We present analytical and numerical solutions for accretion discs subject to a non-zero central torque. We express this in terms of a single parameter, $f$, which is the ratio of outward viscous flux of angular momentum from the inner boundary to the inward advected flux of angular momentum there. The standard "accretion" disc, where the central boundary condition is zero-torque, is represented by $f=0$. A "decretion" disc, where the radial velocity at the inner boundary is zero, is represented by $f\rightarrow\infty$. For $f > 0$ a torque is applied to the disc at the inner boundary, which feeds both angular momentum and energy into the disc. This can arise, for example, in the case of a circumbinary disc where resonances transfer energy and angular momentum from the binary to the disc orbits, or where the disc is around a rotating magnetic star which can allow the disc orbits to be accelerated outwards at the magnetospheric radius. We present steady-state solutions to the disc structure as a function of $f$, and for arbitrary kinematic viscosity $ν$. For time-dependent discs, we solve the equations using a Green's function approach for the specific case of $ν\propto R$ and provide an example numerical solution to the equations for the case of $ν\propto R^{3/2}$. We find that for values of $f\lesssim 0.1$ the disc solutions closely resemble "accretion" discs. For values of $f \gtrsim 10$ the solutions initially resemble "decretion" discs, but at sufficiently late times exhibit the properties of "accretion" discs. We discuss the application of this theory to different astrophysical systems, and in particular the values of the $f$ parameter that are expected in different cases.
Using numerical hydrodynamics calculations and a novel method for densely sampling parameter space, we measure the accretion and torque on a binary system from a circumbinary disk. In agreement with previous studies, we find that the net torque on the binary is positive for mass ratios close to unity, and that accretion always drives the binary towards equal mass. Accretion variability depends sensitively on the numerical sink prescription, but the torque and relative accretion onto each component do not depend on the sink timescale. Positive torque and highly variable accretion occurs only fo…
A luminous body embedded in an accretion disk can generate asymmetric density perturbations that lead to a net torque and thus orbital migration of the body. Linear theory has shown that this heating torque gives rise to a migration term linear in the body's mass that can oppose or even reverse that arising from the sum of gravitational Lindblad and co-orbital torques. We use high-resolution local simulations in an unstratified disk to assess the accuracy and domain of applicability of the linear theory. We find agreement between analytic and simulation results to better than 10\% in the appro…
Most astrophysical accretion disks are likely to be warped. In X-ray binaries the spin evolution of an accreting neutron star is critically dependent on the interaction between the neutron star magnetic field and the accretion disk. There have been extensive investigations on the accretion torque exerted by a coplanar disk that is magnetically threaded by the magnetic field lines from the neutron stars, but relevant works on warped/tilted accretion disks are still lacking. In this paper we develop a simplified two-component model, in which the disk is comprised of an inner coplanar part and an…
The magnetic interaction between a classical T Tauri star and its surrounding accretion disk is thought to influence its rotational evolution. We use 2.5D magnetohydrodynamic, axisymmetric simulations of star-disk interaction, computed via the PLUTO code, to calculate the net torque acting on these stars. We divide the net torque into three contributions: accretion (spin-up), stellar winds (spin-down), and magnetospheric ejections (MEs) (spin-up or down). In Paper I, we explored interaction regimes in which the stellar magnetosphere truncates the inner disk at a location spinning faster than t…
We have extended the analytical model proposed earlier to estimate the inner disk radius of accreting neutron stars in the strong-propeller (SP) phase, and the conditions for the transitions between the strong and weak propeller (WP) phases (Ertan 2017, 2018) to the WP (accretion with spin-down) and the spin-up (SU) phases, and the torque reversals during the WP/SU transitions. The model can account for some basic observed properties of these systems that are not expected in conventional models: (1) accretion on to the star at low X-ray luminosities and the transitions to the SP phase (no accr…
