Mass Accretion Rate Fluctuations Research Articles

What drives the variability in AGN? Explaining the UV-Xray disconnect through propagating fluctuations

ABSTRACT Intensive broad-band reverberation mapping campaigns have shown that AGN variability is significantly more complex than expected from disc reverberation of the variable X-ray illumination. The UV/optical variability is highly correlated and lagged, with longer lags at longer wavelengths as predicted, but the observed time-scales are longer than expected. Worse, the UV/optical light curves are not well correlated with the X-rays, which should drive them. Instead, we consider an intrinsically variable accretion disc, where slow mass accretion rate fluctuations are generated in the optical-UV disc, propagating down to modulate intrinsically faster X-ray variability from the central regions. We match our model to Fairall 9, a well-studied AGN with L ∼ 0.1LEdd, where the spectrum is dominated by the UV/EUV. Our model produces light curves where the X-rays and UV have very different fast variability, yet are well correlated on longer time-scales, as observed. It predicts that the intrinsic variability has optical/UV leading the X-rays, but including reverberation of the variable EUV from an inner wind produces a lagged bound-free continuum that matches the observed UV-optical lags. We conclude that optical/UV AGN variability is likely driven by intrinsic fluctuations within the disc, not X-ray reprocessing: the observed longer than expected lags are produced by reverberation of the EUV illuminating a wind, not by X-ray illumination of the disc: the increasing lag with increasing wavelength is produced by the increased contribution of the (constant lag) bound-free continuum to the spectrum, rather than indicating intrinsically larger reverberation distances for longer wavelengths.

Wavelet spectral timing: X-ray reverberation from a dynamic black hole corona hidden beneath ultrafast outflows

ABSTRACT Spectral timing analyses based upon wavelet transforms provide a new means to study the variability of the X-ray emission from accreting systems, including AGN, stellar mass black holes, and neutron stars, and can be used to trace the time variability of X-ray reverberation from the inner accretion disc. The previously missing iron K reverberation time lags in the AGN IRAS 13224–3809 and MCG–6-30-15 are detected and found to be transitory in nature. Reverberation can be hidden during periods in which variability in the iron K band becomes dominated by ultrafast outflows. Following the time evolution of the reverberation lag between the corona and inner accretion disc, we may observe the short time-scale increase in scale height of the corona as it is accelerated away from the accretion disc during bright X-ray flares in the AGN I Zw 1. Measuring the variation of the reverberation lag that corresponds to the continuous, stochastic variations of the X-ray luminosity sheds new light on the disc–corona connection around accreting black holes. Hysteresis is observed between the X-ray count rate and the scale height of the corona, and a time lag of 10∼40 ks is observed between the rise in luminosity and the increase in reverberation lag. This correlation and lag are consistent with viscous propagation through the inner accretion disc, leading first to an increase in the flux of seed photons that are Comptonized by the corona, before mass accretion rate fluctuations reach the inner disc and are able to modulate the structure of the corona.

The origin of long soft lags and the nature of the hard-intermediate state in black hole binaries

ABSTRACT Fast variability of the X-ray corona in black hole binaries can produce a soft lag by reverberation, where the reprocessed thermalized disc photons lag behind the illuminating hard X-rays. This lag is small, and systematically decreases with increasing mass accretion rate towards the hard–soft transition, consistent with a decreasing truncation radius between the thin disc and X-ray hot inner flow. However, the soft lag suddenly increases dramatically just before the spectrum becomes disc dominated (hard-intermediate state). Interpreting this as reverberation requires that the X-ray source distance from the disc increases dramatically, potentially consistent with switching to X-rays produced in the radio jet. However, this change in lag behaviour occurs without any clear change in hard X-ray spectrum, and before the plasmoid ejection event that might produce such a source (soft-intermediate state). Instead, we show how the soft lag can be interpreted in the context of propagation lags from mass accretion rate fluctuations. These normally produce hard lags, as the model has radial stratification, with fluctuations from larger radii modulating the harder spectra produced at smaller radii. However, all that is required to switch the sign is that the hottest Comptonized emission has seed photons that allow it to extend down in energy below the softer emission from the slower variable turbulent region from the inner edge of the disc. Our model connects the timing change to the spectral change, and gives a smooth transition of the X-ray source properties from the bright hard state to the disc-dominated states.

