Fundamental limitations of high contrast imaging set by small sample statistics

In this paper, we review the impact of small sample statistics on detection thresholds and corresponding confidence levels (CLs) in high contrast imaging at small angles. When looking close to the star, the number of resolution elements decreases rapidly towards small angles. This reduction of the number of degrees of freedom dramatically affects CLs and false alarm probabilities. Naively using the same ideal hypothesis and methods as for larger separations, which are well understood and commonly assume Gaussian noise, can yield up to one order of magnitude error in contrast estimations at fixed CL. The statistical penalty exponentially increases towards very small inner working angles. Even at 5-10 resolution elements from the star, false alarm probabilities can be significantly higher than expected. Here we present a rigorous statistical analysis which ensures robustness of the CL, but also imposes a substantial limitation on corresponding achievable detection limits (thus contrast) at small angles. This unavoidable fundamental statistical effect has a significant impact on current coronagraphic and future high contrast imagers. Finally, the paper concludes with practical recommendations to account for small number statistics when computing the sensitivity to companions at small angles and when exploiting the results of direct imaging planet surveys.Comment: 12 pages, 10 figures, accepted to Ap

Large-Scale Sunyaev-Zel'dovich Effect: Measuring Statistical Properties with Multifrequency Maps

We study the prospects for extracting detailed statistical properties of the Sunyaev-Zel'dovich (SZ) effect associated with large scale structure using upcoming multifrequency CMB experiments. The greatest obstacle to detecting the large-angle signal is the confusion noise provided by the primary anisotropies themselves, and to a lesser degree galactic and extragalactic foregrounds. We employ multifrequency subtraction techniques and the latest foregrounds models to determine the detection threshold for the Boomerang, MAP (several microK) and Planck CMB (sub microK) experiments. Calibrating a simplified biased-tracer model of the gas pressure off recent hydrodynamic simulations, we estimate the SZ power spectrum, skewness and bispectrum through analytic scalings and N-body simulations of the dark matter. We show that the Planck satellite should be able to measure the SZ effect with sufficient precision to determine its power spectrum and higher order correlations, e.g. the skewness and bispectrum. Planck should also be able to detect the cross correlation between the SZ and gravitational lensing effect in the CMB. Detection of these effects will help determine the properties of the as yet undetected gas, including the manner in which the gas pressure traces the dark matter.Comment: 13 ApJ pages, 11 figures; typos and figure 5 revised; submitted to Ap

3-pt Statistics of Cosmological Stochastic Gravitational Waves

We consider the 3-pt function (i.e. the bispectrum or non-Gaussianity) for stochastic backgrounds of gravitational waves. We estimate the amplitude of this signal for the primordial inflationary background, gravitational waves generated during preheating, and for gravitational waves produced by self-ordering scalar fields following a global phase transition. To assess detectability, we describe how to extract the 3-pt signal from an idealized interferometric experiment and compute the signal to noise ratio as a function of integration time. The 3-pt signal for the stochastic gravitational wave background generated by inflation is unsurprisingly tiny. For gravitational radiation generated by purely causal, classical mechanisms we find that, no matter how non-linear the process is, the 3-pt correlations produced vanish in direct detection experiments. On the other hand, we show that in scenarios where the B-mode of the CMB is sourced by gravitational waves generated by a global phase transition, a strong 3-pt signal among the polarization modes could also be produced. This may provide another method of distinguishing inflationary B-modes. To carry out this computation, we have developed a diagrammatic approach to the calculation of stochastic gravitational waves sourced by scalar fluids, which has applications beyond the present scenario.Comment: 16 pages, 5 figure

Robust statistics for deterministic and stochastic gravitational waves in non-Gaussian noise I: Frequentist analyses

Gravitational wave detectors will need optimal signal-processing algorithms to extract weak signals from the detector noise. Most algorithms designed to date are based on the unrealistic assumption that the detector noise may be modeled as a stationary Gaussian process. However most experiments exhibit a non-Gaussian ``tail'' in the probability distribution. This ``excess'' of large signals can be a troublesome source of false alarms. This article derives an optimal (in the Neyman-Pearson sense, for weak signals) signal processing strategy when the detector noise is non-Gaussian and exhibits tail terms. This strategy is robust, meaning that it is close to optimal for Gaussian noise but far less sensitive than conventional methods to the excess large events that form the tail of the distribution. The method is analyzed for two different signal analysis problems: (i) a known waveform (e.g., a binary inspiral chirp) and (ii) a stochastic background, which requires a multi-detector signal processing algorithm. The methods should be easy to implement: they amount to truncation or clipping of sample values which lie in the outlier part of the probability distribution.Comment: RevTeX 4, 17 pages, 8 figures, typos corrected from first version

Improving and Assessing Planet Sensitivity of the GPI Exoplanet Survey with a Forward Model Matched Filter

We present a new matched filter algorithm for direct detection of point sources in the immediate vicinity of bright stars. The stellar Point Spread Function (PSF) is first subtracted using a Karhunen-Lo\'eve Image Processing (KLIP) algorithm with Angular and Spectral Differential Imaging (ADI and SDI). The KLIP-induced distortion of the astrophysical signal is included in the matched filter template by computing a forward model of the PSF at every position in the image. To optimize the performance of the algorithm, we conduct extensive planet injection and recovery tests and tune the exoplanet spectra template and KLIP reduction aggressiveness to maximize the Signal-to-Noise Ratio (SNR) of the recovered planets. We show that only two spectral templates are necessary to recover any young Jovian exoplanets with minimal SNR loss. We also developed a complete pipeline for the automated detection of point source candidates, the calculation of Receiver Operating Characteristics (ROC), false positives based contrast curves, and completeness contours. We process in a uniform manner more than 330 datasets from the Gemini Planet Imager Exoplanet Survey (GPIES) and assess GPI typical sensitivity as a function of the star and the hypothetical companion spectral type. This work allows for the first time a comparison of different detection algorithms at a survey scale accounting for both planet completeness and false positive rate. We show that the new forward model matched filter allows the detection of $50\%$ fainter objects than a conventional cross-correlation technique with a Gaussian PSF template for the same false positive rate.Comment: ApJ accepte