We discuss transportation and redistribution of energy and angular momentum in the magnetic connection (MC) process and Blandford-Payne (BP) process. The MC results in readjusting the interior viscous torque, and its effects are operative not only in but also beyond the MC region. The BP process is invoked to transfer the "excessive" angular momentum from an accretion disc. In addition, we derive a criterion for the interior viscous torque to resolve the puzzle of the overall equilibrium of angular momentum in disc accretion. It turns out that the BP efficiency of extracting angular momentum a…
Recent observations and theoretical work on gamma-ray bursts (GRBs) favor the central engine model of a Kerr black hole (BH) surrounded by a magnetized neutrino-dominated accretion flow (NDAF). The magnetic coupling between the BH and disk through a large-scale closed magnetic field exerts a torque on the disk, and transports the rotational energy from the BH to the disk. We investigate the properties of the NDAF with this magnetic torque. For a rapid spinning BH, the magnetic torque transfers enormous rotational energy from BH into the inner disk. There are two consequences: (i) the luminosit…
Numerical experiments are the primary method of studying the evolution of circumbinary disks due to the strong nonlinearities involved. Many circumbinary simulations also require the use of numerical mass sinks: source terms which prevent gas from unphysically accumulating around the simulated point masses by removing gas at a given rate. However, special care must be taken when drawing physical conclusions from such simulations to ensure that results are not biased by numerical artifacts. We demonstrate how the use of improved sink methods reduces some of these potential biases in vertically-…
Misalignment of the Lense-Thirring precession by an accretion torque
Indian Institute of Technology Indore(印度理工学院印多尔分校);Northwestern University(西北大学);Academy of Sciences(科学院);Nicolaus Copernicus Astronomical Center(尼古拉·哥白尼天文中心);College of Charleston(查尔斯顿学院);Flatiron Institute(平研究所)
We present numerical calculations of spectra and structure of accretion disks models appropriate for near-Eddington luminosity black hole X-ray binaries (BHB). Our work incorporates non-zero torque at the ISCO as well as several dissipation profiles based on first-principles three-dimensional disk interior simulations. We found that significant dissipation near the photosphere can produce steep power law-like spectra for models with moderate viewing angles spanning a range of black hole spins while including inner torque push the spectral peak to higher energies. Consistent with previous studi…
The spin-down rate of PSR J1023+0038, one of the three confirmed transitional millisecond pulsars, was measured in both radio pulsar (RMSP) and X-ray pulsar (LMXB) states. The spin-down rate in the LMXB state is only about 27 % greater than in the RMSP state (Jaodand et al. 2016). The inner disk radius, r_in, obtained recently by Ertan (2017) for the propeller phase, which is close to the co-rotation radius, r_co, and insensitive to the mass-flow rate, can explain the observed torques together with the X-ray luminosities, Lx . The X-ray pulsar and radio pulsar states correspond to accretion wi…
I discuss three mutually-supportive notions or assumptions regarding jets and accretion. The first is magnetocentrifugal acceleration (MCA), the overwhelmingly favored mechanism for the production of jets in most steady accreting systems. The second is the zero-torque inner boundary condition. The third is that effective viscous dissipation is like real dissipation, leading directly to heating. All three assumptions fit nicely together in a manner that is simple, persuasive, and mutually-consistent. All, I argue, are incorrect. For concreteness I focus on protostars. Magnetohydrodynamic (MHD) …
The $γ$-ray pulsar binary system PSR B1259-63 flares in GeV after each periastron. The origin of those flares is still under debate. Recently, [2017ApJ...844..114Y] proposed a mechanism that might explain the GeV flares. In that model, a transient accretion disc is expected to be formed from the matter which was gravity-captured by the neutron star from the main sequence companion's circumstellar disc. The transient accretion disc exerts a spin down torque on the neutron star (propeller effect), which might be traceable via pulsar timing observation of PSR B1259-63. In this paper, we phenomeno…
A stellar mass black hole (BH) surrounded by a neutrino-dominated accretion flow (NDAF) has been discussed in a number of works as the central engine of gamma-ray bursts (GRBs). It is widely believed that NDAF cannot liberate enough energy for bright GRBs. However, these works have been based on the assumption of "no torque" boundary condition, which is invalid when the disk is magnetized. In this paper, we present both numerical and analytical solutions for NDAFs with non-zero boundary stresses, and reexamine their properties. We find that NDAF with such boundary torque can be powerful enough…
