Sturmian morphisms, the braid group B_4, Christoffel words and bases of F_2

We give a presentation by generators and relations of a certain monoid generating a subgroup of index two in the group Aut(F_2) of automorphisms of the rank two free group F_2 and show that it can be realized as a monoid in the group B_4 of braids on four strings. In the second part we use Christoffel words to construct an explicit basis of F_2 lifting any given basis of the free abelian group Z^2. We further give an algorithm allowing to decide whether two elements of F_2 form a basis or not. We also show that, under suitable conditions, a basis has a unique conjugate consisting of two palindromes.Comment: 25 pages, 4 figure

F stars, metallicity, and the ages of red galaxies at z > 1

We explore whether the rest-frame near-UV spectral region, observable in high-redshift galaxies via optical spectroscopy, contains sufficient information to allow the degeneracy between age and metallicity to be lifted. We do this by testing the ability of evolutionary synthesis models to reclaim the correct metallicity when fitted to the near-UV spectra of F stars of known (sub-solar and super-solar) metallicity. F stars are of particular interest because the rest-frame near-UV spectra of the oldest known elliptical galaxies at z > 1 appear to be dominated by F stars near to the main-sequence turnoff. We find that, in the case of the F stars, where the HST ultraviolet spectra have high signal:noise, model-fitting with metallicity allowed to vary as a free parameter is rather successful at deriving the correct metallicity. As a result, the estimated turnoff ages of these stars yielded by the model fitting are well constrained. Encouraged by this we have fitted these same variable- metallicity models to the deep, optical spectra of the z \simeq 1.5 mJy radio galaxies 53W091 and 53W069 obtained with the Keck telescope. While the age-metallicity degeneracy is not so easily lifted for these galaxies, we find that even when metallicity is allowed as a free parameter, the best estimates of their ages are still \geq 3 Gyr, with ages younger than 2 Gyr now strongly excluded. Furthermore, we find that a search of the entire parameter space of metallicity and star formation history using MOPED (Heavens et al., 2000) leads to the same conclusion. Our results therefore continue to argue strongly against an Einstein-de Sitter universe, and favour a lambda-dominated universe in which star formation in at least these particular elliptical galaxies was completed somewhere in the redshift range z = 3 - 5.Comment: 10 pages, LaTeX, uses MNRAS style file, incorporates 14 postscript figures, submitted to MNRAS. Changes include: inclusion of single stellar atmosphere model fits; more rigorous calculation of confidence regions; some re-structurin

Morphometric study of Acipenser nuccurii (Bonaparte, 1836) in fish farm individuals

The main objective of this study was to analyse differences and similarities in morphometric characteristics among specimens of the same year class of Acipenser naccarii (Bonaparte, 1836), comparing fish raised either in Italy or Spain. All specimens were F1 of captive broodstock in Italy. Fifteen biometric variables were measured, and three derived indices were calculated, on 30 individuals of 3+ year class from Lombardy (Italy) and 90 individuals of I+, 2+ and 3+ year class from Riofrio (Granada, Spain). A stepwise discriminate analysis (SDA) was carried out, and the results were contrasted using a non-hierarchical cluster analysis. The two groups proved to be similar, so a principal component analysis and a simple regression analysis were performed on all individuals, taking total length (TI) as the independent variable and all the biometric variables as dependent. The study revealed that although the Soljan index (i.e. ratio of mouth width to snout length) is related to TI, and is a valid taxonomic characteristic, the CA index (i.e. relative position of the barbels) and FB index (i.e. ratio of snout length to width) are also valid characteristics for individuals longer than 57 cm, being independent of TI

Commutative limit of a renormalizable noncommutative model

Renormalizable $\phi^{\star 4}_4$ models on Moyal space have been obtained by modifying the commutative propagator. But these models have a divergent "naive" commutative limit. We explain here how to obtain a coherent such commutative limit for a recently proposed translation-invariant model. The mechanism relies on the analysis of the uv/ir mixing in general Feynman graphs.Comment: 11 pages, 3 figures, minor misprints being correcte

GTC OSIRIS transiting exoplanet atmospheric survey: detection of sodium in XO-2b from differential long-slit spectroscopy

