Steady state shocks in accretion disks around a Kerr black hole

Results of numerical simulations of shock solutions in a geometrical thin accretion disk around a Kerr black hole (BH) are presented. Using the smoothed particle hydrodynamics (SPH) technique, the influence of the central object is included by means of an effective potential, We first present the theory of standing shock formation in accretion disks around a Kerr black hole, and show that the results of our numerical simulation agree very well with the theoretical results. We find that the shocks in an inviscid flow are very stable. We also remove the ambiguity prevalent regarding the location and stability of shocks in adiabatic flows. Finally we sketch some of the astrophysical consequenc…

On the Azimuthal Stability of Shock Waves around Black Holes

Analytical studies and numerical simulations of time dependent axially symmetric flows onto black holes have shown that it is possible to produce stationary shock waves with a stable position both for ideal inviscid and for moderately viscous accretion disks. We perform several two dimensional numerical simulations of accretion flows in the equatorial plane to study shock stability against non-axisymmetric azimuthal perturbations. We find a peculiar new result. A very small perturbation seems to produce an instability as it crosses the shock, but after some small oscillations, the shock wave suddenly transforms into an asymmetric closed pattern, and it stabilizes with a finite radial extent…

Zero‐Energy Rotating Accretion Flows near a Black Hole

We characterize the nature of thin, axisymmetric, inviscid, accretion flows of cold adiabatic gas with zero specific energy in the vicinity of a black hole by the specific angular momentum. Using two-dimensional hydrodynamic simulations in cylindrical geometry, we present various regimes in which the accretion flows behave distinctly differently. When the flow has a small angular momentum $(\lambda\lsim\lambda_b)$, most of the material is accreted into the black hole forming a quasi-spherical flow or a simple disk-like structure around it. When the flow has a large angular momentum (typically, larger than the marginally bound value, $\lambda\gsim\lambda_{mb}$), almost no accretion into the …

Black hole accretion discs and jets at super-Eddington luminosity

Super-Eddington accretion discs with 3 and 15 dot M_E around black holes with mass 10 M_sun are examined by two-dimensional radiation hydrodynamical calculations extending from the inner disc edge to 5*10^4 r_g and lasting up to \sim 10^6 r_g/c. The dominant radiation-pressure force in the inner region of the disc accelerates the gas vertically to the disc plane, and jets with 0.2 -- 0.4$c$ are formed along the rotational axis. In the case of the lower accretion rate, the initially anisotropic high-velocity jet expands outward and becomes gradually isotropic flow in the distant region. The mass-outflow rate from the outer boundary is as large as \sim 10^{19} -- 10^{23} g s^{-1}, but it is v…

Low compressibility accretion disc formation in close binaries: the role of physical viscosity

Aims. Physical viscosity naturally hampers gas dynamics (rarefaction or compression). Such a role should support accretion disc development inside the primary gravitation potential well in a close binary system, even for low compressibility modelling. Therefore, from the astrophysical point of view, highly viscous accretion discs could exist even in the low compressibility regime showing strong thermal differences to high compressibility ones Methods. We performed simulations of stationary Smooth Particle Hydrodynamics (SPH) low compressibility accretion disc models for the same close binary system. Artificial viscosity operates in all models. The absence of physical viscosity and a superso…

Low angular momentum flow model for Sgr A*

We examine the low angular momentum flow model for Sgr A* using two-dimensional hydrodynamical calculations based on the parameters of the specific angular momentum and total energy estimated in the recent analysis of stellar wind of nearby stars around Sgr A*. The accretion flow with the plausible parameters is non-stationary and an irregularly oscillating shock is formed in the inner region of a few tens to a hundred and sixty Schwarzschild radii. Due to the oscillating shock, the luminosity and the mass-outflow rate are modulated by several per cent to a factor of 5 and a factor of 2-7, respectively, on time-scales of an hour to ten days. The flows are highly advected and the radiative e…

Inner Edge Drag by an Asynchronous Primary and Accretion Disc Structure In Close Binaries

In this work a 3-D ‘Smoothed Particle Hydrodynamics’ ([1]; [4]; [5]) accretion disc is simulated where particles at its inner edge are dragged by a fast spinning compact central star, as in the case of the intermediate polars. The angular velocity of the central star is twice the orbital angular velocity w 0. This drag can be attributed mainly to viscous interaction in the dense compact star atmosphere, although magnetic coupling may also play a role.

