Shape Of Power Spectral Density Research Articles

Ensemble power spectral density of SDSS quasars in UV/optical bands

Context. Quasar variability has proven to be a powerful tool to constrain the properties of their inner engine and the accretion process onto supermassive black holes. Correlations between UV/optical variability and physical properties have been long studied with a plethora of different approaches and time-domain surveys, although the detailed picture is not yet clear. Aims. We analysed archival data from the SDSS Stripe-82 region to study how the quasar power spectral density (PSD) depends on the black hole mass, bolometric luminosity, accretion rate, redshift, and rest-frame wavelength. We developed a model-independent analysis framework that could be easily applied to upcoming large surveys such as the Legacy Survey of Space and Time (LSST). Methods. We used light curves of 8042 spectroscopically confirmed quasars, observed in at least six yearly seasons in five filters ugriz. We split the sample into bins of similar physical properties containing at least 50 sources, and we measured the ensemble PSD in each of them. Results. We find that a simple power law is a good fit to the power spectra in the frequency range explored. Variability does not depend on the redshift at a fixed wavelength. Instead, both PSD amplitude and slope depend on the black hole mass, accretion rate, and rest-frame wavelength. We provide scaling relations to model the observed variability as a function of the physical properties, and discuss the possibility of a universal PSD shape for all quasars, where frequencies scale with the black hole mass, while normalization and slope(s) are fixed (at any given wavelength and accretion rate).

Exploring the Link between the X-Ray Power Spectra and Energy Spectra of Active Galactic Nuclei

Active galactic nuclei (AGN) are generally considered the scaled-up counterparts of X-ray binaries (XRBs). It is known that the power spectral density (PSD) of the X-ray emission of XRBs shows significant evolution with spectral state. It is not clear whether AGN follow a similar evolutionary trend, however, though their X-ray emission and the PSD are both variable. In this work, we study a sample of nine AGN with multiple long observations with XMM-Newton, which exhibit significant X-ray spectral variation. We perform Bayesian PSD analysis to measure the PSD shape and variation. We find that a large change in the X-ray energy spectrum (mainly the change in flux state) is often accompanied by a large change in the PSD shape. The emergence of a high-frequency break in the PSD also depends on the spectral state. Among the four sources with significant high-frequency PSD breaks detected, three show the break only in the high-flux state, while the remaining one shows it only in the low-flux state. Moreover, the X-ray rms variability in different spectral states of an AGN is found to vary by as much as 1.0 dex. These results suggest that the different variability properties observed are likely caused by different physical processes dominating different spectral states. Our results also indicate that the intrinsic PSD variation can introduce a significant fraction of the dispersion as reported for the correlations between various X-ray variability properties and the black hole mass.

Normalization of Aperiodic Electrocorticography Components Indicates Fine Motor Recovery After Sensory Cortical Stroke in Mice.

Electrophysiological signatures of ischemic stroke might help to develop a deeper understanding of the mechanisms of recovery. However, to identify critical windows for novel treatment approaches, suitable readout parameters in vivo with the potential to close the gap between functional modifications within the peri-infarct cortex and behavioral outcome on the systems-level are still lacking. Wild-type mice were trained in a skilled reaching task and underwent permanent distal medial cerebral artery occlusion or sham intervention. Functional deficits and their recovery were monitored both behaviorally and electrophysiologically recording multichannel electrocorticography from both hemispheres. Ischemic strokes are located in sensory cortical areas. Affected mice presented fine motor deficits of their contralateral forepaw. Analyses of electrocorticography signals from awake animals demonstrated a modulation of the shape of power spectral density in the vicinity of the infarct. While power spectral density consists of both rhythmic oscillatory and nonrhythmic, aperiodic components, the alteration of spectrum shape was reflected in a transient increase of aperiodic exponents in the peri-infarct cortex. The relative power and frequency of slow oscillations remained unchanged. Exponents derived from motor areas significantly correlated with fine motor recovery, thus indicating functional modifications of neuronal activity. Aperiodic spectral exponents exhibited a unique spatiotemporal profile in the mouse cortex after stroke and might complement future translational studies providing a dynamic link from pathophysiology to behavior.