The magnetic field of ultraluminous X-ray (ULX) pulsars is the key parameter to understand the nature and accretion physics. However, the typical magnetic field values in these ULX pulsars are still under debate. We used six different torque models to study the magnetic fields of ULX pulsars, to see how derived magnetic fields change with different models, and to determine which models are more suitable for ULX pulsars. We took the currently available period, period derivative, and flux data of 7 confirmed ULX pulsars, M82 X-2, ULX NGC 7793 P13, ULX NGC 5907, NGC 300 ULX1, NGC 1313 X-2, M51 UL…
We have investigated the detailed torque-reversal behavior of 4U 1626--67 in the framework of the recently developed comprehensive model of the inner disk radius and torque calculations for neutron stars accreting from geometrically thin disks. The model can reproduce the torque -- X-ray luminosity relation across the torque reversals of 4U 1626--67. Our results imply that: (1) rotational equilibrium is reached when the inner disk radius equals the co-rotation radius, $r_\mathrm{co}$, while the conventional Alfven radius is greater than and close to $r_\mathrm{co}$, (2) both spin-up and spin-d…
We present a coherent timing analysis of the 2003 outburst of the accreting millisecond pulsar XTE J1807-294. We find an upper limit for the spin frequency derivative of 5E-14 Hz/s. The sinusoidal fractional amplitudes of the pulsations are the highest observed among the accreting millisecond pulsars and can reach values of up to 27% (2.5-30 keV). The pulse arrival time residuals of the fundamental follow a linear anti-correlation with the fractional amplitudes that suggests hot spot motion over the surface of the neutron star both in longitude and latitude. An anti-correlation between residua…
We consider the effects of black hole tilt on accretion disk alignment, studying three initial black hole tilts,6 degrees, 12 degrees and 24 degrees, with both magnetohydrodynamic and (inviscid) hydrodynamic evolution. In a number of ways, but not all, the dynamics are homologous in the sense that the alignment fronts resulting from different initial tilts are very similar when analyzed in terms of the fraction of the initial tilt angle. Even when the initial misalignment is 24 degrees, which, for the sound speed studied, is 4 vertical scale heights at the disk fiducial radius, the surface den…
Gaseous disks have been proposed as a mechanism for facilitating mergers of binary black holes. We explore circumbinary disk systems to determine the evolution of the central binary. To do so, we perform 3D, hydrodynamic, locally isothermal simulations of circumbinary disks on a Cartesian grid. We focus on binaries of equal mass ratios on fixed circular orbits. To investigate the orbital evolution of the binary, we examine the various torques exerted on the system. For the case where the disk plane and binary orbital plane are aligned, we find that the total torque is positive so that the semi…
NGC 300 ULX1 is a newly identified ultra-luminous X-ray pulsar. The system is associated with the supernova impostor SN 2010da that was later classified as a possible supergiant Be X-ray binary. In this work we report on the spin period evolution of the neutron star based on all the currently available X-ray observations of the system. We argue that the X-ray luminosity of the system has remained almost constant since 2010, at a level above ten times the Eddington limit. Moreover, we find evidence that the spin period of the neutron star evolved from ~126 s down to ~18 s within a period of abo…
We have investigated the rotational and the X-ray luminosity ($L_{\mathrm{x}}$) observations of 4U 1626--67 accumulated during the last four decades. It has been recorded that the source underwent a torque reversal twice. We have tried to understand whether this eccentrical sign-switch of the period derivative ($\dot{P}$) of the source could be accounted for with the existing torque models. We have found that the observed source properties are better estimated with the distances close to the lower limit of the previously predicted distance range ($5-13$ kpc). Furthermore, assuming an inclined …
We present the spectral and timing analysis of the X-ray pulsar GRO J1744-28 during its 2014 outburst using data collected with the X-ray satellites Swift, INTEGRAL, Chandra, and XMM-Newton. We derived, by phase-connected timing analysis of the observed pulses, an updated set of the source ephemeris. We were also able to investigate the spin-up of the X-ray pulsar as a consequence of the accretion torque during the outburst. Relating the spin-up rate and the mass accretion rate as $\dotν\propto\dot{M}^β$, we fitted the pulse phase delays obtaining a value of $β=0.96(3)$. Combining the results …
Gaseous circumbinary accretion discs provide a promising mechanism to facilitate the mergers of supermassive black holes (SMBHs) in galactic nuclei. We measure the torques exerted on accreting SMBH binaries, using 2D, isothermal, moving-mesh, viscous hydrodynamical simulations of circumbinary accretion discs. Our computational domain includes the entire inner region of the circumbinary disk with the individual black holes (BHs) included as point masses on the grid and a sink prescription to model accretion onto each BH. The BHs each acquire their own well-resolved accretion discs ("minidiscs")…
