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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS2006

Does The Nile Reflect Solar Variability?

Historical records of the Nile water level provide a unique opportunity to investigate the possibility that solar variability influences the Earth's climate. Particularly important are the annual records of the water level, which are uninterrupted for the years 622-1470 A.D. These records are non-stationary, so that standard spectral analyses cannot adequately characterize them. Here the Empirical Mode Decomposition technique, which is designed to deal with nonstationary, nonlinear time series, becomes useful. It allows the identification of two characteristic time scales in the water level data that can be linked to solar variability: the 88 year period and a time scale of about 200 years. These time scales are also present in the concurrent aurora data. Auroras are driven by coronal mass ejections and the rate of auroras is an excellent proxy for solar variability. Analysis of auroral data contemporaneous with the Nile data shows peaks at 88 years and about 200 years. This suggests a physical link between solar variability and the low frequency variations of the Nile water level. The link involves the influence of solar variability on the North Annual Mode of atmospheric variability and its North Atlantic and Indian Oceans patterns that affect rainfall over Eastern Equatorial Africa where the Nile originates.

statistical methods↗
NASA NTRS2011

Variability of African Farming Systems from Phenological Analysis of NDVI Time Series

Food security exists when people have access to sufficient, safe and nutritious food at all times to meet their dietary needs. The natural resource base is one of the many factors affecting food security. Its variability and decline creates problems for local food production. In this study we characterize for sub-Saharan Africa vegetation phenology and assess variability and trends of phenological indicators based on NDVI time series from 1982 to 2006. We focus on cumulated NDVI over the season (cumNDVI) which is a proxy for net primary productivity. Results are aggregated at the level of major farming systems, while determining also spatial variability within farming systems. High temporal variability of cumNDVI occurs in semiarid and subhumid regions. The results show a large area of positive cumNDVI trends between Senegal and South Sudan. These correspond to positive CRU rainfall trends found and relate to recovery after the 1980's droughts. We find significant negative cumNDVI trends near the south-coast of West Africa (Guinea coast) and in Tanzania. For each farming system, causes of change and variability are discussed based on available literature (Appendix A). Although food security comprises more than the local natural resource base, our results can perform an input for food security analysis by identifying zones of high variability or downward trends. Farming systems are found to be a useful level of analysis. Diversity and trends found within farming system boundaries underline that farming systems are dynamic.

Vrieling, Anton↗
NASA NTRS2004

Variable Shadow Screens for Imaging Optical Devices

Variable shadow screens have been proposed for reducing the apparent brightnesses of very bright light sources relative to other sources within the fields of view of diverse imaging optical devices, including video and film cameras and optical devices for imaging directly into the human eye. In other words, variable shadow screens would increase the effective dynamic ranges of such devices. Traditionally, imaging sensors are protected against excessive brightness by use of dark filters and/or reduction of iris diameters. These traditional means do not increase dynamic range; they reduce the ability to view or image dimmer features of an image because they reduce the brightness of all parts of an image by the same factor. On the other hand, a variable shadow screen would darken only the excessively bright parts of an image. For example, dim objects in a field of view that included the setting Sun or bright headlights could be seen more readily in a picture taken through a variable shadow screen than in a picture of the same scene taken through a dark filter or a narrowed iris. The figure depicts one of many potential variations of the basic concept of the variable shadow screen. The shadow screen would be a normally transparent liquid-crystal matrix placed in front of a focal-plane array of photodetectors in a charge-coupled-device video camera. The shadow screen would be placed far enough from the focal plane so as not to disrupt the focal-plane image to an unacceptable degree, yet close enough so that the out-of-focus shadows cast by the screen would still be effective in darkening the brightest parts of the image. The image detected by the photodetector array itself would be used as feedback to drive the variable shadow screen: The video output of the camera would be processed by suitable analog and/or digital electronic circuitry to generate a negative partial version of the image to be impressed on the shadow screen. The parts of the shadow screen in front of those parts of the image with brightness below a specified threshold would be left transparent; the parts of the shadow screen in front of those parts of the image where the brightness exceeded the threshold would be darkened by an amount that would increase with the excess above the threshold.

