Effects of gravitational darkening on the determination of fundamental parameters in fast-rotating B-type stars

Abstract

Abstract. In this paper we develop a calculation code to account for the effects carried by fast rotation on the observed spectra of early-type stars. Stars are assumed to be in rigid rotation, and the grid of plane-parallel model atmospheres used to represent the gravitational darkening are calculated by means of a non-LTE approach. Attention is paid to the relation between the apparent and parent non-rotating counterpart stellar fundamental parameters and apparent, and true Vsin i parameters as a function of the rotation rate Ω/Ω c , stellar mass, and inclination angle. It is shown that omitting of gravitational darkening in the analysis of chemical abundances of CNO elements can produce systematic overestimation or underestimation, depending on the lines used, rotational rate, and inclination angle. The proximity of Be stars to the critical rotation is revised while correcting not only the Vsin i of 130 Be stars, but also their effective temperature and gravity to account for stellar rotationally induced geometrical distortion and for the concomitant gravitational darkening effect. We concluded that the Vsin i increase is accompanied by an even higher value for the stellar equatorial critical velocity, so that the most probable average rate of the angular velocity of Be stars attains Ω/Ω c 0.88.

Critical study of the distribution of rotational velocities of Be stars

“…The stellar sample used in this work has 233 Galactic classical Be stars, which have been previously studied by Chauville et al (2001), Frémat et al (2005), Zorec et al (2005), Frémat et al (2006) and Levenhagen & Leister (2006). They are listed in Table 1.…”

“…Apparent fundamental parameters. Following Frémat et al (2005), the directly observed parameters are called apparent fundamental parameters, which describe only the average properties of the photosphere in the hemisphere projected toward the observer. In the present work we deal with four independent observed apparent quantities: (i) T app eff , is the apparent effective temperature, which corresponds to the effective temperature of a classical nonrotating, plane-parallel model of stellar atmospheres without GD that describes the observed spectrum in a limited wavelength domain.…”

“…Regarding the critical rotation, statistical analyses (Cranmer 2005;Frémat et al 2005) conclude that Be stars are undercritical rotators. Studies of individual stars, based on nonradial pulsation modes (Cameron et al 2008;Saio 2013) and rotational rates inferred from interferometric data (Meilland et al 2012;Domiciano de Souza et al 2014), produce estimates of Ω/Ω c ranging from 0.60 to 0.98, which correspond to linear velocities ratios 0.44 V/V c 0.88 (V c is the critical equatorial linear velocity) or to ratios of centrifugal to gravity accelerations 0.14 a c /a g 0.70.…”

“…Nevertheless, a number of phenomena act either to underestimate or increase the Vsin i of Be stars systematically. In the present paper we only pay attention to the following phenomena: (1) the gravity darkening effect (hereafter GD), which may carry a systematic underestimation of the Vsin i (Stoeckley 1968;Townsend et al 2004;Cranmer 2005;Frémat et al 2005); (2) more or less chaotic macroscopic velocity fields present in atmospheres of active stars, called macroturbulence, and since Unsöld & Struve (1949) and Huang & Struve (1953) are known to contribute a nonrotational broadening component of spectral lines; (3) under certain conditions, the orbital motion increases the apparent value of Vsin i because this phenomenon can concern a large fraction of Be stars that are members of binary systems (Kriz & Harmanec 1975;Harmanec 1987;Gies 2000;Chini et al 2012;Nasseri et al 2013;Oudmaijer & Parr 2010).…”

A working hypothesis about the cause of Be stars: Episodic outward leakage of low-frequency waves excited by the iron-peak κ-mechanism

“…Indeed, the spectroscopically observed rotation velocities of Be stars are higher than those of normal B-type stars. However, careful analyses indicate that their velocities are not high enough to reach the break-up limit (Porter 1996;Frémat et al 2005), though this conclusion is still controversial (e.g., Townsend et al 2004). Some additional mechanisms for the angular momentum transport have been 174 H. Shibahashi examined to bring the already rapid stellar rotation to its critical value at the surface, and allows the star to eject material.…”