The diversity of supernovae and impostors shortly after explosion

Observational surveys are now able to detect an increasing number of transients, such as core-collapse supernovae (SN) and powerful non-terminal outbursts (SN impostors). Dedicated spectroscopic facilities can follow up these events shortly after detection. Here we investigate the properties of these explosions at early times. We use the radiative transfer code CMFGEN to build an extensive library of spectra simulating the interaction of supernovae and their progenitor's winds/circumstellar medium (CSM). We consider a range of progenitor mass-loss rates (Mdot = 5e-4 to 1e-2 Msun/yr), abundances (solar, CNO-processed, and He-rich), and SN luminosities (L = 1.9e8 to 2.5e10 Lsun). The models simulate events ~1 day after explosion, and we assume a fixed location of the shock front as Rin=8.6e13 cm. We show that the large range of massive star properties at the pre-SN stage causes a diversity of early-time interacting SN and impostors. We identify three main classes of early-time spectra consisting of relatively high-ionisation (e.g. Ovi), medium-ionisation (e.g. Ciii), and low-ionisation lines (e.g. Feii/iii). They are regulated by L and the CSM density. Given a progenitor wind velocity Vinf, our models also place a lower limit of Mdot > 5e-4 (Vinf/150 km/s) Msun/yr for detection of CSM interaction signatures in observed spectra. Early-time SN spectra should provide clear constraints on progenitors by measuring H, He, and CNO abundances if the progenitors come from single stars. The connections are less clear considering the effects of binary evolution. Yet, our models provide a clear path for linking the final stages of massive stars to their post-explosion spectra at early times, and guiding future observational follow-up of transients with facilities such as the Zwicky Transient Facility.Comment: Accepted for publication in A&A. 14 pages, 7 figure

Static inconsistencies in certain axiomatic higher-order shear deformation theories for beams, plates and shells

AbstractStatic inconsistencies that arise when modelling the flexural behaviour of beams, plates and shells with clamped boundary conditions using a certain class of axiomatic, higher-order shear deformation theory are discussed. The inconsistencies pertain to displacement-based theories that enforce conditions of vanishing shear strain at the top and bottom surfaces a priori. First it is shown that the essential boundary condition of vanishing Kirchhoff rotation perpendicular to an edge (w,x=0 or w,y=0) is physically inaccurate, as the rotation at a clamped edge may in fact be non-zero due to the presence of transverse shear rotation. As a result, the shear force derived from constitutive equations erroneously vanishes at a clamped edge. In effect, this boundary condition overconstrains the structure leading to underpredictions in transverse bending deflection and overpredictions of axial stresses compared to high-fidelity 3D finite element solutions for thick and highly orthotropic plates. Generalised higher-order theories written in the form of a power series, as in Carrera’s Unified Formulation, do not produce this inconsistency. It is shown that the condition of vanishing shear tractions at the top and bottom surfaces need not be applied a priori, as the transverse shear strains inherently vanish if the order of the theory is sufficient to capture all higher-order effects. Finally, the transverse deflection of the generalised higher-order theories is expanded in a power series of a non-dimensional parameter and used to derive a material and geometry dependent shear correction factor that provides more accurate solutions of bending deflection than the classical value of 5/6

Episodic modulations in supernova radio light curves from luminous blue variable supernova progenitor models

Ideally, one would like to know which type of core-collapse SNe is produced by different progenitors and the channels of stellar evolution leading to these progenitors. These links have to be very well known to use the observed frequency of different types of SN events for probing the star formation rate and massive star evolution in different types of galaxies. We investigate the link between LBV as SN progenitors and the appearance of episodic radio light curve modulations of the SN event. We use the 20Msun and 25Msun models with rotation at solar metallicity, part of an extended grid of stellar models computed by the Geneva team. At their pre-SN stage, these two models have recently been shown to have spectra similar to those of LBV stars and possibly explode as Type IIb SNe. Based on the wind properties before the explosion, we derive the density structure of their circumstellar medium. This structure is used as input for computing the SN radio light curve. We find that the 20Msun model shows radio light curves with episodic luminosity modulations, similar to those observed in some Type IIb SNe. This occurs because the evolution of the 20Msun model terminates in a region of the HR diagram where radiative stellar winds present strong density variations, caused by the bistability limit. The 25Msun model, ending its evolution in a zone of the HR diagram where no change of the mass-loss rates is expected, presents no such modulations in its radio SN light curve. Our results reinforce the link between SN progenitors and LBV stars. We also confirm the existence of a physical mechanism for a single star to have episodic radio light curve modulations. In the case of the 25Msun progenitors, we do not obtain modulations in the radio light curve, but our models may miss some outbursting behavior in the late stages of massive stars.Comment: 5 pages, 3 figures, accepted by Astronomy & Astrophysics Letter

