Spectrally resolved interferometric observations ofαCephei and physical modeling of fast rotating stars

O Delaa,T Ten Brummelaar,A Spang,L Sturmann,A Domiciano De Souza,M Challouf,P J Goldfinger,J Zorec,D Bonneau,J Sturmann,D Mourard,Philippe Bério ,J M Clausse,Xiao Chen ,N Nardetto,Philippe Stee ,N Turner,R Ligi,John D Monnier ,Stefan Kraus ,A Meilland,C Farrington,K Perraut,Y Frémat,Harold A Mcalister

doi:10.1051/0004-6361/201220689

Abstract

Context. When a given observational quantity depends on several stellar physical parameters, it is generally very difficult to obtain observational constraints for each of them individually. Therefore, we studied under which conditions constraints for some individual parameters can be achieved for fast rotators, knowing that their geometry is modified by the rapid rotation which causes a non-uniform surface brightness distribution.Aims. We aim to study the sensitivity of interferometric observables on the position angle of the rotation axis (PA) of a rapidly rotating star, and whether other physical parameters can influence the determination of PA, and also the influence of the surface differential rotation on the determination of the β exponent in the gravity darkening law that enters the interpretation of interferometric observations, using α Cep as a test star.Methods. We used differential phases obtained from observations carried out in the Hα absorption line of α Cep with the VEGA/CHARA interferometer at high spectral resolution, R = 30 000 to study the kinematics in the atmosphere of the star.Results. We studied the influence of the gravity darkening effect (GDE) on the determination of the PA of the rotation axis of α Cep and determined its value, PA = −157-10° +17° . We conclude that the GDE has a weak influence on the dispersed phases. We showed that the surface differential rotation can have a rather strong influence on the determination of the gravity darkening exponent. A new method of determining the inclination angle of the stellar rotational axis is suggested. We conclude that differential phases obtained with spectro-interferometry carried out on the Hα line can in principle lead to an estimate of the stellar inclination angle i . However, to determine both i and the differential rotation parameter α , lines free from the Stark effect and that have collision-dominated source functions are to be preferred.

Highlights

The centrifugal force of rapid rotators induces a strong deformation of the stellar geometry that has been nicely shown observationally, thanks to long-baseline optical interferometrers that today allow observations at high spatial resolution to be performed (van Belle et al 2001, 2006; Domiciano de Souza et al 2003; McAlister et al 2005; Kervella & Domiciano de Souza 2006; Monnier et al 2007; Zhao et al 2009)
We explore whether the inclination angle i can be estimated with interferometric observations and what effects are induced by the surface differential rotation that may hamper the angle i-determination
Because we have at our disposal interferometric observations covering almost the entire Hα line of α Cep, in the present section, we explore whether we can use this line to estimate the inclination angle i of the rotation axis

Summary

Introduction

The centrifugal force of rapid rotators induces a strong deformation of the stellar geometry that has been nicely shown observationally, thanks to long-baseline optical interferometrers that today allow observations at high spatial resolution to be performed (van Belle et al 2001, 2006; Domiciano de Souza et al 2003; McAlister et al 2005; Kervella & Domiciano de Souza 2006; Monnier et al 2007; Zhao et al 2009). Concomitant to the stellar flattening, there is a non-uniform effective temperature distribution, called the gravity darkening effect (GDE; von Zeipel 1924). For stars with conservative rotation laws (rigid rotation is a particular case of a conservative law), whose envelopes are in hydrostatic and radiative equilibrium and where the diffusion approximation to the radiative transfer equation is used, the following relation for the effective temperature distribution as a function of the co-latitude θ holds: Teff(θ) = Tp geff (θ) gp β (1). Where Teff(θ) and geff(θ) are the co-latitude θ dependent effective temperature and effective gravity Tp is the polar effective temperature, and gp is the polar gravity. The value β = 0.08 holds for stars with convective envelopes (Lucy 1967; Reiners 2003).

Objectives

Methods

Findings

Conclusion