ON THE NATURE OF THE PROTOTYPE LUMINOUS BLUE VARIABLE AG CARINAE. II. WITNESSING A MASSIVE STAR EVOLVING CLOSE TO THE EDDINGTON AND BISTABILITY LIMITS

We show that the significantly different effective temperatures (T(eff)) achieved by the luminous blue variable AG Carinae during the consecutive visual minima of 1985-1990 (T(eff) similar or equal to 22,800 K) and 2000-2001 (T(eff) similar or equal to 17,000 K) place the star on different sides of the bistability limit, which occurs in line-driven stellar winds around T(eff) similar to 21,000 K. Decisive evidence is provided by huge changes in the optical depth of the Lyman continuum in the inner wind as T(eff) changes during the S Dor cycle. These changes cause different Fe ionization structures in the inner wind. The bistability mechanism is also related to the different wind parameters during visual minima: the wind terminal velocity was 2-3 times higher and the mass-loss rate roughly two times smaller in 1985-1990 than in 2000-2003. We obtain a projected rotational velocity of 220 +/- 50 km s(-1) during 1985-1990 which, combined with the high luminosity (L(star) = 1.5 x 10(6) L(circle dot)), puts AG Car extremely close to the Eddington limit modified by rotation (Omega Gamma limit): for an inclination angle of 90 degrees, Gamma(Omega) greater than or similar to 1.0 for M(circle dot) less than or similar to 60. Based on evolutionary models and mass budget, we obtain an initial mass of similar to 100 M(circle dot) and a current mass of similar to 60-70 M(circle dot) for AG Car. Therefore, AG Car is close to, if not at, the Omega Gamma limit during visual minimum. Assuming M = 70 M(circle dot), we find that Gamma(Omega) decreases from 0.93 to 0.72 as AG Car expands toward visual maximum, suggesting that the star is not above the Eddington limit during maximum phases.

Phylogeny, species limits, and biogeography of the Brazilian lizards of the genus Eurolophosaurus (Squamata : Tropiduridae) as inferred from mitochondrial DNA sequences

Phylogenetic relationships and divergence times for 10 populations of the three recognized ""species"" of Brazilian lizards of genus Eurolophosaurus were estimated from 1229 bp of cyt b, COI, 12S, and 16S rRNA mitochondrial gene segments. Eurolophosaurus is monophyletic and the basal split within the genus separates E divaricatus from a clade comprising E amathites and E nanuzae. Three populations of E divaricatus, which occurs along the western bank of Rio S (a) over tildeo Francisco, were consistently grouped together. Oil the east bank of the river, E amathites and E nanuzae from state of Bahia were recovered as the sister group of E nanuzae populations from state of Minas Gerais. The paraphyly of E nanuzae and the high divergence levels among populations of E divaricatus strongly suggest that species limits in Eurolophosaurus should be revised. Even considering an extreme evolutionary rate of 2.8% sequence divergence per million years for the four gene segments analyzed together, E. divaricatus would have separated from the two other species by at least 5.5 my ago, and E. amathites from E nanuzae populations from Bahia and Minas Gerais, respectively, by 1.5 and 3.5 my. The paleolacustrine hypothesis and changes in the course of the river potentially explain faunal divergence in the area, but divergences are much older than previously admitted. (C) 2007 Elsevier Inc. All rights reserved.

Paper surfaces and dynamical limits

It is very common in mathematics to construct surfaces by identifying the sides of a polygon together in pairs: For example, identifying opposite sides of a square yields a torus. In this article the construction is considered in the case where infinitely many pairs of segments around the boundary of the polygon are identified. The topological, metric, and complex structures of the resulting surfaces are discussed: In particular, a condition is given under which the surface has a global complex structure (i.e., is a Riemann surface). In this case, a modulus of continuity for a uniformizing map is given. The motivation for considering this construction comes from dynamical systems theory: If the modulus of continuity is uniform across a family of such constructions, each with an iteration defined on it, then it is possible to take limits in the family and hence to complete it. Such an application is briefly discussed.

LIMITS OF TILTING MODULES

We study the problem of when a direct limit of tilting modules is still a tilting module.