We study mass flow rate through a disc resulting from a varying mass supply rate. Variable mass supply rate occurs, e.g., during disc state transitions, and in interacting eccentric binaries. It is, however, damped by the viscosity of the disc. Here, we calculate this damping in detail. We derive an analytical description of the propagation of the flow rate using the solution of Lynden-Bell & Pringle, in which the disc is assumed to extend to infinity. In particular, we derive the accretion-rate Green's function, and its Fourier transform, which gives the fractional damping at a given variability frequency. We then compare this model to that of a finite disc with the mass supply at its outer edge. We find significant differences with respect to the infinite disc solution, which we find to overestimate the viscous damping. In particular, the asymptotic form of the Green's function is power-law for the infinite disc and exponential for the finite one. We then find a simple fitting form for the latter, and also calculate its Fourier transform. In general, the damping becomes very strong when the viscous time at the outer edge of the disc becomes longer than the modulation time scale. We apply our results to a number of astrophysical systems. We find the effect is much stronger in low-mass X-ray binaries, where the disc size is comparable to that of the Roche lobe, than in high-mass binaries, where the wind-fed disc can have a much smaller size.
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…
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 explanatio…
Explaining variability observed in the accretion flows of black hole X-ray binary systems remains challenging, especially concerning timescales less than, or comparable to, the viscous timescale but much larger than the inner orbital period despite decades of research identifying numerous relevant physical mechanisms. We take a simplified but broad approach to study several mechanisms likely relevant to patterns of variability observed in the persistently high-soft Roche-lobe overflow system LMC X-3. Based on simple estimates and upper bounds, we find that physics beyond varying disk/corona bi…
We perform detailed variability analysis of two-dimensional viscous, radiation hydrodynamic numerical simulations of Shakura-Sunyaev thin disks around a stellar mass black hole. Disk models are initialized on both the gas-, as well as radiation-, pressure-dominated branches of the thermal equilibrium curve, with mass accretion rates spanning the range from $\dot{M} = 0.01 L_\mathrm{Edd}/c^2$ to $10 L_\mathrm{Edd}/c^2$. An analysis of temporal variations of the numerically simulated disk reveals multiple robust, coherent oscillations. Considering the local mass flux variability, we find an osci…
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 var…
The standard thin accretion disk model has been successfully used to explain the soft X-ray spectra of Galactic black hole systems and perhaps the UV emission of Active Galactic Nuclei. However, radiation pressure dominated disks are known to be viscously unstable and should produce large amplitude oscillations that are typically not observed. Instead, these sources exhibit stochastic variability which may naturally arise due to viscous fluctuations in a turbulent disk. Here we investigate whether these aperiodic viscous fluctuations can stabilize the inner radiation pressure dominated disks a…
Truncated accretion disks are commonly invoked to explain the spectro-temporal variability from accreting black holes in both small systems, i.e. state transitions in galactic black hole binaries (GBHBs), and large systems, i.e. low-luminosity active galactic nuclei (LLAGNs). In the canonical truncated disk model of moderately low accretion rate systems, gas in the inner region of the accretion disk occupies a hot, radiatively inefficient phase, which leads to a geometrically thick disk, while the gas in the outer region occupies a cooler, radiatively efficient phase that resides in the standa…
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 log-normal 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, w…
The optical/ultraviolet (UV) variability of quasars has been discovered to be correlated with other quasar properties, such as luminosity, black hole mass and rest-frame wavelength. However,the origin of variability has been a puzzle so far. In this work, we upgrade the accretion disc model (Li & Cao 2008), which assumed the variability is caused by the change of global mass accretion rate, by constraining the disc size to match the viscous timescale of accretion disc to the variability timescale observed and by including the irradiation/X-ray reprocessing to make the emitted spectrum become s…
Models of X-ray reverberation from extended coronae are developed from general relativistic ray tracing simulations. Reverberation lags between correlated variability in the directly observed continuum emission and that reflected from the accretion disc arise due to the additional light travel time between the corona and reflecting disc. X-ray reverberation is detected from an increasing sample of Seyfert galaxies and a number of common properties are observed, including a transition from the characteristic reverberation signature at high frequencies to a hard lag within the continuum componen…
We investigate the effects of the convection in the hyperaccretion disk around a stellar-mass black hole, which is considered to be the central engine of gamma-ray bursts (GRBs), with simple analytical calculations. If the convective energy transfer in the vertical direction becomes efficient compared with the inward advective energy transport, the hyperaccretion disk is expected to be hotter and the neutrino emission due to the electron-positron annihilation becomes the most efficient cooling process. We find that the sequence of the thermal equilibrium solutions for the convective hyperaccre…
We study the X-ray variability of SS433 based on data from the ASCA observatory and the MAXI and RXTE/ASM monitoring missions. Based on the ASCA data, we have constructed the power spectrum of SS433 in the frequency range from $10^{-6}$ to 0.1 Hz, which confirms the presence of a flat portion (flat-topped noise) in the spectrum at frequencies $3\times 10^{-5}$ - $10^{-3}$ Hz. The periodic variability (precession, nutation, eclipses) begins to dominate significantly over the stochastic variability at lower frequencies, which does not allow the stochastic variability to be studied reliably. The …
