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John C. B. Papaloizou

Publications and source records attributed to John C. B. Papaloizou.

46 records · Page 3Linked to original sources
arXiv2002

3D-MHD simulations of an accretion disk with star-disk boundary layer

We present global 3D MHD simulations of geometrically thin but unstratified accretion disks in which a near Keplerian disk rotates between two bounding regions with initial rotation profiles that are stable to the MRI. The inner region models the boundary layer between the disk and an assumed more slowly rotating central, non magnetic star. We investigate the dynamical evolution of this system in response to initial vertical and toroidal fields imposed in a variety of domains contained within the near Keplerian disk. Cases with both non zero and zero net magnetic flux are considered and sustained dynamo activity found in runs for up to fifty orbital periods at the outer boundary of the near Keplerian disk. Simulations starting from fields with small radial scale and with zero net flux lead to the lowest levels of turbulence and smoothest variation of disk mean state variables. For our computational set up, average values of the Shakura & Sunyaev (1973) $α$ parameter in the Keplerian disk are typically $0.004\pm 0.002.$ Magnetic field eventually always diffuses into the boundary layer resulting in the build up of toroidal field inward angular momentum transport and the accretion of disk material. The mean radial velocity, while exhibiting large temporal fluctuations is always subsonic. Simulations starting with net toroidal flux may yield an average $α\sim 0.04.$ While being characterized by one order of magnitude larger average $α$, simulations starting from vertical fields with large radial scale and net flux may lead to the formation of persistent non-homogeneous, non-axisymmetric magnetically dominated regions of very low density.

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arXiv2000

The response of an accretion disc to an inclined dipole with application to AA Tau

We compute the warping of a disc induced by an inclined dipole. We consider a magnetised star surrounded by a thin Keplerian diamagnetic disc with an inner edge that corotates with the star. We suppose the stellar field is a dipole with an axis that is slightly misaligned with the stellar rotation axis. The rotation axes of the disc material orbiting at large distances from the star and that of the star are supposed to coincide. The misalignment of the magnetic and rotation axes results in the magnetic pressure not being the same on the upper and lower surfaces of the disc. The resultant net vertical force produces a warp which appears stationary in a frame corotating with the star. We find that, if viscosity is large enough (alpha on the order of 0.01-0.1) to damp bending waves as they propagate away, a smoothly varying warp of the inner region of the disc is produced. The amplitude of the warp can easily be on the order of ten percent of the disc inner radius for reasonably small misalignment angles (less than 30 degrees). Viscous damping also introduces a phase shift between the warp and the forcing torque, which results in the locations of maximum elevation above the disc forming a trailing spiral pattern. We apply these results to recent observations of AA Tau, and show that the variability of its light curve, which occurs with a period comparable to the expected stellar rotation period, could be due to obscuration produced by a warp configuration of the type we obtain.

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arXiv2000

Accretion disc-stellar magnetosphere interaction: field line inflation and the effect on the spin-down torque

We calculate the structure of a force-free magnetosphere which is assumed to corotate with a central star and which interacts with an embedded differentially rotating accretion disc. The magnetic and rotation axes are aligned and the stellar field is assumed to be a dipole. We concentrate on the case when the amount of field line twisting through the disc-magnetosphere interaction is large and consider different outer boundary conditions. In general the field line twisting produces field line inflation (eg. Bardou & Heyvaerts 1996) and in some cases with large twisting many field lines can become open. We calculate the spin-down torque acting between the star and the disc and we find that it decreases significantly for cases with large field line twisting. This suggests that the oscillating torques observed for some accreting neutron stars could be due to the magnetosphere varying between states with low and high field line inflation. Calculations of the spin evolution of T Tauri stars may also have to be revised in light of the significant effect that field line twisting has on the magnetic torque resulting from star-disc interactions.

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arXiv2000

Hydrodynamic Simulations of the Bardeen-Petterson Effect

We present SPH simulations of accretion discs in orbit about rotating compact objects such as black holes and neutron stars, and study the structure of warped discs produced by the Bardeen-Petterson effect. We calculate the transition radius out to which the disc specific angular momentum vector is aligned with that of the black hole. We focus on the parameter regime where the warp dynamics are controlled by bending wave propagation, but also consider models in which warps are subject to diffusion rather than wave transport, and are able to consider the fully nonlinear regime. Because of hydrodynamic or pressure effects, for the parameter range investigated, the transition radius is always found to be much smaller than that obtained by Bardeen & Petterson (1975). For discs with midplane Mach numbers of about 10, the transition occurs between 10 - 16 gravitational radii, whereas for a Mach number of about 30 it occurs at around 30 gravitational radii. A thicker disc with a Mach number of 5 is found to produce no discernible warped structure. The rate of black hole - disc alignment is found to be consistent with the ideas of Ress (1978), with the alignment torque behaving as if it arises from the accreted material transferring its misaligned component of angular momentum at the larger transition radius of Bardeen & Petterson (1975). The inclusion of Einstein precession in the calculations modified both the warped disc structure and, consistent with linear analysis, produced an increased alignment rate by up to a factor of 4 because of the effect that a non Keplerian potential has on the propagation of warps.

