The VLT-FLAMES survey of massive stars: atmospheric parameters and rotational velocity distributions for B-type stars in the Magellanic Clouds

Aims.We aim to provide the atmospheric parameters and rotational velocities for a large sample of O- and early B-type stars, analysed in a homogeneous and consistent manner, for use in constraining theoretical models. Methods: Atmospheric parameters, stellar masses, and rotational velocities have been estimated for approximately 250 early B-type stars in the Large (LMC) and Small (SMC) Magellanic Clouds from high-resolution VLT-FLAMES data using the non-LTE TLUSTY model atmosphere code. This data set has been supplemented with our previous analyses of some 50 O-type stars (Mokiem et al. 2006, 2007) and 100 narrow-lined early B-type stars (Hunter et al. 2006; Trundle et al. 2007) from the same survey, providing a sample of ~400 early-type objects. Results: Comparison of the rotational velocities with evolutionary tracks suggests that the end of core hydrogen burning occurs later than currently predicted and we argue for an extension of the evolutionary tracks. We also show that the large number of the luminous blue supergiants observed in the fields are unlikely to have directly evolved from main-sequence massive O-type stars as neither their low rotational velocities nor their position on the H-R diagram are predicted. We suggest that blue loops or mass-transfer binary systems may populate the blue supergiant regime. By comparing the rotational velocity distributions of the Magellanic Cloud stars to a similar Galactic sample, we find that (at 3s confidence level) massive stars (above 8 M?) in the SMC rotate faster than those in the solar neighbourhood. However there appears to be no significant difference between the rotational velocity distributions in the Galaxy and the LMC. We find that the v sin i distributions in the SMC and LMC can modelled with an intrinsic rotational velocity distribution that is a Gaussian peaking at 175 km s-1 (SMC) and 100 km s-1 (LMC) with a 1/e half width of 150 km s-1. We find that in NGC 346 in the SMC, the 10-25 M? main-sequence stars appear to rotate faster than their higher mass counterparts. It is not expected that O-type stars spin down significantly through angular momentum loss via stellar winds at SMC metallicity, hence this could be a reflection of mass dependent birth spin rates. Recently Yoon et al. (2006) have determined rates of GRBs by modelling rapidly rotating massive star progenitors. Our measured rotational velocity distribution for the 10-25 M? stars is peaked at slightly higher velocities than they assume, supporting the idea that GRBs could come from rapid rotators with initial masses as low as 14 M? at low metallicities.

Whitney's type theorems for infinite dimensional spaces

It is proved that for any $f$ is an element of $C^k(L,R)$, where k is a natural number and L is a closed linear subspace of a nuclear Frechet space $X$, the function $f$ can be extended to a function of class $C^{k-1}$ defined on the entire space $X$. It is also proved that for any $f$ is an element of $C^k(L, R)$, where $k$ is a natural number of infinity and L is a closed linear subspace of a dual $X$ of a nuclear Frechet space, the function $f$ can be extended to a function of class $C^k$ defined on the entire space $X$. In addition, it is proved that under these conditions, the existence of a linear extension operator is equivalent to the complementability of the subspace.

Blue luminous stars in nearby galaxies: Quantitative spectral analysis of M33 B-type supergiant stars

We present the detailed spectral analysis of a sample of M33 B-type supergiant stars, aimed at the determination of their fundamental parameters and chemical composition. The analysis is based on a grid of non-LTE metal line-blanketed model atmospheres including the effects of stellar winds and spherical extension computed with the code FASTWIND. Surface abundance ratios of C, N, and O are used to discuss the chemical evolutionary status of each individual star. The comparison of observed stellar properties with theoretical predictions of massive star evolutionary models shows good agreement within the uncertainties of the analysis. The spatial distribution of the sample allows us to investigate the existence of radial abundance gradients in the disk of M33. The comparison of stellar and H II region O abundances ( based on direct determinations of the electron temperature of the nebulae) shows good agreement. Using a simple linear radial representation, the stellar oxygen abundances result in a gradient of -0.0145 +/- 0.005 dex arcmin(-1) (or -0.06 +/- 0.02 dex kpc(-1)) up to a distance equal to similar to 1.1 times the isophotal radius of the galaxy. A more complex representation cannot be completely discarded by our stellar sample. The stellar Mg and Si abundances follow the trend displayed by O abundances, although with shallower gradients. These differences in gradient slope cannot be explained at this point. The derived abundances of the three alpha-elements yield solar metallicity in the central regions of the disk of M33. A comparison with recent planetary nebula data from Magrini and coworkers indicates that the disk of M33 has not suffered from a significant O enrichment in the last 3 Gyr.

The Impact of Extension and Ecosystem Services on Smallholders’ Credit Constraint.

On formal credit markets, access to formal credit and reasonable credit terms of smallholder farmers
in rural sub-Saharan Africa is limited due to adverse selection. Financial institutions operating in
rural areas often cannot distinguish between borrowers (farmers) that are creditworthy and those that
are not, thus, allocate limited resource to agriculture to reduce credit risk. In the presence of limited business quality signaling by smallholder farmers, financial institutions shall demand for collateral and/or offer unfavorable contract terms. Moreover, agricultural productivity of rural sub-Saharan
Africa, dominated by subsistence or small-scale farmers, is also negatively impacted by the adverse
effect of climate change. A strategy that may make the farming practices of smallholder farmer’s
climate resilient and profitable may also improve smallholder farmer's access to formal credit. This
study investigates to what extent participating in ecosystem and extension services (EES) programs
signals business quality of smallholders, thus granting them credit accessibility. We collected data
on 210 smallholder farmers in 2013, comprising farmers that receive payments for ecosystem
services (PES) and farm management training from the International Small Group Tree Planting
Program (TIST) Kenya to test the aforementioned theory empirically. We use game theory,
particularly a screening and sorting model, to illustrate the prospects for farmers with EES to access
formal credit and to improve their credit terms given that they receive PES and banking services
training. Furthermore, the PES’ long term duration (10 – 30 years) generates stable cash-flow which
may be perceived as collateral substitute. Results suggest that smallholder farmers in the TIST
program were less likely to be credit constraint compared to non-TIST farmers. Distance to market,
education, livestock and farm income are factors that determine access to credit from microfinance
institutions in rural Kenya. Amongst farmers that have obtained loans, those keeping business records
enjoy more favorable formal credit conditions. These farmers were observed to pay ca. 5 percent less
interest rate in microfinance charges. For TIST farmers, this type of farm management practices may
be attributed to the banking services and other training they receive within the program. While the
availability of classical collateral (farmlands) and PES may reduce interest rate, the latter was found
to be statistically insignificant. This research underlines the importance of an effective extension
services in rural areas of developing countries and the need to improve gains from conservation
agriculture and ensuing PES. The benefits associated with EES and PES may encompass agricultural
financing.