We present two transits of the hot-Jupiter exoplanet XO-2b using the Gran Telescopio Canarias (GTC). The time series observations were performed using long-slit spectroscopy of XO-2 and a nearby reference star with the OSIRIS instrument, enabling differential specrophotometric transit lightcurves capable of measuring the exoplanet's transmission spectrum. Two optical low-resolution grisms were used to cover the optical wavelength range from 3800 to 9300{\AA}. We find that sub-mmag level slit losses between the target and reference star prevent full optical transmission spectra from being constructed, limiting our analysis to differential absorption depths over ~1000{\AA} regions. Wider long slits or multi-object grism spectroscopy with wide masks will likely prove effective in minimising the observed slit-loss trends. During both transits, we detect significant absorption in the planetary atmosphere of XO-2b using a 50{\AA} bandpass centred on the Na I doublet, with absorption depths of Delta(R_pl/R_star)^2=0.049+/-0.017 % using the R500R grism and 0.047+/-0.011 % using the R500B grism (combined 5.2-sigma significance from both transits). The sodium feature is unresolved in our low-resolution spectra, with detailed modelling also likely ruling out significant line-wing absorption over an ~800{\AA} region surrounding the doublet. Combined with narrowband photometric measurements, XO-2b is the first hot Jupiter with evidence for both sodium and potassium present in the planet's atmosphere.Comment: 9 pages, 10 figures, 1 table, accepted for publication in MNRA

The unusual protoplanetary disk around the T Tauri star ET Cha

We present new continuum and line observations, along with modelling, of the faint (6-8) Myr old T Tauri star ET Cha belonging to the eta Chamaeleontis cluster. We have acquired HERSCHEL/PACS photometric fluxes at 70 mic and 160 mic, as well as a detection of the [OI] 63 mic fine-structure line in emission, and derived upper limits for some other far-IR OI, CII, CO and o-H2O lines. The HERSCHEL data is complemented by new ANDICAM B-K photometry, new HST/COS and HST/STIS UV-observations, a non-detection of CO J=3-2 with APEX, re-analysis of a UCLES high-resolution optical spectrum showing forbidden emission lines like [OI] 6300A, [SII] 6731A and 6716A, and [NII] 6583A, and a compilation of existing broad-band photometric data. We used the thermo-chemical disk code ProDiMo and the Monte-Carlo radiative transfer code MCFOST to model the protoplanetary disk around ET Cha. Based on these models we can determine the disk dust mass Mdust = (2.E-8 - 5.E-8) Msun, whereas the total disk gas mass is found to be only little constrained, Mgas = (5.E-5 - 3.E-3) Msun. In the models, the disk extends from 0.022 AU (just outside of the co-rotation radius) to only about 10 AU. Larger disks are found to be inconsistent with the CO J=3-2 non-detection. The low velocity component of the [OI] 6300A emission line is consistent with being emitted from the inner disk. The model can also reproduce the line flux of H2 v=1-0 S(1) at 2.122 mic. An additional high-velocity component of the [OI] 6300A emission line, however, points to the existence of an additional jet/outflow of low velocity (40 - 65) km/s with mass loss rate ~1.E-9 Msun/yr. In relation to our low estimations of the disk mass, such a mass loss rate suggests a disk lifetime of only ~(0.05 - 3) Myr, substantially shorter than the cluster age. The evolutionary state of this unusual protoplanetary disk is discussed.Comment: accepted by Astronomy & Astrophysics (18 pages, 11 figures and 7 tables). Additional 9-page appendix with 6 figures, 3 tables and 37 equation

The LQG -- String: Loop Quantum Gravity Quantization of String Theory I. Flat Target Space

We combine I. background independent Loop Quantum Gravity (LQG) quantization techniques, II. the mathematically rigorous framework of Algebraic Quantum Field Theory (AQFT) and III. the theory of integrable systems resulting in the invariant Pohlmeyer Charges in order to set up the general representation theory (superselection theory) for the closed bosonic quantum string on flat target space. While we do not solve the, expectedly, rich representation theory completely, we present a, to the best of our knowledge new, non -- trivial solution to the representation problem. This solution exists 1. for any target space dimension, 2. for Minkowski signature of the target space, 3. without tachyons, 4. manifestly ghost -- free (no negative norm states), 5. without fixing a worldsheet or target space gauge, 6. without (Virasoro) anomalies (zero central charge), 7. while preserving manifest target space Poincar\'e invariance and 8. without picking up UV divergences. The existence of this stable solution is exciting because it raises the hope that among all the solutions to the representation problem (including fermionic degrees of freedom) we find stable, phenomenologically acceptable ones in lower dimensional target spaces, possibly without supersymmetry, that are much simpler than the solutions that arise via compactification of the standard Fock representation of the string. Moreover, these new representations could solve some of the major puzzles of string theory such as the cosmological constant problem. The solution presented in this paper exploits the flatness of the target space in several important ways. In a companion paper we treat the more complicated case of curved target spaces.Comment: 46 p., LaTex2e, no figure

