Global survey of star clusters in the Milky Way I. The pipeline and fundamental parameters in the second quadrant

Aims: On the basis of the PPMXL star catalogue we performed a survey of star clusters in the second quadrant of the Milky Way. Methods: From the PPMXL catalogue of positions and proper motions we took the subset of stars with near-infrared photometry from 2MASS and added the remaining 2MASS stars without proper motions (called 2MAst, i.e. 2MASS with astrometry). We developed a data-processing pipeline including interactive human control of a standardised set of multi-dimensional diagrams to determine kinematic and photometric membership probabilities for stars in a cluster region. The pipeline simultaneously produced the astrophysical parameters of a cluster. From literature we compiled a target list of presently known open and globular clusters, cluster candidates, associations, and moving groups. From established member stars we derived spatial parameters (coordinates of centres and radii of the main morphological parts of clusters) and cluster kinematics (average proper motions and sometimes radial velocities). For distance, reddening, and age determination we used specific sets of theoretical isochrones. Tidal parameters were obtained by a fit of three-parameter King profiles to the observed density distributions of members. Results: We investigated all 871 objects in the 2nd Galactic quadrant, of which we successfully treated 642 open clusters, 2 globular clusters, and 8 stellar associations. The remaining 219 objects (24%) were recognised by us to be nonexistent clusters, duplicate entries, or clusters too faint for 2MAst. We found that our sample is complete in the 2nd quadrant up to a distance of 2 kpc, where the average surface density is 94 clusters per kpc$^{2}$. Compared with literature values we found good agreement in spatial and kinematic data, as well as for optical distances and reddening. Small, but systematic offsets were detected in the age determination.Comment: published in Astronomy and Astrophysics, 10 pages, 7 figures (plus 3 pages of appendices incl. 2 more figures), catalogues will be available at the CDS, all the machine-readable online data described in appendices A, B, and C are also available at: http://www.aip.de/People/rdscholz/kharchenko_etal_2012

Galactic Rotation Parameters from Data on Open Star Clusters

Currently available data on the field of velocities Vr, Vl, Vb for open star clusters are used to perform a kinematic analysis of various samples that differ by heliocentric distance, age, and membership in individual structures (the Orion, Carina--Sagittarius, and Perseus arms). Based on 375 clusters located within 5 kpc of the Sun with ages up to 1 Gyr, we have determined the Galactic rotation parameters Wo =-26.0+-0.3 km/s/kpc, W'o = 4.18+-0.17 km/s/kpc^2, W''o=-0.45+-0.06 km/s/kpc^3, the system contraction parameter K = -2.4+-0.1 km/s/kpc, and the parameters of the kinematic center Ro =7.4+-0.3 kpc and lo = 0+-1 degrees. The Galactocentric distance Ro in the model used has been found to depend significantly on the sample age. Thus, for example, it is 9.5+-0.7 kpc and 5.6+-0.3 kpc for the samples of young (50 Myr) clusters, respectively. Our study of the kinematics of young open star clusters in various spiral arms has shown that the kinematic parameters are similar to the parameters obtained from the entire sample for the Carina-Sagittarius and Perseus arms and differ significantly from them for the Orion arm. The contraction effect is shown to be typical of star clusters with various ages. It is most pronounced for clusters with a mean age of 100 Myr, with the contraction velocity being Kr = -4.3+-1.0 km/s.Comment: 14 pages, 4 figures, 2 table

