¹ Instituto de Astronomia, Geofísica e Ciências Atmosféricas da Universidade de São Paulo, CUASO, 05508-900 São Paulo SP, Brazil
²Institut d'Astrophysique de Paris, UMR 7095 CNRS-Université Pierre & Marie Curie, 98bis Boulevard Arago, 75014 Paris, France

We explore the geometrical distortion and the stellar and circumstellar activity of  Eri (HD 10144), the brightest Be star in the sky. We present a thorough discussion of the fundamental parameters of the object for an independent determination of its rotational distortion. We used stellar atmosphere models and evolutionary tracks calculated for fast rotating early-type stars. If the star is a rigid rotator, its angular velocity rate is /_c   0.8, so that its rotational distortion is smaller than the one inferred from recent interferometric measurements. We then discuss the stellar surface activity using high resolution and high S/N spectroscopic observations of HeI and MgII lines, which concern a period of H line emission decline. The variations in the HeI lines are interpreted as due to non-radial pulsations. Time series analysis of variations was performed with the CLEANEST algorithm, which enabled us to detect the following frequencies: 0.49, 0.76, 1.27 and 1.72 c/d and pulsation degrees ~ (3-4) for = 0.76 c/d, ~ (2-3) for = 1.27 c/d and ~ (3-4) for = 1.72 c/d. The study of the absolute deviation of the HeI 6678Å spectral line revealed mass ejection between 1997 and 1998. We conclude that the lowest frequency found, = 0.49 c/d, is due to the circumstellar environment, which is present even at epochs of low emission in the wings of HeI 6678Å and MgII 4481Å line profiles, as well as during nearly normal aspects of the H line. This suggests that there may be matter around the star affecting some spectral regions, even though the object displays a B-normal like phase. The long-term changes of the H line emission in  Eri are studied. We pay much attention to the H line emission at the epoch of interferometric observations. The H line emission is modeled and interpreted in terms of varying structures of the circumstellar disc. We conclude that during the epoch of interferometric measurements there was enough circumstellar matter near the star to produce 2.2μm flux excess, which could account for the overestimated stellar equatorial angular diameter. From the study of the latest B->Be phase transition of  Eri we concluded that the H line emission formation regions underwent changes so that: a) the low H emission phases are characterized by extended emission zones in the circumstellar disc and a steep outward matter density decline; b) during the strong H emission phases the emitting regions are less extended and have a constant density distribution. The long-term variations of the H line in  Eri seem to have a 14-15 year cyclic B->Be phase transition. The disc formation time scales, interpreted as the periods during which the H line emission increases from zero to its maximum, agree with the viscous decretion model. On the other hand, the time required for the disc dissipation ranges from 6 to 12 years which questions the viscous disc model.

Accepted by A&A
Preprints from zorec@iap.fr