[Paper Review] Cyclic Variability of the Circumstellar Disc of the Be Star $\zeta$ Tau. II. Testing the 2D Global Disc Oscillation Model

A. C. Carciofi, Atsuo T. Okazaki+6 more|arXiv (Cornell University)|Jan 8, 2009

Astrophysics and Star Formation StudiesPhysics and Astronomy33 references69 citations

TL;DR

This study presents a self-consistent 3D NLTE radiative transfer model of the Be star ζ Tauri, testing the global disc oscillation scenario using polarimetric, photometric, spectrophotometric, and VLTI/AMBER interferometric data. It confirms the viscous decretion disc model as the formation mechanism and provides the first quantitative fit of spatially resolved interferometric data, demonstrating that the V/R variations arise from a one-armed spiral density wave precessing in the disc with a ~1430-day period.

ABSTRACT

Aims. In this paper we model, in a self-consistent way, polarimetric, photometric, spectrophotometric and interferometric observations of the classical Be star $\zeta$ Tauri. Our primary goal is to conduct a critical quantitative test of the global oscillation scenario. Methods. We have carried out detailed three-dimensional, NLTE radiative transfer calculations using the radiative transfer code HDUST. For the input for the code we have used the most up-to-date research on Be stars to include a physically realistic description for the central star and the circumstellar disc. We adopt a rotationally deformed, gravity darkened central star, surrounded by a disc whose unperturbed state is given by a steady-state viscous decretion disc model. We further assume that disc is in vertical hydrostatic equilibrium. Results. By adopting a viscous decretion disc model for $\zeta$ Tauri and a rigorous solution of the radiative transfer, we have obtained a very good fit of the time-average properties of the disc. This provides strong theoretical evidence that the viscous decretion disc model is the mechanism responsible for disc formation. With the global oscillation model we have successfully fitted spatially resolved VLTI/AMBER observations and the temporal V/R variations of the H$\alpha$ and Br$\gamma$ lines. This result convincingly demonstrates that the oscillation pattern in the disc is a one-armed spiral. Possible model shortcomings, as well as suggestions for future improvements, are also discussed.

Motivation & Objective

• To conduct a critical quantitative test of the global disc oscillation model for the Be star ζ Tauri using multi-wavelength, multi-technique observations.
• To determine whether the viscous decretion disc model accurately reproduces the time-averaged and time-variable properties of the circumstellar disc.
• To assess the geometry and dynamics of the disc, particularly the nature of the V/R variations and the spatial structure revealed by interferometry.
• To resolve ambiguities in model parameters by simultaneously fitting diverse observational constraints, including interferometric and spectroscopic data.

Proposed method

• Employed the 3D NLTE radiative transfer code HDUST to solve coupled radiative transfer, radiative equilibrium, and statistical equilibrium problems in non-local thermodynamic equilibrium.
• Used a rotationally deformed, gravity-darkened central star model with latitude-dependent radiation field and Kurucz model atmospheres.
• Modeled the unperturbed disc as a steady-state viscous decretion disc in vertical hydrostatic equilibrium, with Keplerian rotation.
• Superposed a global m = 1 one-armed spiral oscillation mode on the disc, based on the Okazaki (1991) and Papaloizou et al. (1992) model.
• Simultaneously fit time-averaged photometric, spectrophotometric, polarimetric, and spatially resolved VLTI/AMBER interferometric data.
• Used Monte Carlo photon tracing to simulate emission and scattering in the 3D disc geometry, accounting for escape to polar regions and local shielding.

Experimental results

Research questions

• RQ1 Does the viscous decretion disc model accurately reproduce the time-averaged global properties of the circumstellar disc in ζ Tauri?
• RQ2 Can the global disc oscillation model with a one-armed spiral density wave quantitatively reproduce the observed V/R cycle of Hα and Brγ lines?
• RQ3 To what extent can the VLTI/AMBER interferometric observations constrain the geometry and structure of the outer disc?
• RQ4 Why does the model fail to reproduce the Br15 line V/R cycle and predict unobserved polarization variations in the inner disc?
• RQ5 How do 3D vertical oscillation effects influence the confinement and amplitude of the m = 1 mode in the disc?

Key findings

• The model achieved an excellent fit to the time-averaged disc properties, providing strong theoretical evidence that the viscous decretion disc mechanism is responsible for disc formation in ζ Tauri.
• The simultaneous fit to VLTI/AMBER interferometric data and the V/R cycles of Hα and Brγ lines confirms that the density wave is a one-armed spiral, with a precession period of approximately 1430 days.
• The inclination angle of the disc was determined to be 95°, confirming that the southern face of the disc is oriented toward Earth, resolving ambiguity from non-spatially resolved polarization measurements.
• The model successfully reproduces the general structure of the outer disc, as evidenced by the interferometric data, but fails to match the Br15 line V/R cycle and predicts unobserved polarization variations in the inner disc.
• The discrepancy in the inner disc suggests that the global oscillation model may not accurately represent the geometry or dynamics in the innermost regions, possibly due to non-isothermal effects or outburst-driven perturbations.
• The study demonstrates that the 3D vertical structure of the oscillation mode, as described by Ogilvie (2008), is expected to influence the outer disc amplitude, motivating further analysis in the next paper of the series.