X-ray variability of transitional millisecond pulsars: a faint, stable, and fluctuating disc

ABSTRACT Transitional millisecond pulsars (tMSPs) have emerged in the last decade as a unique class of neutron stars at the crossroads between accretion- and rotation-powered phenomena. In their (sub-luminous) accretion disc state, with X-ray luminosities of order 1033–1034 erg s−1, they switch rapidly between two distinct X-ray modes: the disc-high (DH) and disc-low (DL) states. We present a systematic XMM–Newton and Chandra analysis of the aperiodic X-ray variability of all three currently known tMSPs, with a main focus on their disc state and separating DH and DL modes. We report the discovery of flat-topped broad-band noise in the DH state of two of them, with break frequencies of 2.8 mHz (PSR J1023 + 0038) and 0.86 mHz (M28-I). We argue that the lowest frequency variability is similar to that seen in disc-accreting X-ray binaries in the hard state, at typical luminosities at least two orders of magnitude higher than tMSPs. We find strong variability in the DH state around 1 Hz, not typical of hard state X-ray binaries, with fractional rms amplitudes close to 30 per cent. We discuss our results and use them to constrain the properties of the accretion disc, assuming that the X-ray variability is produced by fluctuations in mass accretion rate, and that the break frequency corresponds to the viscous time-scale at the inner edge of the disc. In this context, we find that the newly found break frequencies are broadly consistent with a disc truncated close to the light cylinder with $\dot{M}\simeq 10^{13}-5\times 10^{14}$ g s−1 and a viscosity parameter α ≳ 0.2.

Origins of the UV/X-ray relation in Arakelian 120

ABSTRACTWe explore the accretion geometry in Arakelian 120 using intensive UV and X-ray monitoring from Swift. The hard X-rays (1–10 keV) show large amplitude, fast (few-day) variability, so we expect reverberation from the disc to produce UV variability from the varying hard X-ray illumination. We model the spectral energy distribution (SED) including an outer standard disc (optical), an intermediate warm-Comptonization region (UV and soft X-ray), and a hot corona (hard X-rays). Unlike the lower Eddington fraction AGN (NGC 4151 and NGC 5548 at L/LEdd ∼ 0.02 and 0.03, respectively), the SED of Akn 120 (L ∼ 0.05LEdd) is dominated by the UV, restricting the impact of reverberating hard X-rays by energetics alone. Illumination from a hard X-ray corona with height ∼10 Rg produces minimal UV variability. Increasing the coronal scale height to ∼100 Rg improves the match to the observed amplitude of UV variability as the disc subtends a larger solid angle, but results in too much fast variability to match the UV data. The soft X-rays (connected to the UV in the warm-Comptonization model) are more variable than the hard, but again contain too much fast variability to match the observed smoother variability seen in the UV. Results on lower Eddington fraction AGN have emphasized the contribution from reverberation from larger scales (the broad-line region), but reverberation induces lags on similar time-scales to the smoothing, producing a larger delay than is compatible with the data. We conclude that the majority of the UV variability is therefore intrinsic, connected to mass-accretion rate fluctuations in the warm-Comptonization region.

A full spectral-timing model to map the accretion flow in black hole binaries: the low/hard state of MAXI J1820+070