Spectra of Temperature Fluctuations in the Solar Wind

Turbulent cascade transferring the free energy contained within the large scale fluctuations of the magnetic field, velocity and density into the smaller ones is probably one of the most important mechanisms responsible for heating of the solar corona and solar wind, thus the turbulent behavior of these quantities is intensively studied. The temperature is also highly fluctuating quantity but its variations are studied only rarely. There are probably two reasons, first the temperature is tensor and, second, an experimental determination of temperature variations requires knowledge of the full velocity distribution with an appropriate time resolution but such measurements are scarce. To overcome this problem, the Bright Monitor of the Solar Wind (BMSW) on board Spektr-R used the Maxwellian approximation and provided the thermal velocity with a 32 ms resolution, investigating factors influencing the temperature power spectral density shape. We discuss the question whether the temperature spectra determined from Faraday cups are real or apparent and analyze mutual relations of power spectral densities of parameters like the density, parallel and perpendicular components of the velocity and magnetic field fluctuations. Finally, we compare their spectral slopes with the slopes of the thermal velocity in both inertial and kinetic ranges and their evolution in course of solar wind expansion.

A Physical Model for Volcanic Eruption Tremor

AbstractSeismic waves are commonly used to monitor unrest before, during, and after volcanic eruptions. The source of seismic tremor during a sustained explosive volcanic eruption is not well understood. Recent observations of the 2016 eruption of Pavlof Volcano, Alaska, revealed a change in the relationship (hysteresis) between ash plume height and seismic amplitude over time. Based on similarities in physical processes and observed seismic tremor in rivers, we explore two key sources of seismic energy in the volcanic conduit: (1) forces exerted by particle impacts and (2) dynamic pressure changes by the turbulent flow. We develop a physical model calculating the seismic power spectral density (PSD), where forces on the conduit wall are convolved with the Green's function for Rayleigh waves. Using reasonable eruption parameters, the model is able to reproduce the frequency spectrum from the Pavlof eruption, although the modeled amplitudes are generally lower. We test the relative importance of different eruption parameters, including grain size, velocity, and conduit dimensions. We find that turbulence generally dominates over particle impacts. However, to reach the PSD amplitude during the Pavlof eruption, large grain sizes are required, as they have the greatest relative influence on the modeled amplitude. The hysteresis between plume height and seismic amplitude can then potentially be explained by grain size changes. The PSD shape is mostly determined by the Rayleigh‐wave quality factor Q, and substantial variations in seismic amplitude can be modeled assuming a constant mass eruption rate.

Pseudonoise Waveform Design for Spectrum Sharing Systems

With an increasing demand for high-resolution radar and wideband communication systems, the frequency spectrum is becoming a limited resource. Many such systems must coexist in a given frequency band. In order to minimize interference among these systems, a radar waveform design is used. Without a priori knowledge of the transmission channel and communication waveform, one viable strategy is to use spectral nulls for the frequencies used by communication system. This article describes an improved method for generating pseudonoise waveforms with limited range and Doppler sidelobes. The algorithm permits adjustable power spectral density of the generated waveform. An additional parameter, “significance factor,” is a tradeoff between power spectral density shape and sidelobe suppression depth. The method also allows the generation of a set of mutually orthogonal waveforms for multitransmitter scenarios. Effectiveness of the algorithm is confirmed by both numerical simulation and field trials.

Day-to-Day Test-Retest Reliability of EEG Profiles in Children With Autism Spectrum Disorder and Typical Development.