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arXiv1999

The Migration and Growth of Protoplanets in Protostellar Discs

We investigate the gravitational interaction of a Jovian mass protoplanet with a gaseous disc with aspect ratio and kinematic viscosity expected for the protoplanetary disc from which it formed. Different disc surface density distributions have been investigated. We focus on the tidal interaction with the disc with the consequent gap formation and orbital migration of the protoplanet. Nonlinear hydrodynamic simulations are employed using three independent numerical codes. A principal result is that the direction of the orbital migration is always inwards and such that the protoplanet reaches the central star in a near circular orbit after a characteristic viscous time scale of approximately 10,000 initial orbital periods. This was found to be independent of whether the protoplanet was allowed to accrete mass or not. Inward migration is helped through the disappearance of the inner disc, and therefore the positive torque it would exert, because of accretion onto the central star.Our results indicate that a realistic upper limit for the masses of closely orbiting giant planets is approximately 5 Jupiter masses, because of the reduced accretion rates obtained for planets of increasing mass. Assuming some process such as termination of the inner disc through a magnetospheric cavity stops the migration, the range of masses estimated for a number of close orbiting giant planets (Marcy, Cochran, & Mayor 1999; Marcy & Butler 1998) as well as their inward orbital migration can be accounted for by consideration of disc--protoplanet interactions during the late stages of giant planet formation. Maximally accreting protoplanets reached about four Jovian masses on reaching the neighbourhood of the central star.

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arXiv1999

Hydrodynamic Simulations of Propagating Warps and Bending Waves In Accretion Discs

We present the results of a study of propagating warp or bending waves in accretion discs. Three dimensional hydrodynamic simulations were performed using SPH, and the results of these are compared with calculations based on the linear theory of warped discs. We consider primarily the physical regime in which the dimensionless viscosity parameter `alpha' < H/r, the disc aspect ratio, so that bending waves are expected to propagate. We also present calculations in which `alpha' > H/r, where the warps are expected to behave diffusively. Small amplitude perturbations are studied in both Keplerian and slightly non Keplerian discs, and we find that the SPH results can be reasonably well fitted by those of the linear theory. The main results of these calculations are: (1) the warp in Keplerian discs when `alpha' < H/r propagates with little dispersion and damps at a rate expected from estimates of the code viscosity, (2) warps evolve diffusively when `alpha' > H/r, (3) the non Keplerian discs exhibit a substantially more dispersive behaviour of the warps. Initially imposed higher amplitude nonlinear warping disturbances were studied in Keplerian discs. The results indicate that nonlinear warps can lead to the formation of shocks, and that the evolution of the warp becomes less wave-like and more diffusive in character. This work is relevant to the study of the warped accretion discs that may occur around Kerr black holes or in misaligned binary systems. The results indicate that SPH can accurately model the hydrodynamics of warped discs, even when using rather modest numbers of particles.

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arXiv1997

Bending Instabilities in Magnetized Accretion Discs

We study the global bending modes of a thin annular disc subject to both an internally generated magnetic field and a magnetic field due to a dipole embedded in the central star with axis aligned with the disc rotation axis. When there is a significant inner region of the disc corotating with the star, we find spectra of unstable bending modes. These may lead to elevation of the disc above the original symmetry plane facilitating accretion along the magnetospheric field lines. The resulting non-axisymmetric disc configuration may result in the creation of hot spots on the stellar surface and the periodic photometric variations observed in many classical T Tauri stars (CTTS). Time-dependent behaviour may occur including the shadowing of the central source in magnetic accretors even when the dipole and rotation axes are aligned.

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arXiv1996

The hydrodynamical response of a tilted circumbinary disc: linear theory and non-linear numerical simulations

In this paper we present an analytical and numerical study of the response of a circumbinary disc subject to the tidal-forcing of a binary with a fixed circular orbit. We consider fluid discs with a range of thicknesses and binaries with a range of mass ratios, orbital separations and inclination angles. Our numerical simulations are implemented using a SPH code. For our unperturbed disc models, we write a scaling relation for the shear viscosity and deduce that the disc thickness cannot be varied without affecting the viscosity in these kinds of SPH disc models. It is found that maintainance of an inner cavity owing to the tidal truncation of the disc is effective for non-zero orbital inclinations. Also we show that our model discs may precess approximately like rigid bodies, provided that the disc is able to communicate on a length scale comparable to the inner boundary radius by either sonic or viscous effects, in a sufficiently small fraction of the local precession period. Furthermore, the disc precession period may tend to infinity if the disc outer edge is allowed to become arbitrarily large, the disc suffering only a modest quasi-steady warp near the inner boundary. When the disc response is linear, or weakly non-linear, the precession periods and the forms of warping that we measure yield reasonable quantitative agreement with the analytical expressions that we derive from a linear response calculation. For a stronger disc response the results can agree poorly with our linear analysis, although some qualitative features of the response remain intact. We show that the response of a disc of non-interacting particles is qualitatively different from this. The work presented in this paper is of relevance to a number of astrophysical phenomena of current interest in star and planet formation.

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arXiv1994

Variable Smoothing Lengths and Energy Conservation in Smoothed Particle Hydrodynamics

We present a new formulation of the equations of motion used in smoothed particle hydrodynamics (SPH). The spatial resolution in SPH is determined by the smoothing length, $h$, and it has become common practice for each particle to be given its own adaptive smoothing length, $h_i$. Consequently, the dynamic range that may be spatially resolved is greatly increased, but additional ($\nabla h$) terms, which account for the variability of the smoothing lengths, should appear in the equations of motion in order to satisy conservation requirements. Previous implementations of SPH have neglected these additional terms, whereas we have included them. This is achieved by defining a functional form for the $h_i$s, that depends on inter-particle distances only, and then deriving the equations of motion using a Hamiltonian formalism. A number of test calculations are presented. We find that including the $\nabla h$ terms has no detrimental effect on the ability of SPH to model known problems with reasonable accuracy. For problems where the energy conservation was rather poor, including the $\nabla h$ terms results in a dramatic improvement. In particluar non-conservation of energy during a collision between two polytropes can occur at the level of 10% when the $\nabla h$ terms are neglected. When the $\nabla h$ terms are included, then this error reduces to 0.8%.

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