Rms-flux Relation Research Articles

Optical Variability Properties of Southern TESS Blazars

We present a study of high-cadence, high-precision optical light curves from the TESS satellite of 67 blazars in the southern sky. We provide descriptive flux statistics, power spectral density (PSD) model parameters, and characteristic variability timescales. We find that only 15 BL Lacertae objects (BLLs) and 18 flat spectrum radio quasars (FSRQs) from the initial 26 and 41, respectively, exhibit statistically significant variability. We employ an adapted power spectral response method to test the goodness of fit for the PSD function to three power-law variant models. From our best-fitting description of the PSD, we extract the high-frequency power-spectral slopes, and if present, determine the significant bend or break in the model to identify characteristic timescales. We find no significant difference in the excess variance or rms scatter between blazar subpopulations. We identify a linear rms–flux relation in ∼69% of our sample, in which ∼20% show a strong correlation. We find that both subpopulations of blazars show power spectral slopes of α ∼ 2 in which a broken power-law best fits five BLLs and six FSRQs and a bending power-law best fits one BLL and five FSRQs. The shortest timescales of variability in each light-curve range widely from minutes to weeks. Additionally, these objects’ characteristic timescales range from ∼0.8 to 8 days, consistent with optical variability originating in the jet.

Rms–Flux Slope in MAXI J1820+070: A Measure of Disk–Corona Coupling

The linear rms–flux relation has been well established in different spectral states of all accreting systems. In this work, we study the evolution of the frequency-dependent rms–flux relation of MAXI J1820+070 during the initial decaying phase of its 2018 outburst with Insight-HXMT over a broad energy range of 1–150 keV. As the flux decreases, we first observe a linear rms–flux relation at frequencies from 2 mHz to 10 Hz, while such a relation breaks at varying times for different energies, leading to a substantial reduction in the slope. Moreover, we find that the low-frequency variability exhibits the highest sensitivity to the break, which occurs prior to the hard-to-hard state transition time determined through time-averaged spectroscopy, and the time deviation increases with energy. The overall evolution of the rms–flux slope and intercept suggests the presence of a two-component Comptonization system. One component is radially extended, explaining the strong disk–corona coupling before the break, while the other component extends vertically, contributing to a reduction of disk–corona coupling after the break. A further vertical expansion of the latter component is required to accommodate the dynamic evolution observed in the rms–flux slope. In conclusion, we suggest that the rms–flux slope in the 1–150 keV band can be employed as an indicator of disk–corona coupling, and the hard-to-hard state transition in MAXI J1820+070 could be partially driven by changes in the coronal geometry.

Comprehensive Study of the Blazars from Fermi-LAT LCR: The Log-Normal Flux Distribution and Linear rms–Flux Relation

Fermi-LAT LCR provides continuous and regularly sampled gamma-ray light curves, spanning about 14 yr, for a large sample of blazars. The log-normal flux distribution and linear rms–flux relation of the light curves for a few Fermi blazars have been examined in previous studies. However, the probability that blazars exhibit the log-normal flux distribution and linear rms–flux relation in their gamma-ray light curves has not been systematically explored. In this study, we comprehensively research the distribution of γ-ray flux and the statistical characteristics on a large sample of 1414 variable blazars from the Fermi-LAT LCR catalog, including 572 FSRQs, 477 BL Lacs, and 365 BCUs, and statistically compare their flux distributions with normal and log-normal distributions. The results indicate that the probability of not rejecting log-normal is 42.05% for the large sample, and there is still a 2.05% probability of not rejecting normality, based on the joint of Kolmogorov–Smirnov, Shapiro–Wilk, and Normality tests. We further find that the probability that BL Lacs conform to the log-normal distribution is higher than that of FSRQs. Besides, after removing sources with less than 200 data points from this large sample, a sample of 549 blazars, which is still a large sample compared to the previous studies, was obtained. Based on dividing the light curves into segments every 20 points (or 40 points, or one year), we fitted the linear rms–flux relation of these three different sets and found that the Pearson correlation coefficients are all close to 1 for most blazars. This result indicates a strong linear correlation between the rms and the flux of these 549 blazars. The log-normal distribution and linear rms–flux relation indicate that the variability of the γ-ray flux for most blazars is a non-linear and multiplicative process.

