotation period to infer a precise age via both isochrone fitting and gyrochronology simultaneously. We show that incorporating rotation periods with 5% uncertainties into stellar evolution models improves age precision for FGK stars on the main sequence, and can, on average, provide age estimates up to three times more precise than isochrone fitting alone. In addition, we provide a new gyrochronology relation, calibrated to the Praesepe cluster and the Sun, that includes a variance model to capture the rotational behavior of stars whose rotation periods do not lengthen with the square-root of time, and parts of the Hertzsprung-Russell diagram where gyrochronology has not been calibrated. This publication is accompanied by an open source Python package, stardate, for inferring the ages of main-sequence and subgiant FGKM stars from rotation periods, spectroscopic parameters and/or apparent magnitudes and parallaxes.

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arXiv2019

eleanor: An open-source tool for extracting light curves from the TESS Full-Frame Images

During its two year prime mission the Transiting Exoplanet Survey Satellite (TESS) will perform a time-series photometric survey covering over 80% of the sky. This survey comprises observations of 26 24 x 96 degree sectors that are each monitored continuously for approximately 27 days. The main goal of TESS is to find transiting planets around 200,000 pre-selected stars for which fixed aperture photometry is recorded every two minutes. However, TESS is also recording and delivering Full-Frame Images (FFIs) of each detector at a 30 minute cadence. We have created an open-source tool, eleanor, to produce light curves for objects in the TESS FFIs. Here, we describe the methods used in eleanor to produce light curves that are optimized for planet searches. The tool performs background subtraction, aperture and PSF photometry, decorrelation of instrument systematics, and cotrending using principal component analysis. We recover known transiting exoplanets in the FFIs to validate the pipeline and perform a limited search for new planet candidates in Sector 1. Our tests indicate that eleanor produces light curves with significantly less scatter than other tools that have been used in the literature. Cadence-stacked images, and raw and detrended eleanor light curves for each analyzed star will be hosted on MAST, with planet candidates on ExoFOP-TESS as Community TESS Objects of Interest (CTOIs). This work confirms the promise that the TESS FFIs will enable the detection of thousands of new exoplanets and a broad range of time domain astrophysics.

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arXiv2019

The L 98-59 System: Three Transiting, Terrestrial-Sized Planets Orbiting a Nearby M-dwarf

We report the Transiting Exoplanet Survey Satellite (TESS) discovery of three terrestrial-sized planets transiting L 98-59 (TOI-175, TIC 307210830) -- a bright M dwarf at a distance of 10.6 pc. Using the Gaia-measured distance and broad-band photometry we find that the host star is an M3 dwarf. Combined with the TESS transits from three sectors, the corresponding stellar parameters yield planet radii ranging from 0.8REarth to 1.6REarth. All three planets have short orbital periods, ranging from 2.25 to 7.45 days with the outer pair just wide of a 2:1 period resonance. Diagnostic tests produced by the TESS Data Validation Report and the vetting package DAVE rule out common false positive sources. These analyses, along with dedicated follow-up and the multiplicity of the system, lend confidence that the observed signals are caused by planets transiting L 98-59 and are not associated with other sources in the field. The L 98-59 system is interesting for a number of reasons: the host star is bright (V = 11.7 mag, K = 7.1 mag) and the planets are prime targets for further follow-up observations including precision radial-velocity mass measurements and future transit spectroscopy with the James Webb Space Telescope; the near resonant configuration makes the system a laboratory to study planetary system dynamical evolution; and three planets of relatively similar size in the same system present an opportunity to study terrestrial planets where other variables (age, metallicity, etc.) can be held constant. L 98-59 will be observed in 4 more TESS sectors, which will provide a wealth of information on the three currently known planets and have the potential to reveal additional planets in the system.

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arXiv2018

The orbital eccentricity of small planet systems

We determine the orbital eccentricities of individual small Kepler planets, through a combination of asteroseismology and transit light-curve analysis. We are able to constrain the eccentricities of 51 systems with a single transiting planet, which supplement our previous measurements of 66 planets in multi-planet systems. Through a Bayesian hierarchical analysis, we find evidence that systems with only one detected transiting planet have a different eccentricity distribution than systems with multiple detected transiting planets. The eccentricity distribution of the single-transiting systems is well described by the positive half of a zero-mean Gaussian distribution with a dispersion $σ_e = 0.32 \pm 0.06$, while the multiple-transit systems are consistent with $σ_e = 0.083^{+0.015}_{-0.020}$. A mixture model suggests a fraction of $0.76^{+0.21}_{-0.12}$ of single-transiting systems have a moderate eccentricity, represented by a Rayleigh distribution that peaks at $0.26^{+0.04}_{-0.06}$. This finding may reflect differences in the formation pathways of systems with different numbers of transiting planets. We investigate the possibility that eccentricities are "self-excited" in closely packed planetary systems, as well as the influence of long-period giant companion planets. We find that both mechanisms can qualitatively explain the observations. We do not find any evidence for a correlation between eccentricity and stellar metallicity, as has been seen for giant planets. Neither do we find any evidence that orbital eccentricity is linked to the detection of a companion star. Along with this paper we make available all of the parameters and uncertainties in the eccentricity distributions, as well as the properties of individual systems, for use in future studies.

