A Novel Symmetric Four Dimensional Polytope Found Using Optimization Strategies Inspired by Thomson's Problem of Charges on a Sphere

Inspired by, and using methods of optimization derived from classical three dimensional electrostatics, we note a novel beautiful symmetric four dimensional polytope we have found with 80 vertices. We also describe how the method used to find this symmetric polytope, and related methods can potentially be used to find good examples for the kissing and packing problems in D dimensions

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&

2MASS J154043.42-510135.7: a new addition to the 5 pc population

The aim of the project is to find the stars nearest to the Sun and to contribute to the completion of the stellar and substellar census of the solar neighbourhood. We identified a new late-M dwarf within 5 pc, looking for high proper motion sources in the 2MASS-WISE cross-match. We collected astrometric and photometric data available from public large-scale surveys. We complemented this information with low-resolution optical and near-infrared spectroscopy with instrumentation on the ESO NTT to confirm the nature of our candidate. We also present a high-quality medium-resolution VLT/X-shooter spectrum covering the 400 to 2500 nm wavelength range. We classify this new neighbour as an M7.0$\pm$0.5 dwarf using spectral templates from the Sloan Digital Sky Survey and spectral indices. Lithium absorption at 670.8 nm is not detected in the X-shooter spectrum, indicating that the M7 dwarf is older than 600 Myr and more massive than 0.06 M$_{\odot}$. We also derive a trigonometric distance of 4.4 pc, in agreement with the spectroscopic distance estimate, making 2MASS\,J154043.42$-$510135.7 the nearest M7 dwarf to the Sun. This trigonometric distance is somewhat closer than the $\sim$6 pc distance reported by the ALLWISE team, who independently identified this object recently. This discovery represents an increase of 25\% in the number of M7--M8 dwarfs already known at distances closer than 8\,pc from our Sun. We derive a density of $\rho$\,=\,1.9$\pm$0.9$\times$10$^{-3}$\,pc$^{-3}$ for M7 dwarfs in the 8 pc volume, a value similar to those quoted in the literature. This new ultracool dwarf is among the 50 nearest systems to the Sun, demonstrating that our current knowledge of the stellar census within the 5 pc sample remains incomplete. 2M1540 represents a unique opportunity to search for extrasolar planets around ultracool dwarfs due to its proximity and brightness.Comment: 8 pages, 5 figures. Acepted in Astronomy & Astrophysics (15/05/2005

Polar magneto-optic Kerr and Faraday effects in finite periodic \texorpdfstring{PT\mathcal{P}\mathcal{T}}{PT}-symmetric systems

We discuss the anomalous behavior of the Faraday (transmission) and polar Kerr (reflection) rotation angles of the propagating light, in finite periodic parity-time ($\mathcal{P}\mathcal{T}$) symmetric structures, consisting of $N$ cells. The unit cell potential is two complex $\delta$-potentials placed on both boundaries of the ordinary dielectric slab. It is shown that, for a given set of parameters describing the system, a phase transition-like anomalous behavior of Faraday and Kerr rotation angles in a parity-time symmetric systems can take place. In the anomalous phase the value of one of the Faraday and Kerr rotation angles can become negative, and both angles suffer from spectral singularities and give a strong enhancement near the singularities. We also shown that the real part of the complex angle of KR, $\theta^{R}_1$, is always equal to the $\theta^{T}_1$ of FR, no matter what phase the system is in due to the symmetry constraints. The imaginary part of KR angles $\theta^{R^{r/l}}_2$ are related to the $\theta^{T}_2$ of FR by parity-time symmetry. Calculations based on the approach of the generalized nonperturbative characteristic determinant, which is valid for a layered system with randomly distributed delta potentials, show that the Faraday and Kerr rotation spectrum in such structures has several resonant peaks. Some of them coincide with transmission peaks, providing simultaneous large Faraday and Kerr rotations enhanced by an order one or two of magnitude. We provide a recipe for funding a one-to-one relation in between KR and FR

High spatial resolution and high contrast optical speckle imaging with FASTCAM at the ORM

In this paper, we present an original observational approach, which combines, for the first time, traditional speckle imaging with image post-processing to obtain in the optical domain diffraction-limited images with high contrast (1e-5) within 0.5 to 2 arcseconds around a bright star. The post-processing step is based on wavelet filtering an has analogy with edge enhancement and high-pass filtering. Our I-band on-sky results with the 2.5-m Nordic Telescope (NOT) and the lucky imaging instrument FASTCAM show that we are able to detect L-type brown dwarf companions around a solar-type star with a contrast DI~12 at 2" and with no use of any coronographic capability, which greatly simplifies the instrumental and hardware approach. This object has been detected from the ground in J and H bands so far only with AO-assisted 8-10 m class telescopes (Gemini, Keck), although more recently detected with small-class telescopes in the K band. Discussing the advantage and disadvantage of the optical regime for the detection of faint intrinsic fluxes close to bright stars, we develop some perspectives for other fields, including the study of dense cores in globular clusters. To the best of our knowledge this is the first time that high contrast considerations are included in optical speckle imaging approach.Comment: Proceedings of SPIE conference - Ground-based and Airborne Instrumentation for Astronomy III (Conference 7735), San Diego 201

Fluctuation-Stimulated Variable-Range Hopping

Qualitatively new transport mechanism is suggested for hopping of carriers according to which the variable-range hopping (VRH) arises from the resonant tunneling between transport states brought into resonance by Coulomb potentials produced by surrounding sites with fluctuating occupations. A semiquantitative description of the hopping transport is given based on the assumption that fluctuations of energies of hopping sites have spectral density 1/f

Binary frequency of planet-host stars at wide separations: A new brown dwarf companion to a planet-host star

The aim of the project is to improve our knowledge on the multiplicity of planet-host stars at wide physical separations. We cross-matched approximately 6200 square degree area of the Southern sky imaged by the Visible Infrared Survey Telescope for Astronomy (VISTA) Hemisphere Survey (VHS) with the Two Micron All Sky Survey (2MASS) to look for wide common proper motion companions to known planet-host stars. We complemented our astrometric search with photometric criteria. We confirmed spectroscopically the co-moving nature of seven sources out of 16 companion candidates and discarded eight, while the remaining one stays as a candidate. Among these new wide companions to planet-host stars, we discovered a T4.5 dwarf companion at 6.3 arcmin (~9000 au) from HIP70849, a K7V star which hosts a 9 Jupiter mass planet with an eccentric orbit. We also report two new stellar M dwarf companions to one G and one metal-rich K star. We infer stellar and substellar binary frequencies for our complete sample of 37 targets of 5.4+/-3.8% and 2.7+/-2.7% (1 sigma confidence level), respectively, for projected physical separations larger than ~60-160 au assuming the range of distances of planet-host stars (24-75 pc). These values are comparable to the frequencies of non planet-host stars. We find that the period-eccentricity trend holds with a lack of multiple systems with planets at large eccentricities (e > 0.2) for periods less than 40 days. However, the lack of planets more massive than 2.5 Jupiter masses and short periods (<40 days) orbiting single stars is not so obvious due to recent discoveries by ground-based transit surveys and space missions.Comment: Accepted for publication in A&A, 13 pages, 5 figures, 3 tables, optical spectra will be available at CDS Strasbour