Lu, Ed↗
NASA NTRS2011

Optical Polarization and Spectral Variability in the M87 Jet

During the last decade, M87's jet has been the site of an extraordinary variability event, with one knot (HST-1) increasing by over a factor 100 in brightness. Variability was also seen on timescales of months in the nuclear flux. Here we discuss the optical-UV polarization and spectral variability of these components, which show vastly different behavior. HST -1 shows a highly significant correlation between flux and polarization, with P increasing from approx 20% at minimum to > 40% at maximum, while the orientation of its electric vector stayed constant. HST-l's optical-UV spectrum is very hard (alpha(sub uv-0) approx. 0.5, F(sub v) varies as (v(exp -alpha)), and displays "hard lags" during epochs 2004.9-2005.5, including the peak of the flare, with soft lags at later epochs. We interpret the behavior of HST-1 as enhanced particle acceleration in a shock, with cooling from both particle aging and the relaxation of the compression. We set 2alpha upper limits of 0.5 delta parsecs and 1.02c on the size and advance speed of the flaring region. The slight deviation of the electric vector orientation from the jet PA, makes it likely that on smaller scales the flaring region has either a double or twisted structure. By contrast, the nucleus displays much more rapid variability, with a highly variable electric vector orientation and 'looping' in the (I, P) plane. The nucleus has a much steeper spectrum ((alpha(sub uv-0) approx. 1.5) but does not show UV-optical spectral variability. Its behavior can be interpreted as either a helical distortion to a steady jet or a shock propagating through a helical jet.

Perlman, Eric S.↗
NASA NTRS2012

Anomalous Low States and Long Term Variability in the Black Hole Binary LMC X-3

Rossi X-my Timing Explorer observations of the black hole binary LMC X-3 reveal an extended very low X-ray state lasting from 2003 December 13 until 2004 March 18, unprecedented both in terms of its low luminosity (>15 times fainter than ever before seen in this source) and long duration (approx 3 times longer than a typical low/hard state excursion). During this event little to no source variability is observed on timescales of approx hours-weeks, and the X-ray spectrum implies an upper limit of 1.2 x 10(exp 35) erg/s, Five years later another extended low state occurs, lasting from 2008 December 11 until 2009 June 17. This event lasts nearly twice as long as the first, and while significant variability is observed, the source remains reliably in the low/hard spectral state for the approx 188 day duration. These episodes share some characteristics with the "anomalous low states" in the neutron star binary Her X-I. The average period and amplitude of the Variability of LMC X-3 have different values between these episodes. We characterize the long-term variability of LMC X-3 before and after the two events using conventional and nonlinear time series analysis methods, and show that, as is the case in Her X-I, the characteristic amplitude of the variability is related to its characteristic timescale. Furthermore, the relation is in the same direction in both systems. This suggests that a similar mechanism gives rise to the long-term variability, which in the case of Her X-I is reliably modeled with a tilted, warped precessing accretion disk.

Smale, Alan P.↗
NASA NTRS2013

Understanding Brown Dwarf Variability

Surveys of brown dwarf variability continue to find that roughly half of all brown dwarfs are variable. While variability is observed amongst all types of brown dwarfs, amplitudes are typically greatest for L-T transition objects. In my talk I will discuss the possible physical mechanisms that are responsible for the observed variability. I will particularly focus on comparing and contrasting the effects of changes in atmospheric thermal profile and cloud opacity. The two different mechanisms will produce different variability signatures and I will discuss the extent to which the current datasets constrain both mechanisms. By combining constraints from studies of variability with existing spectral and photometric datasets we can begin to construct and test self-consistent models of brown dwarf atmospheres. These models not only aid in the interpretation of existing objects but also inform studies of directly imaged giant planets.

