FASTWIND reloaded: Complete comoving frame transfer for “all” contributing lines

FASTWIND is a unified NLTE atmosphere/spectrum synthesis code originally designed (and frequently used) for the optical/IR spectroscopic analysis of massive stars with winds. Until the previous version (v10), the line transfer for background elements (mostly from the iron-group) was performed in an approximate way, by calculating the individual line-transitions in a single-line Sobolev or comoving frame approach, and by adding up the individual opacities and source functions to quasi-continuum quantities that are used to determine the radiation field for the complete spectrum (see Puls et al. 2005, A&A 435, 669, and updates).We have now updated this approach (v11) and calculate, for all contributing lines (from elements H to Zn), the radiative transfer in the comoving frame, thus also accounting for line-overlap effects in an “exact” way. Related quantities such as temperature, radiative acceleration and formal integral have been improved in parallel. For a typical massive star atmospheric model, the computation times (from scratch, and for a modern desktop computer) are 1.5 h for the atmosphere/NLTE part, and 30 to 45 minutes (when not parallelized) for the formal integral (i.e., SED and normalized flux) in the ranges 900 to 2000 and 3800 to 7000 Å(Δλ = 0.03 Å).We compare our new with analogous results from the alternative code CMFGEN (Hillier & Miller 1998, ApJ 496, 407, and updates), for a grid consisting of 5 O-dwarf and 5 O-supergiant models of different spectral subtype. In most cases, the agreement is very good or even excellent (i.e., for the radiative acceleration), though also certain differences can be spotted. A comparison with results from the previous, approximate method shows equally good agreement, though also here some differences become obvious. Besides the possibility to calculate the (total) radiative acceleration, the new FASTWIND version will allow us to investigate the UV-part of the spectrum in parallel with the optical/IR domain.

Equivariant N-Dof Hamiltonians Via Generalized Normal Forms

In the present paper we study polynomial Hamiltonian systems depending on one or various real parameters. We determine the values that these parameters should take in order to be able to construct formal (asymptotic) integrals of the system. In this respect, a method to calculate the formal integrals of a polynomial Hamiltonian vector field is presented. The original Hamilton function represents a family of dynamical systems composed by a principal part (quadratic terms) plus the perturbation (terms of degree three or bigger). We extend an integral of the principal part to the perturbed system by means of Lie transformations for autonomous Hamiltonian systems. Thus, the procedure is carried out order by order starting with polynomials of degree three. We obtain the conditions that the external parameters have to satisfy so that the integral of the quadratic terms persists for the whole system up to a certain order of approximation. Once the formal integral is computed the departure system has been transformed into a generalized normal form, i.e. a system which is equivalent to the initial one but easier to be analysed by making use of reduction theory. The truncated normal form defines a system with less degrees of freedom than the original Hamiltonian and is written exactly in terms of the polynomial first integrals associated to the quadratic part of the new integral and it contains the qualitative description of the initial system. The theory is illustrated with two examples borrowed from Physics.

Amplitude and phase shift due to caustics

abstract The formal integral solution for an arbitrary ray in a plane parallel-layered, vertically inhomogeneous elastic medium is evaluated using a modified third-order saddle point method. The result, which reduces to the Airy function solution where the latter is valid, is shown to be more generally valid and just as simple to compute. In addition, it is shown that the phase shift due to caustics is intimately related to the occurrence of turning points along the ray. An expression is derived explicitly relating this phase shift to the number of turning points and to whether the ray is on a direct or reverse travel-time branch.

Appraisal of near-field solutions for a Hertzian dipole over a conducting half-space

Various approximations to the exact formal integral representations of the near-field and the impedance are considered. A new approximate form is obtained which appears to be valid even when the dipole is near a poorly conducting earth. Numerical comparisons with the exact integral formula verify some of the conjectures. The result shows that the ground has a significant influence on the input impedance of the dipole, particularly for low heights.

On the Response of an Elastic Half-Space to a Moving Blast Wave

A formal integral transform solution is obtained for the response of an elastic half-space to a radially symmetric pressure signature of variable pressure and variable velocity. An asymptotic approximation to this solution is developed and expressed in terms of the known solution for the response of a half-space to a two-dimensional pulse moving with constant velocity plus a correction that is important only if the blast-wave speed directly above the point of observation is close to the Rayleigh-wave speed.