A new numerical scheme for structures of rotating magnetic stars

We have developed a new numerical scheme for obtaining structures of rapidly rotating stars with strong magnetic fields. In our scheme, both poloidal and toroidal magnetic fields can be treated for stars with compressibility and infinite conductivity. By introducing the vector potential and its integral representation, we can treat the boundary condition for the magnetic fields across the surface properly. We show structures and distributions of magnetic fields as well as the distributions of the currents of rotating magnetic polytropic stars with polytropic index   N = 1.5  . The shapes of magnetic stars are oblate as long as the magnetic vector potential decreases as 1/ r when   r →∞  . For extremely strong magnetic fields, equilibrium configurations can be of toroidal shapes.     

How Fast the Nucleus of Comet Hale–Bopp was Rotating?

At the First International Conference on Comet Hale–Bopp(Canaries, 1998) many astronomers agreed with the value of theperiod of axial rotation of its nucleus, which was obtained byobservers by a comparison of the two sequential patterns of thedust arcs. It was noted that the pattern had been repeated each∼12 hours. The value 11.35^h was taken as the periodof axial rotation. However, alternative periods of 4 and 8 days havealso been suggested. The possible reasons for thisdiscrepancy are discussed. It is shown that a short period could be obtained by a misidentification of the same arc on twosequential images and, as a result, an overestimate of theradial velocity of dust in the arcs. To obtain the half day period one must take the projected velocity of the arc ∼ 1.6 km/s,which exceeds the H₂O gas expansion velocity. If one takes a lower expansion velocity a longer period would be obtained.     

Fan-shaped staurolite in the Bolton syncline, eastern Connecticut: evidence for porphyroblast rotation during growth

Fan‐shaped polycrystalline staurolite porphyroblasts, 3–4 cm in length and 0.5 cm in width, occur together with centimetre‐sized euhedral prismatic staurolite porphyroblasts in pelitic schists of the Littleton Formation on the western overturned limb of the Bolton syncline in eastern Connecticut. The fans consist of intergrown planar splays of [001] elongated prisms, which are crudely radial from a single apex. The apical angles of the radial groupings range up to 70°. The orientations of the individual staurolite prisms are related by a rigid rotation about an axis perpendicular to the fan plane. The zone axes [001] always lie in the plane of the fan. Although the angle between the [100] zone axes of the individual prisms is uniform in each fan, it ranges from +30° to ?30° in different fans. Internally, the fans display: (i) remnants of a passively captured S_i foliation defined by disc‐shaped quartz blebs (type 1 inclusions) and layers of very fine carbonaceous material and tabular ilmenite platelets; (ii) bent staurolite blades and undulose extinction along low‐angle (010) subgrain boundaries near the apex of the fans; (iii) wedge‐shaped dilatational zones containing equigranular inclusion‐free quartz, mica and staurolite, and (iv) growth‐related quartz inclusion trails roughly perpendicular to a crystal face (type 2 inclusions). The S_i inclusion trails are typically perpendicular to the fan surface, radiate parallel to the blades, and show little to no curvature except at the very edge of the fans where they abruptly curve through nearly 90° into parallelism with an external S_e foliation. Careful examination of the three‐dimensional geometry of fans based on U‐stage measurements, serial sections and two‐circle optical goniometric measurements permits a detailed reconstruction of their sequential development. The origin of a fan involves limited intracrystalline deformation and brittle crack dilation, spalling, rotation, and growth of small marginal fragments and of new staurolite along wedge‐shaped zones along the S_i inclusion surfaces. Fans preferentially develop in porphyroblasts in which S_i is subparallel to the 010 cleavage. These internal features reflect the rotation and deformation of a brittle porphyroblast relative to syn‐growth shear stresses.     

Problems, Connections and Expectations of Asteroseismology: a Summary of the Workshop

The workshop took place at the beginning of what promises tobe a golden age of asteroseismology.Ground-based instrumentation is finally reaching a level of stabilitywhich allows detailed investigations of solar-like oscillations in atleast bright, slowly rotating main-sequence stars.Very extensive results are expected from the coming space missions,including data on a broad range of stars from the Eddington mission.The observational situation is therefore extremely promising.To make full use of these promises, major efforts are requiredtowards the efficient utilization of the data, through the developmentof techniques for the analysis and interpretation of the data.A broad range of topics related to these issues is discussed in the presentproceedings. Here I review some of the relevant problems,relate the asteroseismic investigations to broader areas of astrophysics and consider briefly the basis for our great expectations for the developmentof the field.     