Three-dimensional simulation of polytropic accretion discs

Three-dimensional simulations of the formation and evolution of accretion discs in close binary systems,realised with the Smoothed Particle Hydrodynamics method to solve the fluid dynamic equations, are presented. Although the runs presented here refer to an ideal gas with different polytropic indexes, and constitute the first stage of more physically complex forthcoming simulations, they nervertheless give some interesting results: the disc structure and dynamics are in agreement with standard models only for small γ-values; as a consequence of the z-resolution it is found that disc formation is inhibited for γ ≥ 1.2, which means that some 2 D simulations of polytropic discs are meaningles…

A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH

In literature, it is well know that the Smoothed Particle Hydrodynamics method can be affected by numerical noise on the pressure field when dealing with liquids. This can be highly dangerous when an SPH code is dynamically coupled with a structural solver. In this work a simple procedure is proposed to improve the computation of the pressure distribution in the dynamics of liquids. Such a procedure is based on the use of a density diffusion term in the equation for the mass conservation. This diffusion is a pure numerical effect, similar to the well known artificial viscosity originally proposed in SPH method to smooth out the shock discontinuities. As the artificial viscosity, the density…

A model of M87 nuclear emission without ADAF

We present a simple physical model of the central source emission in the M87 galaxy. It is well known that the observed X‐ray luminosity from this galactic nucleus is much lower than the predicted one, if a standard radiative efficiency is assumed. Up to now the main model invoked to explain such a luminosity is the ADAF (Advection‐Dominated‐Accretion‐Flow) model. Our approach supposes only a simple axis‐symmetric adiabatic accretion with a low angular momentum together with the bremsstrahlung emission process in the accreting gas. With no other special hypothesis on the dynamics of the system, this model agrees well enough with the luminosity value measured by Chandra.

Luminosity oscillations in accretion discs around compact objects

A three-dimensional smoothed particle hydrodynamics simulation of the active phase of SS Cyg-type discs and its implications for the mass transfer burst model

We perform a smoothed particle hydrodynamics (SPH) three-dimensional simulation of the outburst phase of the accretion disc of a typical SS Cyg-like dwarf nova in the framework of the mass transfer burst model (MTBM), where we assume that the active phase is triggered by a sudden increase in the accretion rate due to some instability in the secondary's atmosphere. The evolution of the accretion disc is followed for a single orbital period, starting from the initial quiescent disc configuration obtained by us in a previous paper. This is a suitable integration time for determining the geometrical and physical properties of the disc in the impulsive phase and is comparable with observed outbu…

The jets and disc of SS 433 at super-Eddington luminosities

We examine the jets and the disc of SS 433 at super-Eddington luminosities with 600 times Eddington critical accretion rate by time-dependent two-dimensional radiation hydrodynamical calculations, assuming alpha-model for the viscosity. One-dimensional supercritical accretion disc models with mass loss or advection are used as the initial configurations of the disc. As a result, from the initial advective disc models with alpha =0.001 and 0.1, we obtain the total luminosities 2.5x10^{40} and 2.0x10^{40} erg/s. The total mass-outflow rates are 4x10^{-5} and 10^{-4} solar-mass/yr and the rates of the relativistic axial outflows in a small half opening angle of 1 degree are about 10^{-6} solar…

Bending Instability of an Accretion Disc Around a Black Hole

We demonstrate that generically an accretion disk around a compact object could have a new type of instability in that the accretion flow need not be symmetric with respect to the equatorial plane even when matter is supplied symmetrically farther out. We find that this behaviour is mainly due to interaction of outgoing matter bounced off the centrifugal barrier and the incoming accretion. We believe that X-ray variability could be developed by this instability.