Biomarker development is currently a high priority in neurodevelopmental disorder research. For many types of biomarkers (particularly biomarkers of diagnosis), reliability over short periods is critically important. In the field of autism spectrum disorder (ASD), resting electroencephalography (EEG) power spectral densities (PSD) are well-studied for their potential as biomarkers. Classically, such data have been decomposed into pre-specified frequency bands (e.g., delta, theta, alpha, beta, and gamma). Recent technical advances, such as the Fitting Oscillations and One-Over-F (FOOOF) algorithm, allow for targeted characterization of the features that naturally emerge within an EEG PSD, permitting a more detailed characterization of the frequency band-agnostic shape of each individual’s EEG PSD. Here, using two resting EEGs collected a median of 6 days apart from 22 children with ASD and 25 typically developing (TD) controls during the Feasibility Visit of the Autism Biomarkers Consortium for Clinical Trials, we estimate test-retest reliability based on the characterization of the PSD shape in two ways: (1) Using the FOOOF algorithm we estimate six parameters (offset, slope, number of peaks, and amplitude, center frequency and bandwidth of the largest alpha peak) that characterize the shape of the EEG PSD; and (2) using nonparametric functional data analyses, we decompose the shape of the EEG PSD into a reduced set of basis functions that characterize individual power spectrum shapes. We show that individuals exhibit idiosyncratic PSD signatures that are stable over recording sessions using both characterizations. Our data show that EEG activity from a brief 2-min recording provides an efficient window into characterizing brain activity at the single-subject level with desirable psychometric characteristics that persist across different analytical decomposition methods. This is a necessary step towards analytical validation of biomarkers based on the EEG PSD and provides insights into parameters of the PSD that offer short-term reliability (and thus promise as potential biomarkers of trait or diagnosis) vs. those that are more variable over the short term (and thus may index state or other rapidly dynamic measures of brain function). Future research should address the longer-term stability of the PSD, for purposes such as monitoring development or response to treatment.

X-ray variability plane revisited: Role of obscuration

AbstractScaling relations are the most powerful astrophysical tools to set constraints to the physical mechanisms of astronomical sources and to infer properties for objects where they cannot be accessed directly. We have re-investigated one of these scaling relations using powerful type 1 Seyferts; the so-called X-ray variability plane (or mass-luminosity-timescale relation, McHardy et al.2006). This relation links the power-spectral density (PSD) break frequency with the SMBH mass and the bolometric luminosity. We used all available XMM-Newton observations to study the PSD and spectra in short segments within each observation. This allows us to report for the first time that the PSD break frequency varies for each object, showing variations in 19 out of the 22 AGN analyzed. Our analysis of the variability plane confirms the relation between the break frequency and the SMBH mass and finds that the obscuration along the line of sight (or the variations on the obscuration using its standard deviation) is also a required parameter. We constrain a new variability plane of the form: log(vBreak) = – A log (MBH) + B log (NH) – C (or log(vBreak) = – A log (MBH) + B Δ (NH) + C). The X-ray variability plane found by McHardy et al. (2006) is roughly recovered when we use unobscured segments. We speculate the PSD shape is related with the outflowing wind close to the accretion disk at least for these powerful type 1 AGN (Gonzalez-Martin et al. 2018).

Dechirping Compression Method for Nonlinear Frequency Modulation Waveforms

This letter proposes a novel dechirp processing method for wideband nonlinear frequency modulation (NLFM) waveform which enables low sampling rate of data. As we know, NLFM waveform can easily realize optimal shape of power spectral density which helps to achieve better pulse compression result with low range sidelobes without signal-to-noise ratio degradation caused by weighting as we usually do for LFM waveforms. In the approach, hamming window is adopted in the generation of the NLFM waveform for better balance on the low range sidelobes and a relative small bandwidth. In dechirp operation, the NLFM radar echoes are mixed with a local reference LFM signal, and thus narrowband signals are resulted and only low sampling rate is needed. The dechirped NLFM signals are then up-sampled and inverse dechirped by software and finally matched filtering is conducted to complete pulse compression. Both numerically simulated data and real radar data are processed to verify the effectiveness of the proposed method.

