Kepler Mission Stellar and Instrument Noise Properties

Kepler Mission results are rapidly contributing to fundamentally new discoveries in both the exoplanet and asteroseismology fields. The data returned from Kepler are unique in terms of the number of stars observed, precision of photometry for time series observations, and the temporal extent of high duty cycle observations. As the first mission to provide extensive time series measurements on thousands of stars over months to years at a level hitherto possible only for the Sun, the results from Kepler will vastly increase our knowledge of stellar variability for quiet solar-type stars. Here we report on the stellar noise inferred on the timescale of a few hours of most interest for detection of exoplanets via transits. By design the data from moderately bright Kepler stars are expected to have roughly comparable levels of noise intrinsic to the stars and arising from a combination of fundamental limitations such as Poisson statistics and any instrument noise. The noise levels attained by Kepler on-orbit exceed by some 50% the target levels for solar-type, quiet stars. We provide a decomposition of observed noise for an ensemble of 12th magnitude stars arising from fundamental terms (Poisson and readout noise), added noise due to the instrument and that intrinsic to the stars. The largest factor in the modestly higher than anticipated noise follows from intrinsic stellar noise. We show that using stellar parameters from galactic stellar synthesis models, and projections to stellar rotation, activity and hence noise levels reproduces the primary intrinsic stellar noise features.Comment: Accepted by ApJ; 26 pages, 20 figure

The stability of simulation based estimation of the multiperiod multinominal probit model with individual specific covariates

The multi-period multinomial Probit model (MMPM) is seen as a flexible tool to explain individual choices among several alternatives over time. There are two versions of this model: a) for each individual the covariates for all alternatives are known and b) for each individual only the parameters of the alternative which was chosen is known. The main difficulty with the MMPM was the calculation of the probability for the individual sequence of chosen alternatives, which requires the computation of the integral over a high dimensional multivariate Normal density. This remedy was removed by the Smooth Recursive Conditional (SRC) simulator. Several simulation studies have investigated the stability of the MMPM estimates with special emphasis to the number of replications of the SRC routine. In contrast to these studies, which use the case of alternative specific covariates, we use the case of the individual specific covariates. We conclude that the MMPM with individual specific covariates is only weakly identified, generalizing Keane's (1992) result for the one period case. As a consequence the maximization of the simulated likelihood often converges to a singular covariance structure so that the SRC-routine stops iterating. This feature cannot be avoided by increasing the number of replications in the SRC-routine. The percentage of these failures rapidly increases with the number of alternatives. --discrete choice models,multi-period multinomial,probit models,simulated maximum likelihood method,smooth recursive conditional simulator,panel data

Phasing the Mirror Segments of the Keck Telescopes: The Broadband Phasing Algorithm

To achieve its full diffraction limit in the infrared, the primary mirror of the Keck telescope (now telescopes) must be properly phased: The steps or piston errors between the individual mirror segments must be reduced to less than 100 nm. We accomplish this with a wave optics variation of the Shack–Hartmann test, in which the signal is not the centroid but rather the degree of coherence of the individual subimages. Using filters with a variety of coherence lengths, we can capture segments with initial piston errors as large as ± 30 µm and reduce these to 30 nm—a dynamic range of 3 orders of magnitude. Segment aberrations contribute substantially to the residual errors of ~75 nm

Generalized fiducial inference for normal linear mixed models

While linear mixed modeling methods are foundational concepts introduced in any statistical education, adequate general methods for interval estimation involving models with more than a few variance components are lacking, especially in the unbalanced setting. Generalized fiducial inference provides a possible framework that accommodates this absence of methodology. Under the fabric of generalized fiducial inference along with sequential Monte Carlo methods, we present an approach for interval estimation for both balanced and unbalanced Gaussian linear mixed models. We compare the proposed method to classical and Bayesian results in the literature in a simulation study of two-fold nested models and two-factor crossed designs with an interaction term. The proposed method is found to be competitive or better when evaluated based on frequentist criteria of empirical coverage and average length of confidence intervals for small sample sizes. A MATLAB implementation of the proposed algorithm is available from the authors.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1030 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A time-frequency analysis approach for condition monitoring of a wind turbine gearbox under varying load conditions

This paper deals with the condition monitoring of wind turbine gearboxes under varying operating conditions. Generally, gearbox systems include nonlinearities so a simplified nonlinear gear model is developed, on which the time–frequency analysis method proposed is first applied for the easiest understanding of the challenges faced. The effect of varying loads is examined in the simulations and later on in real wind turbine gearbox experimental data. The Empirical Mode Decomposition (EMD) method is used to decompose the vibration signals into meaningful signal components associated with specific frequency bands of the signal. The mode mixing problem of the EMD is examined in the simulation part and the results in that part of the paper suggest that further research might be of interest in condition monitoring terms. For the amplitude–frequency demodulation of the signal components produced, the Hilbert Transform (HT) is used as a standard method. In addition, the Teager–Kaiser energy operator (TKEO), combined with an energy separation algorithm, is a recent alternative method, the performance of which is tested in the paper too. The results show that the TKEO approach is a promising alternative to the HT, since it can improve the estimation of the instantaneous spectral characteristics of the vibration data under certain conditions

PeX 1. Multi-spectral expansion of residual speckles for planet detection

The detection of exoplanets in coronographic images is severely limited by residual starlight speckles. Dedicated post-processing can drastically reduce this "stellar leakage" and thereby increase the faintness of detectable exoplanets. Based on a multi-spectral series expansion of the diffraction pattern, we derive a multi-mode model of the residuals which can be exploited to estimate and thus remove the residual speckles in multi-spectral coronographic images. Compared to other multi-spectral processing methods, our model is physically grounded and is suitable for use in an (optimal) inverse approach. We demonstrate the ability of our model to correctly estimate the speckles in simulated data and demonstrate that very high contrasts can be achieved. We further apply our method to removing speckles from a real data cube obtained with the SPHERE IFS instrument.Comment: accepted for publication in MNRAS on 25th of August 2017, 17 pages, 15 figure