ABSTRACT The nature and geometry of the accretion flow in the low/hard state of black hole binaries is currently controversial. While most properties are generally explained in the truncated disc/hot inner flow model, the detection of a broad residual around the iron line argues for strong relativistic effects from an untruncated disc. Since spectral fitting alone is somewhat degenerate, we combine it with the additional information in the fast X-ray variability and perform a full spectral-timing analysis for NICER and NuSTAR data on a bright low/hard state of MAXI J1820+070. We model the variability with propagating mass accretion rate fluctuations by combining two separate current insights: that the hot flow is spectrally inhomogeneous, and that there is a discontinuous jump in viscous time-scale between the hot flow and variable disc. Our model naturally gives the double-humped shape of the power spectra, and the increasing high-frequency variability with energy in the second hump. Including reflection and reprocessing from a disc truncated at a few tens of gravitational radii quantitatively reproduces the switch in the lag-frequency spectra, from hard lagging soft at low frequencies (propagation through the variable flow) to the soft lagging hard at the high frequencies (reverberation from the hard X-ray continuum illuminating the disc). The viscous time-scale of the hot flow is derived from the model, and we show how this can be used to observationally test ideas about the origin of the jet.

Multi-timescale reverberation mapping of Mrk 335

ABSTRACT Time lags due to X-ray reverberation have been detected in several Seyfert galaxies. The different traveltime between reflected and directly observed rays naturally causes this type of lag, which depends directly on the light-crossing time-scale of the system and hence scales with the mass of the central black hole. Featureless ‘hard lags’ not associated with reverberation, and often interpreted as propagating mass accretion rate fluctuations, dominate the longer time-scale variability. Here we fit our reltrans model simultaneously to the time-averaged energy spectrum and the lag-energy spectra of the Seyfert galaxy Mrk 335 over two time-scales (Fourier frequency ranges). We model the hard lags as fluctuations in the slope and strength of the illuminating spectrum, and self-consistently account for the effects that these fluctuations have on the reverberation lags. The resulting mass estimate is $1.1^{+2.0}_{-0.7} \times 10^6~\mathrm{ M}_\odot$, which is significantly lower than the mass measured with the optical reverberation mapping technique (14–26 million M⊙). When we add the correlated variability amplitudes to the time lags by fitting the full complex cross-spectra, the model is unable to describe the characteristic reverberation Fe K α line and cannot constrain the black hole mass. This may be due to the assumption that the direct radiation is emitted by a point-like source.

Broad-band aperiodic variability in X-ray pulsars: accretion rate fluctuations propagating under the influence of viscous diffusion

We investigate aperiodic X-ray flux variability in accreting highly magnetized neutron stars - X-ray pulsars (XRPs). The X-ray variability is largely determined by mass accretion rate fluctuations at the NS surface, which replicate accretion rate fluctuations at the inner radius of the accretion disc. The variability at the inner radius is due to fluctuations arising all over the disc and propagating inwards under the influence of viscous diffusion. The inner radius varies with mean mass accretion rate and can be estimated from the known magnetic field strength and accretion luminosity of XRPs. Observations of transient XRPs covering several orders of magnitude in luminosity give a unique opportunity to study effects arising due to the changes of the inner disc radius. We investigate the process of viscous diffusion in XRP accretion discs and construct new analytical solutions of the diffusion equation applicable for thin accretion discs truncated both from inside and outside. Our solutions are the most general ones derived in the approximation of Newtonian mechanics. We argue that the break observed at high frequencies in the power density spectra of XRPs corresponds to the minimal time scale of the dynamo process, which is responsible for the initial fluctuations. Comparing data from the bright X-ray transient A 0535+26 with our model, we conclude that the time scale of initial variability in the accretion disc is a few times longer than the local Keplerian time scale.

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.

Modelling hard and soft states of Cygnus X-1 with propagating mass accretion rate fluctuations

We present a timing analysis of threeRossi X-ray Timing Explorer observations of the black hole binary Cygnus X-1 with the propagating mass accretion rate fluctuations model PROPFLUC. The model simultaneously predicts power spectra, time lags, and coherence of the variability as a function of energy. The observations cover the soft and the hard state of the source, and the transition between the two. We find good agreement between model pre-dictions and data in the hard and in the soft state. Our analysis suggests that in the soft state the fluctuations propagate in an optically thin hot flow extending up to large radii above and below a stable optically thick disc. In the hard state, our results are consistent with a truncated disc geometry, where the hot flow extends radially inside the inner radius of the disc. In the transition from soft to hard state, the characteristics of the rapid variability are too complex to be successfully described with PROPFLUC. The surface density profile of the hot flow predicted by our model and the lack of QPOs in the soft and hard state, suggest that the spin of the black hole is aligned with the inner accretion disc and therefore probably with the rotational axis of the binary system.