Emergent Geometry and Gravity from Matrix Models: an Introduction

A introductory review to emergent noncommutative gravity within Yang-Mills Matrix models is presented. Space-time is described as a noncommutative brane solution of the matrix model, i.e. as submanifold of \R^D. Fields and matter on the brane arise as fluctuations of the bosonic resp. fermionic matrices around such a background, and couple to an effective metric interpreted in terms of gravity. Suitable tools are provided for the description of the effective geometry in the semi-classical limit. The relation to noncommutative gauge theory and the role of UV/IR mixing is explained. Several types of geometries are identified, in particular "harmonic" and "Einstein" type of solutions. The physics of the harmonic branch is discussed in some detail, emphasizing the non-standard role of vacuum energy. This may provide new approach to some of the big puzzles in this context. The IKKT model with D=10 and close relatives are singled out as promising candidates for a quantum theory of fundamental interactions including gravity.Comment: Invited topical review for Classical and Quantum Gravity. 57 pages, 5 figures. V2,V3: minor corrections and improvements. V4,V5: some improvements, refs adde

OGLE-2017-BLG-0329L: A Microlensing Binary Characterized with Dramatically Enhanced Precision Using Data from Space-based Observations

Mass measurements of gravitational microlenses require one to determine the microlens parallax π E, but precise π E measurement, in many cases, is hampered due to the subtlety of the microlens-parallax signal combined with the difficulty of distinguishing the signal from those induced by other higher-order effects. In this work, we present the analysis of the binary-lens event OGLE-2017-BLG-0329, for which π E is measured with a dramatically improved precision using additional data from space-based Spitzer observations. We find that while the parallax model based on the ground-based data cannot be distinguished from a zero-π E model at the 2σ level, the addition of the Spitzer data enables us to identify two classes of solutions, each composed of a pair of solutions according to the well-known ecliptic degeneracy. It is found that the space-based data reduce the measurement uncertainties of the north and east components of the microlens-parallax vector π E by factors ~18 and ~4, respectively. With the measured microlens parallax combined with the angular Einstein radius measured from the resolved caustic crossings, we find that the lens is composed of a binary with component masses of either (M1, M2) ~ (1.1, 0.8) M⊙ or ~(0.4, 0.3) M⊙ according to the two solution classes. The first solution is significantly favored but the second cannot be securely ruled out based on the microlensing data alone. However, the degeneracy can be resolved from adaptive optics observations taken ~10 years after the event

Characterization of the gaseous companion {\kappa} Andromedae b: New Keck and LBTI high-contrast observations

We previously reported the direct detection of a low mass companion at a projected separation of 55+-2 AU around the B9 type star {\kappa} Andromedae. The properties of the system (mass ratio, separation) make it a benchmark for the understanding of the formation and evolution of gas giant planets and brown dwarfs on wide-orbits. We present new angular differential imaging (ADI) images of the Kappa Andromedae system at 2.146 (Ks), 3.776 (L'), 4.052 (NB 4.05) and 4.78 {\mu}m (M') obtained with Keck/NIRC2 and LBTI/LMIRCam, as well as more accurate near-infrared photometry of the star with the MIMIR instrument. We derive a more accurate J = 15.86 +- 0.21, H = 14.95 +- 0.13, Ks = 14.32 +- 0.09 mag for {\kappa} And b. We redetect the companion in all our high contrast observations. We confirm previous contrasts obtained at Ks and L' band. We derive NB 4.05 = 13.0 +- 0.2 and M' = 13.3 +- 0.3 mag and estimate Log10(L/Lsun) = -3.76 +- 0.06. We build the 1-5 microns spectral energy distribution of the companion and compare it to seven PHOENIX-based atmospheric models in order to derive Teff = 1900+100-200 K. Models do not set constrains on the surface gravity. ``Hot-start" evolutionary models predict masses of 14+25-2 MJup based on the luminosity and temperature estimates, and considering a conservative age range for the system (30+120-10 Myr). ``warm-start" evolutionary tracks constrain the mass to M >= 11 MJup. Therefore, the mass of {\kappa} Andromedae b mostly falls in the brown-dwarf regime, due to remaining uncertainties in age and mass-luminosity models. According to the formation models, disk instability in a primordial disk could account for the position and a wide range of plausible masses of {\kappa} And b.Comment: 20 pages, 16 figures, accepted for publication in Astronomy and Astrophysics on August 6, 201