arXiv subjects

Eric Agol

Publications and source records attributed to Eric Agol.

At least 55 records · Page 3Linked to original sources

arXiv2020

The Discovery of the Long-Period, Eccentric Planet Kepler-88 d and System Characterization with Radial Velocities and Photodynamical Analysis

We present the discovery of Kepler-88 d ($P_d = 1403\pm14$ days, $M\mathrm{sin}i_d = 965\pm44\,M_\oplus = 3.04\pm0.14\,M_J$, $e_d = 0.41\pm0.03$) based on six years of radial velocity (RV) follow-up from the W. M. Keck Observatory HIRES spectrograph. Kepler-88 has two previously identified planets. Kepler-88 b (KOI-142.01) transits in the NASA \Kepler\ photometry and has very large transit timing variations. \citet{Nesvorny2013} perfomed a dynamical analysis of the TTVs to uniquely identify the orbital period and mass of the perturbing planet (Kepler-88 c), which was later was confirmed with RVs from the Observatoire de Haute-Provence (OHP, Barros et al. 2014). To fully explore the architecture of this system, we performed photodynamical modeling on the \Kepler\ photometry combined with the RVs from Keck and OHP and stellar parameters from spectroscopy and Gaia. Planet d is not detectable in the photometry, and long-baseline RVs are needed to ascertain its presence. A photodynamical model simultaneously optimized to fit the RVs and \Kepler\ photometry yields the most precise planet masses and orbital properties yet for b and c: $P_b = 10.91647\pm0.00014\,\mathrm{days}$, $M_b=9.5\pm1.2\,M_\oplus$, $P_c=22.2649\pm0.0007\,\mathrm{days}$, and $M_c=214.1\pm5.3\,M_\oplus$. The photodynamical solution also finds that planets b and c have low eccentricites and low mutual inclination, are apsidally anti-aligned, and have conjunctions on the same hemisphere of the star. Continued RV follow-up of systems with small planets will improve our understanding of the link between inner planetary system architectures and giant planets.

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arXiv2020

The Stellar Variability Noise Floor for Transiting Exoplanet Photometry with PLATO

One of the main science motivations for the ESA PLAnetary Transit and Oscillations (PLATO) mission is to measure exoplanet transit radii with 3% precision. In addition to flares and starspots, stellar oscillations and granulation will enforce fundamental noise floors for transiting exoplanet radius measurements. We simulate light curves of Earth-sized exoplanets transiting continuum intensity images of the Sun taken by the HMI instrument aboard SDO to investigate the uncertainties introduced on the exoplanet radius measurements by stellar granulation and oscillations. After modeling the solar variability with a Gaussian process, we find that the amplitude of solar oscillations and granulation is of order 100 ppm -- similar to the depth of an Earth transit -- and introduces a fractional uncertainty on the depth of transit of 0.73% assuming four transits are observed over the mission duration. However, when we translate the depth measurement into a radius measurement of the planet, we find a much larger radius uncertainty of 3.6%. This is due to a degeneracy between the transit radius ratio, the limb-darkening, and the impact parameter caused by the inability to constrain the transit impact parameter in the presence of stellar variability. We find that surface brightness inhomogeneity due to photospheric granulation contributes a lower limit of only 2 ppm to the photometry in-transit. The radius uncertainty due to granulation and oscillations, combined with the degeneracy with the transit impact parameter, accounts for a significant fraction of the error budget of the PLATO mission, before detector or observational noise is introduced to the light curve. If it is possible to constrain the impact parameter or to obtain follow-up observations at longer wavelengths where limb-darkening is less significant, this may enable higher precision radius measurements.

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arXiv2020

The TRAPPIST-1 JWST Community Initiative

The upcoming launch of the James Webb Space Telescope (JWST) combined with the unique features of the TRAPPIST-1 planetary system should enable the young field of exoplanetology to enter into the realm of temperate Earth-sized worlds. Indeed, the proximity of the system (12pc) and the small size (0.12 Rsun) and luminosity (0.05 Lsun) of its host star should make the comparative atmospheric characterization of its seven transiting planets within reach of an ambitious JWST program. Given the limited lifetime of JWST, the ecliptic location of the star that limits its visibility to 100d per year, the large number of observational time required by this study, and the numerous observational and theoretical challenges awaiting it, its full success will critically depend on a large level of coordination between the involved teams and on the support of a large community. In this context, we present here a community initiative aiming to develop a well-defined sequential structure for the study of the system with JWST and to coordinate on every aspect of its preparation and implementation, both on the observational (e.g. study of the instrumental limitations, data analysis techniques, complementary space-based and ground-based observations) and theoretical levels (e.g. model developments and comparison, retrieval techniques, inferences). Depending on the outcome of the first phase of JWST observations of the planets, this initiative could become the seed of a major JWST Legacy Program devoted to the study of TRAPPIST-1.

