A monoidal algebraic model for rational SO(2)-spectra

The category of rational SO(2)--equivariant spectra admits an algebraic model. That is, there is an abelian category A(SO(2)) whose derived category is equivalent to the homotopy category of rational$SO(2)--equivariant spectra. An important question is: does this algebraic model capture the smash product of spectra? The category A(SO(2)) is known as Greenlees' standard model, it is an abelian category that has no projective objects and is constructed from modules over a non--Noetherian ring. As a consequence, the standard techniques for constructing a monoidal model structure cannot be applied. In this paper a monoidal model structure on A(SO(2)) is constructed and the derived tensor product on the homotopy category is shown to be compatible with the smash product of spectra. The method used is related to techniques developed by the author in earlier joint work with Roitzheim. That work constructed a monoidal model structure on Franke's exotic model for the K_(p)--local stable homotopy category. A monoidal Quillen equivalence to a simpler monoidal model category that has explicit generating sets is also given. Having monoidal model structures on the two categories removes a serious obstruction to constructing a series of monoidal Quillen equivalences between the algebraic model and rational SO(2)--equivariant spectra.

The VLT-FLAMES Tarantula Survey: XXIII. Two massive double-lined binaries in 30 Doradus

Aims: We investigate the characteristics of two newly discovered short-period, double-lined, massive binary systems in the Large Magellanic Cloud, VFTS 450 (O9.7 II-Ib + O7::) and VFTS 652 (B1 Ib + O9: III:). 

Methods: We perform model-atmosphere analyses to characterise the photospheric properties of both members of each binary (denoting the "primary" as the spectroscopically more conspicuous component). Radial velocities and optical photometry are used to estimate the binary-system parameters. 

Results: We estimate T_eff = 27 kK, log g = 2.9 (cgs) for the VFTS 450 primary spectrum (34 kK, 3.6: for the secondary spectrum); and T_eff = 22 kK, log g = 2.8 for the VFTS 652 primary spectrum (35 kK, 3.7: for the secondary spectrum). Both primaries show surface nitrogen enrichments (of more than 1 dex for VFTS 652), and probable moderate oxygen depletions relative to reference LMC abundances. We determine orbital periods of 6.89 d and 8.59 d for VFTS 450 and VFTS 652, respectively, and argue that the primaries must be close to filling their Roche lobes. Supposing this to be the case, we estimate component masses in the range ∼20-50 M_⊙. 

Conclusions: The secondary spectra are associated with the more massive components, suggesting that both systems are high-mass analogues of classical Algol systems, undergoing case-A mass transfer. Difficulties in reconciling the spectroscopic analyses with the light-curves and with evolutionary considerations suggest that the secondary spectra are contaminated by (or arise in) accretion disks.