(In)finite extent of stationary perfect fluids in Newtonian theory

For stationary, barotropic fluids in Newtonian gravity we give simple criteria on the equation of state and the "law of motion" which guarantee finite or infinite extent of the fluid region (providing a priori estimates for the corresponding stationary Newton-Euler system). Under more restrictive conditions, we can also exclude the presence of "hollow" configurations. Our main result, which does not assume axial symmetry, uses the virial theorem as the key ingredient and generalises a known result in the static case. In the axially symmetric case stronger results are obtained and examples are discussed.Comment: Corrections according to the version accepted by Ann. Henri Poincar

Prehistory of Transit Searches

Nowadays the more powerful method to detect extrasolar planets is the transit method. We review the planet transits which were anticipated, searched, and the first ones which were observed all through history. Indeed transits of planets in front of their star were first investigated and studied in the solar system. The first observations of sunspots were sometimes mistaken for transits of unknown planets. The first scientific observation and study of a transit in the solar system was the observation of Mercury transit by Pierre Gassendi in 1631. Because observations of Venus transits could give a way to determine the distance Sun-Earth, transits of Venus were overwhelmingly observed. Some objects which actually do not exist were searched by their hypothetical transits on the Sun, as some examples a Venus satellite and an infra-mercurial planet. We evoke the possibly first use of the hypothesis of an exoplanet transit to explain some periodic variations of the luminosity of a star, namely the star Algol, during the eighteen century. Then we review the predictions of detection of exoplanets by their transits, those predictions being sometimes ancient, and made by astronomers as well as popular science writers. However, these very interesting predictions were never published in peer-reviewed journals specialized in astronomical discoveries and results. A possible transit of the planet beta Pic b was observed in 1981. Shall we see another transit expected for the same planet during 2018? Today, some studies of transits which are connected to hypothetical extraterrestrial civilisations are published in astronomical refereed journals. Some studies which would be classified not long ago as science fiction are now considered as scientific ones.Comment: Submiited to Handbook of Exoplanets (Springer

Lines of Descent: Kuhn and Beyond

yesThomas S. Kuhn is famous both for his work on the Copernican Revolution and his ‘paradigm’ view of scientific revolutions. But Kuhn later abandoned the notion of paradigm (and related notions) in favour of a more ‘evolutionary’ view of the history of science. Kuhn’s position therefore moved closer to ‘continuity’ models of scientific progress, for instance ‘chain-of-reasoning’ models, originally championed by D. Shapere. The purpose of this paper is to contribute to the debate around Kuhn’s new ‘developmental’ view and to evaluate these competing models with reference to some major innovations in the history of cosmology, from Copernicanism to modern cosmology. This evaluation is made possible through some unexpected overlap between Kuhn’s earlier discontinuity model and various versions of the later continuity models. It is the thesis of this paper that the ‘chain-of-reasoning’ model accounts better for the cosmological evidence than both Kuhn’s early paradigm model and his later developmental view of the history of science

Drivers of plant diversity in Bulgarian dry grasslands vary across spatial scales and functional-taxonomic groups

Questions: Studying dry grasslands in a previously unexplored region, we asked: (a) which environmental factors drive the diversity patterns in vegetation; (b) are taxonomic groups (vascular plants, bryophytes, lichens) and functional vascular plant groups differently affected; and (c) how is fine-grain beta diversity affected by environmental drivers? Location: Northwestern and Central Bulgaria. Methods: We sampled environmental data and vascular plant, terricolous bryophyte and lichen species in 97 10-m2 plots and 15 nested-plot series with seven grain sizes (0.0001–100 m2) of ten grassland sites within the two regions. We used species richness as measure of alpha-diversity and the z-value of the power-law species–area relationship as measure of beta-diversity. We analysed effects of landscape, topographic, soil and land-use variables on the species richness of the different taxonomic and functional groups. We applied generalised linear models (GLMs) or, in the presence of spatial autocorrelation, generalised linear mixed-effect models (GLMMs) in a multi-model inference framework. Results: The main factors affecting total and vascular plant species richness in 10-m2 plots were soil pH (unimodal) and inclination (negative). Species richness of bryophytes was positively affected by rock cover, sand proportion and negatively by inclination. Inclination and litter cover were also negative predictors of lichen species richness. Elevation negatively affected phanerophyte and therophyte richness, but positively that of cryptophytes. A major part of unexplained variance in species richness was associated with the grassland site. The z-values for total richness showed a positive relationship with elevation and inclination. Conclusions: Environmental factors shaping richness patterns strongly differed among taxonomic groups, functional vascular plant groups and spatial scales. The disparities between our and previous findings suggest that many drivers of biodiversity cannot be generalised but rather depend on the regional context. The large unexplained variance at the site level calls for considering more site-related factors such as land-use history

An Isolated Stellar-Mass Black Hole Detected Through Astrometric Microlensing

We report the first unambiguous detection and mass measurement of an isolated stellar-mass black hole (BH). We used the Hubble Space Telescope (HST) to carry out precise astrometry of the source star of the long-duration (t_E ~ 270 days), high-magnification microlensing event MOA-2011-BLG-191/OGLE-2011-BLG-0462, in the direction of the Galactic bulge. HST imaging, conducted at eight epochs over an interval of six years, reveals a clear relativistic astrometric deflection of the background star's apparent position. Ground-based photometry shows a parallactic signature of the effect of the Earth's motion on the microlensing light curve. Combining the HST astrometry with the ground-based light curve and the derived parallax, we obtain a lens mass of 7.1 +/- 1.3 M_Sun and a distance of 1.58 +/- 0.18 kpc. We show that the lens emits no detectable light, which, along with having a mass higher than is possible for a white dwarf or neutron star, confirms its BH nature. Our analysis also provides an absolute proper motion for the BH. The proper motion is offset from the mean motion of Galactic-disk stars at similar distances by an amount corresponding to a transverse space velocity of ~45 km/s, suggesting that the BH received a modest natal 'kick' from its supernova explosion. Previous mass determinations for stellar-mass BHs have come from radial-velocity measurements of Galactic X-ray binaries, and from gravitational radiation emitted by merging BHs in binary systems in external galaxies. Our mass measurement is the first ever for an isolated stellar-mass BH using any technique