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arXiv2020

On the impact of tides on the transit-timing fits to the TRAPPIST-1 system

Transit Timing Variations, or TTVs, can be a very efficient way of constraining masses and eccentricities of multi-planet systems. Recent measurements of the TTVs of TRAPPIST-1 led to an estimate of the masses of the planets, enabling an estimate of their densities. A recent TTV analysis using data obtained in the past two years yields a 34% and 13% increase in mass for TRAPPIST-1b and c, respectively. In most studies to date, a Newtonian N-body model is used to fit the masses of the planets, while sometimes general relativity is accounted for. Using the Posidonius N-body code, we show that in the case of the TRAPPIST-1 system, non-Newtonian effects might be also relevant to correctly model the dynamics of the system and the resulting TTVs. In particular, using standard values of the tidal Love number $k_2$ (accounting for the tidal deformation) and the fluid Love number $k_{2f}$ (accounting for the rotational flattening) leads to differences in the TTVs of TRAPPIST-1b and c similar to the differences caused by general relativity. We also show that relaxing the values of tidal Love number $k_2$ and the fluid Love number $k_{2f}$ can lead to TTVs which differ by as much as a few 10~s on a $3-4$-year timescale, which is a potentially observable level. The high values of the Love numbers needed to reach observable levels for the TTVs could be achieved for planets with a liquid ocean, which, if detected, might then be interpreted as a sign that TRAPPIST-1b and TRAPPIST-1c could have a liquid magma ocean. For TRAPPIST-1 and similar systems, the models to fit the TTVs should potentially account for general relativity, for the tidal deformation of the planets, for the rotational deformation of the planets and, to a lesser extent, for the rotational deformation of the star, which would add up to 7x2+1 = 15 additional free parameters in the case of TRAPPIST-1.

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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

An Automated Method to Detect Transiting Circumbinary Planets

To date a dozen transiting "Tatooines" or circumbinary planets (CBPs) have been discovered, by eye, in the data from the Kepler mission; by contrast, thousands of confirmed circumstellar planets orbiting around single stars have been detected using automated algorithms. Automated detection of CBPs is challenging because their transits are strongly aperiodic with irregular profiles. Here, we describe an efficient and automated technique for detecting circumbinary planets that transit their binary hosts in Kepler light curves. Our method accounts for large transit timing and duration variations (TTVs and TDVs), induced by binary reflex motion, in two ways: 1) We directly correct for large-scale TTVs and TDVs in the light curves by using Keplerian models to approximate binary and CBP orbits; and 2) We allow additional aperiodicities on the corrected light curves by employing the Quasi-periodic Automated Transit Search algorithm (QATS). We demonstrate that our method dramatically improves detection significance using simulated data and two previously identified CBP systems, Kepler-35 and Kepler-64.

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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

Modeling Kepler Eclipsing Binaries: Homogeneous Inference of Orbital & Stellar Properties

We report on the properties of eclipsing binaries from the Kepler mission with a newly developed photometric modeling code, which uses the light curve, spectral energy distribution of each binary, and stellar evolution models to infer stellar masses without the need for radial velocity measurements. We present solutions and posteriors to orbital and stellar parameters for 728 systems, forming the largest homogeneous catalogue of full Kepler binary parameter estimates to date. Using comparisons to published radial velocity measurements, we demonstrate that the inferred properties (e.g., masses) are reliable for well-detached main-sequence binaries, which make up the majority of our sample. The fidelity of our inferred parameters degrades for a subset of systems not well described by input isochrones, such as short-period binaries that have undergone interactions, or binaries with post-main sequence components. Additionally, we identify 35 new systems which show evidence of eclipse timing variations, perhaps from apsidal motion due to binary tides or tertiary companions. We plan to subsequently use these models to search for and constrain the presence of circumbinary planets in Kepler eclipsing binary systems.

