Keplerian Flow Research Articles

Accretion flow dynamics and characteristics of MAXI J153–571-spectral analysis using combination of XSPEC and TCAF models

MAXI J153–571 accretion flow consists of Keplerian (optically thick) and sub-Keplerian (optically thin) flow, and their mass accretion rates seem to regulate other accretion flow characteristics. Hard X-rays are produced when the Keplerian seed soft photons are thermally or inverse comptonized in the Compton cloud/post-shock region by hot electrons. The variations/fluctuations of components of the accretion flow during the hard states create propagating Quasi-periodic oscillation (QPO) when their timescales are roughly matched and resonance phenomena occur. The QPO and its frequency are timing properties and the accretion flow spectra-temporal characteristics can be determined via spectral analysis. In this study, we looked into the accretion flow characteristics of MAXI J153–571 during the hard-intermediate state. Spectral analysis of MAXI J153–571 observed by MAXI/GSC, Swift/BAT, and NuSTAR on the same or close-in epochs was carried out. XSPEC and TCAF models were used in fitting/modeling the data. A robust and statistically acceptable fit spectra with a reduced Chi-squared value of ∼ 0.84 – 1.20 and best-fit photon index of 2.0–2.29 was obtained. The track of the accretion flow characteristics was obtained using models’–fitted parameters and MATLAB written codes of physical equations. Some accretion flow characteristics are positively correlated while others are anti-correlated at different phases and their correlation are statistically significant. The correlation of accretion flow characteristics with one another suggests that saturation effects, variation/fluctuations in the accretion flow, and intermittent/flickering behavior of MAXI J153–571 are tied to the variations/fluctuations of the intrinsic properties; mass accretion rates. Moreover, a resonance condition of 0.70 to 0.83 indicates that the cooling and infall timescales are roughly matched and affirms the presence of QPO in the accretion flow. This suggests that the origin of the photon index–QPO frequency (Γ–vQPO) relation is strongly linked to the variation/fluctuations in mass accretion flow rates. Hence, the accretion flow is dynamic, and independent variations/fluctuations of mass accretion rates could regulate the variation/fluctuations of other accretion flow parameters and perhaps, spectral evolution.

The Doppler Flip in HD 100546 as a Disk Eruption: The Elephant in the Room of Kinematic Protoplanet Searches

The interpretation of molecular-line data using hydrodynamical simulations of planet–disk interactions fosters new hope for the indirect detection of protoplanets. In a model-independent approach, embedded protoplanets should be found at the roots of abrupt Doppler flips in velocity centroid maps. However, the largest velocity perturbation known for an unwarped disk, in the disk of HD 100546, leads to a conspicuous Doppler flip that coincides with a thick dust ring, in contradiction with an interpretation in terms of a ≳1 M jup body. Here we present new ALMA observations of the 12CO(2–1) kinematics in HD 100546, with a factor of 2 finer angular resolutions. We find that the disk rotation curve is consistent with a central mass 2.1 < M ⋆/M ⊙ < 2.3 and that the blueshifted side of the Doppler flip is due to vertical motions, reminiscent of the disk wind proposed previously from blueshifted SO lines. We tentatively propose a qualitative interpretation in terms of a surface disturbance to the Keplerian flow, i.e., a disk eruption, driven by an embedded outflow launched by a ∼10 M earth body. Another interpretation involves a disk-mass-loading hot spot at the convergence of an envelope accretion streamer.

Accretion onto a quintessence contaminated rotating black hole: violating the lower limit for eta over s

Viscous accretion flow around a rotating supermassive black hole sitting in a quintessence tub is studied in this article. To introduce such a dark energy contaminated black hole’s gravitational force, a new pseudo-Newtonian potential is used. This pseudo-Newtonian force can be calculated if we know the distance from the black hole’s center, spin of the black hole and equation of state of the quintessence inside which the black hole is considered to lie. This force helps us to avoid complicated nonlinearity of general relativistic field equations. Transonic, viscous, continuous and Keplerian flow is assumed to take place. Fluid speed, sonic speed profile and specific angular momentum to Keplerian angular momentum ratio are found out for different values of spin parameter and quintessence parameter. Density variation is built and tallied with observations. Shear viscosity to entropy density ratio is constructed for our model and a comparison with theoretical lower limit is done.