Constraining X-Ray Variability of the Blazar 3C 273 Using XMM-Newton Observations over Two Decades

Blazars exhibit relentless variability across diverse spatial and temporal frequencies. The study of long- and short-term variability properties observed in the X-ray band provides insights into the inner workings of the central engine. In this work, we present timing and spectral analyses of the blazar 3C 273 using the X-ray observations from the XMM-Newton telescope covering the period from 2000 to 2020. The methods of timing analyses include estimation of fractional variability, long- and short-term flux distribution, rms–flux relation, and power spectral density analysis. The spectral analysis include estimating a model-independent flux hardness ratio and fitting the observations with multiplicative and additive spectral models such as power law, log-parabola, broken power law, and blackbody. The blackbody represents the thermal emission from the accretion disk, while the other models represent the possible energy distributions of the particles emitting synchrotron radiation in the jet. During the past two decades, the source flux changed by a factor of three, with a considerable fractional variability of 27%. However, the intraday variation was found to be moderate. Flux distributions of the individual observations were consistent with a normal or log-normal distribution, while the overall flux distribution including all observations appears to be rather multimodal and of a complex shape. The spectral analyses indicate that a log-parabola added to a blackbody gives the best fit for most of the observations. The results indicate a complex scenario in which the variability can be attributed to the intricate interaction between the disk/corona system and the jet.

Multiwavelength variability and broad-band SED modelling of BL Lac during a bright flaring period MJD 59000–59943

ABSTRACT We carried out a detailed temporal and spectral study of the BL Lacertae (BL Lac) by using the long-term Fermi-Large Area Telescope (LAT) and Swift-X-ray Telescope (XRT)/Ultraviolet Optical Telescope (UVOT) observations, during the period MJD 59000–59943. The daily-binned γ-ray light curve displays a maximum flux of $1.74\pm 0.09\times 10^{-5} \,\rm photons\, cm^{-2}\, s^{-1}$ on MJD 59868, which is the highest daily γ-ray flux observed from BL Lac. The γ-ray variability is characterized by power spectral density (PSD), rms–flux relation, and flux distribution study. We find that the power-law model fits the PSD with index ∼1, which suggests a long-memory process at work. The observed rms–flux relation exhibits a linear trend, which indicates that the γ-ray flux distribution follows a lognormal distribution. The skewness/Anderson–Darling test and histogram fit reject the normality of flux distribution, and instead suggest that the flux distribution is a lognormal distribution. The fractional variability amplitude shows that the source is more variable in the X-ray band than in optical/ultraviolet/γ-ray bands. In order to obtain an insight into the underlying physical process, we extracted broad-band spectra from different time periods of the light curve. The broad-band spectra are statistically fitted with the convolved one-zone leptonic model with different forms of the particle energy distribution. We found that spectral energy distribution during different flux states can be reproduced well with the synchrotron, synchrotron self-Compton, and external Compton emissions from a broken power-law electron distribution, ensuring equipartition condition. A comparison between the best-fitting physical parameters shows that the variation in different flux states is mostly related to an increase in the bulk Lorentz factor and spectral hardening of the particle distribution.

Study of Optical and Gamma-ray Long-term Variability in Blazars

Blazars, a subset of powerful active galactic nuclei, feature relativistic jets that shine in a broadband electromagnetic radiation, e. g. from radio to TeV emission. Here I present the results of the studies that explore gamma-ray and optical variability properties of a sample of gamma-ray bright sources Several methods of time-series analyses are performed on the decade-long optical and Fermi/LAT observations. The main results are as follows: The sources are found highly variable in both the bands, and the gamma-ray power spectral density is found to be consistent with flicker noise suggesting long-memory processes at work. While comparing two emission, not only the overall optical and the $\gamma$-ray emission are highly correlated but also both the observation distributions exhibit heavy tailed log-normal distribution and linear RMS-flux relation. In addition, in some of the sources indications of quasi-periodic oscillation were revealed with similar characteristic timescales in both the bands. We discuss the results in light of current blazar models with relativistic shocks propagating down the jet viewed close to the line of sight.