Acoustic receptivity and transition modeling of Tollmien-Schlichting disturbances induced by distributed surface roughness

Acoustic receptivity to Tollmien-Schlichting waves in the presence of surface roughness is investigated for a flat plate boundary layer using the time-harmonic incompressible linearized Navier-Stokes equations. It is shown to be an accurate and efficient means of predicting receptivity amplitudes and, therefore, to be more suitable for parametric investigations than other approaches with direct-numerical-simulation-like accuracy. Comparison with the literature provides strong evidence of the correctness of the approach, including the ability to quantify non-parallel flow effects. These effects are found to be small for the efficiency function over a wide range of frequencies and local Reynolds numbers. In the presence of a two-dimensional wavy-wall, non-parallel flow effects are quite significant, producing both wavenumber detuning and an increase in maximum amplitude. However, a smaller influence is observed when considering an oblique Tollmien-Schlichting wave. This is explained by considering the non-parallel effects on receptivity and on linear growth which may, under certain conditions, cancel each other out. Ultimately, we undertake a Monte Carlo type uncertainty quantification analysis with two-dimensional distributed random roughness. Its power spectral density (PSD) is assumed to follow a power law with an associated uncertainty following a probabilistic Gaussian distribution. The effects of the acoustic frequency over the mean amplitude of the generated two-dimensional Tollmien-Schlichting waves are studied. A strong dependence on the mean PSD shape is observed and discussed according to the basic resonance mechanisms leading to receptivity. The growth of Tollmien-Schlichting waves is predicted with non-linear parabolized stability equations computations to assess the effects of stochasticity in transition location.

Frequency-dependent core shifts and parameter estimation for the blazar 3C 454.3

We study the core shift effect in the parsec scale jet of the blazar 3C 454.3 using the 4.8 GHz - 36.8 GHz radio light curves obtained from three decades of continuous monitoring. From a piecewise Gaussian fit to each flare, time lags $\Delta t$ between the observation frequencies $\nu$ and spectral indices $\alpha$ based on peak amplitudes $A$ are determined. From the fit $\Delta t \propto \nu^{1/k_r}$, $k_r = 1.10 \pm 0.18$ indicating equipartition between the magnetic field energy density and the particle energy density. From the fit $A \propto \nu^\alpha$, $\alpha$ is in the range $-0.24$ to $1.52$. A mean magnetic field strength at 1 pc, $B_1 = 0.5 \pm 0.2$ G, and at the core, $B_{\rm core} = 46 \pm 16$ mG, are inferred, consistent with previous estimates. The measure of core position offset is $\Omega_{r\nu} = 6.4 \pm 2.8$ pc GHz$^{1/k_r}$ when averaged over all frequency pairs. Based on the statistical trend shown by the measured core radius $r_{\rm core}$ as a function of $\nu$, we infer that the synchrotron opacity model may not be valid for all cases. A Fourier periodogram analysis yields power law slopes in the range $-1.6$ to $-3.5$ describing the power spectral density shape and gives bend timescales in the range $0.52 - 0.66~$yr. This result, and both positive and negative $\alpha$, indicate that the flares originate from multiple shocks in a small region. Important objectives met in our study include: the demonstration of the computational efficiency and statistical basis of the piecewise Gaussian fit; consistency with previously reported results; evidence for the core shift dependence on observation frequency and its utility in jet diagnostics in the region close to the resolving limit of very long baseline interferometry observations.

The remarkable timing properties of a ‘hypersoft’ state in GRO J1655-40

We report the identification and study of an unusual soft state of the black hole low-mass X-ray binary GRO J1655-40, observed during its 2005 outburst by the Rossi X-ray Timing Explorer. Chandra X-ray grating observations have revealed a high mass-outflow accretion disc wind in this state, and we show that the broadband X-ray spectrum is remarkably similar to that observed in the so-called `hypersoft' state of the high mass X-ray binary Cyg X-3, which possesses a strong stellar wind from a Wolf-Rayet secondary. The power-spectral density (PSD) of GRO J1655-40 shows a bending power-law shape, similar to that of canonical soft states albeit with larger fractional rms. However, the characteristic bend-frequency of the PSD is strongly correlated with the X-ray flux, such that the bend-frequency increases by two decades for less than a factor 2 increase in flux. The strong evolution of PSD bend-frequency for very little change in flux or X-ray spectral shape seems to rule out the suppression of high-frequency variability by scattering in the wind as the origin of the PSD bend. Instead, we suggest that the PSD shape is intrinsic to the variability process and may be linked to the evolution of the scale-height in a slim disc. An alternative possibility is that variability is introduced by variable absorption and scattering in the wind. We further argue that the hypersoft state in GRO J1655-40 and Cyg X-3 is associated with accretion close to or above the Eddington limit.

