Evolution of Collisionally Merged Massive Stars

We investigate the evolution of collisionally merged stars with mass of ~100 Msun which might be formed in dense star clusters. We assumed that massive stars with several tens Msun collide typically after ~1Myr of the formation of the cluster and performed hydrodynamical simulations of several collision events. Our simulations show that after the collisions, merged stars have extended envelopes and their radii are larger than those in the thermal equilibrium states and that their interiors are He-rich because of the stellar evolution of the progenitor stars. We also found that if the mass-ratio of merging stars is far from unity, the interior of the merger product is not well mixed and the elemental abundance is not homogeneous. We then followed the evolution of these collision products by a one dimensional stellar evolution code. After an initial contraction on the Kelvin-Helmholtz (thermal adjustment) timescale (~10^{3-4} yr), the evolution of the merged stars traces that of single homogeneous stars with corresponding masses and abundances, while the initial contraction phase shows variations which depend on the mass ratio of the merged stars. We infer that, once runaway collisions have set in, subsequent collisions of the merged stars take place before mass loss by stellar winds becomes significant. Hence, stellar mass loss does not inhibit the formation of massive stars with mass of ~1000Msun

Relations between some invariants of algebraic varieties in positive characteristic

We discuss relations between certain invariants of varieties in positive characteristic, like the a-number and the height of the Artin-Mazur formal group. We calculate the a-number for Fermat surfacesComment: 13 page

How Do Black Holes Predict the Sign of the Fourier Coefficients of Siegel Modular Forms?

Single centered supersymmetric black holes in four dimensions have spherically symmetric horizon and hence carry zero angular momentum. This leads to a specific sign of the helicity trace index associated with these black holes. Since the latter are given by the Fourier expansion coefficients of appropriate meromorphic modular forms of Sp(2,Z) or its subgroup, we are led to a specific prediction for the signs of a subset of these Fourier coefficients which represent contributions from single centered black holes only. We explicitly test these predictions for the modular forms which compute the index of quarter BPS black holes in heterotic string theory on T^6, as well as in Z_N CHL models for N=2,3,5,7.Comment: LaTeX file, 17 pages, 1 figur

The Top Ten solar analogs in the ELODIE library

Several solar analogs have been identified in the library of high resolution stellar spectra taken with the echelle spectrograph ELODIE. A purely differential method has been used, based on the chi2 comparison of a large number of G dwarf spectra to 8 spectra of the Sun, taken on the Moon and Ceres. HD 146233 keeps its status of closest ever solar twin (Porto de Mello & da Silva 1997). Some other spectroscopic analogs have never been studied before, while the two planet-host stars HD095128 and HD186427 are also part of the selection. The fundamental parameters found in the literature for these stars show a surprising dispersion, partly due to the uncertainties which affect them. We discuss the advantages and drawbacks of photometric and spectroscopic methods to search for solar analogs and conclude that they have to be used jointly to find real solar twins.Comment: 12 pages, accepted in A&

On the Quantum Invariant for the Spherical Seifert Manifold

We study the Witten--Reshetikhin--Turaev SU(2) invariant for the Seifert manifold $S^3/\Gamma$ where $\Gamma$ is a finite subgroup of SU(2). We show that the WRT invariants can be written in terms of the Eichler integral of the modular forms with half-integral weight, and we give an exact asymptotic expansion of the invariants by use of the nearly modular property of the Eichler integral. We further discuss that those modular forms have a direct connection with the polyhedral group by showing that the invariant polynomials of modular forms satisfy the polyhedral equations associated to $\Gamma$.Comment: 36 page

Analysis of Peculiarities of the Stellar Velocity Field in the Solar Neighborhood

Based on a new version of the Hipparcos catalogue and an updated Geneva-Copenhagen survey of F and G dwarfs, we analyze the space velocity field of about 17000 single stars in the solar neighborhood. The main known clumps, streams, and branches (Pleiades, Hyades, Sirius, Coma Berenices, Hercules, Wolf 630-alpha Ceti, and Arcturus) have been identified using various approaches. The evolution of the space velocity field for F and G dwarfs has been traced as a function of the stellar age. We have managed to confirm the existence of the recently discovered KFR08 stream. We have found 19 Hipparcos stars, candidates for membership in the KFR08 stream, and obtained an isochrone age estimate for the stream, 13 Gyr. The mean stellar ages of the Wolf 630-alpha Ceti and Hercules streams are shown to be comparable, 4--6 Gyr. No significant differences in the metallicities of stars belonging to these streams have been found. This is an argument for the hypothesis that these streams owe their origin to a common mechanism.Comment: 23 pages, 9 figure