Rms–flux relation and disc–jet connection in blazars in the context of the internal shocks model

ABSTRACT Recent analysis of blazar variability has revealed a proportionality between the mean flux and the root mean squared (rms) fluctuations about the mean flux. Although such rms–flux relation has been previously observed in the accretion disc/corona variability of X-ray binaries and Seyfert galaxies, and has been extensively modelled, its emergence in the jet light curves of blazars calls for a revised theoretical understanding of this feature. In this work, we analyse the time variability properties of realistic multiwavelength jet light curves, simulated in the context of a simplified version of the internal shocks model, particularly focusing on the rms–flux relation. These shocks accelerate the jet electrons to relativistic energies, which then cool radiatively via synchrotron and inverse-Compton processes. We find that the rms–flux relation may be consistently recovered in the cases, in which the shocks have different amplitudes based on the speed of the colliding blobs generating them as opposed to all shocks having the same amplitude. We observe that the slope of the rms–flux relation depends on the wavelength at which the variability is observed and the energy distribution of the electron population. We find that the accretion disc and the jet variability are anticorrelated, with the latter lagging that of the disc. Our results provide crucial constraints on the physical properties of the jet, and the mode of connection through which the accretion disc and jet may be related.

Characterizing Long-term Optical Variability Properties of γ-Ray-bright Blazars

Abstract Optical observations of a sample of 12 γ-ray-bright blazars from four optical data archives—American Association of Variable Star Observers, Small and Moderate Aperture Research Telescope System, Catalina, and Steward Observatory—are compiled to create densely sampled light curves spanning more than a decade. As a part of the blazar multiwavelength studies, several methods of analysis, e.g., flux distribution and rms–flux relation, are performed on the observations with the aim to compare the results with the similar ones in the γ-ray band presented in Bhatta & Dhital. It is found that, similar to the γ-ray band, blazars display significant variability in the optical band that can be characterized with lognormal flux distribution and a power-law dependence of rms on flux. It could be an indication of a possible inherent linear rms–flux relation, yet the scatter in the data does not allow to rule out other possibilities. When comparing variability properties in the two bands, the blazars in the γ-rays are found to exhibit stronger variability with a steeper possible linear rms–flux relation and a flux distribution that is more skewed toward higher fluxes. The cross-correlation study shows that except for source 3C 273, the overall optical and the γ-ray emission in the sources are highly correlated, suggesting a cospatial existence of the particles responsible for both the optical and γ-ray emission. Moreover, sources S5 0716+714, Mrk 421, Mrk 501, PKS 1424-418, and PKS 2155-304 revealed possible evidence of quasiperiodic oscillations in the optical emission with the characteristic timescales, which are comparable to those in the γ-ray band detected in our previous work.

Short-Term X-ray Variability during Different Activity Phases of Blazars S5 0716+714 and PKS 2155-304

We explored the statistical properties of short-term X-ray variability using long-exposure XMM-Newton data during high X-ray variability phases of blazars S5 0716+714 and PKS 2155-304. In general, the hardness ratio shows correlated variations with the source flux state (count rate), but in a few cases, mainly the bright phases, the trend is complex with both correlation and anti-correlation, indicating spectral evolution. Stationarity tests suggest the time series are non-stationarity or have trend stationarity. Except for one, none of the histogram fits resulted in a reduced-χ2∼1 for a normal and log-normal profile but a normal profile is favored in general. On the contrary, the Anderson–Darling test favors log-normal with a test-statistic value lower for log-normal over normal for all the observations, even if out of significance limits. None of the IDs show linear RMS-flux relation. The contrary inferences from different widely used statistical methods indicate that a careful analysis is needed while the complex behavior of count rate with hardness ratio suggests spectral evolution over a few 10 s of kilo-seconds during bright phases of the sources. In these cases, the spectrum extracted from whole observation may not be meaningful for spectral studies and certainly not a true representation of the spectral state of the source.

Looking for the underlying cause of black hole X-ray variability in GRMHD simulations

ABSTRACT Long-term observations have shown that black hole X-ray binaries exhibit strong, aperiodic variability on time-scales of a few milliseconds to seconds. The observed light curves display various characteristic features like a lognormal distribution of flux and a linear rms–flux relation, which indicate that the underlying variability process is stochastic in nature. It is also thought to be intrinsic to accretion. This variability has been modelled as inward propagating fluctuations of mass accretion rate, although the physical process driving the fluctuations remains puzzling. In this work, we analyse five exceptionally long-duration general relativistic magnetohydrodynamic (GRMHD) simulations of optically thin, geometrically thick, black hole accretion flows to look for hints of propagating fluctuations in the simulation data. We find that the accretion profiles from these simulations do show evidence for inward propagating fluctuations below the viscous frequency by featuring strong radial coherence and positive time lags when comparing smaller to larger radii, although these time lags are generally shorter than the viscous time-scale and are frequency-independent. Our simulations also support the notion that the fluctuations in $\dot{M}$ build up in a multiplicative manner, as the simulations exhibit linear rms–mass flux relations, as well as lognormal distributions of their mass fluxes. When combining the mass fluxes from the simulations with an assumed emissivity profile, we additionally find broad agreement with observed power spectra and time lags, including a recovery of the frequency dependency of the time lags.

