Evidence of Intermittent Cascades from Discrete Hierarchical Dissipation in Turbulence

We present the results of a search of log-periodic corrections to scaling in the moments of the energy dissipation rate in experiments at high Reynolds number (2500) of three-dimensional fully developed turbulence. A simple dynamical representation of the Richardson-Kolmogorov cartoon of a cascade shows that standard averaging techniques erase by their very construction the possible existence of log-periodic corrections to scaling associated with a discrete hierarchy. To remedy this drawback, we introduce a novel ``canonical'' averaging that we test extensively on synthetic examples constructed to mimick the interplay between a weak log-periodic component and rather strong multiplicative and phase noises. Our extensive tests confirm the remarkable observation of statistically significant log-periodic corrections to scaling, with a prefered scaling ratio for length scales compatible with the value gamma = 2. A strong confirmation of this result is provided by the identification of up to 5 harmonics of the fundamental log-periodic undulations, associated with up to 5 levels of the underlying hierarchical dynamical structure. A natural interpretation of our results is that the Richardson-Kolmogorov mental picture of a cascade becomes a realistic description if one allows for intermittent births and deaths of discrete cascades at varying scales.Comment: Latex document of 40 pages, including 18 eps figure

Investigating Light Curve Modulation via Kernel Smoothing. I. Application to 53 fundamental mode and first-overtone Cepheids in the LMC

Recent studies have revealed a hitherto unknown complexity of Cepheid pulsation. We implement local kernel regression to search for both period and amplitude modulations simultaneously in continuous time and to investigate their detectability, and test this new method on 53 classical Cepheids from the OGLE-III catalog. We determine confidence intervals using parametric and non-parametric bootstrap sampling to estimate significance and investigate multi-periodicity using a modified pre-whitening approach that relies on time-dependent light curve parameters. We find a wide variety of period and amplitude modulations and confirm that first overtone pulsators are less stable than fundamental mode Cepheids. Significant temporal variations in period are more frequently detected than those in amplitude. We find a range of modulation intensities, suggesting that both amplitude and period modulations are ubiquitous among Cepheids. Over the 12-year baseline offered by OGLE-III, we find that period changes are often non-linear, sometimes cyclic, suggesting physical origins beyond secular evolution. Our method more efficiently detects modulations (period and amplitude) than conventional methods reliant on pre-whitening with constant light curve parameters and more accurately pre-whitens time series, removing spurious secondary peaks effectively.Comment: Re-submitted including revisions to Astronomy and Astrophysic

Adaptive window selection and smoothing of Lomb periodogram for time-frequency analysis of time series

The 47th Midwest Symposium on Circuits and Systems Conference, Salt Lake City, Utah, USA, 25-28 July 2004This article introduces a new adaptive Lomb periodogram for time-frequency analysis of time series, which are possibly non-uniformly sampled. It extends the conventional Lomb spectrum by windowing the observations and adaptively selects the window length by the intersection of confidence intervals (ICI) rule. To further reduce the variance of the Lomb periodogram due to time smoothing alone, time-frequency smoothing using local polynomial regression (LPR) is proposed. An orientation analysis is performed in order to derive a directional kernel in the time-frequency plane for adaptive smoothing of the periodogram. The support of this directional kernel is also adaptively selected using the ICI rule. Simulation results show that the proposed adaptive Lomb periodogram with time-frequency smoothing offers better time and frequency resolutions as well as lower variance than the conventional Lomb periodogram.published_or_final_versio

New Evidence of Discrete Scale Invariance in the Energy Dissipation of Three-Dimensional Turbulence: Correlation Approach and Direct Spectral Detection

We extend the analysis of [Zhou and Sornette, Physica D 165, 94-125, 2002] showing statistically significant log-periodic corrections to scaling in the moments of the energy dissipation rate in experiments at high Reynolds number ($\approx 2500$) of three-dimensional fully developed turbulence. First, we develop a simple variant of the canonical averaging method using a rephasing scheme between different samples based on pairwise correlations that confirms Zhou and Sornette's previous results. The second analysis uses a simpler local spectral approach and then performs averages over many local spectra. This yields stronger evidence of the existence of underlying log-periodic undulations, with the detection of more than 20 harmonics of a fundamental logarithmic frequency $f = 1.434 \pm 0.007$ corresponding to the preferred scaling ratio $\gamma = 2.008 \pm 0.006$.Comment: 9 RevTex4 papes including 8 eps figure