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arXiv2018

Compact multi-planet systems are more common around metal poor hosts

In systems with detected planets, hot-Jupiters and compact systems of multiple planets are nearly mutually exclusive. We compare the relative occurrence of these two architectures as a fraction of detected planetary systems to determine the role that metallicity plays in planet formation. We show that compact multi-planet systems occur more frequently around stars of increasingly lower metallicities using spectroscopically derived abundances for more than 700 planet hosts. At higher metallicities, compact multi-planet systems comprise a nearly constant fraction of the planet hosts despite the steep rise in the fraction of hosts containing hot and cool-Jupiters. Since metal poor stars have been underrepresented in planet searches, this implies that the occurrence rate of compact multis is higher than previously reported. Due to observational limits, radial velocity planet searches have focused mainly on high-metallicity stars where they have a higher chance of finding giant planets. New extreme-precision radial velocity instruments coming online that can detect these compact multi-planet systems can target lower metallicity stars to find them.

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arXiv2018

STARRY: Analytic Occultation Light Curves

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.

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arXiv2018

A Robust Method to Measure Centroids of Spectral Lines

Measuring the centroid of a spectral line is a common problem in astronomy. Many methods have been devised to overcome limitations due to either noise in the spectra or asymmetric profiles, the most common of which are the intensity weighted averages (first moment) or fits of analytical (typically Gaussian) profiles. If the spectral line can be considered a single component, we demonstrate that a simple quadratic fit to the pixel of maximum intensity and its two neighboring pixels provides a robust measure of the line centroid. This approach allows for a sub-velocity resolution precision on the line centroid, without be biases by noise or asymmetric features in the line profile and outperforming traditional methods in most situations.

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arXiv2018

A Kinematical Detection of Two Embedded Jupiter Mass Planets in HD 163296

We present the first kinematical detection of embedded protoplanets within a protoplanetary disk. Using archival ALMA observations of HD 163296, we demonstrate a new technique to measure the rotation curves of CO isotopologue emission to sub-percent precision relative to the Keplerian rotation. These rotation curves betray substantial deviations caused by local perturbations in the radial pressure gradient, likely driven by gaps carved in the gas surface density by Jupiter-mass planets. Comparison with hydrodynamic simulations shows excellent agreement with the gas rotation profile when the disk surface density is perturbed by two Jupiter mass planets at 83 au and 137 au. As the rotation of the gas is dependent on the pressure of the total gas component, this method provides a unique probe of the gas surface density profile without incurring significant uncertainties due to gas-to-dust ratios or local chemical abundances which plague other methods. Future analyses combining both methods promise to provide the most accurate and robust measures of embedded planetary mass. Furthermore, this method provides a unique opportunity to explore wide-separation planets beyond the mm continuum edge and to trace the gas pressure profile essential in modelling grain evolution in disks.

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arXiv2018

Inference of stellar parameters from brightness variations

It has been demonstrated that the time variability of a star's brightness at different frequencies can be used to infer its surface gravity, radius, mass, and age. With large samples of light curves now available from Kepler and K2, and upcoming surveys like TESS, we wish to quantify the overall information content of this data and identify where the information resides. As a first look into this question we ask which stellar parameters we can predict from the brightness variations in red-giant stars data and to what precision, using a data-driven model. We demonstrate that the long-cadence (30-minute) Kepler light curves for 2000 red-giant stars can be used to predict their $T_{\rm eff}$ and $\log g$. Our inference makes use of a data-driven model of a part of the autocorrelation function (ACF) of the light curve, where we posit a polynomial relationship between stellar parameters and the ACF pixel values. We find that this model, trained using 1000 stars, can be used to recover the temperature $T_{\rm eff}$ to $<$100 K, the surface gravity to $<$ 0.1 dex, and the asteroseismic power-spectrum parameters $\rm ν_{max}$ and $\rm Δν$ to $<11$ $μ$Hz and $<0.9$ $μ$Hz ($\lesssim$ 15\%). We recover $T_{\rm eff}$ from range of time-lags 0.045 $<$ $T_{\rm lag}$ $<$ 370 days and the $\log g$, $\rm ν_{max}$ and $\rm Δν$ from the range 0.045 $<$ $T_{\rm lag}$ $<$ 35 days. We do not discover any information about stellar metallicity. The information content of the data about each parameter is empirically quantified using this method, enabling comparisons to theoretical expectations about convective granulation.

