Elena Toscano

Black hole accretion discs and jets at super-Eddington luminosity

Super-Eddington accretion discs with 3 ˙ ME and 15 ˙ ME around black holes with mass 10 M� are examined by two-dimensional radiation hydrodynamical calculations extending from the inner disc edge to 5 × 10 4 r g and lasting up to ∼10 6 rg/c. The dominant radiation pressure force in the inner region of the disc accelerates the gas vertically to the disc plane, and jets with 0.2‐0.4c 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 ∼10 19 ‐10 23 gs −1 ,b ut it is variable and intermittent with time; that is, the outflow switches occasionally to inflow in the distant region. The luminosity also varies as ∼10 40 ‐10 42 erg s −1 on a long time-scale. On the other hand, the jet in the case of the higher accretion rate maintains its initial anisotropic shape even after it goes far away. The mass-outflow rate and the luminosity attain steady values of 3 × 10 19 gs −1 and 1.3 × 10 40 erg s −1 , respectively. In accordance with the local analysis of the slim accretion disc model, the disc is thermally unstable in the case of 3 ˙ ME but stable in the case of 15 ˙ ME. The super-Eddington model with 15 ˙

A smoothed particle interpolation scheme for transient electromagnetic simulation

In this paper, the fundamentals of a mesh-free particle numerical method for electromagnetic transient simulation are presented. The smoothed particle interpolation methodology is used by considering the particles as interpolation points in which the electromagnetic field components are computed. The particles can be arbitrarily placed in the problem domain: No regular grid, nor connectivity laws among the particles, have to be initially stated. Thus, the particles can be thickened only in distinct confined areas, where the electromagnetic field rapidly varies or in those regions in which objects of complex shape have to be simulated. Maxwells equations with the assigned boundary and initial conditions in time domain are numerically solved by means of the proposed method. Validation of the model is carried out by comparing the results with those obtained by the FDTD method for a one-dimensional (1-D) case study in order to easily show the capability of the proposed scheme

On the use of a meshless solver for PDEs governing electromagnetic transients

In this paper some key elements of the Smoothed Particle Hydrodynamics methodology suitably reformulated for analyzing electromagnetic transients are investigated. The attention is focused on the interpolating smoothing kernel function which strongly influences the computational results. Some issues are provided by adopting the polynomial reproducing conditions. Validation tests involving Gaussian and cubic B-spline smoothing kernel functions in one and two dimensions are reported.

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 M 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 discs for a set of values of a and M. 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 the initial configurations we tested. We find significant convective heat flux that increases the instability development time, but is not strong enough to inhibit the disc collapse. A physical explanation of the lack of the expansion phase is proposed considering the role of the radial heat advection. Our finding is relevant since it excludes the formation of the hot Comptonizing corona - often suggested to be present - around the central object by the mechanism of the Shakura-Sunyaev instability. We also show that, in the ranges of a and M values we simulated, accretion discs are crossed by significant amplitude acoustic waves.

A Mesh-free Particle Method for Transient Full-wave Simulation

A mesh-free particle method is presented for electromagnetic (EM) transient simulation. The basic idea is to obtain numerical solutions for the partial differential equations describing the EM problem in time domain, by using a set of particles, considered as spatial interpolation points of the field variables, arbitrarily placed in the problem domain and by avoiding the use of a regular mesh. Irregular problems geometry with diffused non-homogeneous media can be modeled only with an initial set of arbitrarily distributed particles. The time dependence is accounted for with an explicit finite difference scheme. Moreover the particle discretization can be improved during the process time stepping, by inserting and/or removing particles without the need of overlapping sub-grids. These features lead to a reduction of the global computational complexity in comparison with traditional grid based frames. Canonical application examples are discussed and validated

Ab initio simulations of accretion disc instability

We show that accretion discs, both in the subcritical and supercritical accretion rate regime, may exhibit significant amplitude luminosity oscillations. The luminosity time behaviour has been obtained by performing a set of time-dependent two-dimensional smoothed particle hydrodynamics simulations of accretion discs with different values of a and accretion rate. In this study, to avoid any influence of the initial disc configuration, we produced the discs injecting matter from an outer edge far from the central object. The period of oscillations is 2-50 s for the two cases, and the variation amplitude of the disc luminosity is 10 38 -10 39 erg s -1 . An explanation of this luminosity behaviour is proposed in terms of limit cycle instability; the disc 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 radiation from the disc surface (the well-known thermal instability mechanism). We support this hypothesis showing that the limit cycle behaviour produces a sequence of collapsing and refilling states of the innermost disc region.

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 is observed in the black hole candidate GRS 1915+105.

Hardware and Software Platforms for Distributed Computing on Resource Constrained Devices

The basic idea of distributed computing is that it is possible to solve a large problem by using the resources of various computing devices connected in a network. Each device interacts with each other in order to process a part of a problem, contributing to the achievement of a global solution. Wireless sensor networks (WSNs) are an example of distributed computing on low resources devices. WSNs encountered a considerable success in many application areas. Due to the constraints related to the small sensor nodes capabilities, distributed computing in WSNs allows to perform complex tasks in a collaborative way, reducing power consumption and increasing battery life. Many hardware platforms compose the ecosystem of WSNs and some lightweight operating systems have also been designed to ease application deployment, to ensure efficient resources management, and to decrease energy consumption. In this chapter we focus on distributed computing from several points of view emphasizing important aspects, ranging from hardware platforms to applications on resource constrained devices.

Mauro Picone, Sandro Faedo, and the numerical solution of partial differential equations in Italy (1928---1953)

In this paper we revisit the pioneering work on the numerical analysis of partial differential equations (PDEs) by two Italian mathematicians, Mauro Picone (1885–1977) and Sandro Faedo (1913–2001). We argue that while the development of constructive methods for the solution of PDEs was central to Picone’s vision of applied mathematics, his own work in this area had relatively little direct influence on the emerging field of modern numerical analysis. We contrast this with Picone’s influence through his students and collaborators, in particular on the work of Faedo which, while not the result of immediate applied concerns, turned out to be of lasting importance for the numerical analysis of time-dependentPDEs.

The Poisson problem: A comparison between two approaches based on SPH method

Abstract In this paper two approaches to solve the Poisson problem are presented and compared. The computational schemes are based on Smoothed Particle Hydrodynamics method which is able to perform an integral representation by means of a smoothing kernel function by involving domain particles in the discrete formulation. The first approach is derived by means of the variational formulation of the Poisson problem, while the second one is a direct differential method. Numerical examples on different domain geometries are implemented to verify and compare the proposed approaches; the computational efficiency of the developed methods is also studied.