Crystal structures and freezing of dipolar fluids

We investigate the crystal structure of classical systems of spherical particles with an embedded point dipole at T=0. The ferroelectric ground state energy is calculated using generalizations of the Ewald summation technique. Due to the reduced symmetry compared to the nonpolar case the crystals are never strictly cubic. For the Stockmayer (i.e., Lennard-Jones plus dipolar) interaction three phases are found upon increasing the dipole moment: hexagonal, body-centered orthorhombic, and body-centered tetragonal. An even richer phase diagram arises for dipolar soft spheres with a purely repulsive inverse power law potential $\sim r^{-n}$. A crossover between qualitatively different sequences of phases occurs near the exponent $n=12$. The results are applicable to electro- and magnetorheological fluids. In addition to the exact ground state analysis we study freezing of the Stockmayer fluid by density-functional theory.Comment: submitted to Phys. Rev.

Magnetization of ferrofluids with dipolar interactions - a Born--Mayer expansion

For ferrofluids that are described by a system of hard spheres interacting via dipolar forces we evaluate the magnetization as a function of the internal magnetic field with a Born--Mayer technique and an expansion in the dipolar coupling strength. Two different approximations are presented for the magnetization considering different contributions to a series expansion in terms of the volume fraction of the particles and the dipolar coupling strength.Comment: 19 pages, 11 figures submitted to PR

Virtual Testing of Experimental Continuation

We present a critical advance in experimental testing of nonlinear structures. Traditional quasi-static experimental methods control the displacement or force at one or more load-introduction points on a structure. This approach is unable to traverse limit points in the control parameter, as the immediate equilibrium beyond these points is statically unstable, causing the structure to snap to another equilibrium. As a result, unstable equilibria---observed numerically---are yet to be verified experimentally. Based on previous experimental work, and a virtual testing environment developed herein, we propose a new experimental continuation method that can path-follow along unstable equilibria and traverse limit points. To support these developments, we provide insightful analogies between a fundamental building block of our technique---shape control---and analysis concepts such as the principle of virtual work and Galerkin's method. The proposed testing method will enable the validation of an emerging class of nonlinear structures that exploit instabilities for novel functionality

Shape Control for Experimental Continuation

An experimental method has been developed to locate unstable equilibria of nonlinear structures quasi-statically. The technique involves loading a structure by application of either a force or a displacement at a main actuation point, while simultaneously controlling the overall shape using additional probe points. The method is applied to a shallow arch, and unstable segments of its equilibrium path are identified experimentally for the first time. Shape control is a fundamental building block for the experimental---as opposed to numerical---continuation of nonlinear structures, which will significantly expand our ability to measure their mechanical response.Comment: Updated Figure 6 experimental results with correct calibration factor for linear transducer. Updated Figure 6 finite element results with correct load multiplier for half-model. Updated paper text to reflect these changes. 5 pages, 6 figure

Inhomogeneous magnetization in dipolar ferromagnetic liquids

At high densities fluids of strongly dipolar spherical particles exhibit spontaneous long-ranged orientational order. Typically, due to demagnetization effects induced by the long range of the dipolar interactions, the magnetization structure is spatially inhomogeneous and depends on the shape of the sample. We determine this structure for a cubic sample by the free minimization of an appropriate microscopic density functional using simulated annealing. We find a vortex structure resembling four domains separated by four domain walls whose thickness increases proportional to the system size L. There are indications that for large L the whole configuration scales with the system size. Near the axis of the mainly planar vortex structure the direction of the magnetization escapes into the third dimension or, at higher temperatures, the absolute value of the magnetization is strongly reduced. Thus the orientational order is characterized by two point defects at the top and the bottom of the sample, respectively. The equilibrium structure in an external field and the transition to a homogeneous magnetization for strong fields are analyzed, too.Comment: 17 postscript figures included, submitted to Phys. Rev.