Black-Hole Accretion Discs and Jets at Super-Eddington Luminosity

Super-Eddington accretion discs with 3 and 15 dot M_E around black holes with mass 10 M_sun are examined by two-dimensional radiation hydrodynamical calculations extending from the inner disc edge to 5*10^4 r_g and lasting up to \sim 10^6 r_g/c. The dominant radiation-pressure force in the inner region of the disc accelerates the gas vertically to the disc plane, and jets with 0.2 -- 0.4$c$ are formed along the rotational axis. In the case of the lower accretion rate, the initially anisotropic high-velocity jet expands outward and becomes gradually isotropic flow in the distant region. The mass-outflow rate from the outer boundary is as large as \sim 10^{19} -- 10^{23} g s^{-1}, but it is v…

A Simple Model of Radiative Emission in M87

We present a simple physical model of the central source emission in the M87 galaxy. It is well known that the observed X-ray luminosity from this galactic nucleus is much lower than the predicted one, if a standard radiative efficiency is assumed. Up to now the main model invoked to explain such a luminosity is the ADAF (Advection-Dominated-Accretion-Flow) model. Our approach supposes only a simple axis-symmetric adiabatic accretion with a low angular momentum together with the bremsstrahlung emission process in the accreting gas. With no other special hypothesis on the dynamics of the system, this model agrees well enough with the luminosity value measured by Chandra.

Linking ecological and physical features in the Strait of Sicily preliminary results of air - sea interaction.

Parallelization of a Smoothed Particle Hydrodynamic Code for Simulation of Shocks in Accretion Disks

Radiative Shocks in Rotating Accretion Flows around Black Holes

It is well known that the rotating inviscid accretion flows with adequate injection parameters around black holes could form shock waves close to the black holes, after the flow passes through the outer sonic point and can be virtually stopped by the centrifugal force. We examine numerically such shock waves in 1D and 2D accretion flows, taking account of cooling and heating of the gas and radiation transport. The numerical results show that the shock location shifts outward compared with that in the adiabatic solutions and that the more rarefied ambient density leads to the more outward shock location. In the 2D-flow, we find an intermediate frequency QPO behavior of the shock location as …

The effect of cooling on time dependent behaviour of accretion flows around black holes

We present the results of several numerical simulations of two dimensional axi-symmetric accretion flows around black holes using Smoothed Particle Hydrodynamics (SPH) in the presence of cooling effects. We consider both stellar black holes and super-massive black holes. We observe that due to {\it both radial and vertical oscillation} of shock waves in the accretion flow, the luminosity and average thermal energy content of the inner disk exhibit very interesting behaviour. When power density spectra are taken, quasi-periodic variabilities are seen at a few Hz and also occasionally at hundreds of Hz for stellar black holes. For super-massive black holes, the time scale of the oscillations …

Stima dei flussi di calore latente e sensibile in differenti aree del Mediterraneo Centrale, attraverso strumentazione acustica e tradizionale.

QPOs expected in rotating accretion flows around a supermassive black hole

AbstractIt is well known that rotating inviscid accretion flows with adequate injection parameters around black holes could form shock waves close to the black holes, after the flow passes through the outer sonic point and can be virtually stopped by the centrifugal force. We numerically examine such shock waves in 2D accretion flows with 10−5 to 106 Eddington critical accretion rates around a supermassive black hole with 106M⊙. As the results, the luminosities show QPO phenomena with modulations of a factor 2–3 and with quasi-periods of a few to several hours.

Low angular momentum flow model for Sgr A*

Can gravity perturbations explain QPOs?

We show the results of some numerical simulations trying to reproduce the QPO behavior in black hole and neutron star sources. Our simulations are based on the idea that a nearly periodic luminosity oscillation can be obtained from a perturbation of the source gravitational field with a sinusoidal time behavior. We find that some specific features of the QPO phenomenon can be described by this simple model, but the required amplitude of the gravity perturbation is more than 1% of the unperturbed gravitational field. If the hypothesis is formed that such a perturbation is due to a density fluctuation (of the accretion disk or the source itself, in the case of the neutron star) going around t…

Viscosity prescriptions in accretion discs with shock waves

QPOs from Radial and Vertical Oscillation of Shocks in Advective Accretion Flows

SPH simulations of Shakura-Sunyaev instability at intermediate accretion rates

We show that a standard Shakura-Sunyaev accretion disc around a black hole with an accretion rate lower than the critical Eddington limit does show the instability in the radiation pressure dominated zone. We obtain this result performing time-dependent simulations of accretion disks for a set of values of the viscosity parameter and accretion rate. In particular we always find the occurrence of the collapse of the disc: the instability develops always towards a collapsed gas pressure dominated disc and not towards the expansion. This result is valid for all initial configurations we tested. We find significant convective heat flux that increases the instability development time, but is not…