Turbulence in electromagnetically driven Keplerian flows

Abstract

Origin of hydrodynamic instability from noise: From laboratory flow to accretion disk

We attempt to address the old problem of plane shear flows: the origin of turbulence and hence transport of angular momentum in accretion flows as well as laboratory flows, such as plane Couette flow. We undertake the problem by introducing an extra force in Orr-Sommerfeld and Squire equations along with the Coriolis force mimicking the local region of the accretion disk. For plane Couette flow, the Coriolis term drops. Subsequently we solve the equations by WKB approximation method. We investigate the dispersion relation for the Keplerian flow and plane Couette flow for all possible combinations of wave vectors. Due to the very presence of extra force, we show that both the flows are unstable for a certain range of wave vectors. However, the nature of instability between the flows is different. We also study the Argand diagrams of the perturbation eigenmodes. It helps us to compare the different time scales corresponding to the perturbations as well as accretion. We ultimately conclude with this formalism that fluid gets enough time to be unstable and hence plausibly turbulent particularly in the local regime of the Keplerian accretion disks. Repetition of the analysis throughout the disk explains the transport of angular momentum and matter along outward and inward direction respectively.

Perturbation dynamics in Keplerian flow under external stochastic forcing

ABSTRACT We investigate the dynamics of linear perturbations in Keplerian flow under external stochastic force. To abstract from the details of flow structure and boundary conditions, we consider the problem in the shearing box approximation. An external force is assumed to have zero mean, even so, induced perturbations form a steady state, which provides angular momentum transfer to the periphery of the flow. The most effective scenario is based on the transient amplification of induced vortices with the following emission of a shearing sound wave, wherein the maximum of the flux linearly depends on Reynolds number. Thus such a mechanism is significant for astrophysical flows, for which enormous Reynolds numbers are typical. At the same time, addressing the problem analytically, we find that for incompressible fluid in the shearing box approximation stochastic forcing does not lead to average angular momentum transfer. Thus the compressibility of the fluid plays an important role here, and one cannot neglect it.

Analysis of azimuthal magnetorotational instability of rotating magnetohydrodynamic flows and Tayler instability via an extended Hain-Lüst equation.

We consider a differentially rotating flow of an incompressible electrically conducting and viscous fluid subject to an external axial magnetic field and to an azimuthal magnetic field that is allowed to be generated by a combination of an axial electric current external to the fluid and electrical currents in the fluid itself. In this setting we derive an extended version of the celebrated Hain-Lüst differential equation for the radial Lagrangian displacement that incorporates the effects of the axial and azimuthal magnetic fields, differential rotation, viscosity, and electrical resistivity. We apply the Wentzel-Kramers-Brillouin method to the extended Hain-Lüst equation and derive a comprehensive dispersion relation for the local stability analysis of the flow to three-dimensional disturbances. We confirm that in the limit of low magnetic Prandtl numbers, in which the ratio of the viscosity to the magnetic diffusivity is vanishing, the rotating flows with radial distributions of the angular velocity beyond the Liu limit, become unstable subject to a wide variety of the azimuthal magnetic fields, and so is the Keplerian flow. In the analysis of the dispersion relation we find evidence of a new long-wavelength instability which is caught also by the numerical solution of the boundary value problem for a magnetized Taylor-Couette flow.

