Moduli Spaces and Formal Operads

Let overline{M}_{g,n} be the moduli space of stable algebraic curves of genus g with n marked points. With the operations which relate the different moduli spaces identifying marked points, the family (overline{M}_{g,n})_{g,n} is a modular operad of projective smooth Deligne-Mumford stacks, overline{M}. In this paper we prove that the modular operad of singular chains C_*(overline{M};Q) is formal; so it is weakly equivalent to the modular operad of its homology H_*(overline{M};Q). As a consequence, the "up to homotopy" algebras of these two operads are the same. To obtain this result we prove a formality theorem for operads analogous to Deligne-Griffiths-Morgan-Sullivan formality theorem, the existence of minimal models of modular operads, and a characterization of formality for operads which shows that formality is independent of the ground field.Comment: 36 pages (v3: some typographical corrections

The first confirmation of V-type asteroids among the Mars crosser population

The Mars crossing region constitutes a path to deliver asteroids from the Inner Main Belt to the Earth crossing space. While both the Inner Main Belt and the population of Earth crossing asteroids contains a significant fraction of asteroids belonging to the V taxonomic class, only two of such V-type asteroids has been detected in the Mars crossing region up to now. In this work, we searched for asteroids belonging to the V class among the population of Mars crossing asteroids, in order to support alternative paths to the delivery of this bodies into the Earth crossing region. We selected 18 candidate V-type asteroids in the Mars crossing region using observations contained in the Sloan Digital Sky Survey Moving Objects Catalog. Then, we observed 4 of these candidates to take their visible spectra using the Southern Astrophysical Research Telescope (SOAR). We also performed the numerical simulation of the orbital evolution of the observed asteroids. We confirmed that 3 of the observed asteroids belong to the V class, and one of these may follow a path that drives it to an Earth collision in some tens of million years

Taxonomy of asteroid families among the Jupiter Trojans: Comparison between spectroscopic data and the Sloan Digital Sky Survey colors

We present a comparative analysis of the spectral slope and color distributions of Jupiter Trojans, with particular attention to asteroid families. We use a sample of data from the Moving Object Catalogue of the Sloan Digital Sky Survey, together with spectra obtained from several surveys. A first sample of 349 observations, corresponding to 250 Trojan asteroids, were extracted from the Sloan Digital Sky Survey, and we also extracted from the literature a second sample of 91 spectra, corresponding to 71 Trojans. The spectral slopes were computed by means of a least-squares fit to a straight line of the fluxes obtained from the Sloan observations in the first sample, and of the rebinned spectra in the second sample. In both cases the reflectance fluxes/spectra were renormalized to 1 at 6230 $\textrm{\AA}$. We found that the distribution of spectral slopes among Trojan asteroids shows a bimodality. About 2/3 of the objects have reddish slopes compatible with D-type asteroids, while the remaining bodies show less reddish colors compatible with the P-type and C-type classifications. The members of asteroid families also show a bimodal distribution with a very slight predominance of D-type asteroids, but the background is clearly dominated by the D-types. The L4 and L5 swarms show different distributions of spectral slopes, and bimodality is only observed in L4. These differences can be attributed to the asteroid families since the backgraound asteroids show the same slope distribtuions in both swarms. The analysis of individual families indicates that the families in L5 are taxonomically homogeneous, but in L4 they show a mixture of taxonomic types. We discuss a few scenarios that might help to interpret these results.Comment: 20 pages, 15 figures, 2 table

Chemical abundances and kinematics of barium stars

In this paper we present an homogeneous analysis of photospheric abundances based on high-resolution spectroscopy of a sample of 182 barium stars and candidates. We determined atmospheric parameters, spectroscopic distances, stellar masses, ages, luminosities and scale height, radial velocities, abundances of the Na, Al, $alpha$-elements, iron-peak elements, and s-process elements Y, Zr, La, Ce, and Nd. We employed the local-thermodynamic-equilibrium model atmospheres of Kurucz and the spectral analysis code {\sc moog}. We found that the metallicities, the temperatures and the surface gravities for barium stars can not be represented by a single gaussian distribution. The abundances of $alpha$-elements and iron peak elements are similar to those of field giants with the same metallicity. Sodium presents some degree of enrichment in more evolved stars that could be attributed to the NeNa cycle. As expected, the barium stars show overabundance of the elements created by the s-process. By measuring the mean heavy-element abundance pattern as given by the ratio [s/Fe], we found that the barium stars present several degrees of enrichment. We also obtained the [hs/ls] ratio by measuring the photospheric abundances of the Ba-peak and the Zr-peak elements. Our results indicated that the [s/Fe] and the [hs/ls] ratios are strongly anti-correlated with the metallicity. Our kinematical analysis showed that 90% of the barium stars belong to the thin disk population. Based on their luminosities, none of the barium stars are luminous enough to be an AGB star, nor to become self-enriched in the s-process elements. Finally, we determined that the barium stars also follow an age-metallicity relation.Comment: 30 pages, 26 figures, 18 tables, accepted for publication in MNRA

Dendroecology of Aspidosperma polyneuron Müll. Arg. (Apocynaceae) trees in two different geomorphological growth conditions in Atlantic forests, Paraná State, Brazil.

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