2.5D global-disk oscillation models of the Be shell star ζ Tauri

I. Spectroscopic and polarimetric analysis^⋆

¹ Instituto de Astronomia, Geofísica e Ciencias Atmosféricas, Universidade de São Paulo, Rua do Matão 1226, Cidade Universitária, 05508-090 São Paulo SP, Brazil
e-mail: cyril.escolano@usp.br
² Hokkai-Gakuen University, Toyohira-ku, 062-8605 Sapporo, Japan
³ ESO – European Organisation for Astronomical Research in the Southern Hemisphere, Casilla 19001 Santiago, Chile
⁴ ESO – European Organisation for Astronomical Research in the Southern Hemisphere, Karl-Schwarzschild-Str. 2, 85748 Garching, Germany
⁵ ALMA – Atacama Large Millimeter Array, Alonso de Córdova 3107, Vitacura, 763 0355 Santiago, Chile

Received: 2 December 2014
Accepted: 4 February 2015

Abstract

Context. A large number of Be stars exhibit intensity variations of their violet and red emission peaks in their H i lines observed in emission. This is the so-called V/R phenomenon, usually explained by the precession of a one-armed spiral density perturbation in the circumstellar disk. That global-disk oscillation scenario was confirmed, both observationally and theoretically, in the previous series of two papers analyzing the Be shell star ζ Tauri. The vertically averaged (2D) global-disk oscillation model used at the time was able to reproduce the V/R variations observed in Hα, as well as the spatially resolved interferometric data from AMBER/VLTI. Unfortunately, that model failed to reproduce the V/R phase of Br15 and the amplitude of the polarization variation, suggesting that the inner disk structure predicted by the model was incorrect.

Aims. The first aim of the present paper is to quantify the temporal variations of the shell-line characteristics of ζ Tauri. The second aim is to better understand the physics underlying the V/R phenomenon by modeling the shell-line variations together with the V/R and polarimetric variations. The third aim is to test a new 2.5D disk oscillation model, which solves the set of equations that describe the 3D perturbed disk structure but keeps only the equatorial (i.e., 2D) component of the solution. This approximation was adopted to allow comparisons with the previous 2D model, and as a first step toward a future 3D model.

Methods. We carried out an extensive analysis of ζ Tauri’s spectroscopic variations by measuring various quantities characterizing its Balmer line profiles: red and violet emission peak intensities (for Hα, Hβ, and Br15), depth and asymmetry of the shell absorption (for Hβ, Hγ, and Hδ), and the respective position (i.e., radial velocity) of each component. We attempted to model the observed variations by implementing in the radiative transfer code HDUST the perturbed disk structure computed with a recently developed 2.5D global-disk oscillation model.

Results. The observational analysis indicates that the peak separation and the position of the shell absorption both exhibit variations following the V/R variations and, thus, may provide good diagnostic tools of the global-disk oscillation phenomenon. The shell absorption seems to become slightly shallower close to the V/R maximum, but the scarcity of the data does not allow the exact pattern to be identified. The asymmetry of the shell absorption does not seem to correlate with the V/R cycle; no significant variations of this parameter are observed, except during certain periods where Hα and Hβ exhibit perturbed emission profiles. The origin of these so-called triple-peak phases remains unknown. On the theoretical side, the new 2.5D formalism appears to improve the agreement with the observed V/R variations of Hα and Br15, under the proviso that a large value of the viscosity parameter, α = 0.8, be adopted. It remains challenging for the models to reproduce consistently the amplitude and the average level of the polarization data. The 2D formalism provides a better match to the peak separation, although the variation amplitude predicted by both the 2D and 2.5D models is smaller than the observed value. Shell-line variations are difficult for the models to reproduce, whatever formalism is adopted.