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Global 3D Simulations of Disc Accretion onto the classical T Tauri Star BP Tauri

The magnetic field of the classical T Tauri star BP Tau can be approximated as a superposition of dipole and octupole moments with respective strengths of the polar magnetic fields of 1.2 kG and 1.6 kG (Donati et al. 2008). We adopt the measured properties of BP Tau and model the disc accretion onto the star. We observed in simulations that the disc is disrupted by the dipole component and matter flows towards the star in two funnel streams which form two accretion spots below the dipole magnetic poles. The octupolar component becomes dynamically important very close to the star and it redirects the matter flow to higher latitudes. The spots are meridionally elongated and are located at higher latitudes, compared with the pure dipole case, where crescent-shaped, latitudinally elongated spots form at lower latitudes. The position and shape of the spots are in good agreement with observations. The disk-magnetosphere interaction leads to the inflation of the field lines and to the formation of magnetic towers above and below the disk. The magnetic field of BP Tau is close to the potential only near the star, inside the magnetospheric surface, where magnetic stress dominates over the matter stress. A series of simulation runs were performed for different accretion rates. They show that an accretion rate is lower than obtained in many observations, unless the disc is truncated close to the star. The torque acting on the star is about an order of magnitude lower than that which is required for the rotational equilibrium. We suggest that a star could lose most of its angular momentum at earlier stages of its evolution.Comment: 11 pages, 13 figures, submitted to MNRA

Global 3D Simulations of Disc Accretion onto the classical T Tauri Star V2129 Oph

The magnetic field of the classical T Tauri star V2129 Oph can be modeled approximately by superposing slightly tilted dipole and octupole moments, with polar magnetic field strengths of 0.35kG and 1.2kG respectively (Donati et al. 2007). Here we construct a numerical model of V2129 Oph incorporating this result and simulate accretion onto the star. Simulations show that the disk is truncated by the dipole component and matter flows towards the star in two funnel streams. Closer to the star, the flow is redirected by the octupolar component, with some of the matter flowing towards the high-latitude poles, and the rest into the octupolar belts. The shape and position of the spots differ from those in a pure dipole case, where crescent-shaped spots are observed at the intermediate latitudes. Simulations show that if the disk is truncated at the distance of 6.2 R_* which is comparable with the co-rotation radius, 6.8 R_*, then the high-latitude polar spots dominate, but the accretion rate obtained from the simulations is about an order of magnitude lower than the observed one. The accretion rate matches the observed one if the disk is disrupted much closer to the star, at 3.4 R_*. However, the octupolar belt spots strongly dominate. Better match has been obtained in experiments with a dipole field twice as strong. The torque on the star from the disk-magnetosphere interaction is small, and the time-scale of spin evolution, 2 x10^7-10^9 years is longer than the 2x10^6 years age of V2129 Oph. The external magnetic flux of the star is strongly influenced by the disk: the field lines connecting the disk and the star inflate and form magnetic towers above and below the disk. The potential (vacuum) approximation is still valid inside the Alfv\'en (magnetospheric) surface where the magnetic stress dominates over the matter stress.Comment: 15 pages, 15 figures, after major revision, added 3 figures, 2 tables. Accepted to MNRA

Accretion dynamics in the classical T Tauri star V2129 Oph

We analyze the photometric and spectroscopic variability of the classical T Tauri star V2129 Oph over several rotational cycles to test the dynamical predictions of magnetospheric accretion models. The photometric variability and the radial velocity variations in the photospheric lines can be explained by rotational modulation due to cold spots, while the radial velocity variations of the He I (5876 \AA) line and the veiling variability are due to hot spot rotational modulation. The hot and cold spots are located at high latitudes and about the same phase, but the hot spot is expected to sit at the chromospheric level, while the cold spot is at the photospheric level. Using the dipole+octupole magnetic-field configuration previously proposed in the literature for the system, we compute 3D MHD magnetospheric simulations of the star-disk system. We use the simulation's density, velocity and scaled temperature structures as input to a radiative transfer code, from which we calculate theoretical line profiles at all rotational phases. The theoretical profiles tend to be narrower than the observed ones, but the qualitative behavior and the observed rotational modulation of the H\alpha and H\beta emission lines are well reproduced by the theoretical profiles. The spectroscopic and photometric variability observed in V2129 Oph support the general predictions of complex magnetospheric accretion models with non-axisymmetric, multipolar fields.Comment: Accepted by Astronomy and Astrophysic

Three-dimensional simulations of rotationally-induced line variability from a Classical T Tauri star with a misaligned magnetic dipole