We present numerical spectral and vertical structure calculations appropriate for near-Eddington-luminosity, radiation-pressure-dominated accretion disks around stellar-mass black holes. We cover a wide range of black hole spins and incorporate dissipation profiles based on first-principles three-dimensional MHD disk interior simulations. We also include nonzero stresses at the innermost stable circular orbit, which results in the disk effective temperature increasing rapidly toward the black hole and gives rise to rather extreme conditions with high temperatures and low surface densities. We …
In this paper, we present the complete structure of a quasi-Keplerian thin accretion disk with an internal dynamo around a magnetized neutron star. We assume a full quasi-Keplerian disk with the azimuthal velocity deviating from the Keplerian fashion by a factor of $ξ$ ($0<ξ<2$). In our approach, we vertically integrate the radial component of the momentum equation to obtain the radial pressure gradient equation for a thin quasi-Keplerian accretion disk. Our results show that, at large radial distance, the accretion disk behaves in a Keplerian fashion. However, close to the neutron star, press…
Several X-ray pulsars have been observed to experience torque reversals, which provide important observational clues to the interaction between the neutron star magnetic field and the accretion disk. We review the current models proposed for the torque reversals and discuss their viability based on the observations of the quasi-periodic oscillations (QPOs) in 4U 1626-67. Most of these models seem to be incompatible with the evolution of the QPO frequencies if they are interpreted in terms of the beat frequency model. We suggest that winds or outflows from the neutron star and the accretion dis…
Millisecond pulsars are rather weakly-magnetized neutron stars which are thought to have been spun up by disc accretion, with magnetic linkage between the star and the disc playing a key role. Their spin history depends sensitively on details of the magnetic field structure, but idealized models from the 1980s and 1990s are still commonly used for calculating the magnetic field components. This paper is the third in a series presenting results from a step-by-step analysis which we are making of the problem, starting with very simple models and then progressively including additional features o…
Using only physical mechanisms, i.e., 3D MHD with no phenomenological viscosity, we have simulated the dynamics of a moderately thin accretion disk subject to torques whose radial scaling mimics those produced by lowest-order post-Newtonian gravitomagnetism. In this simulation, we have shown how, in the presence of MHD turbulence, a time-steady transition can be achieved between an inner disk region aligned with the equatorial plane of the central mass's spin and an outer region orbiting in a different plane. The position of the equilibrium orientation transition is determined by a balance bet…
We consider a geometrically thin, Keplerian disk in the orbital plane of a binary black hole (BHBH) consisting of a spinning primary and low-mass secondary (mass ratio q < 1). To account for the principle effects of general relativity (GR), we propose a modification of the standard Newtonian evolution equation for the (orbit-averaged) time-varying disk surface density. In our modified equation the viscous torque in the disk is treated in full GR, while the tidal torque is handled in the Newtonian limit. Our GR-hybrid treatment is reasonable because the tidal torque is concentrated near the orb…
We review the pulse profile evolution of the unique accretion powered X-ray pulsar 4U 1626-67 over the last 40 years since its discovery. This pulsar showed two distinct eras of steady spin-up separated by a steady spin-down episode for about 18 years. In the present work, using data from different observatories active during each phase of spin-up and spin-down we establish a clear correlation between the accretion torque acting on this pulsar and its pulse profile. The energy resolved pulse profiles are identical in both the spin-up eras and quite different in the spin-down era, especially in…
When an accretion disk surrounds a binary rotating in the same sense, the binary exerts strong torques on the gas. Analytic work in the 1D approximation indicated that these torques sharply diminish or even eliminate accretion from the disk onto the binary. However, recent 2D and 3D simulational work has shown at most modest diminution. We present new MHD simulations demonstrating that for binaries with mass ratios of 1 and 0.1 there is essentially no difference between the accretion rate at large radius in the disk and the accretion rate onto the binary. To resolve the discrepancy with earlie…
