Instability strips of SPB and beta Cephei stars: the effect of the updated OP opacities and of the metal mixture

The discovery of $\beta$ Cephei stars in low metallicity environments, as well as the difficulty in theoretically explaining the excitation of the pulsation modes observed in some $\beta$ Cephei and hybrid SPB-$\beta$ Cephei pulsators, suggest that the ``iron opacity bump'' provided by stellar models could be underestimated. We analyze the effect of uncertainties in the opacity computations and in the solar metal mixture, on the excitation of pulsation modes in B-type stars. We carry out a pulsational stability analysis for four grids of main-sequence models with masses between 2.5 and 12 $\rm M_\odot$ computed with OPAL and OP opacity tables and two different metal mixtures. We find that in a typical $\beta$ Cephei model the OP opacity is 25% larger than OPAL in the region where the driving of pulsation modes occurs. Furthermore, the difference in the Fe mass fraction between the two metal mixtures considered is of the order of 20%. The implication on the excitation of pulsation modes is non-negligible: the blue border of the SPB instability strip is displaced at higher effective temperatures, leading to a larger number of models being hybrid SPB-$\beta$ Cephei pulsators. Moreover, higher overtone p-modes are excited in $\beta$ Cephei models and unstable modes are found in a larger number of models for lower metallicities, in particular $\beta$ Cephei pulsations are also found in models with Z=0.01.Comment: Accepted for publication in MNRAS Letter

A functional central limit theorem for a Markov-modulated infinite-server queue

The production of molecules in a chemical reaction network is modelled as a Poisson process with a Markov-modulated arrival rate and an exponential decay rate. We analyze the distributional properties of $M$, the number of molecules, under specific time-scaling; the background process is sped up by $N^{\alpha}$, the arrival rates are scaled by $N$, for $N$ large. A functional central limit theorem is derived for $M$, which after centering and scaling, converges to an Ornstein-Uhlenbeck process. A dichotomy depending on $\alpha$ is observed. For $\alpha\leq1$ the parameters of the limiting process contain the deviation matrix associated with the background process.Comment: 4 figure

Coriolis force corrections to g-mode spectrum in 1D MHD model

The corrections to g-mode frequencies caused by the presence of a central magnetic field and rotation of the Sun are calculated. The calculations are carried out in the simple one dimensional magnetohydrodynamical model using the approximations which allow one to find the purely analytical spectra of magneto-gravity waves beyond the scope of the JWKB approximation and avoid in a small background magnetic field the appearance of the cusp resonance which locks a wave within the radiative zone. These analytic results are compared with the satellite observations of the g-mode frequency shifts which are of the order one per cent as given in the GOLF experiment at the SoHO board. The main contribution turns out to be the magnetic frequency shift in the strong magnetic field which obeys the used approximations. In particular, the fixed magnetic field strength 700 KG results in the mentioned value of the frequency shift for the g-mode of the radial order n=-10. The rotational shift due to the Coriolis force appears to be small and does not exceed a fracton of per cent, \alpha_\Omega < 0.003.Comment: RevTeX4, 9 pages, 4 eps figures; accepted for publication in Astronomy Reports (Astronomicheskii Zhurnal

The Generalized Ricci Flow for 3D Manifolds with One Killing Vector

We consider 3D flow equations inspired by the renormalization group (RG) equations of string theory with a three dimensional target space. By modifying the flow equations to include a U(1) gauge field, and adding carefully chosen De Turck terms, we are able to extend recent 2D results of Bakas to the case of a 3D Riemannian metric with one Killing vector. In particular, we show that the RG flow with De Turck terms can be reduced to two equations: the continual Toda flow solved by Bakas, plus its linearizaton. We find exact solutions which flow to homogeneous but not always isotropic geometries