Mass of dusty clumps with temperature and density structure

We consider a dusty clump in two cases of spherical and cylindrical symmetry to investigate the effect of temperature and density gradients on the observed flux density. Conversely, we evaluate how the presence of these gradients affects the calculation of the clump mass from the observed flux. We provide approximate expressions relating flux density and mass in the optically thick and thin limits and in the Rayleigh-Jeans regime, and we discuss the reliability of these expressions by comparing them to the outcome of a numerical code. Finally, we present the application of our calculations to three examples taken from the literature, which shows how the correction introduced after taking into account temperature and density gradients may affect our conclusions on the stability of the clumps.

3D MHD simulations and synthetic radio emission from an oblique rotating magnetic massive star

ABSTRACT We have performed 3D isothermal MHD simulation of a magnetic rotating massive star with a non-zero dipole obliquity and predicted the radio/sub-mm observable light curves and continuum spectra for a frequency range compatible with ALMA. From these results we also compare the model input mass-loss to that calculated from the synthetic thermal emission. Spherical and cylindrical symmetry is broken due to the obliquity of the stellar magnetic dipole resulting in an inclination and phase dependence of both the spectral flux and inferred mass-loss rate, providing testable predictions of variability for oblique rotator. Both quantities vary by factors between 2 and 3 over a full rotational period of the star, demonstrating that the role of rotation as critical in understanding the emission. This illustrates the divergence from a symmetric wind, resulting in a two-armed spiral structure indicative of an oblique magnetic rotator. We show that a constant spectral index, α, model agrees well with our numerical prediction for a spherical wind for ν < 103 GHz; however it is unable to capture the behaviour of emission at ν > 103 GHz. As such we caution the use of such constant α models for predicting emission from non-spherical winds such as those which form around magnetic massive stars.

Green's functions for polarized radiative transfer equation in different geometries

A review of some earlier exact analytic solutions of monochromatic stationary vector radiative transfer equation in homogeneous infinite medium is given. It is stressed that Green's functions for plane-parallel, spherical and cylindrical symmetry are expressed through derivatives and integrals from basically one and the same set of functions.

SOLITONS OF SCALAR FIELD WITH INDUCED NONLINEARITY AND THEIR STABILITY

Exact particle-like static, spherically and/or cylindrically symmetric solutions to the equations of interacting scalar and electromagnetic field system have been obtained. We considered FRW and Gödel universes as external gravitational field with spherical and cylindrical symmetry respectively. Beside the usual solitons some special regular solutions know as droplets, antidroplets and hats (confined in finite interval and having trivial value beyond it) have been obtained. It has been shown that in FRW space–time equations with different interaction terms may have stable solutions while within the scope of Gödel model only the droplet-like and the hat-like configurations may be stable, providing they are located in the region where g00>0.

MAGNETIZATION REVERSAL BY NUCLEATION

The exact static solutions of the Landau-Lifshitz equations for the magnetization, which have been identified as describing nucleation centers for the magnetization reversal in ferromagnets, are compared with those of phenomenological models of spherical and cylindrical symmetry. It is found that the latter have higher critical fields.