We use the XMM-Newton EPIC-pn instrument in timing mode to extend spectral time-lag studies of hard state black hole X-ray binaries into the soft X-ray band. We show that variations of the disc blackbody emission substantially lead variations in the power-law emission, by tenths of a second on variability time-scales of seconds or longer. The large lags cannot be explained by Compton scattering but are consistent with time-delays due to viscous propagation of mass accretion fluctuations in the disc. However, on time-scales less than a second the disc lags the power-law variations by a few ms, …
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 w…
Magnetic Configuration Imprints on Quasi-Periodic Variability in GRMHD Simulations of Thin Accretion Disks
Tsung-Dao Lee Institute, Shanghai Jiao Tong University（李政道研究所，上海交通大学）；Institute of Fundamental Physics and Quantum Technology, School of Physical Science and Technology, Ningbo University（宁波大学物理科学与技术学院基础物理与量子技术研究所）；School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）；Key Laboratory for Particle Physics, Astrophysics and Cosmology (MOE), Shanghai Key Laboratory for Particle Physics and Cosmology, Shanghai Jiao Tong University（粒子物理、天体物理与宇宙学教育部重点实验室，上海粒子物理与宇宙学重点实验室，上海交通大学）；Institut für Theoretische Physik, Goethe-Universität Frankfurt（法兰克福歌德大学理论物理研究所）
Flickering, and more specifically aperiodic broad-band variability, is an important phenomenon used in understanding the geometry and dynamics of accretion flows. Although the inner regions of accretion flows are known to generate variability on relatively fast timescales, the broad-band variability generated in the outer regions have mostly remained elusive due to their long intrinsic variability timescales. Ultra-compact AM CVn systems are relatively small when compared to other accreting binaries and are well suited to search and characterise low frequency variability. Here we present the f…
We propose the thick-disc model of Gu et al. 2016 to interpret the transition between soft ultraluminous state (SUL) and supersoft ultraluminous (SSUL) state in NGC 247. As accretion rate increases, the inner disc will puff up and act as shield to block the innermost X-ray emission regions and absorb both soft and hard X-ray photons. The absorbed X-ray emission will be re-radiated as a much softer blackbody X-ray spectrum. Hence NGC 247 shows flux dips in the hard X-ray band and transits from the SUL state to the SSUL state. The $\sim 200$s transition timescale can be explained by the viscous …
Using archival RXTE data, we show that the ultracompact X-ray binary in NGC 1851 exhibits large amplitude X-ray flux varations of more than a factor of 10 on timescales of days to weeks and undergoes sustained periods of months where the time-averaged luminosty varies by factors of two. Variations of this magnitude and timescale have not been reported previously in other ultracompact X-ray binaries. Mass transfer in ultracompact binaries is thought to be driven by gravitational radiation and the predicted transfer rates are so high that the disks of ultracompact binaries with orbits as short a…
We study viscous accretion disc around black holes, and all possible accretion solutions, including shocked as well as shock free accretion branches. Shock driven bipolar outflows from a viscous accretion disc around a black hole has been investigated. One can identify two critical viscosity parameters $α_{cl}$ and $α_{cu}$, within which the stationary shocks may occur, for each set of boundary conditions. Adiabatic shock has been found for upto viscosity parameter $α=0.3$, while in presence of dissipation and massloss we have found stationary shock upto $α=0.15$. The mass outflow rate may inc…
Context: Low mass X-ray binaries were found to have very low frequency breaks in their power density spectra below which the power density spectra are nearly in white noise structure and at higher frequencies they approximately follow the $P_ν\propto ν^{-1.3}$ law. Aims: In 2005, Gilfanov and Arefiev studied X-ray variability of persistent LMXBs in the $10^{-8}-10^{-1}$ Hz frequency range and To determine whether high mass X-ray binary power density spectra have similar properties and the findings for low mass X-ray binaries are also valid for high mass binaries, we analyzed the time series of…
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 disk state, with X-ray luminosities of order $10^{33}-10^{34}$ erg s$^{-1}$, they switch rapidly between two distinct X-ray modes: the disk-high (DH) and disk-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 disk state and separating DH and DL modes. We report the di…
Aperiodic broad-band variability (also known as flickering) is observed throughout all types of accreting compact objects. Many statistical properties of this variability can be naturally explained with the fluctuating accretion disk model, where variations in the mass-transfer rate through the disk are modulated on the local viscous timescale and propagate towards the central compact object. Here, a recently developed implementation of the model is applied for the first time to the time-averaged, high-frequency variability of a cataclysmic variable star (MV Lyrae) observed with the Kepler sat…
Using the anelastic approximation of linearized hydrodynamic equations, we investigate the development of axially symmetric small perturbations in thin Keplerian discs. Dispersion relation is found as a solution of general Sturm-Liouville eigenvalue problem for different values of relevant physical parameters (viscosity, heat conductivity, disc semithickness). The analysis reveals the appearance of overstable mode for Prandtl parameter higher than some critical value. These modes have a viscous-convective nature and can serve as a seed for turbulence in astrophysical discs even in the absence …
We study local stability of the advection-dominated optically thick (slim) and optically thin discs with purely toroidal magnetic field and the radial viscous force using a linear perturbation analysis. Our dispersion relation indicates that the presence of magnetic fields and radial viscous force cannot give rise to any new mode of the instability. We find, however, that growth rate of the thermal mode in the slim discs and that of the acoustic modes in the slim and optically thin discs are dramatically affected by the radial viscous force. This force tends to strongly decrease the growth rat…
Recent observations of extreme variability in Active Galactic Nuclei have pushed standard viscous accretion disc models over an edge. "Extreme reprocessing" where an erratically variable central quasi-point source is entirely responsible for heating an otherwise cold and passive low-viscosity disc, may be the best route forward.
