Slopes Of Structure Function Research Articles

Analysis of the Intranight Variability of BL Lacertae during Its 2020 August Flare

We present an analysis of the BVRI photometry of the blazar BL Lacertae on diverse timescales from 2020 mid-July to mid-September. We have used 11 different optical telescopes around the world and have collected data over 84 observational nights. The observations cover the onset of a new activity phase of BL Lacertae that started in 2020 August (termed as the 2020 August flare by us), and the analysis is focused on the intranight variability. On short-term timescales, (i) flux varied with ∼2.2 mag in the R band, (ii) the spectral index was found to be weakly dependent on the flux (i.e., the variations could be considered mildly chromatic), and (iii) no periodicity was detected. On intranight timescales, BL Lacertae was found to predominantly show bluer-when-brighter chromatism. We also found two cases of significant interband time lags of the order of a few minutes. The duty cycle of the blazar during the 2020 August flare was estimated to be quite high (∼90% or higher). We decomposed the intranight light curves into individual flares and determined their characteristics. On the basis of our analysis and assuming the turbulent jet model, we determined some characteristics of the emitting regions: Doppler factor, magnetic field strength, electron Lorentz factor, and radius. The radii determined were discussed in the framework of the Kolmogorov theory of turbulence. We also estimated the weighted mean structure function slope on intranight timescales, related it to the slope of the power spectral density, and discussed it with regard to the origin of intranight variability.

Optical Variability of Eight FRII-type Quasars with 13 yr Photometric Light Curves

We characterize the optical variability properties of eight lobe-dominated radio quasars (QSOs): B2 0709+37, FBQS J095206.3+235245, PG 1004+130, [HB89] 1156+631, [HB89] 1425+267, [HB89] 1503+691, [HB89] 1721+343, and 4C +74.26, systematically monitored for a duration of 13 yr since 2009. The quasars are radio-loud objects with extended radio lobes that indicate their orientation close to the sky plane. Five of the eight QSOs are classified as giant radio quasars. All quasars showed variability during our monitoring, with magnitude variations between 0.3 and 1 mag for the least variable and the most variable QSOs, respectively. We performed both structure function (SF) analysis and power spectral density (PSD) analysis for the variability characterization and search for characteristic timescales and periodicities. As a result of our analysis, we obtained relatively steep SF slopes (α ranging from 0.49 to 0.75) that are consistent with the derived PSD slopes (∼2–3). All the PSDs show a good fit to single power-law forms, indicating a red-noise character of variability between timescales of ∼13 yr and weeks. We did not measure reliable characteristic timescales of variability from the SF analysis, which indicates that the duration of the gathered data is too short to reveal them. The absence of bends in the PSDs (change of slope from ≥1 to ∼0) on longer timescales indicates that optical variations are most likely caused by thermal instabilities in the accretion disk.

Statistical analysis of the causes of excess variance in the 21 cm signal power spectra obtained with the Low-Frequency Array

Context.The detection of the 21 cm signal of neutral hydrogen from the Epoch of Reionization (EoR) is challenging due to bright foreground sources, radio frequency interference (RFI), and the ionosphere as well as instrumental effects. Even after correcting for these effects in the calibration step and applying foreground removal techniques, the remaining residuals in the observed 21 cm power spectra are still above the thermal noise, which is referred to as the “excess variance.”Aims.We study a number of potential causes of this excess variance based on 13 nights of data obtained with the Low-Frequency Array (LOFAR).Methods.We focused on the impact of gain errors, the sky model, and ionospheric effects on the excess variance by correlating the relevant parameters such as the gain variance over time or frequency, local sidereal time (LST), diffractive scale, and phase structure–function slope with the level of excess variance.Results.Our analysis shows that the excess variance, at the current level, is neither strongly correlated with gain variance nor the ionospheric parameters. Rather, excess variance has an LST dependence, which is related to the power from the sky. Furthermore, the simulated StokesIpower spectra from bright sources and the excess variance show a similar progression over LST with the minimum power appearing at LST bin 6h to 9h. This LST dependence is also present in sky images of the residual StokesIof the observations. In very-wide sky images based on one night of observation after direction-dependent calibration, we demonstrate that the extra power comes exactly from the direction of bright and distant sources Cassiopeia A and Cygnus A with the array beam patterns.Conclusions.These results suggest that the level of excess variance in the 21 cm signal power spectra is related to sky effects and, hence, it depends on LST. In particular, very bright and distant sources such as Cassiopeia A and Cygnus A can dominate the effect. This is in line with earlier studies and offers a path forward toward a solution, since the correlation between the sky-related effects and the excess variance is non-negligible.