We present three-dimensional (3-D) simulations of rotationally induced line variability arising from complex circumstellar environment of classical T Tauri stars (CTTS) using the results of the 3-D magnetohydrodynamic (MHD) simulations of Romanova et al., who considered accretion onto a CTTS with a misaligned dipole magnetic axis with respect to the rotational axis. The density, velocity and temperature structures of the MHD simulations are mapped on to the radiative transfer grid, and corresponding line source function and the observed profiles of neutral hydrogen lines (H-beta, Pa-beta and Br-gamma) are computed using the Sobolev escape probability method. We study the dependency of line variability on inclination angles (i) and magnetic axis misalignment angles (Theta). By comparing our models with the Pa-beta profiles of 42 CTTS observed by Folha & Emerson, we find that models with a smaller misaligngment angle (Theta<~15 deg.) are more consistent with the observations which show that majority of Pa-beta are rather symmetric around the line centre. For a high inclination system with a small dipole misalignment angle (Theta ~ 15 deg.), only one accretion funnel (on the upper hemisphere) is visible to an observer at any given rotational phase. This can cause an anti-correlation of the line equivalent width in the blue wing (v0) over a half of a rotational period, and a positive correlation over other half. We find a good overall agreement of the line variability behaviour predicted by our model and those from observations. (Abridged)Comment: 15 pages, 13 figures. Accepted for publication in MNRAS. A version with full resolution figures can be downloaded from http://www.physics.unlv.edu/~rk/preprint/inclined_dipole.pd

Variability Profiles of Millisecond X-Ray Pulsars: Results of Pseudo-Newtonian 3D MHD Simulations

We model the variability profiles of millisecond period X-ray pulsars. We performed three-dimensional magnetohydrodynamic simulations of disk accretion to millisecond period neutron stars with a misaligned magnetic dipole moment, using the pseudo-Newtonian Paczynski-Wiita potential to model general relativistic effects. We found that the shapes of the resulting funnel streams of accreting matter and the hot spots on the surface of the star are quite similar to those for more slowly rotating stars obtained from earlier simulations using the Newtonian potential. The funnel streams and hot spots rotate approximately with the same angular velocity as the star. The spots are bow-shaped (bar-shaped) for small (large) misalignment angles. We found that the matter falling on the star has a higher Mach number when we use the Paczynski-Wiita potential than in the Newtonian case. Having obtained the surface distribution of the emitted flux, we calculated the variability curves of the star, taking into account general relativistic, Doppler and light-travel-time effects. We found that general relativistic effects decrease the pulse fraction (flatten the light curve), while Doppler and light-travel-time effects increase it and distort the light curve. We also found that the light curves from our hot spots are reproduced reasonably well by spots with a gaussian flux distribution centered at the magnetic poles. We also calculated the observed image of the star in a few cases, and saw that for certain orientations, both the antipodal hot spots are simultaneously visible, as noted by earlier authors.Comment: 9 pages, 10 figures, accepted for publication in ApJ; corrected some typo

Protoplanet Magnetosphere Interactions

In this paper, we study a simple model of an orbiting protoplanet in a central magnetospheric cavity, the entry into such a cavity having been proposed as a mechanism for halting inward orbital migration. We have calculated the gravitational interaction of the protoplanet with the magnetosphere using a local model and determined the rate of evolution of the orbit. The interaction is found to be determined by the outward flux of MHD waves and thus the possibility of the existence of such waves in the cavity is significant. The estimated orbital evolution rates due to gravitational and other interactions with the magnetosphere are unlikely to be significant during protoplanetary disk lifetimes.Comment: Accepted for publication in A&

An investigation of magnetic field distortions in accretion discs around neutron stars. I. Analysis of the poloidal field component

We report results from calculations investigating stationary magnetic field configurations in accretion discs around magnetised neutron stars. Our strategy is to start with a very simple model and then progressively improve it providing complementary insight into results obtained with large numerical simulations. In our first model, presented here, we work in the kinematic approximation and consider the stellar magnetic field as being a dipole aligned with the stellar rotation axis and perpendicular to the disc plane, while the flow in the disc is taken to be steady and axisymmetric. The behaviour in the radial direction is then independent of that in the azimuthal direction. We investigate the distortion of the field caused by interaction with the disc matter, solving the induction equation numerically in full 2D. The influence of turbulent diffusivity and fluid velocity on the poloidal field configuration is analysed, including discussion of outflows from the top and bottom of the disc. We find that the distortions increase with increasing magnetic Reynolds number R_m (calculated using the radial velocity). However, a single global parameter does not give an adequate description in different parts of the disc and we use instead a `magnetic distortion function' D_m(r,\theta) (a magnetic Reynolds number defined locally). Where D_m<<1 (near to the inner edge of the disc) there is little distortion, but where D_m>1 (most of the rest of the disc), there is considerable distortion and the field becomes weaker than the dipole would have been. Between these two regions, there is a transition zone where the field is amplified and can have a local minimum and maximum. The location of this zone depends sensitively on the diffusivity. The results depend very little on the boundary conditions at the top of the disc.Comment: Published in A&A; 10 pages and 8 figures; ver. 4: compactification of content

Packing of concave polyhedra with continuous rotations using nonlinear optimisation

We study the problem of packing a given collection of arbitrary, in general concave, polyhedra into a cuboid of minimal volume. Continuous rotations and translations of polyhedra are allowed. In addition, minimal allowable distances between polyhedra are taken into account. We derive an exact mathematical model using adjusted radical free quasi phi-functions for concave polyhedra to describe non-overlapping and distance constraints. The model is a nonlinear programming formulation. We develop an efficient solution algorithm, which employs a fast starting point algorithm and a new compaction procedure. The procedure reduces our problem to a sequence of nonlinear programming subproblems of considerably smaller dimension and a smaller number of nonlinear inequalities. The benefit of this approach is borne out by the computational results, which include a comparison with previously published instances and new instances