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Register a new userOn Correlated-noise Analyses Applied To Exoplanet Light Curves
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Time-correlated noise is a significant source of uncertainty when modeling exoplanet light-curve data. A correct assessment of correlated noise is fundamental to determine the true statistical significance of our findings. Here we review three of the most widely used correlated-noise estimators in the exoplanet field, the time-averaging, residual-permutation, and wavelet-likelihood methods. We argue that the residual-permutation method is unsound in estimating the uncertainty of parameter estimates. We thus recommend to refrain from this method altogether. We characterize the behavior of the time averagings rms-vs.-bin-size curves at bin sizes similar to the total observation duration, which may lead to underestimated uncertainties. For the wavelet-likelihood method, we note errors in the published equations and provide a list of corrections. We further assess the performance of these techniques by injecting and retrieving eclipse signals into synthetic and real Spitzer light curves, analyzing the results in terms of the relative-accuracy and coverage-fraction statistics. Both the time-averaging and wavelet-likelihood methods significantly improve the estimate of the eclipse depth over a white-noise analysis (a Markov-chain Monte Carlo exploration assuming uncorrelated noise). However, the corrections are not perfect, when retrieving the eclipse depth from Spitzer datasets, these methods covered the true (injected) depth within the 68% credible region in only $sim$45--65% of the trials. Lastly, we present our open-source model-fitting tool, Multi-Core Markov-Chain Monte Carlo ({MC$^3$}). This package uses Bayesian statistics to estimate the best-fitting values and the credible regions for the parameters for a (user-provided) model. {MC$^3$} is a Python/C code, available at https://github.com/pcubillos/MCcubed.
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We use a planetary albedo model to investigate variations in visible wavelength phase curves of exoplanets. The presence of clouds on these exoplanets significantly alters their planetary albedo spectra. We confirm that non-uniform cloud coverage on the dayside of tidally locked exoplanets will manifest as changes to the magnitude and shift of the phase curve. In this work, we first investigate a test case of our model using a Jupiter-like planet, at temperatures consistent to 2.0 AU insolation from a solar type star, to consider the effect of H2O clouds. We then extend our application of the model to the exoplanet Kepler-7b and consider the effect of varying cloud species, sedimentation efficiency, particle size, and cloud altitude. We show that, depending on the observational filter, the largest possible shift of the phase curve maximum will be 2-10 deg for a Jupiter-like planet, and up to 30 deg (0.08 in fractional orbital phase) for hot-Jupiter exoplanets at visible wavelengths as a function of dayside cloud distribution with a uniformly averaged thermal profile. Finally, we tailor our model for comparison with, and confirmation of, the recent optical phase-curve observations of Kepler-7b with the Kepler space telescope. The average planetary albedo can vary between 0.1-0.6 for the 1300 cloud scenarios that were compared to the observations. We observe that smaller particle size and increasing cloud altitude have a strong effect on increasing albedo. In particular, we show that a set of models where Kepler-7b has roughly half of its dayside covered in small-particle clouds high in the atmosphere, made of bright minerals like MgSiO3 and Mg2SiO4, provide the best fits to the observed offset and magnitude of the phase-curve, whereas Fe clouds are found to have too dark to fit the observations.
The number of known transiting exoplanets is rapidly increasing, which has recently inspired significant interest as to whether they can host a detectable moon. Although there has been no such example where the presence of a satellite was proven, several methods have already been investigated for such a detection in the future. All these methods utilize post-processing of the measured light curves, and the presence of the moon is decided by the distribution of a timing parameter. Here we propose a method for the detection of the moon directly in the raw transit light curves. When the moon is in transit, it puts its own fingerprint on the intensity variation. In realistic cases, this distortion is too little to be detected in the individual light curves, and must be amplified. Averaging the folded light curve of several transits helps decrease the scatter, but it is not the best approach because it also reduces the signal. The relative position of the moon varies from transit to transit, the moons wing will appear in different positions on different sides of the planets transit. Here we show that a careful analysis of the scatter curve of the folded light curves enhances the chance of detecting the exomoons directly.
We develop a non-linear semi-parametric Gaussian process model to estimate periods of Miras with sparsely-sampled light curves. The model uses a sinusoidal basis for the periodic variation and a Gaussian process for the stochastic changes. We use maximum likelihood to estimate the period and the parameters of the Gaussian process, while integrating out the effects of other nuisance parameters in the model with respect to a suitable prior distribution obtained from earlier studies. Since the likelihood is highly multimodal for period, we implement a hybrid method that applies the quasi-Newton algorithm for Gaussian process parameters and search the period/frequency parameter over a dense grid. A large-scale, high-fidelity simulation is conducted to mimic the sampling quality of Mira light curves obtained by the M33 Synoptic Stellar Survey. The simulated data set is publicly available and can serve as a testbed for future evaluation of different period estimation methods. The semi-parametric model outperforms an existing algorithm on this simulated test data set as measured by period recovery rate and quality of the resulting Period-Luminosity relations.
We present nine newly observed transits of TrES-3, taken as part of a transit timing program using the RISE instrument on the Liverpool Telescope. A Markov-Chain Monte-Carlo analysis was used to determine the planet-star radius ratio and inclination of the system, which were found to be Rp/Rstar=0.1664^{+0.0011}_{-0.0018} and i = 81.73^{+0.13}_{-0.04} respectively, consistent with previous results. The central transit times and uncertainties were also calculated, using a residual-permutation algorithm as an independent check on the errors. A re-analysis of eight previously published TrES-3 light curves was conducted to determine the transit times and uncertainties using consistent techniques. Whilst the transit times were not found to be in agreement with a linear ephemeris, giving chi^2 = 35.07 for 15 degrees of freedom, we interpret this to be the result of systematics in the light curves rather than a real transit timing variation. This is because the light curves that show the largest deviation from a constant period either have relatively little out-of-transit coverage, or have clear systematics. A new ephemeris was calculated using the transit times, and was found to be T_c(0) = 2454632.62610 +- 0.00006 HJD and P = 1.3061864 +- 0.0000005 days. The transit times were then used to place upper mass limits as a function of the period ratio of a potential perturbing planet, showing that our data are sufficiently sensitive to have probed for sub-Earth mass planets in both interior and exterior 2:1 resonances, assuming the additional planet is in an initially circular orbit.
We infer the number of planets-per-star as a function of orbital period and planet size using $Kepler$ archival data products with updated stellar properties from the $Gaia$ Data Release 2. Using hierarchical Bayesian modeling and Hamiltonian Monte Carlo, we incorporate planet radius uncertainties into an inhomogeneous Poisson point process model. We demonstrate that this model captures the general features of the outcome of the planet formation and evolution around GK stars, and provides an infrastructure to use the $Kepler$ results to constrain analytic planet distribution models. We report an increased mean and variance in the marginal posterior distributions for the number of planets per $GK$ star when including planet radius measurement uncertainties. We estimate the number of planets-per-$GK$ star between 0.75 and 2.5 $R_{oplus}$ and 50 to 300 day orbital periods to have a $68%$ credible interval of $0.49$ to $0.77$ and a posterior mean of $0.63$. This posterior has a smaller mean and a larger variance than the occurrence rate calculated in this work and in Burke et al. (2015) for the same parameter space using the $Q1-Q16$ (previous $Kepler$ planet candidate and stellar catalog). We attribute the smaller mean to many of the instrumental false positives at longer orbital periods being removed from the $DR25$ catalog. We find that the accuracy and precision of our hierarchical Bayesian model posterior distributions are less sensitive to the total number of planets in the sample, and more so on the characteristics of the catalog completeness and reliability and the span of the planet parameter space.
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