On the impossibility of representing infinite utility streams

We show that, independently of the topology chosen on the set of all infinity utility streams, there is no Social Welfare Function preserving the von Weizsäcker’s overtaking criterion. With our proof we extend the impossibility result of Basu and Mitra

Rotational modulation of the linear polarimetric variability of the cool dwarf TVLM 513−-46546

Aims: We aimed to monitor the optical linear polarimetric signal of the magnetized, rapidly rotating M8.5 dwarf TVLM 513$-$46546. Methods: $R$- and $I$-band linear polarimetry images were collected with the ALFOSC instrument of the 2.56-m Nordic Optical Telescope on two consecutive nights covering about 0.5 and 4 rotation cycles in the $R$ and $I$ filters, respectively. We also obtained simultaneous intensity curves by means of differential photometry. The typical precision of the data is $\pm$0.46\% ($R$), $\pm$0.35\% ($I$) in the linear polarization degree and $\pm$9 mmag ($R$), $\pm$1.6 mmag ($I$) in the differential intensity curves. Results: Strong and variable linear polarization is detected in the $R$ and $I$ filters, with values of maximum polarization ($p^{*}$ = 1.30$\pm$0.35 \%) similar for both bands. The intensity and the polarimetric curves present a sinusoid-like pattern with a periodicity of $\sim$1.98 h, which we ascribe to structures in TVLM 513$-$46's surface synchronized with rotation. We found that the peaks of the intensity and polarimetric curves occur with a phase difference of 0.18$\pm$0.01, and that the maximum of the linear polarization happens nearly half a period (0.59$\pm$0.03) after the radio pulse. We discussed different scenarios to account for the observed properties of the light curves.Comment: Accepted for publication in Astronomy and Astrophysic

Simultaneous optical and near-infrared linear spectropolarimetry of the earthshine

Aims: We aim to extend our current observational understanding of the integrated planet Earth spectropolarimetry from the optical to the near-infrared wavelengths. Major biomarkers like O$_{\rm 2}$ and water vapor are strong flux absorbents in the Earth atmosphere and some linear polarization of the reflected stellar light is expected to occur at these wavelengths. Methods: Simultaneous optical ($0.4-0.9$ $\mu$m) and near-infrared ($0.9-2.3$ $\mu$m) linear spectropolarimetric data of the earthshine were acquired by observing the nightside of the waxing Moon. The data have sufficient spectral resolution (2.51 nm in the optical, and 1.83 and 2.91 nm in the near-infrared) to resolve major molecular species present in the Earth atmosphere. Results: We find the highest values of linear polarization ($\ge 10\%$) at the bluest wavelengths, which agrees with the literature. Linear polarization intensity steadily decreases towards red wavelengths reaching a nearly flat value beyond $\sim$0.8 $\mu$m. In the near-infrared, we measured a polarization degree of $\sim4.5 \%$ for the continuum. We report the detection of molecular features due to O$_{2}$ at $0.760, 1.25 \mu$m and H$_{2}$O at 0.653$-$0.725 $\mu$m, 0.780$-$0.825 $\mu$m, 0.93 and 1.12 $\mu$m in the spectropolarimetric data; most of them show high linear polarimetry degrees above the continuum. In particular, the broad H$_{2}$O 1.12 $\mu$m band displays a polarimetric intensity as high as that of the blue optical. These features may become a powerful tool to characterize Earth-like planets in polarized light.Comment: 4 pages, 3 figures. Accepted for publication as Letter in Astronomy and Astrophysics on 23/01/201

On the impossibility of representing infinite utility streams

We show that, independently of the topology chosen on the set of all infinity utility streams, there is no Social Welfare Function preserving the von Weizsäcker’s overtaking criterion. With our proof we extend the impossibility result of Basu and Mitra.

Membership and Multiplicity among Very Low-Mass Stars and Brown Dwarfs in the Pleiades Cluster

We present near-infrared photometry and optical spectroscopy of very low-mass stars and brown dwarf candidates in the Pleiades open cluster. The membership status of these objects is assessed. Eight objects out of 45 appear to be non-members. A search for companions among 34 very low-mass Pleiades members (M$\le$0.09 M$_\odot$) in high-spatial resolution images obtained with the Hubble Space Telescope and the adaptive optics system of the Canada-France-Hawaii telescope produced no resolved binaries with separations larger than 0.2 arcsec (a ~ 27 AU; P ~ 444 years). Nevertheless, we find evidence for a binary sequence in the color-magnitude diagrams, in agreement with the results of Steele & Jameson (1995) for higher mass stars. We compare the multiplicity statistics of the Pleiades very low-mass stars and brown dwarfs with that of G and K-type main sequence stars in the solar neighborhood (Duquennoy & Mayor 1991). We find that there is some evidence for a deficiency of wide binary systems (separation >27 AU) among the Pleiades very low-mass members. We briefly discuss how this result can fit with current scenarios of brown dwarf formation. We correct the Pleiades substellar mass function for the contamination of cluster non-members found in this work. We find a contamination level of 33% among the brown dwarf candidates identified by Bouvier et al. (1998). Assuming a power law IMF across the substellar boundary, we find a slope dN/dM ~ M^{-0.53}, implying that the number of objects per mass bin is still rising but the contribution to the total mass of the cluster is declining in the brown dwarf regime.Comment: to be published in The Astrophysical Journa