Influences of protoplanet-induced three-dimensional gas flow on pebble accretion

Context. The pebble accretion model has the potential to explain the formation of various types of planets. The main difference between this and the planetesimal accretion model is that pebbles not only experience the gravitational interaction with the growing planet but also a gas drag force from the surrounding protoplanetary disk gas. Aims. A growing planet embedded in a disk induces three-dimensional (3D) gas flow, which may influence pebble accretion. However, so far the conventional pebble accretion model has only been discussed in the unperturbed (sub-)Keplerian shear flow. In this study, we investigate the influence of 3D planet-induced gas flow on pebble accretion. Methods. Assuming a nonisothermal, inviscid gas disk, we perform 3D hydrodynamical simulations on the spherical polar grid, which has a planet located at its center. We then numerically integrate the equation of motion of pebbles in 3D using hydrodynamical simulation data. Results. We find that the trajectories of pebbles in the planet-induced gas flow differ significantly from those in the unperturbed shear flow for a wide range of investigated pebble sizes (St = 10−3–100, where St is the Stokes number). The horseshoe flow and outflow of the gas alter the motion of the pebbles, which leads to a reduction of the width of the accretion window, wacc, and the accretion cross section, Aacc. On the other hand, the changes in trajectories also cause an increase in the relative velocity of pebbles to the planet, which offsets the reduction of wacc and Aacc. As a consequence, in the Stokes regime, the accretion probability of pebbles, Pacc, in the planet-induced gas flow is comparable to that in the unperturbed shear flow except when the Stokes number is small, St ~ 10−3, in 2D accretion, or when the thermal mass of the planet is small, m = 0.03, in 3D accretion. In contrast, in the Epstein regime, Pacc in the planet-induced gas flow becomes smaller than that in the shear flow in the Stokes regime in both 2D and 3D accretion, regardless of assumed St and m. Conclusions. Our results combined with the spacial variety of turbulence strength and pebble size in a disk, suggest that the 3D planet-induced gas flow may be helpful to explain the distribution of exoplanets and the architecture of the Solar System.

Kinematic detection of a planet carving a gap in a protoplanetary disk

We still do not understand how planets form, or why extra-solar planetary systems are so different from our own solar system. But the last few years have dramatically changed our view of the discs of gas and dust around young stars. Observations with the Atacama Large Millimeter/submillimeter Array (ALMA) and extreme adaptive-optics systems have revealed that most --- if not all --- discs contain substructure, including rings and gaps, spirals, azimuthal dust concentrations, and shadows cast by misaligned inner discs. These features have been interpreted as signatures of newborn protoplanets, but the exact origin is unknown. Here we report the kinematic detection of a few Jupiter-mass planet located in a gas and dust gap at 130 au in the disc surrounding the young star HD 97048. An embedded planet can explain both the disturbed Keplerian flow of the gas, detected in CO lines, and the gap detected in the dust disc at the same radius. While gaps appear to be a common feature in protoplanetary discs, we present a direct correspondence between a planet and a dust gap, indicating that at least some gaps are the result of planet-disc interactions.

Experimental confirmation of the standard magnetorotational instability mechanism with a spring-mass analogue

The magnetorotational instability (MRI) has long been considered a plausibly ubiquitous mechanism to destabilize otherwise stable Keplerian flows to support radially outward transport of angular momentum. Such an efficient transport process would allow fast accretion in astrophysical objects such as stars and black holes to release copious kinetic energy that powers many of the most luminous sources in the universe. But the standard MRI under a purely vertical magnetic field has heretofore never been directly measured despite numerous efforts over more than a decade. Here we report an unambiguous laboratory demonstration of the spring-mass analogue to the standard MRI by comparing motion of a spring-tethered ball within different rotating flows. The experiment corroborates the theory: efficient outward angular momentum transport manifests only for cases with a weak spring in quasi-Keperian flow. Our experimental method accomplishes this in a new way, thereby connecting solid and fluid mechanics to plasma astrophysics.