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arXiv2019

K2-146: Discovery of Planet c, Precise Masses from Transit Timing, and Observed Precession

K2-146 is a mid-M dwarf ($M_\star = 0.331 \pm 0.009 M_\odot$; $R_\star = 0.330 \pm 0.010 R_\odot$), observed in Campaigns 5, 16, and 18 of the K2 mission. In Campaign 5 data, a single planet was discovered with an orbital period of $2.6$~days and large transit timing variations due to an unknown perturber. Here we analyze data from Campaigns 16 and 18, detecting the transits of a second planet, c, with an orbital period of $4.0$~days, librating in a 3:2 resonance with planet b. Large, anti-correlated timing variations of both planets exist due to their resonant perturbations. The planets have a mutual inclination of $2.40^\circ\pm0.25^\circ$, which torqued planet c more closely into our line-of-sight. Planet c was grazing in Campaign 5 and thus missed in previous searches; in Campaigns 16 and 18 it is fully transiting, and its transit depth is three times larger. We improve the stellar properties using data from Gaia DR2, and using dynamical fits find that both planets are sub-Neptunes: their masses are $5.77\pm0.18$ and $7.50\pm0.23 M_{\oplus}$ and their radii are $2.04\pm0.06$ and $2.19\pm0.07$ R$_\oplus$, respectively. These mass constraints set the precision record for small exoplanets (a few gas giants have comparable relative precision). These planets lie in the photoevaporation valley when viewed in Radius-Period space, but due to the low-luminosity M-dwarf host star, they lie among the atmosphere-bearing planets when viewed in Radius-Irradiation space. This, along with their densities being 60%-80% that of Earth, suggests that they may both have retained a substantial gaseous envelope.

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arXiv2019

EXOFASTv2: A public, generalized, publication-quality exoplanet modeling code

We present the next generation public exoplanet fitting software, EXOFASTv2. It is capable of fitting an arbitrary number of planets, radial velocity data sets, astrometric data sets, and/or transits observed with any combination of wavelengths. We model the star simultaneously in the fit and provide several state-of-the-art ways to constrain its properties, including taking advantage of the now-ubiquitous all-sky catalog photometry and Gaia parallaxes. EXOFASTv2 can model the star by itself, too. Multi-planet systems are modeled self-consistently with the same underlying stellar mass that defines their semi-major axes through Kepler's law and the planetary period. Transit timing, duration, and depth variations can be modeled with a simple command line option. We explain our methodology and rationale as well as provide an improved version of the core transit model that is both 25\% faster and more accurate. We highlight several potential pitfalls in exoplanet modeling, including the handling of eccentricity in transit-only fits, that the standard exoplanet convention for $ω$ uses a left-handed coordinate system, contrary to most modern textbooks, how to avoid an important degeneracy when allowing negative companion masses, and a widely unappreciated, potential 10-minute ambiguity in the reported transit times. EXOFASTv2 is available at https://github.com/jdeast/EXOFASTv2 . The code is written in IDL, and includes an executable that can be run freely and legally without an IDL license or any knowledge of the language. Extensive documentation and tutorials are included in the distribution for a variety of example fits. Advanced amateurs and undergrads have successfully performed sophisticated global fits of complex planetary systems with EXOFASTv2. It is therefore a powerful tool for education and outreach as well as the broader professional community.

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arXiv2019

Stellar Properties of Active G and K Stars: Exploring the Connection Between Starspots and Chromospheric Activity

We gathered high resolution spectra for an ensemble of 55 bright active and inactive stars using the ARC 3.5 m Telescope Echelle Spectrograph at Apache Point Observatory ($R\approx$31,500). We measured spectroscopic effective temperatures, surface gravities and metallicities for most stars in the sample with SME and MOOG. Our stellar property results are consistent with the photometric effective temperatures from the Gaia DR2 pipeline. We also measured their chromospheric $S$ and $\log R^\prime_\mathrm{HK}$ indices to classify the stars as active or inactive and study the connection between chromospheric activity and starspots. We then attempted to infer the starspot covering fractions on the active stars by modeling their spectra as a linear combination of hot and cool inactive stellar spectral templates. We find that it is critical to use precise colors of the stars to place stringent priors on the plausible spot covering fractions. The inferred spot covering fractions generally increase with the chromospheric activity indicator $\log R^\prime_\mathrm{HK}$, though we are largely insensitive to spot coverages smaller than $f_S \lesssim 20$%. We find a dearth of stars with small $\log R^\prime_\mathrm{HK}$ and significant spot coverages.