Broad-Band Variability in Accreting Compact Objects

Cataclysmic variable stars are in many ways similar to X-ray binaries. Both types of systems possess an accretion disk, which in most cases can reach the surface (or event horizon) of the central compact object. The main difference is that the embedded gravitational potential well in X-ray binaries is much deeper than those found in cataclysmic variables. As a result, X-ray binaries emit most of their radiation at X-ray wavelengths, as opposed to cataclysmic variables which emit mostly at optical/ultraviolet wavelengths. Both types of systems display aperiodic broad-band variability which can be associated to the accretion disk. Here, the properties of the observed X-ray variability in XRBs are compared to those observed at optical wavelengths in CVs. In most cases the variability properties of both types of systems are qualitatively similar once the relevant timescales associated with the inner accretion disk regions have been taken into account. The similarities include the observed power spectral density shapes, the rms-flux relation as well as Fourier-dependant time lags. Here a brief overview on these similarities is given, placing them in the context of the fluctuating accretion disk model which seeks to reproduce the observed variability.

X-RAY VARIABILITY AND THE INNER REGION IN ACTIVE GALACTIC NUCLEI

We present theoretical models of X-ray variability attributable to orbital signatures from an accretion disk including emission region size, quasi-periodic oscillations (QPOs) and its quality factor $Q$, and the emergence of a break frequency in the power spectral density shape. We find a fractional variability amplitude of $F_{var}\propto M^{-0.4}_{\bullet}$. We conduct a time series analysis on X-ray light curves ($0.3-10$ keV) of a sample of active galactic nuclei (AGNs). A statistically significant bend frequency is inferred in 9 of 58 light curves (16 %) from 3 AGNs for which the break timescale is consistent with the reported BH spin but not with the reported BH mass. Upper limits of $2.85 \times 10^7 M_\odot$ in NGC 4051, $8.02 \times 10^7 M_\odot$ in MRK 766 and $4.68 \times 10^7 M_\odot$ in MCG-6-30-15 are inferred for maximally spinning BHs. For REJ 1034+396, where a QPO at 3733 s was reported, we obtain an emission region size of $(6 - 6.5) M$ and a BH spin $a\lesssim$ 0.08. The relativistic inner region of a thin disk, dominated by radiation pressure and electron scattering is likely to host the orbital features as the simulated $Q$ ranges from $6.3 \times 10^{-2}$ to $4.25 \times 10^6$, containing the observed $Q$. The derived value of $Q \sim$ 32 for REJ 1034+396 therefore suggests that the AGN hosts a thin disk.

The spectral energy distribution of compact jets powered by internal shocks

Internal shocks caused by fluctuations of the outflow velocity are likely to power the radio to IR emission of the compact jets of X-ray binaries. The dynamics of internal shocks and the resulting spectral energy distribution (SED) of the jet are very sensitive to the time-scales and amplitudes of the velocity fluctuations injected at the base of the jet. I present a new code designed to simulate the synchrotron emission of a compact jet powered by internal shocks. I also develop a semi-analytical formalism allowing one to estimate the observed SED of the jet as a function of the Power Spectral Density (PSD) of the assumed fluctuations of the Lorentz factor. I discuss the cases of a sine modulation of the Lorentz factor and Lorentz factor fluctuations with a power-law PSD shape. Independently of the details of the model, the observed nearly flat SEDs are obtained for PSDs of Lorentz factor fluctuations that are close to a flicker noise spectrum (i.e. P(f)~1/f). The model also presents a strong wavelength dependent variability that is similar to that observed in these sources.