L1 Stream Deflection and Ballistic Launching at the Disk Bow Shock: An Absorption-line Velocity Analysis in Semi-detached Binaries

Abstract Observations of semi-detached interacting binaries reveal orbital modulation in the optical, UV, and X-ray bands, indicating the presence of absorbing material obscuring the disk and accreting primary star at specific orbital phases consistent with L1 stream material overflowing the disk edge. We simulate the L1 stream interaction with the disk using tests particles within the context of the Roche model in the restricted three-body problem. At the disk bow shock the L1 stream particles are deflected and launched onto ballistic trajectories above the disk (as would normally occurs at the front of a detached shock in the hypersonic flow past a blunt body). At a given scale height, the material is assumed to continue without being affected by the disk, while at lower altitude it is being launched at an increasing elevation, as well as gradually being dragged by the Keplerian flow. Near the disk midplane (z ≪ H) the material is assumed to become part of the disk. We follow the stream material ballistic trajectories over the disk surface, where they reach a maximum height z/r at a binary phase Φ ∼ 0.75 and land on the disk at a smaller radius around phase Φ ∼ 0.5. The phase of the maximum height, the phase of the landing site, and the phase of the hot spot itself, all decrease significantly with decreasing radius. The radial velocity for each L1 stream ballistic trajectory along the line of sight (of the observer) to the hot inner parts of the disk is computed as a function of the orbital phase for a binary configuration matching the dwarf nova U Geminorum. The computed velocity amplitudes, phases, and pattern match the observed velocity offsets of the metal lines in the FUSE spectrum of U Gem during outburst. As ballistic trajectories are much easier to compute than realistic 3D hydrodynamical simulations, we propose the use of the L1 stream deflection and ballistic launching as a way to analyze the absorption-line orbital variability in semi-detached binaries and to assess or confirm, with some limitations, system parameters such as the mass ratio, inclination, and disk outer radius.

Supertransient magnetohydrodynamic turbulence in Keplerian shear flows: The role of the Hall effect

Space and astrophysical plasmas are frequently found in the regime of differential rotation, where the presence of a magnetic field can result in the magnetorotational instability, directly responsible for important phenomena such as turbulent angular-momentum transport in accretion disks. In the absence of an imposed magnetic field, a nonlinear dynamo is necessary for this transport mechanism to take place. In protoplanetary disks there are regions with high density and very low temperatures, which are two necessary conditions for the Hall effect to operate, affecting the development of the dynamo and the associated turbulence. In this work we perform local magnetohydrodynamic (MHD) simulations to study transition to weak turbulence in Keplerian shear flows with Hall effect. The Hall effect is shown to lead the system to long-lived turbulent transients whose decay time follows an exponential dependence on the magnetic Reynolds number and the Hall parameter.

Subcritical transition to turbulence in accretion disc boundary layer

Context. Enhanced angular momentum transfer through the boundary layer near the surface of weakly magnetised accreting star is required in order to explain the observed accretion timescales in low-mass X-ray binaries, cataclysmic variables, or young stars with massive protoplanetary discs. The accretion disc boundary layer is locally represented by incompressible homogeneous and boundless flow of the cyclonic type, which is linearly stable. Its non-linear instability at the shear rates of the order of the rotational frequency remains an issue. Aims. We put forward a conjecture that hydrodynamical subcritical turbulence in such a flow is sustained by the non-linear feedback from essentially three-dimensional vortices, which are generated by quasi-two-dimensional trailing shearing spirals grown to high amplitude via the swing amplification. We refer to those three-dimensional vortices as cross-rolls, since they are aligned in the shearwise direction in contrast to streamwise rolls generated by the anti-lift-up mechanism in rotating shear flow on the Rayleigh line. Methods. Transient growth of cross-rolls is studied analytically and further confronted with direct numerical simulations (DNS) of the dynamics of non-linear perturbations in the shearing box approximation. Results. A substantial decrease of transition Reynolds number RT is revealed as one changes a cubic box to a tall box. DNS performed in a tall box show that RT as a function of shear rate accords with the line of constant maximum transient growth of cross-rolls. The transition in the tall box has been observed until the shear rate is three times higher than the rotational frequency, when RT ∼ 50 000. Conclusions. Assuming that the cross-rolls are also responsible for turbulence in the Keplerian flow, we estimate R T ≲ 108 in this case. Our results imply that non-linear stability of Keplerian flow should be verified by extending turbulent solutions found in the cyclonic regime across the solid-body line rather than entering a quasi-Keplerian regime from the side of the Rayleigh line. The most favourable shear rate to test the existence of turbulence in the quasi-Keplerian regime may be sub-Keplerian and equal approximately to 1/2.

