The detection of periodic signals from transiting exoplanets is often impeded by extraneous aperiodic photometric variability, either intrinsic to the star or arising from the measurement process. Frequently, these variations are autocorrelated wherein later flux values are correlated with previous ones. In this work, we present the methodology of the Autoregessive Planet Search (ARPS) project which uses Autoregressive Integrated Moving Average (ARIMA) and related statistical models that treat a wide variety of stochastic processes, as well as nonstationarity, to improve detection of new planetary transits. Providing a time series is evenly spaced or can be placed on an evenly spaced grid with missing values, these low-dimensional parametric models can prove very effective. We introduce a planet-search algorithm to detect periodic transits in the residuals after the application of ARIMA models. Our matched-filter algorithm, the Transit Comb Filter (TCF), is closely related to the traditional Box-fitting Least Squares and provides an analogous periodogram. Finally, if a previously identified or simulated sample of planets is available, selected scalar features from different stages of the analysis -the original light curves, ARIMA fits, TCF periodograms, and folded light curves -can be collectively used with a multivariate classifier to identify promising candidates while efficiently rejecting false alarms. We use Random Forests for this task, in conjunction with Receiver Operating Characteristic (ROC) curves, to define discovery criteria for new, high fidelity planetary candidates. The ARPS methodology can be applied to both evenly spaced satellite light curves and densely cadenced ground-based photometric surveys.
The 4 yr light curves of 156,717 stars observed with NASA’s Kepler mission are analyzed using the autoregressive planet search (ARPS) methodology described by Caceres et al. The three stages of processing are maximum-likelihood ARIMA modeling of the light curves to reduce stellar brightness variations, constructing the transit comb filter periodogram to identify transit-like periodic dips in the ARIMA residuals, and Random Forest classification trained on Kepler team confirmed planets using several dozen features from the analysis. Orbital periods between 0.2 and 100 days are examined. The result is a recovery of 76% of confirmed planets, 97% when period and transit depth constraints are added. The classifier is then applied to the full Kepler data set; 1004 previously noticed and 97 new stars have light-curve criteria consistent with the confirmed planets, after subjective vetting removes clear false alarms and false positive cases. The 97 Kepler ARPS candidate transits mostly have periods of P < 10 days; many are ultrashort period hot planets with radii <1% of the host star. Extensive tabular and graphical output from the ARPS time series analysis is provided to assist in other research relating to the Kepler sample.
Celestial objects exhibit a wide range of variability in brightness at different wavebands. Surprisingly, the most common methods for characterizing time series in statistics-parametric autoregressive modeling-are rarely used to interpret astronomical light curves. We review standard ARMA, ARIMA, and ARFIMA (autoregressive moving average fractionally integrated) models that treat short-memory autocorrelation, long-memory 1/f α "red noise," and nonstationary trends. Though designed for evenly spaced time series, moderately irregular cadences can be treated as evenly-spaced time series with missing data. Fitting algorithms are efficient and software implementations are widely available. We apply ARIMA models to light curves of four variable stars, discussing their effectiveness for different temporal characteristics. A variety of extensions to ARIMA are outlined, with emphasis on recently developed continuous-time models like CARMA and CARFIMA designed for irregularly spaced time series. Strengths and weakness of ARIMA-type modeling for astronomical data analysis and astrophysical insights are reviewed.Keywords: time domain astronomy, irregularly sampled time series, variable stars, quasars, statistical methods, time series analysis, autoregressive modeling, ARIMA THE VARIABILITY OF COSMIC POPULATIONSExcept for five roving planets and an occasional comet or nova, the nighttime sky seems immutable to the human eye. The pattern and brightness of stars appears unchanging as from our childhood to old age. Myths from ancient Egyptian, Greek, and Australian Aboriginal cultures suggest that a few stars (such as Algol, Mira, and Aldeberan) were recognized as variables [1,2]. As telescopic studies proliferated from the seventeenth through twenty first centuries, more variable stars were found with a wide range of characteristics. Some are periodic due to pulsations, rotationally modulated spots, or eclipses of binary companions. Others vary in irregular ways from magnetic flares, eruptions, pulsations, accretion of gas from companions, and most spectacularly, nova and supernova explosions. Ten thousand stars in two dozen categories were cataloged by Kukarkin and Parenago [3]; this catalog now has over 50,000 stars with >100 classes [4]. NASA's Kepler mission has recently shown that most ordinary stars are variable when observed with ∼0.001% accuracy and dense cadences [5].The study of celestial objects with variable brightness has broadened hugely in recent decades, emerging as a recognized discipline called "time domain astronomy" [6]. The brightest sources in the X-ray and gamma-ray sky are highly variable, typically from accretion of gas onto neutron stars and black holes. Timescales range from milliseconds to decades with a bewildering range of
One important prediction of acceleration of particles in the supernova caused shock in the magnetic wind of exploding Wolf Rayet and Red Super Giant stars is the production of an energetic particle component with a E −2 spectrum, at a level of a few percent in flux at injection. After allowing for transport effects, so steepening the spectrum to E −7/3 , this component of electrons produces electromagnetic radiation and readily explains the WMAP haze from the Galactic Center region in spectrum, intensity and radial profile. This requires the diffusion time scale for cosmic rays in the Galactic Center region to be much shorter than in the Solar neighborhood: the energy for cosmic ray electrons at the transition between diffusion dominance and loss dominance is shifted to considerably higher particle energy. We predict that more precise observations will find a radio spectrum of ν −2/3 , at higher frequencies ν −1 , and at yet higher frequencies finally ν −3/2 .
Previously, it has been argued that the anomalous emission from the region around the Galactic Center observed by WMAP, known as the "WMAP Haze", may be the synchrotron emission from relativistic electrons and positrons produced in dark matter annihilations. In particular, the angular distribution, spectrum, and intensity of the observed emission are consistent with the signal expected to result from a WIMP with an electroweak-scale mass and an annihilation cross section near the value predicted for a thermal relic. In this article, we revisit this signal within the context of supersymmetry, and evaluate the parameter space of the Constrained Minimal Supersymmetric Standard Model (CMSSM). We find that, over much of the supersymmetric parameter space, the lightest neutralino is predicted to possess the properties required to generate the WMAP Haze. In particular, the focus point, A-funnel, and bulk regions typically predict a neutralino with a mass, annihilation cross section, and dominant annihilation modes which are within the range required to produce the observed features of the WMAP Haze. The stau-coannihilation region, in contrast, is disfavored as an explanation for the origin of this signal.
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