Why Canonical Disks Cannot Produce Advection-dominated Flows

Using simple arguments we show that the canonical thin keplerian accretion disks cannot smoothly match any plain advection dominated flow (ADAF) model. By 'plain' ADAF model we mean the ones with zero cooling. The existence of sonic points in exact solutions is critical and imposes constraints that cannot be surpassed adopting 'reasonable' physical conditions at the hypothetical match point. Only the occurrence of new critical physical phenomena may produce a transition. We propose that exact advection models are a class of solutions which don't necessarily involve the standard thin cool disks and suggest a different scenario in which good ADAF solutions could eventually occur.

Free-surface flows solved by means of SPH schemes with numerical diffusive terms

A novel system of equations has been defined which contains diffusive terms in both the continuity and energy equations and, at the leading order, coincides with a standard weakly-compressible SPH scheme with artificial viscosity. A proper state equation is used to associate the internal energy variation to the pressure field and to increase the speed of sound when strong deformations/compressions of the fluid occur. The increase of the sound speed is associated to the shortening of the time integration step and, therefore, allows a larger accuracy during both breaking and impact events. Moreover, the diffusive terms allows reducing the high frequency numerical acoustic noise and smoothing …

Radiative 2D Shocks, Super-Eddington Disks and Jets around Black Holes

It is well known that rotating inviscid accretion flows with adequate injection parameters around black holes could form shock waves close to the black holes, after the flow passes through the outer sonic point and can be virtually stopped by the centrifugal force. Such shock waves in 2D accretion flows are examined by 2D radiation hydrodynamical calculations. We also examine super‐Eddington accretion disks with 15 ṀE around black holes, focusing on a small collimation degree of the jet and a large mass‐outflow rate observed in the X‐ray source SS 433.

Three-dimensional numerical simulation of gaseous flow structure in semidetached binaries

The results of 3D hydrodynamic simulation of mass transfer in semidetached binaries of different types (cataclysmic variables and low-mass X-ray binaries) are presented. We find that taking into account of a circumbinary envelope leads to significant changes in the stream-disc morphology. In particular, the obtained steady-state self-consistent solutions show an absence of impact between gas stream from the inner Lagrangian point L1 and forming accretion disc. The stream deviates under the action of gas of circumbinary envelope, and does not cause the shock perturbation of the disc boundary (traditional `hotspot'). At the same time, the gas of circumbinary envelope interacts with the stream…

A shallow water SPH model with PML boundaries

Abstract We focus on the study and implementation of Smoothed Particle Hydrodynamics (SPH) numerical code to deal with non-reflecting boundary conditions, starting from the Perfect Matched Layer (PML) approach. Basically, the method exploits the concept of a physical damping which acts on a fictitious layer added to the edges of computational domain. In this paper, we develop the study of time dependent shallow waves propagating on a finite 2D-XY plane domain and their behavior in the presence of circular and, more generic, rectangular boundary absorbing layers. In particular, an analysis of variation of the layer׳s thickness versus the absorbing efficiency is conducted. In our model, the m…

Perspectives

We discuss a special case of formation of axisymmetric shocks in the accretion flow of ideal gas onto a Schwarzschild black hole: when the total energy of the flow is negative. The result of our analysis enlarges the parameter space for which these steady shocks are exhibited in the accretion of gas rotating around relativistic stellar objects. Since keplerian disks have negative total energy, we guess that, in this energy range, the production of the shock phenomenon might be easier than in the case of positive energy. So our outcome reinforces the view that sub-keplerian flows of matter may significantly affect the physics of the high energy radiation emission from black hole candidates. …

QPOs expected in rotating accretion flows around a supermassive black hole

It is well known that rotating inviscid accretion flows with adequate injection parameters around black holes could form shock waves close to the black holes, after the flow passes through the outer sonic point and can be virtually stopped by the centrifugal force. We numerically examine such shock waves in 2D accretion flows with 10−5 to 106 Eddington critical accretion rates around a supermassive black hole with 106 M. As the results, the luminosities show QPO phenomena with modulations of a factor 2–3 and with quasi-periods of a few to several hours.

