Non-radial Forces Research Articles

Dynamical theory of topological defects II: universal aspects of defect motion

We study the dynamics of topological defects in continuum theories governed by a free energy minimization principle, building on our recently developed framework (Romano et al 2023 J. Stat. Mech. 083211). We show how the equation of motion of point defects, domain walls, disclination lines and any other singularity can be understood with one unifying mathematical framework. For disclination lines, this also allows us to study the interplay between the internal line tension and the interaction with other lines. This interplay is non-trivial, allowing defect loops to expand, instead of contracting, due to external interaction. We also use this framework to obtain an analytical description of two long-lasting problems in point defect motion, namely the scale dependence of the defect mobility and the role of elastic anisotropy in the motion of defects in liquid crystals. For the former, we show that the effective defect mobility is strongly problem-dependent, but it can be computed with high accuracy for a pair of annihilating defects. For the latter, we show that at the first order in perturbation theory, anisotropy causes a non-radial force, making the trajectory of annihilating defects deviate from a straight line. At higher orders, it also induces a correction in the mobility, which becomes non-isotropic for the +1/2 defect. We argue that, due to its generality, our method can help to shed light on the motion of singularities in many different systems, including driven and active non-equilibrium theories.

Intrinsic polarization of Wolf-Rayet stars due to the rotational modulation of the stellar wind

Context. Fast rotating Wolf-Rayet stars are expected to be progenitors of long duration gamma-ray bursts. However, the observational test of this model is problematic. Spectral lines of Wolf-Rayet stars originate in expanding stellar wind, therefore a reliable spectroscopical determination of their rotational velocities is difficult. Intrinsic polarization of Wolf-Rayet stars due to the rotational modulation of the stellar wind may provide an indirect way to determine the rotational velocities of these stars. However, detailed wind models are required for this purpose. Aims. We determine the intrinsic polarization of Wolf-Rayet stars from hydrodynamical wind models as a function of rotational velocity. Methods. We used 2.5D hydrodynamical simulations to calculate the structure of rotating winds of Wolf-Rayet stars. The simulations account for the deformation of the stellar surface due to rotation, gravity darkening, and nonradial forces. From the derived models, we calculated the intrinsic stellar polarization. The mass loss rate was scaled to take realistic wind densities of Wolf-Rayet stars into account. Results. The hydrodynamical wind models predict a prolate wind structure, which leads to a relatively low level of polarization. Even relatively large rotational velocities are allowed by observational constrains. The obtained wind structure is similar to that obtained previously for rotating optically thin winds. Conclusions. Derived upper limits of rotational velocities of studied Wolf-Rayet stars are not in conflict with the model of long duration gamma-ray bursts.

The applicability of the wind compression model

Compression of the stellar winds from rapidly rotating hot stars is described by the wind compression model. However, it was also shown that rapid rotation leads to rotational distortion of the stellar surface, resulting in the appearance of non-radial forces acting against the wind compression. In this note we justify the wind compression model for moderately rotating white dwarfs and slowly rotating giants. The former could be conducive to understanding density/ionization structure of the mass outflow from symbiotic stars and novae, while the latter can represent an effective mass-transfer mode in the wide interacting binaries.

Non-radial interaction forces between superpartials in B2 and L12ordered alloys

Non-radial interaction forces between superpartials in B2 and L1₂ordered alloys

Non-radial interaction forces between superpartials in B2 and L1 2 ordered alloys

Tangential interaction forces acting between superlattice partial dislocations in the L1 2 ordered alloys affect decisively the cross-slip of the dislocations and are thus a fundamental part of the models, explaining the so-called anomalous dependence of the flow stress with increasing temperature. A complex nature of the interaction forces between the 1/2 superpartials in the B2 structure is analysed and compared with the 1/2 superpartials in the L1 2 structure for all the orientations of dislocation lines on the {101}, {121} and {111}, {010} glide planes respectively. The similarities and differences of the dislocation behaviour in the two superlattices studied are pointed out. The stable dissociation of the screw dislocations lies in B2 and L1 2 on the {121} and {010} planes, respectively, which are in both cases inclined to the {101} and {111} primary slip planes. The stable dissociation plane of the edge dislocations is again in both cases perpendicular to the Burgers vector. Consequences for dislocation motion following from the presented results are discussed.

Effect of Instability-Generated Clumping on Wind Compressed Disk Inhibition

AbstractIn rapidly rotating stars with a purely radially driven stellar wind, conservation of wind angular momentum can lead to formation of an equatorial Wind Compressed Disk (WCD). However, for a line-driven stellar wind, recent 2D hydrodynamical simulations based on a localized, Sobolev treatment of the line-force indicate that nonradial components of the line-force can effectively inhibit formation of such a WCD. This presentation will describe current efforts to extend such 2D simulations to a nonlocal, smooth-source-function treatment of the line-force that can incorporate the intrinsically strong instability of line-driving to formation of small-scale, clumped structure. Key questions are how such small-scale clumped structure affects the nonradial line-force components that arise from large-scale velocity-gradient asymmetries, and in particular whether such nonradial forces can still inhibit WCD formation in a clumped flow. The results have important implications for the viability of the WCD mechanism as a paradigm for disk formation in Be stars.