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arXiv2018

The Habitability of Proxima Centauri b I: Evolutionary Scenarios

We analyze the evolution of the potentially habitable planet Proxima Centauri b to identify environmental factors that affect its long-term habitability. We consider physical processes acting on size scales ranging from the galactic to the stellar system to the planet's core. We find that there is a significant probability that Proxima Centauri has had encounters with its companion stars, Alpha Centauri A and B, that are close enough to destabilize an extended planetary system. If the system has an additional planet, as suggested by the discovery data, then it may perturb planet b's eccentricity and inclination, possibly driving those parameters to non-zero values, even in the presence of strong tidal damping. We also model the internal evolution of the planet, evaluating the roles of different radiogenic abundances and tidal heating and find that magnetic field generation is likely for billions of years. We find that if planet b formed in situ, then it experienced 169 +/- 13 million years in a runaway greenhouse as the star contracted during its formation. This early phase could remove up to 5 times as much water as in the modern Earth's oceans, possibly producing a large abiotic oxygen atmosphere. On the other hand, if Proxima Centauri b formed with a substantial hydrogen atmosphere (0.01 - 1% of the planet's mass), then this envelope could have shielded the water long enough for it to be retained before being blown off itself. After modeling this wide range of processes we conclude that water retention during the host star's pre-main sequence phase is the biggest obstacle for Proxima b's habitability. These results are all obtained with a new software package called VPLANET.

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arXiv2018

Scalable backpropagation for Gaussian Processes using celerite

This research note presents a derivation and implementation of efficient and scalable gradient computations using the celerite algorithm for Gaussian Process (GP) modeling. The algorithms are derived in a "reverse accumulation" or "backpropagation" framework and they can be easily integrated into existing automatic differentiation frameworks to provide a scalable method for evaluating the gradients of the GP likelihood with respect to all input parameters. The algorithm derived in this note uses less memory and is more efficient than versions using automatic differentiation and the computational cost scales linearly with the number of data points.

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arXiv2017

Long Term Photometric Variability in Kepler Full Frame Images: Magnetic Cycles of Sun-Like Stars

Photometry from the Kepler mission is optimized to detect small, short duration signals like planet transits at the expense of long-term trends. This long-term variability can be recovered in photometry from the Full Frame Images (FFIs), a set of calibration data collected approximately monthly during the Kepler mission. Here, we present f3, an open-source package to perform photometry on the Kepler FFIs in order to detect changes in the brightness of stars in the Kepler field of view over long time baselines. We apply this package to a sample of 4,000 Sun-like stars with measured rotation periods. We find $\approx 10\%$ of these targets have long-term variability in their observed flux. For the majority of targets we identify the luminosity variations are either correlated or anticorrelated with the short-term variability due to starspots on the stellar surface. We find a transition between anticorrelated (starspot-dominated) variability and correlated (facula-dominated) variability between rotation periods of 15 and 25 days, suggesting the transition between the two modes is complete for stars at the age of the Sun. We also identify a sample of stars with apparently complete cycles, as well as a collection of short-period binaries with extreme photometric variation over the Kepler mission.

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arXiv2017

Linear models for systematics and nuisances

The target of many astronomical studies is the recovery of tiny astrophysical signals living in a sea of uninteresting (but usually dominant) noise. In many contexts (i.e., stellar time-series, or high-contrast imaging, or stellar spectroscopy), there are structured components in this noise caused by systematic effects in the astronomical source, the atmosphere, the telescope, or the detector. More often than not, evaluation of the true physical model for these nuisances is computationally intractable and dependent on too many (unknown) parameters to allow rigorous probabilistic inference. Sometimes, housekeeping data---and often the science data themselves---can be used as predictors of the systematic noise. Linear combinations of simple functions of these predictors are often used as computationally tractable models that can capture the nuisances. These models can be used to fit and subtract systematics prior to investigation of the signals of interest, or they can be used in a simultaneous fit of the systematics and the signals. In this Note, we show that if a Gaussian prior is placed on the weights of the linear components, the weights can be marginalized out with an operation in pure linear algebra, which can (often) be made fast. We illustrate this model by demonstrating the applicability of a linear model for the non-linear systematics in K2 time-series data, where the dominant noise source for many stars is spacecraft motion and variability.

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