Identifying birth places of young isolated neutron stars

Young isolated radio-quiet neutron stars are still hot enough to be detectable at X-ray and optical wavelengths due to their thermal emission and can hence probe cooling curves. An identification of their birth sites can constrain their age. For that reason we try to identify the parent associations for four of the so-called Magnificent Seven neutron stars for which proper motion and distance estimates are available. We are tracing back in time each neutron star and possible birth association centre to find close encounters. The associated time of the encounter expresses the kinematic age of the neutron star which can be compared to its characteristic spin-down age. Owing to observational uncertainties in the input data, we use Monte-Carlo simulations and evaluate the outcome of our calculations statistically. RX J1856.5-3754 most probably originated from the Upper Scorpius association about 0.3 Myr ago. RX 0720.4-3125 was either born in the young local association TWA about 0.4 Myr ago or in Tr 10 0.5 Myr in the past. Also RX J1605.3+3249 and RBS 1223 seem to come from a nearby young association such as the Sco-Cen complex or the extended Corona-Australis association. For RBS 1223 also a birth in Sct OB2 is possible. We also give constraints on the observables as well as on the radial velocity of the neutron star. Given the birth association, its age and the flight time of the neutron star, we estimate the mass of the progenitor star. Some of the potential supernovae were located very nearby (<100pc) and thus should have contributed to the 10Be and 60Fe material found in the Earth's crust. In addition we reinvestigate the previously suggested neutron star/ runaway pair PSR B1929+10/ zeta Ophiuchi and conclude that it is very likely that both objects were ejected during the same supernova event.Comment: 14 figures, 13 table

Zeta-values of arithmetic schemes at negative integers and Weil-étale cohomology

This work is dedicated to interpreting in cohomological terms the special values of zeta functions of arithmetic schemes. Baptiste Morin and Matthias Flach gave a construction of Weil-étale cohomology using Bloch's cycle complexes and stated a precise conjecture for the special values of proper regular arithmetic schemes at any integer argument s=n. The goal of this thesis is to generalize their constructions to arbitrary arithmetic schemes (possibly singular or non-proper), while restricting to the case n We prove that the resulting conjecture is compatible with the decomposition of an arbitrary scheme into an open subscheme and its closed complement. We also show that this conjecture for an arithmetic scheme X at s=n is equivalent to the conjecture for A^r_X at s=n-r, for any r >= 0. It follows that, taking as an input the schemes for which the conjecture is known, it is possible to construct new schemes, possibly singular or non-proper, for which the conjecture holds as well. This is the main unconditional outcome of the machinery developed in this thesis. </table

Zeta-values of arithmetic schemes at negative integers and Weil-étale cohomology

This work is dedicated to interpreting in cohomological terms the special values of zeta functions of arithmetic schemes. Baptiste Morin and Matthias Flach gave a construction of Weil-étale cohomology using Bloch's cycle complexes and stated a precise conjecture for the special values of proper regular arithmetic schemes at any integer argument s=n. The goal of this thesis is to generalize their constructions to arbitrary arithmetic schemes (possibly singular or non-proper), while restricting to the case n We prove that the resulting conjecture is compatible with the decomposition of an arbitrary scheme into an open subscheme and its closed complement. We also show that this conjecture for an arithmetic scheme X at s=n is equivalent to the conjecture for A^r_X at s=n-r, for any r >= 0. It follows that, taking as an input the schemes for which the conjecture is known, it is possible to construct new schemes, possibly singular or non-proper, for which the conjecture holds as well. This is the main unconditional outcome of the machinery developed in this thesis. ALGANT DOC ProgramNumber theory, Algebra and Geometr

Hyman Minsky's financial instability hypothesis and the Greek debt crisis

This article attempts to analyze the current debt crisis in Greece based on the financial instability hypothesis developed by Hyman Minsky. This article shows that the hypothesis provides an understanding of how an economy endogenously becomes “financially fragile” and thus prone to crises. The authors analyze how public and private sector behavior in the Greek economy led to the country's debt crisis. In particular, based on a sample of 36 Greek companies, the authors show that between 2001 and 2014, the majority of those companies had switched to fragile financial structures. Special attention is devoted to the negative consequences of applying the neoclassical doctrine of “austerity measures” in Greece as the principal “anti-crisis” concept of mainstream economic science

Rational points on analytic varieties

These are expanded notes of the mini-courses on Pila's work that Yuri Bilu gave in Basel in April 2011, Yaroslavl in August 2011 and Chennai in February 2012. The topics covered include the Bombieri-Pila theorem, its extensions and applications to some prominent conjectures (Manin-Mumford, Andr\'e-Oort).Comment: Lecture notes; accepted for publication at the "EMS Surveys in Mathematical Sciences