Marley, Mark S.↗
NASA NTRS2013

Calibration Variable Selection and Natural Zero Determination for Semispan and Canard Balances

Independent calibration variables for the characterization of semispan and canard wind tunnel balances are discussed. It is shown that the variable selection for a semispan balance is determined by the location of the resultant normal and axial forces that act on the balance. These two forces are the first and second calibration variable. The pitching moment becomes the third calibration variable after the normal and axial forces are shifted to the pitch axis of the balance. Two geometric distances, i.e., the rolling and yawing moment arms, are the fourth and fifth calibration variable. They are traditionally substituted by corresponding moments to simplify the use of calibration data during a wind tunnel test. A canard balance is related to a semispan balance. It also only measures loads on one half of a lifting surface. However, the axial force and yawing moment are of no interest to users of a canard balance. Therefore, its calibration variable set is reduced to the normal force, pitching moment, and rolling moment. The combined load diagrams of the rolling and yawing moment for a semispan balance are discussed. They may be used to illustrate connections between the wind tunnel model geometry, the test section size, and the calibration load schedule. Then, methods are reviewed that may be used to obtain the natural zeros of a semispan or canard balance. In addition, characteristics of three semispan balance calibration rigs are discussed. Finally, basic requirements for a full characterization of a semispan balance are reviewed.

Ulbrich, Norbert M.↗
NASA NTRS2014

Brown Dwarf Variability: What's Varying and Why?

Surveys by ground based telescopes, HST, and Spitzer have revealed that brown dwarfs of most spectral classes exhibit variability. The spectral and temporal signatures of the variability are complex and apparently defy simplistic classification which complicates efforts to model the changes. Important questions include understanding if clearings are forming in an otherwise uniform cloud deck or if thermal perturbations, perhaps associated with breaking gravity waves, are responsible. If clouds are responsible how long does it take for the atmospheric thermal profile to relax from a hot cloudy to a cooler cloudless state? If thermal perturbations are responsible then what atmospheric layers are varying? How do the observed variability timescales compare to atmospheric radiative, chemical, and dynamical timescales? I will address such questions by presenting modeling results for time-varying partly cloudy atmospheres and explore the importance of various atmospheric processes over the relevant timescales for brown dwarfs of a range of effective temperatures. Regardless of the origin of the observed variability, the complexity seen in the atmospheres of the field dwarfs hints at the variability that we may encounter in the next few years in directly imaged young Jupiters. Thus understanding the nature of variability in the field dwarfs, including sensitivity to gravity and metallicity, is of particular importance for exoplanet characterization.

brown dwarfs↗
NASA NTRS2013

The Galex Time Domain Survey. I. Selection And Classification of Over a Thousand Ultraviolet Variable Sources

We present the selection and classification of over a thousand ultraviolet (UV) variable sources discovered in approximately 40 deg(exp 2) of GALEX Time Domain Survey (TDS) NUV images observed with a cadence of 2 days and a baseline of observations of approximately 3 years. The GALEX TDS fields were designed to be in spatial and temporal coordination with the Pan-STARRS1 Medium Deep Survey, which provides deep optical imaging and simultaneous optical transient detections via image differencing. We characterize the GALEX photometric errors empirically as a function of mean magnitude, and select sources that vary at the 5 sigma level in at least one epoch. We measure the statistical properties of the UV variability, including the structure function on timescales of days and years. We report classifications for the GALEX TDS sample using a combination of optical host colors and morphology, UV light curve characteristics, and matches to archival X-ray, and spectroscopy catalogs. We classify 62% of the sources as active galaxies (358 quasars and 305 active galactic nuclei), and 10% as variable stars (including 37 RR Lyrae, 53 M dwarf flare stars, and 2 cataclysmic variables). We detect a large-amplitude tail in the UV variability distribution for M-dwarf flare stars and RR Lyrae, reaching up to absolute value(Δm) = 4.6 mag and 2.9 mag, respectively. The mean amplitude of the structure function for quasars on year timescales is five times larger than observed at optical wavelengths. The remaining unclassified sources include UV-bright extragalactic transients, two of which have been spectroscopically confirmed to be a young core-collapse supernova and a flare from the tidal disruption of a star by dormant supermassive black hole. We calculate a surface density for variable sources in the UV with NUV less than 23 mag and absolute value(Δm) greater than 0.2 mag of approximately 8.0, 7.7, and 1.8 deg(exp −2) for quasars, active galactic nuclei, and RR Lyrae stars, respectively. We also calculate a surface density rate in the UV for transient sources, using the effective survey time at the cadence appropriate to each class, of approximately 15 and 52 deg(exp −2 yr−1 for M dwarfs and extragalactic transients, respectively.