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arXiv2019

APOGEE/Kepler Overlap Yields Orbital Solutions for a Variety of Eclipsing Binaries

Spectroscopic Eclipsing Binaries (SEBs) are fundamental benchmarks in stellar astrophysics and today are observed in breathtaking detail by missions like TESS, Kepler, and APOGEE. We develop a methodology for simultaneous analysis of high precision Kepler light curves and high resolution near-IR spectra from APOGEE and present orbital solutions and evolutionary histories for a subset of SEBs within this overlap. Radial velocities extracted from APOGEE spectra using the Broadening Function technique are combined with Kepler light curves and to yield binary orbital solutions. The Broadening Function approach yields more precise radial velocities than the standard Cross-Correlation Function, which in turn yields more precise orbital parameters and enables the identification of tertiary stars. The orbital periods of these seven SEBs range from 4 to 40 days. Four of the systems (KIC 5285607, KIC 6864859, KIC 6778289, and KIC 4285087) are well-detached binaries. The remaining three systems have apparent tertiary companions, but each exhibits two eclipses along with at least one spectroscopically varying component (KIC 6449358, KIC 6131659, and KIC 6781535). Gaia distances are available for four targets which we use to estimate temperatures of both members of these SEBs. We explore evolutionary histories in H-R diagram space and estimate ages for this subset of our sample. Finally, we consider the implications for the formation pathways of close binary systems via interactions with tertiary companions. Our methodology combined with the era of big data and observation overlap opens up the possibility of discovering and analyzing large numbers of diverse SEBs, including those with high flux ratios and those in triple systems.

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arXiv2019

The Mass of the White Dwarf Companion in the Self-Lensing Binary KOI-3278: Einstein vs. Newton

KOI-3278 is a self-lensing stellar binary consisting of a white-dwarf secondary orbiting a Sun-like primary star. Kruse and Agol (2014) noticed small periodic brightenings every 88.18 days in the Kepler photometry and interpreted these as the result of microlensing by a white dwarf with about 63$\%$ of the mass of the Sun. We obtained two sets of spectra for the primary that allowed us to derive three sets of spectroscopic estimates for its effective temperature, surface gravity, and metallicity for the first time. We used these values to update the Kruse and Agol (2014) Einsteinian microlensing model, resulting in a revised mass for the white dwarf of $0.539^{+0.022}_{-0.020} \, M_{\odot}$. The spectra also allowed us to determine radial velocities and derive orbital solutions, with good agreement between the two independent data sets. An independent Newtonian dynamical MCMC model of the combined velocities yielded a mass for the white dwarf of $0.5122^{+0.0057}_{-0.0058} \, M_{\odot}$. The nominal uncertainty for the Newtonian mass is about four times better than for the Einsteinian, $\pm 1.1\%$ vs. $\pm 4.1\%$ and the difference between the two mass determinations is $5.2 \%$. We then present a joint Einsteinian microlensing and Newtonian radial velocity model for KOI-3278, which yielded a mass for the white dwarf of $0.5250^{+0.0082}_{-0.0089} \, M_{\odot}$. This joint model does not rely on any white dwarf evolutionary models or assumptions on the white dwarf mass-radius relation. We discuss the benefits of a joint model of self-lensing binaries, and how future studies of these systems can provide insight into the mass-radius relation of white dwarfs.

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arXiv2019

Kepler-62f: Kepler's First Small Planet in the Habitable Zone, but Is It Real?