A Search for Variability in Exoplanet Analogues and Low-Gravity Brown Dwarfs

We report the results of a $J$-band survey for photometric variability in a sample of young, low-gravity objects using the New Technology Telescope (NTT) and the United Kingdom InfraRed Telescope (UKIRT). Surface gravity is a key parameter in the atmospheric properties of brown dwarfs and this is the first large survey that aims to test the gravity dependence of variability properties. We do a full analysis of the spectral signatures of youth and assess the group membership probability of each target using membership tools from the literature. This results in a 30 object sample of young low-gravity brown dwarfs. Since we are lacking in objects with spectral types later than L9, we focus our statistical analysis on the L0-L8.5 objects. We find that the variability occurrence rate of L0-L8.5 low-gravity brown dwarfs in this survey is $30^{+16}_{-8}\%$. We reanalyse the results of Radigan 2014 and find that the field dwarfs with spectral types L0-L8.5 have a variability occurrence rate of $11^{+13}_{-4}\%$. We determine a probability of $98\%$ that the samples are drawn from different distributions. This is the first quantitative indication that the low-gravity objects are more likely to be variable than the field dwarf population. Furthermore, we present follow-up $J_S$ and $K_S$ observations of the young, planetary-mass variable object PSO 318.5-22 over three consecutive nights. We find no evidence of phase shifts between the $J_S$ and $K_S$ bands and find higher $J_S$ amplitudes. We use the $J_S$ lightcurves to measure a rotational period of $8.45\pm0.05~$hr for PSO 318.5-22.Comment: accepted for publication in MNRA

Exoplanets or Dynamic Atmospheres? The Radial Velocity and Line Shape Variations of 51 Pegasi and Tau Bootis

Because of our relatively low spectral resolution, we compare our observations with Gray's line bisector data by fitting observed line profiles to an expansion in terms of orthogonal (Hermite) functions. To obtain an accurate comparison, we model the emergent line profiles from rotating and pulsating stars, taking the instrumental point spread function into account. We describe this modeling process in detail. We find no evidence for line profile or strength variations at the radial velocity period in either 51 Peg or in Tau Boo. For 51 Peg, our upper limit for line shape variations with 4.23-day periodicity is small enough to exclude with 10 sigma confidence the bisector curvature signal reported by Gray & Hatzes; the bisector span and relative line depth signals reported by Gray (1997) are also not seen, but in this case with marginal (2 sigma) confidence. We cannot, however, exclude pulsations as the source of 51 Peg's radial velocity variation, because our models imply that line shape variations associated with pulsations should be much smaller than those computed by Gray & Hatzes; these smaller signals are below the detection limits both for Gray & Hatzes' data and for our own. Tau Boo's large radial velocity amplitude and v*sin(i) make it easier to test for pulsations in this star. Again we find no evidence for periodic line-shape changes, at a level that rules out pulsations as the source of the radial velocity variability. We conclude that the planet hypothesis remains the most likely explanation for the existing data.Comment: 44 pages, 19 figures, plain TeX, accepted to ApJS (companion to letter astro-ph/9712279

Color Difference Makes a Difference: Four Planet Candidates around τ Ceti

The removal of noise typically correlated in time and wavelength is one of the main challenges for using the radial-velocity (RV) method to detect Earth analogues. We analyze τ Ceti RV data and find robust evidence for wavelength-dependent noise. We find that this noise can be modeled by a combination of moving average models and the so-called "differential radial velocities." We apply this noise model to various RV data sets for τ Ceti, and find four periodic signals at 20.0, 49.3, 160, and 642 days, which we interpret as planets. We identify two new signals with orbital periods of 20.0 and 49.3 days while the other two previously suspected signals around 160 and 600 days are quantified to a higher precision. The 20.0 days candidate is independently detected in Keck data. All planets detected in this work have minimum masses less than 4M⊕ with the two long-period ones located around the inner and outer edges of the habitable zone, respectively. We find that the instrumental noise gives rise to a precision limit of the High Accuracy Radial Velocity Planet Searcher (HARPS) around 0.2 m s−1. We also find correlation between the HARPS data and the central moments of the spectral line profile at around 0.5 m s−1 level, although these central moments may contain both noise and signals. The signals detected in this work have semi-amplitudes as low as 0.3 m s−1, demonstrating the ability of the RV technique to detect relatively weak signals

A 2.15 Hour Orbital Period for the Low Mass X-Ray Binary XB 1832-330 in the Globular Cluster NGC 6652

We present a candidate orbital period for the low mass X-ray binary XB 1832-330 in the globular cluster NGC 6652 using a 6.5 hour Gemini South observation of the optical counterpart of the system. Light curves in g' and r' for two LMXBs in the cluster, sources A and B in previous literature, were extracted and analyzed for periodicity using the ISIS image subtraction package. A clear sinusoidal modulation is evident in both of A's curves, of amplitude ~0.11 magnitudes in g' and ~0.065 magnitudes in r', while B's curves exhibit rapid flickering, of amplitude ~1 magnitude in g' and ~0.5 magnitudes in r'. A Lomb-Scargle test revealed a 2.15 hour periodic variation in the magnitude of A with a false alarm probability less than 10^-11, and no significant periodicity in the light curve for B. Though it is possible saturated stars in the vicinity of our sources partially contaminated our signal, the identification of A's binary period is nonetheless robust.Comment: 7 pages, 7 figures, ApJ in pres