The interaction of a rotating star's magnetic field with a surrounding plasma disk lies at the heart of many questions posed by neutron stars in X-ray binaries. We consider the opening of stellar magnetic flux due to differential rotation along field lines coupling the star and disk, using a simple model for the disk-opened flux, the torques exerted on the star by the magnetosphere, and the power extracted by the electromagnetic wind. We examine the conditions under which the system enters an equilibrium spin state, in which the accretion torque is instantaneously balanced by the pulsar wind t…
We combine cosmological hydrodynamic simulations with analytic models to evaluate the role of galaxy-scale gravitational torques on the evolution of massive black holes at the centers of star-forming galaxies. We confirm and extend our earlier results to show that torque-limited growth yields black holes and host galaxies evolving on average along the Mbh-Mbulge relation from early times down to z = 0 and that convergence onto the scaling relation occurs independent of the initial conditions and with no need for mass averaging through mergers or additional self-regulation processes. Smooth acc…
BlackHoleWeather -- Spin-coupled chaotic cold accretion across the meso scale: Variability and kinematics
University of Modena and Reggio Emilia(摩德纳和雷焦艾米利亚大学);Universidad de Santiago de Chile(智利圣地亚哥大学);CIRAS, Universidad de Santiago de Chile(智利圣地亚哥大学 CIRAS);Science and Technology Institute, Universities Space Research Association(美国大学空间研究协会科学与技术研究所);NASA Ames Research Center(NASA 艾姆斯研究中心);INAF – Astronomical Observatory of Rome(意大利国家天体物理研究所罗马天文台);Instituto de Estudios Astrofísicos, Facultad de Ingeniería y Ciencias, Universidad Diego Portales(迭戈·波特莱斯大学工程与科学学院天体物理研究所)
Accretion discs are common in binary systems, and they are often found to be misaligned with respect to the binary orbit. The gravitational torque from a companion induces nodal precession in misaligned disc orbits. We calculate whether this precession is strong enough to overcome the internal disc torques communicating angular momentum. For typical parameters precession wins: the disc breaks into distinct planes that precess effectively independently. We run hydrodynamical simulations to check these results, and confirm that disc breaking is widespread and generally enhances accretion on to t…
We present the first three-dimensional magnetohydrodynamic (MHD) simulations of a circumbinary disk surrounding an equal mass binary. The binary maintains a fixed circular orbit of separation $a$. As in previous hydrodynamical simulations, strong torques by the binary can maintain a gap of radius $\simeq 2a$. Streams curve inward from $r \simeq 2a$ toward the binary; some of their mass passes through the inner boundary, while the remainder swings back out to the disk. However, we also find that near its inner edge the disk develops both a strong $m=1$ asymmetry and growing orbital eccentricity…
MRI Turbulence versus $α$-Viscosity in Circumbinary Disks: Implications for Gravitational-Wave Dephasing and Accretion Variability
Center for Cosmology and Particle Physics, Physics Department, New York University(纽约大学物理系宇宙学与粒子物理中心);Center for Computational Astrophysics, Flatiron Institute(西蒙斯平顿研究所计算天体物理学中心)
In this study we present a method to estimate posterior distributions for standard accretion torque model parameters and binary orbital parameters for X-ray binaries using a nested sampling algorithm for Bayesian Parameter Estimation. We study the spin evolution of two Be X-ray binary systems in the Magellanic Clouds, RX J0520.5-6932 and RX J0209-7427, during major outbursts, in which they surpassed the Eddington-limit. Moreover, we apply our method to the recently discovered Swift J0243.6+6124; the only known Galactic pulsating ultra-luminous X-ray source. This is an excellent candidate for s…
We investigate evolution of an accretion disc in binary black hole (BBH) systems and possible electromagnetic counterparts of the gravitational waves from mergers of BBHs. Perna et al. (2016) proposed a novel evolutionary scenario of an accretion disc in BBHs in which a disc eventually becomes "dead", i.e., the magnetorotational instability (MRI) becomes inactive. In their scenario, the dead disc survives until {\it a few seconds before} the merger event. We improve the dead disc model and propose another scenario, taking account of effects of the tidal torque from the companion and the critic…
Be stars are rapidly rotating B stars with Balmer emission lines that indicate the presence of a Keplerian, rotationally supported, circumstellar gas disc. Current disc models, referred to as "decretion discs", make use of the zero torque inner boundary condition typically applied to accretion discs, with the 'decretion' modelled by adding mass to the disc at a radius of about two per cent larger than the inner disc boundary. We point out that, in this model, the rates at which mass and energy need to be added to the disc are implausibly large. What is required is that the disc has not only a …