Dynamical passage to approximate equilibrium shapes for spinning, gravitating rubble asteroids

Many asteroids are thought to be particle aggregates held together principally by self-gravity. Here we study — for static and dynamical situations — the equilibrium shapes of spinning asteroids that are permitted for rubble piles. As in the case of spinning fluid masses, not all shapes are compatible with a granular rheology. We take the asteroid to always be an ellipsoid with an interior modeled as a rigid-plastic, cohesion-less material with a Drucker-Prager yield criterion. Using an approximate volume-averaged procedure, based on the classical method of moments, we investigate the dynamical process by which such objects may achieve equilibrium. We first collapse our dynamical approach to its statical limit to derive regions in spin-shape parameter space that allow equilibrium solutions to exist. At present, only a graphical illustration of these solutions for a prolate ellipsoid following the Drucker-Prager failure law is available [Sharma, I., Jenkins, J.T., Burns, J.A., 2005a. Bull. Am. Astron. Soc. 37, 643; Sharma, I., Jenkins, J.T., Burns, J.A., 2005b. Equilibrium shapes of ellipsoidal soil asteroids. In: García-Rojo, R., Hermann, H.J., McNamara, S. (Eds.), Proceedings of the 5th International Conference on Micromechanics of Granular Media, vol. 1. A.A. Balkema, UK; Holsapple, K.A., 2007. Icarus 187, 500-509]. Here, we obtain the equilibrium landscapes for general triaxial ellipsoids, as well as provide the requisite governing formulae. In addition, we demonstrate that it may be possible to better interpret the results of Richardson et al. [Richardson, D.C., Elankumaran, P., Sanderson, R.E., 2005. Icarus 173, 349-361] within the context of a Drucker-Prager material. The graphical result for prolate ellipsoids in the static limit is the same as those of Holsapple [Holsapple, K.A., 2007. Icarus 187, 500-509] because, when worked out, his final equations will match ours. This is because, though the formalisms to reach these expressions differ, in statics, at the lowest level of approximation, volume-averaging and the approach of Holsapple [Holsapple, K.A., 2007. Icarus 187, 500-509] coincide. We note that the approach applied here was obtained independently [Sharma, I., Jenkins, J.T., Burns, J.A., 2003. Bull. Am. Astron. Soc. 35, 1034; Sharma, I., 2004. Rotational Dynamics of Deformable Ellipsoids with Applications to Asteroids. Ph.D. thesis, Cornell University] and it provides a general, though approximate, framework that is amenable to systematic improvements and is flexible enough to incorporate the dynamical effects of a changing shape, different rheologies and complex rotational histories. To demonstrate our technique, we investigate the non-equilibrium dynamics of rigid-plastic, spinning, prolate asteroids to examine the simultaneous histories of shape and spin rate for rubble piles. We have succeeded in recovering most results of Richardson et al. [Richardson, D.C., Elankumaran, P., Sanderson, R.E., 2005. Icarus 173, 349-361], who obtained equilibrium shapes by studying numerically the passage into equilibrium of aggregates containing discrete, interacting, frictionless, spherical particles. Our mainly analytical approach aids in understanding and quantifying previous numerical simulations.     

Oscillations of rapidly rotating superfluid stars

Using time evolutions of the relevant linearized equations, we study non-axisymmetric oscillations of rapidly rotating and superfluid neutron stars. We consider perturbations of Newtonian axisymmetric background configurations and account for the presence of superfluid components via the standard two-fluid model. Within the Cowling approximation, we are able to carry out evolutions for uniformly rotating stars up to the mass-shedding limit. This leads to the first detailed analysis of superfluid neutron star oscillations in the fast rotation regime, where the star is significantly deformed by the centrifugal force. For simplicity, we focus on background models where the two fluids (superfluid neutrons and protons) corotate, are in β-equilibrium and co-exist throughout the volume of the star. We construct sequences of rotating stars for two analytical model equations of state. These models represent relatively simple generalizations of single fluid, polytropic stars. We study the effects of entrainment, rotation and symmetry energy on non-radial oscillations of these models. Our results show that entrainment and symmetry energy can have a significant effect on the rotational splitting of non-axisymmetric modes. In particular, the symmetry energy modifies the inertial mode frequencies considerably in the regime of fast rotation.     

An analysis of v sin (i) correlations in early-type binaries

We use information on the   v sin ( i )  values of early-type binaries in order to search for correlations which may constrain the relative orientation of the stellar spin axes in binary systems. We find correlations in the case of close binaries which suggest that tidal synchronization is effective for binaries whose separation exceeds the stellar radius by more than an order of magnitude, in line with the theoretical predictions of Goldreich & Nicholson and the previous observational analysis of Giuricin et al. In the case of wide binaries, the   v sin ( i )  values are not well correlated, which requires that the magnitude of the spin speeds is not tightly correlated. Under this assumption, we then find that the data provide no significant constraints on the degree of alignment of spin axes. The data are therefore compatible with scenarios (such as disc fragmentation or capture) which differ widely in the expected degree of spin alignment.