Transport properties of Keplerian flows in extended local domains with no imposed field

We compare transport statistics of elongated incompressible shearing boxes for different Reynolds and magnetic Prandtl numbers, Re and Pm, and aspect ratios, L|$z$|/Lx. We find that at fixed aspect ratio L|$z$|/Lx = 4 and |$\mathrm{ Re}\,=\,10\, 000$|⁠, the turbulent stresses for Pm ≲ 1 do not show considerable variation and follow a power law ∼Pm3/2 for Pm > 1. This is qualitatively consistent with previous results based on net imposed flux and small box L|$z$|/Lx ∼ 1 simulations but the power-law exponent is different. The saturated level of stresses, the ratio of Maxwell stress to the magnetic energy and Reynolds to Maxwell stress ratio are roughly invariant as L|$z$|/Lx is increased. For cases where the boxes are elongated in both the azimuth and vertical direction, the transport coefficient α ∈ [0.1, 1.0], that is 10–100 times larger than the case with Ly/Lx = 2 and large L|$z$|/Lx. Overall, our results suggest that the saturated state of turbulence is sensitive to both dissipation coefficients and aspect ratio (both L|$z$|/Lx and Ly/Lx) motivating further work on this problem.

Planet–disc interactions with discontinuous Galerkin methods using GPUs

We present a two-dimensional Cartesian code based on high order discontinuous Galerkin methods, implemented to run in parallel over multiple GPUs. A simple planet-disc setup is used to compare the behaviour of our code against the behaviour found using the FARGO3D code with a polar mesh. We make use of the time dependence of the torque exerted by the disc on the planet as a mean to quantify the numerical viscosity of the code. We find that the numerical viscosity of the Keplerian flow can be as low as a few $10^{-8}r^2\Omega$, $r$ and $\Omega$ being respectively the local orbital radius and frequency, for fifth order schemes and resolution of $\sim 10^{-2}r$. Although for a single disc problem a solution of low numerical viscosity can be obtained at lower computational cost with FARGO3D (which is nearly an order of magnitude faster than a fifth order method), discontinuous Galerkin methods appear promising to obtain solutions of low numerical viscosity in more complex situations where the flow cannot be captured on a polar or spherical mesh concentric with the disc.

Local study of helical magnetorotational instability in viscous Keplerian disks

In this paper, regarding the recent detection of significant azimuthal magnetic field in some accretion disks such as protostellar (Donati et al. in Nature 438:466, 2005), the multi-fluid model has been employed to analysis the stability of Keplerian rotational viscous dusty plasma system in a current-free helical magnetic field structure. Using the fluid-Maxwell equations, the general dispersion relation of the excited modes in the system has been obtained by applying the local approximation method in the linear perturbation theory. The typical numerical analysis of the obtained dispersion relation in the high-frequency regime shows that the presence of azimuthal magnetic field component in Keplerian flow has a considerable role in the stability conditions of the system. It also shows that the magnetic field helicity has a stabilization role against the magnetorotational instability (MRI) in the system due to contraction of the unstable wavelength region and decreasing the maximum growth rate of the instability. In this sense, the stabilization role of the viscosity term is more considerable for HMRI (instability in the presence of azimuthal magnetic field component) than the corresponding MRI (instability in the absence of azimuthal magnetic field component). Moreover, considering the discovered azimuthal magnetic field in these systems, the MRI can be arisen in the over-all range of dust grains construction values in contract with traditional MRI. This investigation can greatly contribute to better understanding the physics of some astrophysical phenomena, such as the main source of turbulence and angular momentum transport in protostellar and the other sufficiently ionized astrophysical disks, where the azimuthal magnetic field component in these systems can play a significant role.

Viscorotational shear instability of Keplerian granular flows.