Gezari, S.↗
NASA NTRS2015

A Coordinated X-Ray and Optical Campaign of the Nearest Massive Eclipsing Binary, Delta Orionis Aa. II. X-Ray Variability

We present time-resolved and phase-resolved variability studies of an extensive X-ray high-resolution spectral data set of the delta Ori Aa binary system. The four observations, obtained with Chandra ACIS (Advanced CCD Imaging Spectrometer) HETGS (High Energy Transmission Grating), have a total exposure time approximately equal to 479 kiloseconds and provide nearly complete binary phase coverage. Variability of the total X-ray flux in the range of 5-25 angstroms is confirmed, with a maximum amplitude of about plus or minus15 percent within a single approximately equal to125 kiloseconds observation. Periods of 4.76 and 2.04 days are found in the total X-ray flux, as well as an apparent overall increase in the flux level throughout the nine-day observational campaign. Using 40 kiloseconds contiguous spectra derived from the original observations, we investigate the variability of emission line parameters and ratios. Several emission lines are shown to be variable, including S (sub XV), Si (sub XIII), and Ne (sub IX). For the first time, variations of the X-ray emission line widths as a function of the binary phase are found in a binary system, with the smallest widths at phi = 0.0 when the secondary delta Ori Aa2 is at the inferior conjunction. Using 3D hydrodynamic modeling of the interacting winds, we relate the emission line width variability to the presence of a wind cavity created by a wind-wind collision, which is effectively void of embedded wind shocks and is carved out of the X-ray-producing primary wind, thus producing phase-locked X-ray variability.

X-ray flux↗
NASA NTRS2015

Groundwater Variability Across Temporal and Spatial Scales in the Central and Northeastern U.S.

Depth-to-water measurements from 181 monitoring wells in unconfined or semi-confined aquifers in nine regions of the central and northeastern U.S. were analyzed. Groundwater storage exhibited strong seasonal variations in all regions, with peaks in spring and lows in autumn, and its interannual variability was nearly unbounded, such that the impacts of droughts, floods, and excessive pumping could persist for many years. We found that the spatial variability of groundwater storage anomalies (deviations from the long term mean) increases as a power function of extent scale (square root of area). That relationship, which is linear on a log-log graph, is common to other hydrological variables but had never before been shown with groundwater data. We describe how the derived power function can be used to determine the number of wells needed to estimate regional mean groundwater storage anomalies with a desired level of accuracy, or to assess uncertainty in regional mean estimates from a set number of observations. We found that the spatial variability of groundwater storage anomalies within a region often increases with the absolute value of the regional mean anomaly, the opposite of the relationship between soil moisture spatial variability and mean. Recharge (drainage from the lowest model soil layer) simulated by the Variable Infiltration Capacity (VIC) model was compatible with observed monthly groundwater storage anomalies and month-to-month changes in groundwater storage.

water cycle↗
NASA NTRS2015

Spatial and Temporal Variability of Carbon Dioxide Using Structure Functions in Urban Areas: Insights for Future Active Remote CO2 Sensors