Kepler-62f is the first exoplanet small enough to plausibly have a rocky composition orbiting within the habitable zone (HZ) discovered by the Kepler Mission. The planet is 1.4 times the size of the Earth and has an orbital period of 267 days. At the time of its discovery, it had the longest period of any small planet in the habitable zone of a multi-planet system. Because of its long period, only four transits were observed during Kepler's interval of observations. It was initially missed by the Kepler pipeline, but the first three transits were identified by an independent search by Eric Agol, and it was identified as a planet candidate in subsequent Kepler catalogs. However in the latest catalog of exoplanets (Thompson et al., 2018), it is labeled as a false positive. Recent exoplanet catalogues have evolved from subjective classification to automatic classifications of planet candidates by algorithms (such as `Robovetter'). While exceptionally useful for producing a uniform catalogue, these algorithms sometimes misclassify planet candidates as a false positive, as is the case of Kepler-62f. In particularly valuable cases, i.e., when a small planet has been found orbiting in the habitable zone (HZ), it is important to conduct comprehensive analyses of the data and classification protocols to provide the best estimate of the true status of the detection. In this paper we conduct such analyses and show that Kepler-62f is a true planet and not a false positive. The table of stellar and planet properties has been updated based on GAIA results.

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arXiv2019

Discovery and Characterization of Kepler-36b

We describe the circumstances that led to the discovery of Kepler-36b, and the subsequent characterization of its host planetary system. The Kepler-36 system is remarkable for its physical properties: the close separation of the planets, the contrasting densities of the planets despite their proximity, and the short chaotic timescale. Its discovery and characterization was also remarkable for the novelty of the detection technique and for the precise characterization due to the large transit-timing variations caused by the close proximity of the planets, as well as the precise stellar parameters due to asteroseismology. This was the first multi-planet system whose transit data was processed using a fully consistent photometric-dynamical model, using population Markov Chain Monte Carlo techniques to precisely constrain system parameters. Amongst those parameters, the stellar density was found to be consistent with a complementary, concurrent asteroseismic analysis. In a first, the 3D orientation of the planets was constrained from the lack of transit-duration variations. The system yielded insights into the composition and evolution of short-period planet systems. The denser planet appears to have an Earth-like composition, with uncertainties comparable to the highest precision rocky exoplanet measurements, and the planet densities foreshadowed the rocky/gaseous boundary. The formation of this system remains a mystery, but should yield insights into the migration and evolution of compact exoplanet systems.

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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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arXiv2019

Near-resonance in a system of sub-Neptunes from TESS

We report the Transiting Exoplanet Survey Satellite ($TESS$) detection of a multi-planet system orbiting the $V=10.9$ K0 dwarf TOI 125. We find evidence for up to five planets, with varying confidence. Three high signal-to-noise transit signals correspond to sub-Neptune-sized planets ($2.76$, $2.79$, and $2.94\ R_{\oplus}$), and we statistically validate the planetary nature of the two inner planets ($P_b = 4.65$ days, $P_c = 9.15$ days). With only two transits observed, we report the outer object ($P_{.03} = 19.98$ days) as a high signal-to-noise ratio planet candidate. We also detect a candidate transiting super-Earth ($1.4\ R_{\oplus}$) with an orbital period of only $12.7$ hours and a candidate Neptune-sized planet ($4.2\ R_{\oplus}$) with a period of $13.28$ days, both at low signal-to-noise. This system is amenable to mass determination via radial velocities and transit timing variations, and provides an opportunity to study planets of similar size while controlling for age and environment. The ratio of orbital periods between TOI 125 b and c ($P_c/P_b = 1.97$) is slightly smaller than an exact 2:1 commensurability and is atypical of multiple planet systems from $Kepler$, which show a preference for period ratios just $wide$ of first-order period ratios. A dynamical analysis refines the allowed parameter space through stability arguments and suggests that, despite the nearly commensurate periods, the system is unlikely to be in resonance.

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arXiv2019

The Solar Benchmark: Rotational Modulation of the Sun Reconstructed from Archival Sunspot Records

We use archival daily spot coverage measurements from Howard et al. (1984) to study the rotational modulation of the Sun as though it were a distant star. A quasi-periodic Gaussian process measures the solar rotation period $P_\mathrm{rot} = 26.3 \pm 0.1$ days, and activity cycle period $P_\mathrm{cyc} = 10.7 \pm 0.3$ years. We attempt to search for evidence of differential rotation in variations of the apparent rotation period throughout the activity cycle and do not detect a clear signal of differential rotation, consistent with the null results of the hare-and-hounds exercise of Aigrain et al. (2015). The full reconstructed solar light curve is available online.

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