Gaussian mixture model approximation of total spatial power spectral density for multiple incoherently distributed sources

Practically, the spatial power spectral density (PSD) of single or multiple incoherently distributed (ID) sources is often unknown, and the total spatial PSD is suitable to model the spatial distribution characteristic of signals if the number of multiple ID sources is also unknown. In this study, the Gaussian mixture model (GMM) is employed to characterise the total spatial PSD of multiple ID sources, and two algorithms are proposed to estimate the parameters of the GMM. The first one is the covariance fitting method for multiple ID sources with Gaussian PSD, and the other is the iterative expectation maximisation (EM) algorithm. Simulation studies demonstrate that the EM algorithm outperforms other methods in approximating the shape of the total spatial PSD, especially for small spatial spread.

Variance error, interpolation and experiment design

We investigate how the variance error associated with the prediction error identification is related to the power spectral densities of the input and the additive noise at the output. Let Φ(eiω) be the ratio of the input power spectral density (PSD) to the output-noise PSD. We characterize the set of all functions Φ for which the variance error remains constant. This analysis results a minimal, finite-dimensional, affine parameterization of the variance error. This parameterization connects our analysis with the theory of Nevanlinna–Pick interpolation. It is shown that the set of all Φ for which the variance error remains constant can be characterized by the solutions of a Nevanlinna–Pick interpolation problem. This insight has interesting consequences in optimal input design, where it is possible to use some recent tools in analytic interpolation theory to tune shape of the input PSD to suit certain needs.

Fatigue life prediction for broad-band multiaxial loading with various PSD curve shapes

The fatigue calculation procedure analysed here applies the power spectral density (PSD) function of the equivalent stress together with the known spectral method for estimating the probability density function of stress amplitudes included in random loading. Here, the narrow-band approximation, Wirsching–Light, Benasciutti–Tovo and Dirlik models are used, together with the SWT parameter. The prediction capability of these four methods was verified on a set of 107 tests results obtained under random axial, torsion and combined axial and torsion loading applied to a tubular specimen with a one-sided hole. Several PSD shapes and combinations of loading were applied. It is shown that the results for fatigue life calculated using the Benasciutti–Tovo and Dirlik methods are well correlated with the results of experiments under this type of loading.

A simulation model for generation of multiple uncorrelated Rayleigh fading waveforms

This paper presents a new discrete-time ergodic simulation model for the efficient generation of multiple time uncorrelated Rayleigh waveforms. It uses the inverse discrete Fourier transform (IDFT) to generate the transmission coefficients with only one random number generator. The model and its statistical characteristics are derived as a function of the channel power spectral density (PSD). Irrespective of the channel PSD shape, the proposed model will be an ergodic complex random process with correct ensemble averages.

The Energy‐dependent X‐Ray Timing Characteristics of the Narrow‐Line Seyfert 1 Mrk 766

We present the energy-dependent power spectral density (PSD) and cross-spectral properties of Mkn 766, obtained from combining data obtained during an XMM-Newton observation spanning six revolutions in 2005 with data obtained from an XMM-Newton long-look in 2001. The PSD shapes and rms-flux relations are found to be consistent between the 2001 and 2005 observations, suggesting the 2005 observation is simply a low-flux extension of the 2001 observation and permitting us to combine the two data sets. The resulting PSD has the highest temporal frequency resolution for any AGN PSD measured to date. Applying a broken power-law model yields break frequencies which increase in temporal frequency with photon energy. Obtaining a good fit when assuming energy-independent break frequencies requires the presence of a Lorentzian at 4.6 +/- 0.4 x 10(exp -4)Hz whose strength increases with photon energy, a behavior seen in black hole X-ray binaries. The cross-spectral properties are measured; temporal frequency-dependent soft-to-hard time lags are detected in this object for the first time. Cross-spectral results are consistent with those for other accreting black hole systems. The results are discussed in the context of several variability models, including those based on inwardly-propagating viscosity variations in the accretion disk.