On the angular momentum transfer on to compact stars in binary systems

Results of three-dimensional numerical simulations of the gas transfer in close binary systems show that, in addition to the formation of a tidally induced spiral shock wave, it is also possible for accretion streams to be produced, having low specific angular momentum in a region close to the accreting star. These streams are mainly placed above the orbital disc but are also unevenly present in the equatorial plane. The relevance of such flows is related to formation of hot coronae or bulges in regions very close to the accretor centre. The eventual formation of such bulges and shock-heated flows is interesting in the context of advection-dominated solutions and for the explanation of spec…

Numerical Simulations of the Thermal Instability Collapse in Radiation Pressure Dominated Disks

We show that accretion disks, both in the subcritical and supercritical accretion rate regime, may exhibit significant amplitude luminosity oscillations. The luminosity time behavior has been obtained by performing a set of time‐dependent 2D SPH simulations of accretion disks with different values of α and accretion rate. An explanation of this luminosity behavior is proposed in terms of limit‐cycle instability: the disk oscillates between a radiation pressure dominated configuration (with a high luminosity value) and a gas pressure dominated one (with a low luminosity value). The origin of this instability is the difference between the heat produced by viscosity and the energy emitted as r…

Periodic massloss from viscous accretion flows around black holes

We investigate the behaviour of low angular momentum viscous accretion flows around black holes using Smooth Particle Hydrodynamics (SPH) method. Earlier, it has been observed that in a significant part of the energy and angular momentum parameter space, rotating transonic accretion flow undergoes shock transition before entering in to the black hole and a part of the post-shock matter is ejected as bipolar outflows, which are supposed to be the precursor of relativistic jets. In this work, we simulate accretion flows having injection parameters from the inviscid shock parameter space, and study the response of viscosity on them. With the increase of viscosity, shock becomes time dependent …

Smoothed particles hydrodynamics numerical simulations of droplets walking on viscous vibrating liquid

We study the phenomenon of the "walking droplet", by means of numerical fluid dynamics simulations using the Smoothed Particle Hydrodynamics numerical method. This phenomenon occurs when a millimetric drop is released on the surface of an oil of the same composition, contained in a tank and subjected to vertical oscillations of frequency and amplitude very close to the Faraday instability threshold. At appropriate values of the parameters of the system under study, the oil droplet jumps permanently on the surface of the vibrating liquid forming a localized wave-particle system, reminding the behaviour of a wave particle quantum system as suggested by de Broglie. In our study, we made releva…

On the use of an alternative water state equation in SPH

In this work new equations of state for water are formulated, they improve both the consistency and the accuracy of the Smoothed Particles Hydrodynamics (SPH) method to treat incompressible fluid dynamics. When, both physical and artificial viscous terms are introduced, entropy increases. In liquids, the influence of this entropy variation is negligible, but common SPH formulations treats the water as a weakly compressible gas. Therefore, for violent fluid motions, this increase cannot be neglected anymore and the energy equation has to be introduced. This equation has been time integrated, and connected to alternative water state equations which have been studied heuristically. These equat…

Ab initiosimulations of accretion disc instability

We show that accretion disks, both in the subcritical and supercritical accretion rate regime, may exhibit significant amplitude luminosity oscillations. The luminosity time behavior has been obtained by performing a set of time-dependent 2D SPH simulations of accretion disks with different values of alpha and accretion rate. In this study, to avoid any influence of the initial disk configuration, we produced the disks injecting matter from an outer edge far from the central object. The period of oscillations is 2 - 50 s respectively for the two cases, and the variation amplitude of the disc luminosity is 10^38 - 10^39 erg/s. An explanation of this luminosity behavior is proposed in terms o…

Stima dei flussi energetici all’interfaccia aria-mare con l’impiego di SST da Satellite e dati rilevati in situ.