The power spectral density (PSD) of the X-ray emission variability from the accretion disc-corona region of black hole X-ray binaries and active galactic nuclei has a broken power law shape with a characteristic break time-scale. If the disc and the jet are connected, the jet variability may also contain a characteristic time-scale related to that of the disc-corona. Recent observations of the blazar Mrk 421 have confirmed the broken power law shape of the PSD of its jet X-ray variability. We model the time variability of a blazar, in which emitting particles are assumed to be accelerated by s…
Using the anelastic approximation of linearised hydrodynamic equations, we investigate the development of axially symmetric small perturbations in thin Keplerian discs. The sixth-order dispersion equation is derived and numerically solved for different values of relevant physical parameters (viscosity, heat conductivity, disc semi-thickness and vertical structure). The analysis reveals the appearance of two overstable modes which split out from the classical Rayleigh inertial modes in a wide range of the parameters in both ionized and neutral gases. These modes have a viscous-convective nature…
(Abridged) Recent XMM-Newton studies of X-ray variability in the hard states of black hole X-ray binaries (BHXRBs) imply that the variability is generated in the 'standard' optically-thick accretion disc. The variability originates in the disc as mass-accretion fluctuations and propagates through the disc to 'light up' inner disc regions, eventually modulating the power-law emission that is produced relatively centrally. We present a comparative spectral-timing study of XMM-Newton data from the BHXRB SWIFT J1753.5-0127 in a bright 2009 hard state with that from the significantly fainter 2006 h…
Evolution of variability properties of Galactic transient sources is a diagnostic tool to understand various regimes of the accretion flow and its dynamics close to the central black hole. In this paper, we concentrate on the variability properties of the X-ray transient XTE J1650-500 and investigate the evolution of viscous delay, time lag, QPO frequency, and their energy dependence throughout the rising phase as observed by RXTE during its outburst in 2001. Our analysis reveals (1) a delay of 12 \pm 1 days between one day averaged hard (5-12 keV) and soft (1.5-3 keV) photon light-curves as o…
We present the results of 2D, moving-mesh, viscous hydrodynamical simulations of an accretion disc around a merging supermassive black hole binary (SMBHB). The simulation is pseudo-Newtonian, with the BHs modeled as point masses with a Paczynski-Wiita potential, and includes viscous heating, shock heating, and radiative cooling. We follow the gravitational inspiral of an equal-mass binary with a component mass M_bh=10^6 M_sun from an initial separation of 60r_g (where r_g=GM_bh/c^2 is the gravitational radius) to the merger. We find that a central, low-density cavity forms around the binary, a…
We carry out 2D viscous hydrodynamics simulations of circumbinary disk (CBD) accretion using {\footnotesize AREPO}. We resolve the accretion flow from a large-scale CBD down to the streamers and disks around individual binary components. Extending our recent studies \citep{mun19}, we consider circular binaries with various mass ratios ($0.1\leq q_{\rm{b}}\leq1$) and study accretion from ``infinite'', steady-supply disks and from finite-sized, viscously spreading tori. For ``infinite'' disks, a global steady state can be reached, and the accretion variability has a dominant frequency ${\sim}0.2…
We present a model of a viscously evolving accretion disc around a magnetized neutron star. The model features the varying outer radius of the hot ionized part of the disc due to cooling and the varying inner radius of the disc due to interaction with the magnetosphere. It also includes hindering of accretion on the neutron star because of the centrifugal barrier and irradiation of the outer disc and companion star by X-rays from the neutron star and disc. When setting inner boundary conditions, we take into account that processes at the inner disc occur on a time scale much less than the visc…
Physical damping, regarding the nonlinear Navier-Stokes viscous flow dynamics, refers to a tensorial turbulent dissipation term, attributed to adjacent moving macroscopic flow components. Mutual dissipation among these parts of fluid is described by a braking term in the momentum equation together with a heating term in the energy equation, both responsible of the damping of the momentum variation and of the viscous conversion of mechanical energy into heat. A macroscopic mixing scale length is currently the only characteristic length needed in the nonlinear modelling of viscous fluid dynamics…