Finding benchmark brown dwarfs to probe the IMF as a function of time

Using a simulated disk brown dwarf (BD) population, we find that new large area infrared surveys are expected to identify enough BDs covering wide enough mass--age ranges to potentially measure the mass function down to ~0.03Mo, and the BD formation history out to 10 Gyr, at a level capable of establishing if BD formation follows star formation. We suggest these capabilities are best realised by spectroscopic calibration of BD properties (Teff, g and [M/H]) which, when combined with a measured luminosity and an evolutionary model can give BD mass and age relatively independent of BD atmosphere models. Such calibration requires an empirical understanding of how BD spectra are affected by variations in these properties, and thus the identification and study of "benchmark BDs" whose age and composition can be established independently. We identify the best sources of benchmark BDs as young open cluster members, moving group members, and wide (>1000AU) BD companions to both subgiant stars and high mass white dwarfs (WDs). We have used 2MASS to measure a wide L dwarf companion fraction of 2.7(+0.7/-0.5)%, which equates to a BD companion fraction of 34(+9/-6)% for an alpha~1 companion mass function. Using this value we simulate populations of wide BD binaries, and estimate that 80(+21/-14) subgiant--BD binaries, and 50(+13/-10) benchmark WD--BD binaries could be identified using current and new facilities. The WD--BD binaries should all be identifiable using the Large Area Survey component of UKIDSS combined with Sloan. Discovery of the subgiant--BD binaries will require a NIR imaging campaign around a large (~900) sample of Hipparcos subgiants. If identified, spectral studies of these benchmark brown dwarfs could reveal the spectral sensitivities across the Teff, g and [M/H] space probed by new surveys.Comment: 18 pages, 12 figures, accepted for publication in MNRA

Ultracool dwarf benchmarks with \emph{Gaia} primaries

This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society. © 2017 The Author(s). Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.We explore the potential of \emph{Gaia} for the field of benchmark ultracool/brown dwarf companions, and present the results of an initial search for metal-rich/metal-poor systems. A simulated population of resolved ultracool dwarf companions to \emph{Gaia} primary stars is generated and assessed. Of order $\sim$24,000 companions should be identifiable outside of the Galactic plane ($|b| > 10\,$deg) with large-scale ground- and space-based surveys including late M, L, T, and Y types. Our simulated companion parameter space covers $0.02 \le M/M_{\odot} \le 0.1$, $0.1 \le {\rm age/Gyr} \le 14$, and $-2.5 \le {\rm [Fe/H]} \le 0.5$, with systems required to have a false alarm probability $$0.6\, kau}\,Peer reviewedFinal Accepted Versio

Black Hole Entropy Function, Attractors and Precision Counting of Microstates

In these lecture notes we describe recent progress in our understanding of attractor mechanism and entropy of extremal black holes based on the entropy function formalism. We also describe precise computation of the microscopic degeneracy of a class of quarter BPS dyons in N=4 supersymmetric string theories, and compare the statistical entropy of these dyons, expanded in inverse powers of electric and magnetic charges, with a similar expansion of the corresponding black hole entropy. This comparison is extended to include the contribution to the entropy from multi-centered black holes as well.Comment: LaTeX file, 196 pages, based on lectures given at various schools; v2: added appendix E containing analysis of the multiple D5-brane system, expanded discussion on duality orbits, other minor changes, references added; v3: equations (5.6.20) and (5.6.21) corrected; v4: minor corrections to equations (C.19), (C.20

HIPPARCOS age-metallicity relation of the solar neighbourhood disc stars

We derive age-metallicity relations (AMRs) and orbital parameters for the 1658 solar neighbourhood stars to which accurate distances are measured by the HIPPARCOS satellite. The sample stars comprise 1382 thin disc stars, 229 thick disc stars, and 47 halo stars according to their orbital parameters. We find a considerable scatter for thin disc AMR along the one-zone Galactic chemical evolution (GCE) model. Orbits and metallicities of thin disc stars show now clear relation each other. The scatter along the AMR exists even if the stars with the same orbits are selected. We examine simple extension of one-zone GCE models which account for inhomogeneity in the effective yield and inhomogeneous star formation rate in the Galaxy. Both extensions of one-zone GCE model cannot account for the scatter in age - [Fe/H] - [Ca/Fe] relation simultaneously. We conclude, therefore, that the scatter along the thin disc AMR is an essential feature in the formation and evolution of the Galaxy. The AMR for thick disc stars shows that the star formation terminated 8 Gyr ago in thick disc. As already reported by Gratton et.al. (2000) and Prochaska et.al. (2000), thick disc stars are more Ca-rich than thin disc stars with the same [Fe/H]. We find that thick disc stars show a vertical abundance gradient. These three facts, the AMR, vertical gradient, and [Ca/Fe]-[Fe/H] relation, support monolithic collapse and/or accretion of satellite dwarf galaxy as thick disc formation scenario.Comment: 45 pages, 21 figures, and 5 tables. Accepted to Astronomy & Astrophysic