The mid-infrared variability of the SDSS optical quasars

Based on the Seventh Data Release (DR7) quasar catalog from the Sloan Digital Sky Survey, we investigate the variability of optical quasars in W1, W2, W3 and W4 bands of the Wide-field Infrared Survey Explorer (WISE) and the Near-Earth Object Wide-field Infrared Survey Explorer (NEOWISE). Adopting the structure function (SF) method, we calculate the SF (δ t = 1 yr) which shows no obvious correlations with the bolometric luminosity, the black hole mass and the Eddington ratio. The ensemble SFs in W1 and W2 bands show that the SF slopes are steeper than those in previous studies which may be caused by different cadence and observational epoch number. We further investigate the relation of variability amplitude σm between mid-infrared band and optical band, but no obvious correlation is found. No correlation is found between W1–W2 and g – r color. We think that the mid-infrared emission of quasars may be smoothed out by the extended dust distribution, thus leading to no obvious correlation. For the radio-loud quasar sub-sample, we further analyze the relation between the variability amplitude in the mid-infrared band and the radio luminosity at 6 cm, but no obvious correlations are found, which indicate the mid-infrared emission contributed from the synchrotron radiation of the relativistic jet is very weak.

The Vertical Structure of Open-Ocean Submesoscale Variability during a Full Seasonal Cycle

AbstractSubmesoscale dynamics are typically intensified at boundaries and assumed to weaken below the mixed layer in the open ocean. Here, we assess both the seasonality and the vertical distribution of submesoscale motions in an open-ocean region of the northeast Atlantic. Second-order structure functions, or variance in properties separated by distance, are calculated from submesoscale-resolving ocean glider and mooring observations, as well as a 1/48° numerical ocean model. This dataset combines a temporal coverage that extends through a full seasonal cycle, a horizontal resolution that captures spatial scales as small as 1 km, and vertical sampling that provides near-continuous coverage over the upper 1000 m. While kinetic and potential energies undergo a seasonal cycle, being largest during the winter, structure function slopes, influenced by dynamical characteristics, do not exhibit a strong seasonality. Furthermore, structure function slopes show weak vertical variations; there is not a strong change in properties across the base of the mixed layer. Additionally, we compare the observations to output from a high-resolution numerical model. The model does not represent variability associated with superinertial motions and does not capture an observed reduction in submesoscale kinetic energy that occurs throughout the water column in spring. Overall, these results suggest that the transfer of mixed layer submesoscale variability down to depths below the traditionally defined mixed layer is important throughout the weakly stratified subpolar mode waters.

Mapping Spatial Variations of H i Turbulent Properties in the Small and Large Magellanic Cloud

Abstract We developed methods for mapping spatial variations of the spatial power spectrum (SPS) and structure function slopes, with the goal of connecting the statistical properties of neutral hydrogen (H i) with the turbulent drivers. The new methods were applied to the H i observations of the Small and Large Magellanic Clouds (SMC and LMC). In the case of the SMC, we find highly uniform turbulent properties of H i, with no evidence for local enhancements of turbulence due to stellar feedback. These properties could be caused by a significant turbulent driving on large scales. Alternatively, the significant line-of-sight depth of the SMC could be masking out localized regions with a steeper SPS slope caused by stellar feedback. In contrast to the SMC, the LMC H i shows a large diversity in terms of its turbulent properties. Across most of the LMC, the small-scale SPS slope is steeper than the large-scale slope due to the presence of the H i disk. On small spatial scales, we find several areas of localized steepening of the SPS slope around major H ii regions, with the 30 Doradus region being the most prominent. This is in agreement with predictions from numerical simulations, which suggest a steepening of the SPS slope due to stellar feedback that erodes and destroys interstellar clouds. We also find a localized steepening of the large-scale SPS slope in the outskirts of the LMC. This is likely caused by the flaring of the H i disk, or alternatively, by ram-pressure stripping of the LMC disk due to the interactions with the surrounding halo gas.