Cross-spectral modelling of the black hole X-ray binary XTE J1550-564: challenges to the propagating fluctuations paradigm

Timing properties of black hole X-ray binaries in outburst can be modeled with mass accretion rate fluctuations propagating towards the black hole. Such models predict time lags between energy bands due to propagation delays. First application of a propagating fluctuations model to black hole power spectra showed good agreement with the data. Indeed, hard lags observed from these systems appear to be in agreement with this generic prediction. Our PROPFLUC code allows to simultaneously predict power spectra, time lags, and coherence of the variability as a function of energy. This was successfully applied to Swift data on the black hole MAXIJ1659-152, fitting jointly the power spectra in two energy bands and the cross-spectrum between these two bands. In the current work, we attempt to to model two high signal to noise Rossi X-ray Timing Explorer (RXTE) observations of the black hole XTE J1550-564. We find that neither observation can be adequately explained by the model even when considering, additionally to previous PROPFLUC versions, different propagation speeds of the fluctuations. After extensive exploration of model extensions, we tentatively conclude that the quantitative and qualitative discrepancy between model predictions and data is generic to the propagating fluctuations paradigm. This result encourages further investigation of the fundamental hypotheses of the propagating fluctuations model. We discuss some of these hypotheses with an eye to future works.

INTERFERENCE AS AN ORIGIN OF THE PEAKED NOISE IN ACCRETING X-RAY BINARIES

ABSTRACT We propose a physical model for the peaked noise in the X-ray power density spectra of accreting X-ray binaries. We interpret its appearance as an interference of two Comptonization continua: one coming from the upscattering of seed photons from the cold thin disk and the other fed by the synchrotron emission of the hot flow. Variations of both X-ray components are caused by fluctuations in mass accretion rate, but there is a delay between them corresponding to the propagation timescale from the disk Comptonization radius to the region of synchrotron Comptonization. If the disk and synchrotron Comptonization are correlated, the humps in the power spectra are harmonically related and the dips between them appear at frequencies related as odd numbers 1:3:5. If they are anti-correlated, the humps are related as 1:3:5, but the dips are harmonically related. Similar structures are expected to be observed in accreting neutron star binaries and supermassive black holes. The delay can be easily recovered from the frequency of peaked noise and further used to constrain the combination of the viscosity parameter and disk height-to-radius ratio α(H/R)2 of the accretion flow. We model multi-peak power spectra of black hole X-ray binaries GX 339–4 and XTE J1748–288 to constrain these parameters.

Modelling the cross-spectral variability of the black hole binary MAXI J1659-152 with propagating accretion rate fluctuations

The power spectrum of the X-ray fluctuations of accreting black holes often consists of two broad humps. We quantitatively investigate the hypothesis that the lower frequency hump orig- inates from variability in a truncated thin accretion disc, propagating into a large scale-height inner hot flow which, in turn, itself is the origin of the higher frequency hump. We extend the propagating mass accretion rate fluctuations model PROPFLUC to accommodate double hump power spectra in this way. Furthermore, we extend the model to predict the cross-spectrum between two energy bands in addition to their power spectra, allowing us to constrain the model using the observed time lags, which in the model result from both propagation of fluc- tuations from the disc to the hot flow, and inside the hot flow. We jointly fit soft and hard power spectrum, and the cross-spectrum between the two bands using this model for 5 Swift X-ray Telescope observations of MAXI J1659-152. The new double hump model provides a better fit to the data than the old single hump model for most of our observations. The data show only a small phase lag associated with the low frequency hump. We demonstrate quan- titatively that this is consistent with the model. We compare the truncation radius measured from our fits with that measured purely by spectral fitting and find agreement within a factor of two. This analysis encompasses the first joint fits of stellar-mass black hole cross-spectra and power spectra with a single self-consistent physical model.