The substellar mass function in sigma Orionis. II. Optical, near-infrared and IRAC/Spitzer photometry of young cluster brown dwarfs and planetary-mass objects

We investigate the mass function in the substellar domain down to a few Jupiter masses in the young sigma Orionis open cluster (3+/-2 Ma, d = 360^+70_-60 pc). We have performed a deep IJ-band search, covering an area of 790 arcmin^2 close to the cluster centre. This survey was complemented with an infrared follow-up in the HKs- and Spitzer 3.6-8.0 mum-bands. Using colour-magnitude diagrams, we have selected 49 candidate cluster members in the magnitude interval 16.1 mag < I < 23.0 mag. Accounting for flux excesses at 8.0 mum and previously known spectral features of youth, 30 objects are bona fide cluster members. Four are first identified from our optical-near infrared data. Eleven have most probable masses below the deuterium burning limit and are classified as planetary-mass object candidates. The slope of the substellar mass spectrum (Delta N / Delta M = a M^-alpha) in the mass interval 0.11 Msol M < 0.006 Msol is alpha = +0.6+/-0.2. Any opacity mass-limit, if these objects form via fragmentation, may lie below 0.006 Msol. The frequency of sigma Orionis brown dwarfs with circumsubstellar discs is 47+/-15 %. The continuity in the mass function and in the frequency of discs suggests that very low-mass stars and substellar objects, even below the deuterium-burning mass limit, may share the same formation mechanism.Comment: Accepted for publication in A&A (12/04/2007). It has not been edited for language ye

VLT X-shooter spectroscopy of the nearest brown dwarf binary

The aim of the project is to characterise both components of the nearest brown dwarf sytem to the Sun, WISE J104915.57-531906.1 (=Luhman16AB) at optical and near-infrared wavelengths. We obtained high signal-to-noise intermediate-resolution (R~6000-11000) optical (600-1000 nm) and near-infrared (1000-2480nm) spectra of each component of Luhman16AB, the closest brown dwarf binary to the Sun, with the X-Shooter instrument on the Very Large Telescope. We classify the primary and secondary of the Luhman16 system as L6-L7.5 and T0+/-1, respectively, in agreement with previous measurements published in the literature. We present measurements of the lithium pseudo-equivalent widths, which appears of similar strength on both components (8.2+/-1.0 Angstroms and 8.4+/-1.5 Angstroms for the L and T components, respectively). The presence of lithium (Lithium 7) in both components imply masses below 0.06 Msun while comparison with models suggests lower limits of 0.04 Msun. The detection of lithium in the T component is the first of its kind. Similarly, we assess the strength of other alkali lines (e.g. pseudo-equivalent widths of 6-7 Angstroms for RbI and 4-7 Angstroms for CsI) present in the optical and near-infrared regions and compare with estimates for L and T dwarfs. We also derive effective temperatures and luminosities of each component of the binary: -4.66+/-0.08 dex and 1305(+180)(-135) for the L dwarf and -4.68+/-0.13 dex and 1320(+185)(-135) for the T dwarf, respectively. Using our radial velocity determinations, the binary does not appear to belong to any of the well-known moving group. Our preliminary theoretical analysis of the optical and J-band spectra indicates that the L- and T-type spectra can be reproduced with a single temperature and gravity but different relative chemical abundances which impact strongly the spectral energy distribution of L/T transition objects.Comment: 12 pages, 9 figure, 3 tables, accepted to A&

The Brown Dwarf Mass Function from Pixel Microlensing

We argue that gravitational microlensing is a feasible technique for measuring the mass function of brown dwarf stars in distant galaxies. Microlensing surveys of the bulge of M31, and of M87 in the Virgo cluster, may provide enough events to differentiate the behaviour of the mass function of lenses below the hydrogen burning limit (though we find that M87 is a more favourable target). Such objects may provide a significant supply of baryonic dark matter, an interesting possibility for the study of galactic dynamics. Furthermore, these systems have different metallicities than the solar neighbourhood, which may affect the mass function. These considerations are relevant in the context of star formation studies.Comment: 5 pages, 7 figures, using mn.sty, revised versio