Photometric Variability of Luminous Blue Variable Stars on Different Time-Scales

AbstractWe have compiled historical observations, spanning ∼100 years, for a dozen of the best-studied LBVs in the Local Group. We described how we prepared structure functions for their light-curves and calculated two parameters (the structure function slope and the characteristic time-scale) to describe the behaviour of the LBVs. The sensitivity of those parameters to the variability behaviour of the stars was tested with a number of photometric data sets. The slope of the structure function may anticorrelate with the time-scale. These types of variable stellar objects are crucial to studies of stellar variability and the final stages of stellar evolution.

RADIO SYNCHROTRON FLUCTUATION STATISTICS AS A PROBE OF MAGNETIZED INTERSTELLAR TURBULENCE

ABSTRACT We investigate how observations of synchrotron intensity fluctuations can be used to probe the sonic and Alfvénic Mach numbers of interstellar turbulence, based on mock observations performed on simulations of magnetohydrodynamic turbulence. We find that the structure function slope and a diagnostic of anisotropy that we call the integrated quadrupole ratio modulus both depend on the Alfvénic Mach number. However, these statistics also depend on the orientation of the mean magnetic field in the synchrotron emitting region relative to our line of sight, and this creates a degeneracy that cannot be broken by observations of synchrotron intensity alone. We conclude that the polarization of synchrotron emission could be analyzed to break this degeneracy, and suggest that this will be possible with the Square Kilometre Array.

Estimates of Ocean Macroturbulence: Structure Function and Spectral Slope from Argo Profiling Floats

AbstractThe Argo profiling float network has repeatedly sampled much of the World Ocean. This study uses Argo temperature and salinity data to form the tracer structure function of ocean variability at the macroscale (10–1000 km, mesoscale and above). Here, second-order temperature and salinity structure functions over horizontal separations are calculated along either pressure or potential density surfaces, which allows analysis of both active and passive tracer structure functions. Using Argo data, a map of global variance is created from the climatological average and each datum. When turbulence is homogeneous, the structure function slope from Argo can be related to the wavenumber spectrum slope in ocean temperature or salinity variability. This first application of structure function techniques to Argo data gives physically meaningful results based on bootstrapped confidence intervals, showing geographical dependence of the structure functions with slopes near ⅔ on average, independent of depth.

Second‐order structure function analysis of scatterometer winds over the Tropical Pacific

AbstractKolmogorov second‐order structure functions are used to quantify and compare the small‐scale information contained in near‐surface ocean wind products derived from measurements by ASCAT on MetOp‐A and SeaWinds on QuikSCAT. Two ASCAT and three SeaWinds products are compared in nine regions (classified as rainy or dry) in the tropical Pacific between 10°S and 10°N and 140° and 260°E for the period November 2008 to October 2009. Monthly and regionally averaged longitudinal and transverse structure functions are calculated using along‐track samples. To ease the analysis, the following quantities were estimated for the scale range 50 to 300 km and used to intercompare the wind products: (i) structure function slopes, (ii) turbulent kinetic energies ( ), and (iii) vorticity‐to‐divergence ratios. All wind products are in good qualitative agreement, but also have important differences. Structure function slopes and differ per wind product, but also show a common variation over time and space. Independent of wind product, longitudinal slopes decrease when sea surface temperature exceeds the threshold for onset of deep convection (about 28°C). In rainy areas and in dry regions during rainy periods, ASCAT has larger divergent than SeaWinds, while SeaWinds has larger vortical than ASCAT. Differences between SeaWinds and ASCAT vortical and vorticity‐to‐divergence ratios for the convectively active months of each region are large.

The ensemble optical variability of type-1 AGN in the Sloan Digital Sky Survey Data Release 7

We use a sample of over 5000 active galactic nuclei (AGN) with extended morphologies at z < 0.8 from the Sloan Digital Sky Survey (SDSS) to study the ensemble optical variability as a function of rest-frame time lag and AGN luminosity with the aim of investigating these parameter relationships at lower luminosities than previously studied. We compare photometry from imaging data with spectrophotometry obtained weeks to years later in the Sloan g, r, and i bands. We employ quasar and galaxy eigenspectra fitting to separate the AGN and host galaxy components. A strong correlation between the variability amplitude and rest-frame time lag is observed, in agreement with quasar structure functions but extending to AGN several magnitudes fainter than previously studied. The structure function slopes for our fainter AGN sample are slightly shallower than those found in quasars studies. An anticorrelation with luminosity is clearly detected, with lower luminosity AGN displaying greater variability amplitudes. We demonstrate for the first time that this anticorrelation extends to AGN as faint as MAGNi ∼ -18.5, with a slight trend towards shallower slopes at luminosities fainter than MAGNi ∼ -20.2.