Studies in Astronomical Time-series Analysis. VII. An Enquiry Concerning Nonlinearity, the rms–Mean Flux Relation, and Lognormal Flux Distributions

Abstract A broad and widely used class of stationary, linear, additive time-series models can have statistical properties that many authors have asserted imply that the underlying process must be nonlinear, nonstationary, multiplicative, or inconsistent with shot noise. This result is demonstrated with exact and numerical evaluation of the model flux distribution function and dependence of flux standard deviation on mean flux (here and in the literature called the rms–flux relation). These models can (1) exhibit normal, lognormal, or other flux distributions; (2) show linear or slightly nonlinear rms–mean flux dependencies; and (3) match arbitrary second-order statistics of the time-series data. Accordingly, the above assertions cannot be made on the basis of statistical time-series analysis alone. Also discussed are ambiguities in the meaning of terms relevant to this study—linear, stationary, and multiplicative—and functions that can transform observed fluxes to a normal distribution as well as or better than the logarithm.

The flux distribution of Sgr A*

The Galactic center black hole Sagittarius A* is a variable near-infrared (NIR) source that exhibits bright flux excursions called flares. When flux from Sgr A* is detected, the light curve has been shown to exhibit red noise characteristics and the distribution of flux densities is non-linear, non-Gaussian, and skewed to higher flux densities. However, the low-flux density turnover of the flux distribution is below the sensitivity of current single-aperture telescopes. For this reason, the median NIR flux has only been inferred indirectly from model fitting, but it has not been directly measured. In order to explore the lowest flux ranges, to measure the median flux density, and to test if the previously proposed flux distributions fit the data, we use the unprecedented resolution of the GRAVITY instrument at the VLTI. We obtain light curves using interferometric model fitting and coherent flux measurements. Our light curves are unconfused, overcoming the confusion limit of previous photometric studies. We analyze the light curves using standard statistical methods and obtain the flux distribution. We find that the flux distribution of Sgr A* turns over at a median flux density of (1.1 ± 0.3) mJy. We measure the percentiles of the flux distribution and use them to constrain the NIR K-band spectral energy distribution. Furthermore, we find that the flux distribution is intrinsically right-skewed to higher flux density in log space. Flux densities below 0.1 mJy are hardly ever observed. In consequence, a single powerlaw or lognormal distribution does not suffice to describe the observed flux distribution in its entirety. However, if one takes into account a power law component at high flux densities, a lognormal distribution can describe the lower end of the observed flux distribution. We confirm the rms–flux relation for Sgr A* and find it to be linear for all flux densities in our observation. We conclude that Sgr A* has two states: the bulk of the emission is generated in a lognormal process with a well-defined median flux density and this quiescent emission is supplemented by sporadic flares that create the observed power law extension of the flux distribution.

Non-stationary variability in accreting compact objects

Accreting compact objects show variations in source flux over a broad range of timescales and in all wavebands. The light curves typically show a lognormal distribution of flux and a linear relation between flux and rms. It has been demonstrated that an exponential transform of an underlying (and unobserved) Gaussian stochastic process provides a very good description of the light curves with these observed properties. Recently, a non-stationary power spectrum was observed on fast timescales (~ days) in the active galaxy, IRAS 13224--3809, as well as a non-lognormal flux distribution and non-linear rms-flux relation. Here, we investigate the affects of piecewise non-stationary power spectra on the resultant flux distribution and rms-flux relation. We demonstrate that the simple "exponentiation" model successfully reproduces the observed quantities, even when the light curves are non-stationary. We also demonstrate how non-lognormal flux distributions and rms-flux relations inconsistent with a linear model can be erroneously produced from poorly sampled PSDs. This is of particular importance for AGN surveys where very long baselines are required to sample the PSD down to low enough frequencies.