High resolution in-situ CO2 measurements were recorded onboard the NASA P-3B during the DISCOVER-AQ (Deriving Information on Surface Conditions from Column and Vertically Resolved Observations Relevant to Air Quality) Field Campaigns during July 2011 over Washington DC/Baltimore, MD; January-February 2013 over the San Joaquin Valley, CA; September 2013 over Houston, TX; and July-August 2014 over Denver, CO. Each of these campaigns have approximately two hundred vertical soundings of CO2 within the lower troposphere (surface to about 5 kilometers) at 6-8 different sites in each of the urban areas. In this study, we used structure function analysis, which is a useful way to quantify spatial and temporal variability, by displaying differences with average observations, to evaluate the variability of CO2 in the 0-2 kilometers range (representative of the planetary boundary layer). These results can then be used to provide guidance in the development of science requirements for the future ASCENDS (Active Sensing of CO2 Emissions over Nights, Days, and Seasons) mission to measure near-surface CO2 variability in different urban areas. We also compare the observed in-situ CO2 variability with the variability of the CO2 column-averaged optical depths in the 0-1 kilometer and 0-3.5 kilometers altitude ranges in the four geographically different urban areas, using vertical weighting functions for potential future ASCENDS lidar CO2 sensors operating in the 1.57 and 2.05 millimeter measurement regions. In addition to determining the natural variability of CO2 near the surface and in the column, radiocarbon method using continuous CO2 and CO measurements are used to examine the variation of emission quantification between anthropogenic and biogenic sources in the DC/Maryland urban site.

Choi, Yonghoon↗
NASA NTRS2016

A42F-03: Small-Scale Variability in Tropical Tropopause Layer Humidity

Recent advances in statistical parameterizations of cirrus cloud processes for use in global models are highlighting the need for information about small-scale fluctuations in upper tropospheric humidity and the physical processes that control the humidity variability. To address these issues, we have analyzed high-resolution airborne water vapor measurements obtained in the Airborne Tropical TRopopause EXperiment (ATTREX) over the tropical Pacific between 14 and 20 km. Using accurate and precise 1-Hz water vapor measurements along approximately-level aircraft flight legs, we calculate structure functions spanning horizontal scales ranging from about 0.2 to 50 km, and we compare the water vapor variability in the lower (about 14 km) and upper (16-19 km) Tropical Tropopause Layer (TTL). We also compare the magnitudes and scales of variability inside TTL cirrus versus in clear-sky regions. The measurements show that in the upper TTL, water vapor concentration variance is stronger inside cirrus than in clear-sky regions. Using simulations of TTL cirrus formation, we show that small variability in clear-sky humidity is amplified by the strong sensitivity of ice nucleation rate to supersaturation, which results in highly-structured clouds that subsequently drive variability in the water vapor field. In the lower TTL, humidity variability is correlated with recent detrainment from deep convection. The structure functions indicate approximately power-law scaling with spectral slopes ranging from about minus 5 divided by 3, to minus 2.

water vapor↗
NASA NTRS2019

Significant Spatial Variability in Radar-Derived West Antarctic Accumulation Linked to Surface Winds and Topography

Across the Antarctic Ice Sheet, accumulation heavily influences firn compaction and surface height changes. Therefore, accumulation varies over short distances (<25 km), complicating the derivation of ice sheet mass changes from altimetry and reducing how accurately field measurements can be spatially extrapolated. However, current atmospheric reanalyses have grid spacings (>25 km) that are too coarse to resolve this variability. To address this limitation, we construct a fine-scale accumulation product from airborne snow radar observations by superimposing along-track fluctuations in accumulation onto an atmospheric reanalysis product. Our resulting airborne product reflects large-scale (>25 km) orographic precipitation patterns while providing robust and unprecedented insight into Antarctic accumulation variability on subgrid scales. On these smaller scales, we find significant, regionally dependent accumulation variability (𝜎(sub relative) > 40%). This variability in accumulation is correlated with variability in topographic surface slope in the wind direction (p < 0.01), confirming that subgrid-scale accumulation variability is driven by snow redistribution by wind.

Dattler, Marissa E.↗
NASA NTRSDate not supplied

Publishing Variables Archived at GES DISC to Earth System Grid Federation (ESGF)

We present a straightforward and low-cost approach to publish variables archived at NASA Goddard Earth Sciences Data and Information Services Center (GES DISC) to the Earth System Grid Federation (ESGF). An ESGF publication requires a single standard-name variable aggregated over time to facilitate data inter-comparison. It also contains significant metadata to enable searching in ESGF. We look up standard names on high demand in ESGF search history, and using OPeNDAP and NcML technologies we aggregate the corresponding variables available in the GES DISC archive with augmented metadata required by CMIP6 and obs4MIPs Data Specification version 2.1. At this writing 10 variables from a standard product of the Atmospheric Infrared Sounder along with the Tech Notes are published in ESGF by NASA Center for Climate Simulation (NCCS). Users can view, analyze, and subset remotely, and download these aggregated variables via links in any ESGF node after searching. We plan to work on and publish more variables and data from different NASA missions and experiments in our archive.