The structure function of Galactic H i opacity fluctuations on au scales based on MERLIN, VLA and VLBA data

We use MERLIN, VLA and VLBA observations of Galactic \HI absorption towards 3C~138 to estimate the structure function of the \HI opacity fluctuations at AU scales. Using Monte Carlo simulations, we show that there is likely to be a significant bias in the estimated structure function at signal-to-noise ratios characteristic of our observations, if the structure function is constructed in the manner most commonly used in the literature. We develop a new estimator that is free from this bias and use it to estimate the true underlying structure function slope on length scales ranging $5$ to $40$~AU. From a power law fit to the structure function, we derive a slope of $0.81^{+0.14}_{-0.13}$, i.e. similar to the value observed at parsec scales. The estimated upper limit for the amplitude of the structure function is also consistent with the measurements carried out at parsec scales. Our measurements are hence consistent with the \HI opacity fluctuation in the Galaxy being characterized by a power law structure function over length scales that span six orders of magnitude. This result implies that the dissipation scale has to be smaller than a few AU if the fluctuations are produced by turbulence. This inferred smaller dissipation scale implies that the dissipation occurs either in (i) regions with densities $\gtrsim 10^3 $cm$^-3$ (i.e. similar to that inferred for "tiny scale" atomic clouds or (ii) regions with a mix of ionized and atomic gas (i.e. the observed structure in the atomic gas has a magneto-hydrodynamic origin).

A comparison between grid and particle methods on the statistics of driven, supersonic, isothermal turbulence

We compare the statistics of driven, supersonic turbulence at high Mach number using FLASH a widely used Eulerian grid-based code and PHANTOM, a Lagrangian SPH code at resolutions of up to 512^3 in both grid cells and SPH particles. We find excellent agreement between codes on the basic statistical properties: a slope of k^-1.95 in the velocity power spectrum for hydrodynamic, Mach 10 turbulence, evidence in both codes for a Kolmogorov-like slope of k^-5/3 in the variable rho^1/3 v as suggested by Kritsuk et al. and a log-normal PDF with a width that scales with Mach number and proportionality constant b=0.33-0.5 in the density variance-Mach number relation. The measured structure function slopes are not converged in either code at 512^3 elements. We find that, for measuring volumetric statistics such as the power spectrum slope and structure function scaling, SPH and grid codes give roughly comparable results when the number of SPH particles is approximately equal to the number of grid cells. In particular, to accurately measure the power spectrum slope in the inertial range, in the absence of subgrid models, requires at least 512^3 computational elements in either code. On the other hand the SPH code was found to be better at resolving dense structures, giving max. densities at a resolution of 128^3 particles that were similar those resolved in the grid code at 512^3 cells, reflected also in the high density tail of the PDF. We find SPH to be more dissipative at comparable numbers of computational elements in statistics of the velocity field, but correspondingly less dissipative than the grid code in the statistics of density weighted quantities such as rho^1/3 v. For SPH simulations of high Mach number turbulence we find it important to use sufficient non-linear beta-viscosity to prevent particle interpenetration in shocks (we require beta=4 instead of the default beta=2).

Daily observations of interstellar scintillation in PSR B0329+54

Quasi-continuous observations of PSR B03239+54 over 20 d using the Nanshan 25-m telescope at 1540 MHz have been used to study the effects of refractive scintillation on the pulsar flux density and diffractive scintillation properties. Dynamic spectra were obtained from data sets of 90 min duration and diffractive parameters derived from a two-dimensional auto-correlation analysis. Secondary spectra were also computed but these showed no significant evidence for arc structure. Cross-correlations between variations in the derived parameters were much lower than predicted by thin-screen models and in one case was of opposite sign to the prediction. Observed modulation indices were larger than predicted by thin-screen models with a Kolmogorov fluctuation spectrum. Structure functions were computed for the flux density, diffractive time-scale and decorrelation bandwidth. These indicated a refractive time-scale of 8 +/- 2 h, much shorter than predicted by the thin-screen model. The measured structure function slope of 0.4 +/- 0.2 is also inconsistent with scattering by a single thin screen for which a slope of 2.0 is expected. All observations are consistent with scattering by an extended medium having a Kolmogorov fluctuation spectrum which is concentrated towards the pulsar. This interpretation is also consistent with recent observations of multiple diffuse scintillation arcs for this pulsar.