The remarkable X-ray variability of IRAS 13224–3809 – I. The variability process

We present a detailed X-ray timing analysis of the highly variable NLS1 galaxy, IRAS 13224-3809. The source was recently monitored for 1.5 Ms with XMM-Newton which, combined with 500 ks archival data, makes this the best studied NLS1 galaxy in X-rays to date. We apply standard time- and Fourier-domain in order to understand the underlying variability process. The source flux is not distributed lognormally, as would be expected for accreting sources. The first non-linear rms-flux relation for any accreting source in any waveband is found, with $\mathrm{rms} \propto \mathrm{flux}^{2/3}$. The light curves exhibit significant strong non-stationarity, in addition to that caused by the rms-flux relation, and are fractionally more variable at lower source flux. The power spectrum is estimated down to $\sim 10^{-7}$ Hz and consists of multiple peaked components: a low-frequency break at $\sim 10^{-5}$ Hz, with slope $\alpha < 1$ down to low frequencies; an additional component breaking at $\sim 10^{-3}$ Hz. Using the high-frequency break we estimate the black hole mass $M_\mathrm{BH} = [0.5-2] \times 10^{6} M_{\odot}$, and mass accretion rate in Eddington units, $\dot m_{\rm Edd} \gtrsim 1$. The non-stationarity is manifest in the PSD with the normalisation of the peaked components increasing with decreasing source flux, as well as the low-frequency peak moving to higher frequencies. We also detect a narrow coherent feature in the soft band PSD at $0.7$ mHz, modelled with a Lorentzian the feature has $Q \sim 8$ and an $\mathrm{rms} \sim 3$ %. We discuss the implication of these results for accretion of matter onto black holes.

Characterization of the infrared/X-ray subsecond variability for the black hole transient GX 339-4

We present a detailed analysis of the X-ray/IR fast variability of the Black-Hole Transient GX 339-4 during its low/hard state in August 2008. Thanks to simultaneous high time-resolution observations made with the VLT and RXTE, we performed the first characterisation of the sub-second variability in the near-infrared band - and of its correlation with the X-rays - for a low-mass X-ray binary, using both time and frequency-domain techniques. We found a power-law correlation between the X-ray and infrared fluxes when measured on timescales of 16 seconds, with a marginally variable slope, steeper than the one found on timescales of days at similar flux levels. We suggest the variable slope - if confirmed - could be due to the infrared flux being a non-constant combination of both optically thin and optically thick synchrotron emission from the jet, as a result of a variable self-absorption break. From cross spectral analysis we found an approximately constant infrared time lag of $\approx$ 0.1s, and a very high coherence of $\approx$ 90 per cent on timescales of tens of seconds, slowly decreasing toward higher frequencies. Finally, we report on the first detection of a linear rms-flux relation in the emission from a low-mass X-ray binary jet, on timescales where little correlation is found between the X-rays and the jet emission itself. This suggests that either the inflow variations and jet IR emission are coupled by a non-linear or time-variable transform, or that the IR rms-flux relation is not transferred from the inflow to the jet, but is an intrinsic property of emission processes in the jet.

Propagating mass accretion rate fluctuations in X-ray binaries under the influence of viscous diffusion

Many statistical properties of X-ray aperiodic variability from accreting compact objects can be explained by the propagating fluctuations model applied to the accretion disc. The mass accretion rate fluctuations originate from variability of viscosity, which arises at every radius and causes local fluctuations of the density. The fluctuations diffuse through the disc and result in local variability of the mass accretion rate, which modulates the X-ray flux from the inner disc in the case of black holes, or from the surface in the case of neutron stars. A key role in the theoretical explanation of fast variability belongs to the description of the diffusion process. The propagation and evolution of the fluctuations is described by the diffusion equation, which can be solved by the method of Green functions. We implement Green functions in order to accurately describe the propagation of fluctuations in the disc. For the first time we consider both forward and backward propagation. We show that (i) viscous diffusion efficiently suppress variability at time scales shorter than the viscous time, (ii) local fluctuations of viscosity affect the mass accretion rate variability both in the inner and the outer parts of accretion disc, (iii) propagating fluctuations give rise not only to hard time lags as previously shown, but also produce soft lags at high frequency similar to those routinely attributed to reprocessing, (iv) deviation from the linear rms-flux relation is predicted for the case of very large initial perturbations. Our model naturally predicts bumpy power spectra.