Testing propagating mass accretion rate fluctuations model PROPFLUC on black hole X‐ray binaries

AbstractOver the past 20 years, a consistent phenomenology has been established to describe the variability properties of black hole X‐ray binaries. However, the physics behind the observational data is still poorly understood. The recently proposed model PROPFLUC assumes a truncated disc/hot inner flow geometry, with mass accretion rate fluctuations propagating through a precessing inner flow. These two processes give rise respectively to broad band variability and a quasi‐periodic oscillation (QPO) on the precession frequency. We recently applied systematically for the first time PROPFLUC on a black hole candidate (MAXI J1543‐564) in order to compare the results of phenomenological and physical modeling of the source power spectrum and to give a physical interpretation of the rising phase of the source outburst. Here we resume the results of our study on MAXI J1543‐564 and we discuss future PROPFLUC implementations. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modelling aperiodic X‐ray variabiity in black hole binaries as propagating mass accretion rate fluctuations: A short review

AbstractBlack hole binary systems can emit very bright and rapidly varying X‐ray signals when material from the companion accretes onto the black hole, liberating huge amounts of gravitational potential energy. Central to this process of accretion is turbulence. In the propagating mass accretion rate fluctuations model, turbulence is generated throughout the inner accretion flow, causing fluctuations in the accretion rate. Fluctuations from the outer regions propagate towards the black hole, modulating the fluctuations generated in the inner regions. Here, I present the theoretical motivation behind this picture before reviewing the array of statistical variability properties observed in the light curves of black hole binaries that are naturally explained by the model. I also discuss the remaining challenges for the model, both in terms of comparison to data and in terms of including more sophisticated theoretical considerations. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Geometrical constraints on the origin of timing signals from black holes

We present a systematic study of the orbital inclination effects on black-hole transients fast time-variability properties. We have considered all the black-hole binaries that have been densely monitored by the Rossi XTE satellite. We find that the amplitude of low-frequency quasi periodic oscillations (QPOs) depends on the orbital inclination. Type-C QPOs are stronger for nearly edge-on systems (high inclination), while type-B QPOs are stronger when the accretion disk is closer to face-on (low inclination). Our results also suggest that the noise associated with type-C QPOs is consistent with being stronger for low-inclination sources, while the noise associated to type-B QPOs seems inclination independent. These results are consistent with a geometric origin of the type-C QPOs - for instance arising from relativistic precession of the inner flow within a truncated disk - while the noise would correspond to intrinsic brightness variability from mass accretion rate fluctuations in the accretion flow. The opposite behavior of type-B QPOs - stronger in low inclinations sources - supports the hypothesis that type-B QPOs are related to the jet, the power of which is the most obvious measurable parameter expected to be stronger in nearly face-on sources.

Evolution of the hot flow of MAXI J1543-564

We present a spectral and timing analysis of the black hole candidate MAXI J1543-564 during its 2011 outburst. As shown in previous work, the source follows the standard evolution of a black hole outburst. During the rising phase of the outburst we detect an abrupt change in timing behavior associated with the occurrence of a type-B quasi-periodic oscillation (QPO). This QPO and the simultaneously detected radio emission mark the transition between hard and soft intermediate state. We fit power spectra from the rising phase of the outburst using the recently proposed model propfluc. This assumes a truncated disc / hot inner flow geometry, with mass accretion rate fluctuations propagating through a precessing inner flow. We link the propfluc physical parameters to the phenomenological multi-Lorentzian fit parameters. The physical parameter dominating the QPO frequency is the truncation radius, while broad band noise characteristics are also influenced by the radial surface density and emissivity profiles of the flow. In the outburst rise we found that the truncation radius decreases from $r_o \sim 24$ to $10 R_g$, and the surface density increases faster than the mass accretion rate, as previously reported for XTE J1550-564. Two soft intermediate state observations could not be fitted with propfluc, and we suggest that they are coincident with the ejection of material from the inner regions of the flow in a jet or accretion of these regions into the BH horizon, explaining the drop in QPO frequency and suppression of broad band variability preferentially at high energy bands coincident with a radio flare.