The Formation and Structure of Circumstellar Disks

AbstractSeveral theories have been proposed to explain the origin of Be star disks. Among them are Wind-Compressed Disks, accretion disks, decretion disks, and “explosive” ejections. In reviewing these mechanisms, I first concentrate on the current status of the Wind-Compressed Disk model. In particular, I discuss how non-radial forces may prevent disk formation and then discuss various physical effects that may restore the disk. Second, I examine the observational evidence and what it tells us about the structure of the disk. Of particular interest is evidence in favor of Keplerian disks. Finally, I discuss theories for Keplerian disk formation and some of the constraints such theories must satisfy.

Wind-Compressed Disks

AbstractWe discuss the wind-compressed disk (WCD) model and its ability to produce disks in the outflows from rapidly rotating stars. In particular, we discuss the recently discovered non-radial force components that may inhibit the formation of the disk and present preliminary investigations of the ionization distribution and associated line profiles in the WCD model.

Inhibition of Wind-Compressed Disk Formation by Nonradial Line Forces in Rotating Hot-Star Winds

We investigate the effects of nonradial line forces on the formation of a wind-compressed (WCD) around a rapidly rotating B star. Such nonradial forces can arise both from asymmetries in the line resonances in the rotating wind and from rotational distortion of the stellar surface. They characteristically include a latitudinal force component directed away from the equator and an azimuthal force component acting against the sense of rotation. Here we present results from radiation-hydrodynamical simulations showing that these nonradial forces can lead to an effective suppression of the equatorward flow needed to form a WCD as well as a modest (~20%) spin-down of the wind rotation. Furthermore, contrary to previous expectations that the wind mass flux should be enhanced by the reduced effective gravity near the equator, we show here that gravity darkening effects can actually lead to a reduced mass loss, and thus lower density, in the wind from the equatorial region. Overall, the results here thus imply a flow configuration that is markedly different from that derived in previous models of winds from rotating early-type stars. In particular, a major conclusion is that equatorial wind compression effects should be effectively suppressed in any radiatively driven stellar wind for which, as in the usual CAK formalism, the driving includes a significant component from optically thick lines. This presents a serious challenge to the WCD paradigm as an explanation for disk formation around Be and other rapidly rotating hot stars thought to have CAK-type, line-driven winds.

Mass Loss from Rotating Hot-stars: Inhibition of Wind Compressed Disks by Nonradial Line-forces

We review the dynamics of radiatively driven mass loss from rapidly rotating hot-stars. We first summarize the angular momentum conservation process that leads to formation of a Wind Compressed Disk(WCD) when material from a rapidly rotating star is driven gradually outward in the radial direction. We next describe how stellar oblateness and asymmetries in the Sobolev line-resonance generally leads to nonradialcomponents of the driving force is a line-driven wind, including an azimuthal spin-down force acting against the sense of the wind rotation, and a latitudinal force away from the equator. We summarize results from radiation-hydrodynamical simulations showing that these nonradial forces can lead to an effective suppressionof the equatorward flow needed to form a WCD, as well as a modest (∼ 25%) spin-downof the wind rotation. Furthermore, contrary to previous expectations that the wind mass flux should be enhanced by the reduced effective gravity near the equator, we show here that gravity darkening effects can actually lead to a reducedmass loss, and thus lower density, in the wind from the equatorial region. Finally, we examine the equatorial bistability model, and show that a sufficiently strong jump in wind driving parameters can, in principle, overcome the effect of reduced radiative driving flux, thus still allowing moderate enhancements in density in an equatorial, bistability zone wind.

The propagation of coronal mass ejection transients

Measurements of the direction of propagation of 29 coronal mass ejection events observed during the Skylab epoch (1973–1974) and 19 events observed during the SMM epoch (1980) reveal that the former undergo an average 2.2° equatorward deflection, while the latter do not deviate significantly from radial motion. No differences between eruptive prominence‐associated or flare‐associated events can be detected for either epoch. The results suggest that coronal mass ejection events are influenced by the background coronal magnetic and flow patterns; the nonradial forces affecting the Skylab epoch mass ejections arise from the large‐scale dipolar magnetic field and flow configuration present at that time.

Dynamical Instabilities in Spherical Stellar Systems

Equlibrium spherical stellar systems exhibiting instabilities on a dynamical timescale were first studied by Henon (1973), using a spherically symmetric N-body code. We have re-examined Henon's models using an improved code which includes non-radial forces to quadrupole order. In addition to the radial instability reported by Henon, two new non-radial instabilities are also observed. In one, found in models with highly circular orbits, the mass distribution exhibits quadrupole-mode oscillations. In the other, seen in models with highly radial orbits, the system spontaneously breaks spherical symmetry and settles into a tri-axial ellipsoid. These instabilities, which are driven by fluctuations of the mean field, offer some analogies to the well-known dynamical instabilities of a cold disk of stars. While our models are rather artificial, they indicate that dynamical instabilities may be more common in spherical systems than had been thought.