BlackHoleWeather -- Spin-coupled chaotic cold accretion across the meso-scale: Morphology and thermodynamics
University of Modena and Reggio Emilia(摩德纳和雷焦艾米利亚大学);Universidad de Santiago de Chile(智利圣地亚哥大学);CIRAS, Universidad de Santiago de Chile(智利圣地亚哥大学 CIRAS);INAF – Osservatorio Astronomico di Trieste(意大利国家天体物理研究所的里雅斯特天文台);Science and Technology Institute, Universities Space Research Association(大学太空研究协会科学与理工学院);INAF – Astronomical Observatory of Rome(意大利国家天体物理研究所罗马天文台);Department of Physics, University of Rome “Tor Vergata”(罗马托尔维尔加塔大学物理系)
Tidal torques acting on a gaseous accretion disk around a binary black hole can create a gap in the disk near the orbital radius. At late times, when the binary inspiral timescale due to gravitational wave emission becomes shorter than the viscous timescale in the disk, the binary decouples from the disk and eventually merges. Prior to decoupling the balance between tidal and viscous torques drives the disk to a quasistationary equilibrium state, perturbed slightly by small amplitude, spiral density waves emanating from the edges of the gap. We consider a black hole binary with a companion of …
Accretion discs and black holes (BHs) have angular momenta that are generally misaligned with respect to each other, which can lead to warps in the discs and bends in any jets produced. We consider a disc that is misaligned at large radii and torqued by Lense-Thirring (LT) precession and a Blandford-Znajek (BZ) jet torque. We consider a variety of disc states that include radiatively inefficient thick discs, radiatively efficient thin discs, and super-Eddington accretion discs. The magnetic field strength of the BZ jet is chosen as either from standard equipartition arguments or from magnetica…
We present a series of simulations in both pure hydrodynamics (HD) and magnetohydrodynamics (MHD) exploring the degree to which alignment of disks subjected to external precessional torques (e.g., as in the `Bardeen-Petterson' effect) is dependent upon the disk sound speed c_s. Across the range of sound speeds examined, we find that the influence of the sound speed can be encapsulated in a simple "lumped-parameter" model proposed by Sorathia et al. (2013a). In this model, alignment fronts propagate outward at a speed ~0.2 rOmega_precess(r), where Omega_precess is the local test-particle preces…
GRO J1008-57, as a Be/X-ray transient pulsar, is considered to have the highest magnetic field in known neutron star X-ray binary systems. Observational data of the X-ray outbursts in GRO J1008-57 from 2017 to 2020 were collected by the Insight-HXMT satellite. In this work, the spin period of the neutron star in GRO J1008-57 was determined to be about 93.28 seconds in August 2017, 93.22 seconds in February 2018, 93.25 seconds in June 2019 and 93.14 seconds in June 2020. GRO J1008-57 evolved in the spin-up process with a mean rate of $-(2.10\pm 0.05)\times$10$^{-4}$ s/d from 2009 -- 2018, and t…
Many galaxies are expected to harbor binary supermassive black holes (SMBHs) in their centers. Their interaction with the surrounding gas results in accretion and exchange of angular momentum via tidal torques, facilitating binary inspiral. Here we explore the non-trivial coupling between these two processes and analyze how the global properties of externally supplied circumbinary disks depend on the binary accretion rate. By formulating our results in terms of the angular momentum flux driven by internal stresses, we come up with a very simple classification of the possible global disk struct…
Chaotic migration of LISA Extreme Mass Ratio Inspirals in a turbulent accretion disk: effect on waveform de-phasing
Center for Cosmology and Particle Physics, Physics Department, New York University(纽约大学物理系宇宙学与粒子物理中心);Department of Astrophysics, University of Zurich(苏黎世大学天体物理学系);Shanghai Astronomical Observatory, Chinese Academy of Sciences(中国科学院上海天文台);National Astronomical Observatory of Japan(日本国立天文台);Department of Astronomy & Astrophysics, University of California, Santa Cruz(加州大学圣克鲁兹分校天文与天体物理学系);Institute for Advanced Studies, Tsinghua University(清华大学高等研究院)
We study the general-relativistic dynamics of matter being accreted onto and ejected by a magnetised and nonrotating neutron star. The dynamics is followed in the framework of fully general relativistic magnetohydrodynamics (GRMHD) within the ideal-MHD limit and in two spatial dimensions. More specifically, making use of the numerical code BHAC, we follow the evolution of a geometrically thick matter torus driven into accretion by the development of a magnetorotational instability. By making use of a number of simulations in which we vary the strength of the stellar dipolar magnetic field, we …