Modeling the response of a standard accretion disc to stochastic viscous fluctuations

The observed variability of X-ray binaries over a wide range of time-scales can be understood in the framework of a stochastic propagation model, where viscous fluctuations at different radii induce accretion rate variability that propagate inwards to the X-ray producing region. The scenario successfully explains the power spectra, the linear rms-flux relation as well as the time-lag between different energy photons. The predictions of this model have been obtained using approximate analytical solutions or empirically motivated models which take into account the effect of these propagating variability on the radiative process of complex accretion flows. Here, we study the variation of the accretion rate due to such viscous fluctuations using a hydro-dynamical code for the standard geometrically thin, gas pressure dominated α-disc with a zero torque boundary condition. Our results confirm earlier findings that the time-lag between a perturbation and the resultant inner accretion rate variation depends on the frequency (or time-period) of the perturbation. Here we have quantified that the time-lag tlag∝f−0.54, for time-periods less than the viscous time-scale of the perturbation radius and is nearly constant otherwise. This, coupled with radiative process would produce the observed frequency dependent time-lag between different energy bands. We also confirm that if there are random Gaussian fluctuations of the α-parameter at different radii, the resultant inner accretion rate has a power spectrum which is a power-law.

New structures of power density spectra for four Kepler active galactic nuclei

Many nearby AGNs display a significant short-term variability. In this work we re-analyze photometric data of four active galactic nuclei observed by Kepler in order to study the flickering activity, having as main goal that of searching for multiple components in the power density spectra. We find that all four objects have similar characteristics, with two break frequencies at approximately log(f/Hz)=-5.2 and -4.7. We consider some physical phenomena whose characteristic time-scales are consistent with those observed, in particular mass accretion fluctuations in the inner geometrically thick disc (hot X-ray corona) and unstable relativistic Rayleigh-Taylor modes. The former is supported by detection of the same break frequencies in the Swift X-ray data of ZW229-15. We also discuss rms-flux relations, and we detect a possible typical linear trend at lower flux levels. Our findings support the hypothesis of a multiplicative character of variability, in agreement with the propagating accretion fluctuation model.

The rms-flux relation in accreting objects: not a simple “volume control”

The light curves of a diverse range of accreting objects show characteristic linear relationships between the short-term rms amplitude of variability and the flux as measured on longer time-scales. This behaviour is thought to be imprinted on the light curves by accretion rate fluctuations on different time-scales, propagating and coupling together through the accretion flow. Recently, a simple mathematical interpretation has been proposed for the rms-flux relation, where short-term variations are modulated by a single slower process. Here we show that this model was already considered and ruled out by another publication on the grounds that it did not produce the observed broad time-scale dependence of the rms-flux relation and associated lognormal flux distribution. We demonstrate the problems with the model via mathematical arguments and a case-study of Cyg X-1 data compared with numerical simulations. We also highlight another conclusion of our original work, which is that a linear rms-flux relation is easy to produce using a variety of models with positively skewed flux distributions. Observing such a relation in a non-accreting object (e.g. in solar flares) does not necessarily imply a phenomenological connection with the behaviour of accretion flows, unless the relation is seen over a similarly broad range of time-scales.

TESTING THE PROPAGATING FLUCTUATIONS MODEL WITH A LONG, GLOBAL ACCRETION DISK SIMULATION

ABSTRACT The broadband variability of many accreting systems displays characteristic structures; log-normal flux distributions, root-mean square (rms)-flux relations, and long inter-band lags. These characteristics are usually interpreted as inward propagating fluctuations of the mass accretion rate in an accretion disk driven by stochasticity of the angular momentum transport mechanism. We present the first analysis of propagating fluctuations in a long-duration, high-resolution, global three-dimensional magnetohydrodynamic (MHD) simulation of a geometrically thin (h/r ≈ 0.1) accretion disk around a black hole. While the dynamical-timescale turbulent fluctuations in the Maxwell stresses are too rapid to drive radially coherent fluctuations in the accretion rate, we find that the low-frequency quasi-periodic dynamo action introduces low-frequency fluctuations in the Maxwell stresses, which then drive the propagating fluctuations. Examining both the mass accretion rate and emission proxies, we recover log-normality, linear rms-flux relations, and radial coherence that would produce inter-band lags. Hence, we successfully relate and connect the phenomenology of propagating fluctuations to modern MHD accretion disk theory.