Characteristics of the continuum variability of the nucleus of NGC 4151 in the optical from 1989-1996

The Structure Function (SF) analysis of variable fluxes of the Seyfert galaxy NGC 4151 obtained during its extraordinary brightening in 1989{1996 in the UBVRI bands is reported. More than 1500 measurements were made in each spectral band. The logarithmic slopes of SFs for all samples of flux observations are found to be dierent for intranight and extranight flux variations: 0.81{0.96 and 0.44{0.60, respectively. The dependence of the SF slopes on the phase of nucleus activity was revealed. The SF slopes increased for intranight variations in accordance with the nucleus brightening and decreased for yearly variations. The processes causing the flux variations evolved during the nucleus brightening in dierent directions: for intranight variations the process evolved from flicker{noise to extreme shot{noise; for yearly variations { vice versa. The obtained data provide evidence in favor of the supposition that intranight and extranight variations are caused by dierent sources. As a result, the variable source of the NGC 4151 nucleus during the active phase in the UBVRI bands exhibited characteristics of radio loud AGNs. The highest values of logarithmic slopes of SF for variations on a time scale of years were in the range 0:8 b 1:1, and for 10{150 day flares they were as high as 2.2. There was flattening of the optical spectrum with increasing nucleus brightness. The brightness amplitude of the nucleus in the U band reduced to an aperture D =5 00 over 7.3 years increased by a factor of more than 50. The brightness in the U band varied by a factor of more than 10 per year. The obtained characteristics of the variable source acting in the NGC 4151 nucleus from 1990{1996 do not contradict the model where the increasing nucleus brightening is caused by clouds of synchrotron radiation ejected from the nucleus during its active period.

First Results from the Las Campanas QSO Brightness Monitoring Program

We have examined optical brightness changes in 151 luminous, moderate-redshift QSOs with unknown variability properties. Short exposures were obtained using CCD detectors on the 40 inch (102 cm) Swope Telescope at Las Campanas Observatory. Some of the observations were taken as early as 1987, with the bulk of them beginning in 1990 and continuing through the beginning of 1994. Observations of individual QSOs were typically taken several times per year in V and/or Gunn r filters. Brightness variations have been determined relative to stars contained in an ≈ 6 arcmin2 field. We investigated the characteristics of the brightness variations using the ensemble structure function for three QSO object classes: radio quiet QSOs with broad absorption lines (BALs) in their spectra, radio quiet QSOs without BALs, and radio-loud quasars that systematically lack BALs. We find that ≈ 2/3 of the entire sample show very quiescent variations, with changes typically less than 0.15 mag yr-1 (proper time), corresponding to individual structure function slopes less than 0.0225 mag2 yr-1. We have designated these objects optically weak variables (OWVs), while the remainder of the sample with larger variations are designated optically strong variables (OSVs). Over the time of the observations, we were able to find only subtle statistical differences in the variability properties of radio quiet non-BAL and BAL QSOs. Although there is a slight tendency for the rate of change of continuum brightness to be larger in the radio-quiet non-BAL QSOs, to first order in both object classes the mean rate of change is similar and the characteristic timescale of variation appears to be greater than 1.2 yr (proper time). Consistent with the finding of slightly larger rates of change in radio-quiet non-BAL QSOs, we also find that the fraction of OSVs is marginally larger in the non-BAL QSOs in comparison to the BAL QSOs. However, the optical variability properties of the radio-loud quasars are clearly different. For the radio-loud quasars, while their rate of change in brightness is similar to changes observed in radio-quiet QSOs, their characteristic timescale of variation is statistically shorter, ≈ 0.6-0.8 yr (proper time). Collectively, these results have implications for models of QSO geometry and future methods of conducting QSO optical variability surveys. The results also illustrate the limitations of methods for discovering QSOs on the basis of optical variability alone.