La conoscenza dei flussi energetici scambiati fra oceano e bassa atmosfera è un requisito utile per modellare e comprendere il sistema climatico e la dinamica degli oceani. L’elevata difficoltà di effettuare misure in situ ed in continuo in ambiente marino induce spesso all’utilizzo ausiliario di strumentazione satellitare. Nel presente lavoro è stato effettuato un confronto tra la stima dei flussi energetici superficiali valutati con dati provenienti da satellite e quelli ottenuti da misure in situ. In particolare, per il confronto, sono stati utilizzati i dati SST acquisiti dal satellite NOAA e i dati raccolti in situ dai sensori istallati a bordo della Nave Oceanografica Urania nel corso…

How initial and boundary conditions affect protoplanetary migration in a turbulent sub-Keplerian accretion disc: 2D non-viscous SPH simulations

Current theories on planetary formation establish that giant planet formation should be contextual to their quick migration towards the central star due to the protoplanets-disc interactions on a timescale of the order of $10^5$ years, for objects of nearly 10 terrestrial masses. Such a timescale should be smaller by an order of magnitude than that of gas accretion onto the protoplanet during the hierarchical growing-up of protoplanets by collisions with other minor objects. These arguments have recently been analysed using N-body and/or fluid-dynamics codes or a mixing of them. In this work, inviscid 2D simulations are performed, using the SPH method, to study the migration of one protopla…

Simple absorbing layer conditions for shallow wave simulations with Smoothed Particle Hydrodynamics

Abstract We study and implement a simple method, based on the Perfectly Matched Layer approach, to treat non reflecting boundary conditions with the Smoothed Particles Hydrodynamics numerical algorithm. The method is based on the concept of physical damping operating on a fictitious layer added to the computational domain. The method works for both 1D and 2D cases, but here we illustrate it in the case of 1D and 2D time dependent shallow waves propagating in a finite domain.

Linking air–sea energy fluxes and European anchovy potential spawning ground.

The physical and chemical processes of the sea greatly affect the reproductive biology of fishes, mainly influencing both the numbers of spawned eggs and the survivorship of early stages up to the recruitment period. In the central Mediterranean, the European anchovy constitutes one of the most important fishery resource. Because of its short living nature and of its recruitment variability, associated to high environmental variability, this small pelagic species undergo high interannual fluctuation in the biomass levels. Despite several efforts were addressed to characterize fishes spawning habitat from the oceanographic point of view, very few studies analyze the air-sea exchanges effects…

New progress of the filament theory

Interaction of accretion shocks with winds

Accretion shocks are known to oscillate in presence of cooling processes in the disk. This oscillation may also cause quasi-periodic oscillations of black holes. In the presence of strong winds, these shocks have oscillations in vertical direction as well. We show examples of shock oscillations under the influence of both the effects. When the shocks are absent and the flow is cooler, the wind becomes weaker and the vertical oscillation becomes negligible.

The 35-d modulation of the X-ray emission of Her X-1 in the framework of the SOD model: results of a three-dimensional SPH simulation

Several models have been proposed to explain the 35-d X-ray periodicity observed in Her X-1. We present the results of six three-dimensional quasi-polytropic smoothed particle hydrodynamics (SPH) simulations of the tilted, twisted accretion disc of Her X-1 carried out in the light of Roberts' slaved orienting disc model (SOD) with the intention of finding some limits to the inclination of the rotation axis of the secondary and to the value of the polytropic index γ. These results show that a γ value between 1.05 and 1.1 and an inclination angle φ of the order of 45° are the most suitable for enabling the SOD model to work in three-dimensional space. The simulated disc is rather small and th…

Shock oscillation model for quasi-periodic oscillations in stellar mass and supermassive black holes

We numerically examine centrifugally supported shock waves in 2D rotating accretion flows around a stellar-mass (10M_sun) and a supermassive (10^6M_sun) black holes over a wide range of input accretion rates of 10^7 >\dot M/\dot M_E>10^{-4}. The resultant 2D-shocks are unstable with time and the luminosities show quasi-periodic oscillations (QPOs) with modulations of a factor of 2-3 andwith periods of a tenth seconds to several hours, depending on the black hole masses. The shock oscillation model may explain the intermediate frequency QPOs with 1-10 Hz observed in the stellar-mass black hole candidates and also suggest the existence of QPOs with the period of hours in AGNs. When the accret…

The thermal instability collapse in radiation pressure dominated discs

COS-B Observations of Long Term Variability and Absorption Phenomena in the X-ray Emission from Cen X-3

The COS-B satellite has observed the X-ray source Cen X-3 in the energy range 2 to 12 keV

A simple model of radiative emission in M87