The linear stability of viscous Keplerian flow around a gravitating center is studied using the rheological granular fluid model. The linear rheological instability triggered by the interplay of the shear rheology and Keplerian differential rotation of incompressible dense granular fluids is found. Instability sets in in granular fluids, where the viscosity parameter grows faster than the square of the local shear rate (strain rate) at constant pressure. Found instability can play a crucial role in the dynamics of dense planetary rings and granular flows in protoplanetary disks.

SUSTAINED TURBULENCE IN DIFFERENTIALLY ROTATING MAGNETIZED FLUIDS AT A LOW MAGNETIC PRANDTL NUMBER

ABSTRACT We show for the first time that sustained turbulence is possible at a low magnetic Prandtl number in local simulations of Keplerian flows with no mean magnetic flux. Our results indicate that increasing the vertical domain size is equivalent to increasing the dynamical range between the energy injection scale and the dissipative scale. This has important implications for a large variety of differentially rotating systems with low magnetic Prandtl number such as protostellar disks and laboratory experiments.

Transition to subcritical turbulence in a tokamak plasma

Tokamak turbulence, driven by the ion-temperature gradient and occurring in the presence of flow shear, is investigated by means of local, ion-scale, electrostatic gyrokinetic simulations (with both kinetic ions and electrons) of the conditions in the outer core of the Mega-Ampere Spherical Tokamak (MAST). A parameter scan in the local values of the ion-temperature gradient and flow shear is performed. It is demonstrated that the experimentally observed state is near the stability threshold and that this stability threshold is nonlinear: sheared turbulence is subcritical, i.e. the system is formally stable to small perturbations, but, given a large enough initial perturbation, it transitions to a turbulent state. A scenario for such a transition is proposed and supported by numerical results: close to threshold, the nonlinear saturated state and the associated anomalous heat transport are dominated by long-lived coherent structures, which drift across the domain, have finite amplitudes, but are not volume filling; as the system is taken away from the threshold into the more unstable regime, the number of these structures increases until they overlap and a more conventional chaotic state emerges. Whereas this appears to represent a new scenario for transition to turbulence in tokamak plasmas, it is reminiscent of the behaviour of other subcritically turbulent systems, e.g. pipe flows and Keplerian magnetorotational accretion flows.

Exploring non-normality in magnetohydrodynamic rotating shear flows: Application to astrophysical accretion disks

The emergence of turbulence in shear flows is a well-investigated field. Yet, there are some lingering issues that have not been sufficiently resolved. One of them is the apparent contradiction between the results of linear stability analysis showing a flow to be stable and yet experiments and simulations proving it to be otherwise. There is some success, in particular in astrophysical systems, based on magnetorotational instability (MRI), revealing turbulence. However, MRI requires the system to be weakly magnetized. Such instability is neither a feature of general magnetohydrodynamic (MHD) flows nor revealed in purely hydrodynamic flows. Nevertheless, linear perturbations of such flows are non-normal in nature, which argues for a possible origin of nonlinearity therein. The concept behind this is that non-normal perturbations could produce huge transient energy growth (TEG), which may lead to nonlinearity and further turbulence. However, so far, non-normal effects in shear flows have not been explored much in the presence of magnetic fields. In this spirit, here we consider the perturbed viscoresistive MHD shear flows with rotation in general. Basically we recast the magnetized momentum balance and associated equations into the magnetized version of Orr-Sommerfeld and Squire equations and their magnetic analogs. We also assume the flow to be incompressible and in the presence of Coriolis effect solve the equations using a pseudospectral eigenvalue approach. We investigate the possible emergence of instability and large TEG in three different types of flows, namely, the Keplerian flow, the Taylor-Couette (or constant angular momentum) flow, and plane Couette flow. We show that, above a certain value of magnetic field, instability and TEG both stop occurring. We also show that TEG is maximum in the vicinity of regions of instability in the wave number space for a given magnetic field and Reynolds number, leading to nonlinearity and plausible turbulence. Rotating shear flows are ubiquitous in astrophysics, especially accretion disks, where molecular viscosity is too low to account for observed data. The primary accepted cause of energy-momentum transport therein is turbulent viscosity. Hence, these results would have important implications in astrophysics.