The environment of the fast rotating star Achernar

Abstract

Context. Rotation significantly impacts on the structure and life of stars. In phases of high rotation velocity (close to critical), the photospheric structure can be highly modified, and present in particular geometrical deformation (rotation flattening) and latitudinaldependent flux (gravity darkening). The fastest known rotators among the nondegenerate stars close to the main sequence, Be stars, are key targets for studying the effects of fast rotation on stellar photospheres. Aims. We seek to determine the purely photospheric parameters of Achernar based on observations recorded during an emission-free phase (normal B phase). Methods. Several recent works proved that optical/IR long-baseline interferometry is the only technique able to sufficiently spatially resolve and measure photospheric parameters of fast rotating stars. We thus analyzed ESO-VLTI (PIONIER and AMBER) interferometric observations of Achernar to measure its photospheric parameters by fitting our physical model CHARRON using a Markov chain Monte Carlo method. This analysis was also complemented by spectroscopic, polarimetric, and photometric observations to investigate the status of the circumstellar environment of Achernar during the VLTI observations and to cross-check our model-fitting results. Results. Based on VLTI observations that partially resolve Achernar, we simultaneously measured five photospheric parameters of a Be star for the first time: equatorial radius (equatorial angular diameter), equatorial rotation velocity, polar inclination, position angle of the rotation axis projected on the sky, and the gravity darkening β coefficient (effective temperature distribution). The close circumstellar environment of Achernar was also investigated based on contemporaneous polarimetry, spectroscopy, and interferometry, including image reconstruction. This analysis did not reveal any important circumstellar contribution, so that Achernar was essentially in a normal B phase at least from mid-2009 to end-2012, and the model parameters derived in this work provide a fair description of its photosphere. Finally, because Achernar is the flattest interferometrically resolved fast rotator to-date, the measured β and flattening, combined with values from previous works, provide a crucial test for a recently proposed gravity darkening model. This model offers a promising explanation to the fact that the measured β parameter decreases with flattening and shows significantly lower values than the classical prediction of von Zeipel.

Critical study of the distribution of rotational velocities of Be stars

“…which shows that this exponent varies from β 1 = 1 at η = 0 to Rieutord (2011) and Domiciano de Souza et al (2014). According to this dependence of β 1 with η, the contrast between the emitted polar and equatorial radiative fluxes reduces significantly when η → 1 as compared to predictions obtained with β 1 = 1.…”

“…Other formulations of this relation for conservative and nonconservative rotation laws, produce , von Zeipel 1924;Lucy 1967;Smith & Worley 1974;Kippenhahn 1977;Hadrava 1992;Maeder 1999Maeder , 2009Lovekin et al 2006;Gillich et al 2008;Dall & Sbordone 2011;Espinosa Lara & Rieutord 2011;Claret 2012). Moreover, because of the simple fact that β 1 is colatitude θ-dependent, an observed β 1 is necessarily a function of the aspect angle (Domiciano de Souza et al 2014;Rieutord 2016;Zorec et al 2016). Holding forcibly β 1 = const.…”

“…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. These rates suggest that the surface rotational velocities of Be stars are undoubtedly very high, but they are not necessarily critical.…”

Gravity-darkening exponents for neutron and non-relativistic stars

“…However, for the fourth system, β Cas, the authors found a discrepancy with their theoretical prediction and explained it to be due to the small inclination angle of this system. More recent comparisons with observations can be found in Domiciano et al (2014), where six fast rotators were compared with the mentioned theoretical predictions. The authors concluded (their Fig.…”

Capabilities of future intensity interferometers for observing fast-rotating stars: imaging with two- and three-telescope correlations

“…For modern amplitude interferometers the uncertainties on the model parameters range typically of the order of ≃ 1% − 10%, depending on the parameter (e.g. Domiciano de Souza et al 2014;Monnier et al 2012). Since the (u, v) coverage of CTA can be so dense, we rather adopt model-independent image reconstruction strategies described in Sec.…”