An exact analytic treatment of propagating mass accretion rate fluctuations in X-ray binaries

Many statistical properties of the aperiodic variability observed in X-ray radiation from accreting compact objects can be naturally explained by the propagating fluctuations model. This considers variations in mass accretion rate to be stirred up throughout the accretion flow. Variations from the outer regions of the accretion flow will propagate towards the central object, modulating the variations from the inner regions and eventually modulating the radiation, giving rise to the observed linear RMS-flux relation and also Fourier frequency dependent time lags. Previous treatments of this model have relied on computationally intensive Monte Carlo simulations which can only yield an estimate of statistical properties such as the power spectrum. Here, we find exact and analytic expressions for the power spectrum and lag spectrum predicted by the same model. We use our calculation to fit the model of Ingram & Done (2012) to a power spectrum of XTE J1550-564. The result we present here will apply to any treatment of the propagating fluctuations model and thus provides a very powerful tool for future theoretical modelling.

Modelling variability in black hole binaries: linking simulations to observations

Black hole accretion flows show rapid X-ray variability. The Power Spectral Density (PSD) of this is typically fit by a phenomenological model of multiple Lorentzians for both the broad band noise and Quasi-Periodic Oscillations (QPOs). Our previous paper (Ingram & Done 2011) developed the first physical model for the PSD and fit this to observational data. This was based on the same truncated disc/hot inner flow geometry which can explain the correlated properties of the energy spectra. This assumes that the broad band noise is from propagating fluctuations in mass accretion rate within the hot flow, while the QPO is produced by global Lense-Thirring precession of the same hot flow. Here we develop this model, making some significant improvements. Firstly we specify that the viscous frequency (equivalently, surface density) in the hot flow has the same form as that measured from numerical simulations of precessing, tilted accretion flows. Secondly, we refine the statistical techniques which we use to fit the model to the data. We re-analyse the PSD from the 1998 rise to outburst of XTE J1550-564 with our new model in order to assess the impact of these changes. We find that the derived outer radii of the hot flow (set by the inner radius of the truncated disc) are rather similar, changing from ~68-13 Rg throughout the outburst rise. However, the more physical assumptions of our new model also allow us to constrain the scale height of the flow. This decreases as the outer radius of the flow decreases, as expected from the spectral evolution. The spectrum steepens in response to the increased cooling as the as the truncation radius sweeps in, so gas pressure support for the flow decreases. The new model, propfluc, is publically available within the xspec spectral fitting package.

A physical model for the continuum variability and quasi-periodic oscillation in accreting black holes

The power spectra of black hole binaries have been well studied for decades, giving a detailed phenomenological picture of the variability properties and their correlation with the energy spectrum (spectral state) of the source. Here we take the truncated disc/hot inner flow picture which can describe the spectral changes, and show that propagating mass accretion rate fluctuations in the hot flow can match the broad band power spectral properties seen in black hole binaries, i.e. give approximately band limited noise between a low and high frequency break. The low frequency break marks the viscous timescale at the outer edge of the hot inner flow, which is the inner edge of the truncated disc. The model also predicts the Lense-Thirring precession timescale of the hot flow, as this is set by the surface density of the flow which is self consistently calculated from the propagating fluctuations. We show that this naturally gives the observed relation between the low frequency break and QPO frequency as the outer radius of the flow moves inwards, and that this model predicts many of the observed QPO properties such as correlation of coherence with frequency, and of the recently discovered correlation of frequency with flux on short timescales. We fit this total model of the variability to a sequence of 5 observed power spectra from the bright black hole binary XTE J1550-564 as the source transitioned from a low/hard to very high state. This is the first time that a power spectrum from a black hole binary has been fit with a physical model for the variability. The data are well fit if the inner radius of the flow remains constant, while the outer radius sweeps inwards from ~60-12 Rg. This range of radii agrees with models of the energy spectral evolution, giving the first self consistent description of the evolution of both the spectrum and variability of BHB.