Fan Fang↗
NASA NTRS2020

Radiography in High Mass X-Ray Binaries: Micro-Structure of the Stellar Wind Through Variability of the Column Density

Context. In high mass X-ray binaries, an accreting compact object orbits a high mass star, which loses mass through a dense and in homogeneous wind. Aims. Using the compact object as an X-ray backlight, the time variability of the absorbing column density in the wind can be exploited in order to shed light on the micro-structure of the wind and obtain unbiased stellar mass-loss rates for high mass stars. Methods. We developed a simplified representation of the stellar wind where all the matter is gathered in spherical “clumps” that are radially advected away from the star. This model enables us to explore the connections between the stochastic properties of the wind and the variability of the column density for a comprehensive set of parameters related to the orbit and to the wind micro-structure, such as the size of the clumps and their individual mass. In particular, we focus on the evolution with the orbital phase of the standard deviation of the column density and of the characteristic duration of enhanced absorption episodes. Using the porosity length, we derive analytical predictions and compare them to the standard deviations and coherence time scales that were obtained. Results. We identified the favorable systems and orbital phases to determine the wind micro-structure. The coherence time scale of the column density is shown to be the self-crossing time of a single clump in front of the compact object. We thus provide a procedure to get accurate measurements of the size and of the mass of the clumps, purely based on the observable time variability of the column density. Conclusions. The coherence time scale grants direct access to the size of the clumps, while their mass can be deduced separately from the amplitude of the variability. We further show how monitoring the variability at superior conjunctions can probe the onset of the clump-forming region above the stellar photosphere. If the high column density variations in some high mass X-ray binaries are due to unaccreted clumps which are passing by the line-of-sight, this would require high mass clumps to reproduce the observed peak-to-peak amplitude and coherence time scales. These clump properties are marginally compatible with the ones derived from radiative-hydrodynamics simulations. Alternatively, the following components could contribute to the variability of the column density: larger orbital scale structures produced by a mechanism that has yet to be identified or a dense environment in the immediate vicinity of the accretor, such as an accretion disk, an outflow, or a spherical shell surrounding the magnetosphere of the accreting neutron star.

stars: mass loss↗
NASA NTRS2018

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) per cent⁠. 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) per cent⁠. We determine a probability of 98 per cent 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) light curves to measure a rotational period of 8.45 ± 0.05 h for PSO 318.5–22.

Johanna M. Vos↗
NASA NTRS2021

The Stochastic X-ray Variability of the Accreting Millisecond Pulsar IGR J17062-6143

This work presents an investigation of the stochastic X-ray variability from the 164 Hz accreting millisecond pulsar IGR J17062–6143, based on regular observations collected with the Neutron Star Interior Composition Explorer between 2017 July and 2020 August. Over this period, the power density spectrum showed a stable morphology, with broad ∼ 25% rms band-limited noise below 16 Hz. Quasiperiodic oscillations (QPOs) were occasionally observed, with the most notably detections including a low-frequency QPO centered at 2.7 Hz and a sharp QPO centered at 115 Hz that may be a 2:3 resonance with the spin frequency. Further, the energy dependence of the band-limited noise is studied through a spectroscopic analysis of the complex covariance in two frequency intervals. It is found that the power law continuum is the primary driver for the observed variability, although the thermal (blackbody) emission also appears to be intrinsically variable in area (5% rms) and temperature (1% rms). Notably, the 1 keV emission feature seen in all X-ray spectra of IGR J17062–6143 varies with the same amplitude as the power law, but systematically lags behind that continuum emission. These results appear consistent with a scenario in which a time variable Compton-scattering corona is the primary source for the observed stochastic variability, with the variability observed in the emission feature and at the lowest photon energies being due to the disk reflection of the power law continuum.

Petrus Bult↗