Internal dynamics and membership of the NGC 3603 Young Cluster from microarcsecond astrometry

We have analyzed two epochs of HST/WFPC2 observations of the young Galactic starburst cluster in NGC 3603 with the aim to study its internal dynamics and stellar population. Relative proper motions measured over 10.15 yrs of more than 800 stars enable us to distinguish cluster members from field stars. The best-fitting isochrone yields Av=4.6-4.7 mag, a distance of 6.6-6.9 kpc, and an age of 1 Myr for NGC 3603 Young Cluster (NYC). We identify pre-main-sequence/main-sequence transition stars located in the short-lived radiative-convective gap, which in the NYC occurs in the mass range 3.5-3.8 Msun. We also identify a sparse population of stars with an age of 4 Myr, which appear to be the lower mass counterparts to previously discovered blue supergiants located in the giant HII region NGC 3603. For the first time, we are able to measure the internal velocity dispersion of a starburst cluster from 234 stars with I < 18.5 mag to {\sigma}_pm1D=141+/-27 {\mu}as/yr (4.5+/-0.8 km/s at a distance of 6.75 kpc). As stars with masses between 1.7 and 9 Msun all exhibit the same velocity dispersion, the cluster stars have not yet reached equipartition of kinetic energy (i.e., the cluster is not in virial equilibrium). The results highlight the power of combining high-precision astrometry and photometry, and emphasize the role of NYC as a benchmark object for testing stellar evolution models and dynamical models for young clusters and as a template for extragalactic starburst clusters.Comment: 5 pages, 2 figure

Simple Model for the Variation of Superfluid Density with Zn Concentration in YBCO

We describe a simple model for calculating the zero-temperature superfluid density of Zn-doped YBa_2Cu_3O_{7-\delta} as a function of the fraction x of in-plane Cu atoms which are replaced by Zn. The basis of the calculation is a ``Swiss cheese'' picture of a single CuO_2 layer, in which a substitutional Zn impurity creates a normal region of area $\pi\xi_{ab}^2$ around it as originally suggested by Nachumi et al. Here $\xi_{ab}$ is the zero-temperature in-plane coherence length at x = 0. We use this picture to calculate the variation of the in-plane superfluid density with x at temperature T = 0, using both a numerical approach and an analytical approximation. For $\delta = 0.37$, if we use the value $\xi_{ab}$ = 18.3 angstrom, we find that the in-plane superfluid decreases with increasing x and vanishes near $x_c = 0.01$ in the analytical approximation, and near $x_c = 0.014$ in the numerical approach. $x_c$ is quite sensitive to $\xi_{ab}$, whose value is not widely agreed upon. The model also predicts a peak in the real part of the conductivity, Re$\sigma_e(\omega, x)$, at concentrations $x \sim x_c$, and low frequencies, and a variation of critical current density with x of the form $J_c(x) \propto n_{S,e}(x)^{7/4}$ near percolation, where $n_{S,e}(x)$ is the in-plane superfluid density.Comment: 19 pages including 6 figures, submitted to Physica

A dusty pinwheel nebula around the massive star WR 104

Wolf-Rayet (WR) stars are luminous massive blue stars thought to be immediate precursors to the supernova terminating their brief lives. The existence of dust shells around such stars has been enigmatic since their discovery some 30 years ago; the intense radiation field from the star should be inimical to dust survival. Although dust-creation models, including those involving interacting stellar winds from a companion star, have been put forward, high-resolution observations are required to understand this phenomena. Here we present resolved images of the dust outflow around Wolf-Rayet WR 104, obtained with novel imaging techniques, revealing detail on scales corresponding to about 40 AU at the star. Our maps show that the dust forms a spatially confined stream following precisely a linear (or Archimedian) spiral trajectory. Images taken at two separate epochs show a clear rotation with a period of 220 +/- 30 days. Taken together, these findings prove that a binary star is responsible for the creation of the circumstellar dust, while the spiral plume makes WR 104 the prototype of a new class of circumstellar nebulae unique to interacting wind systems.Comment: 7 pages, 2 figures, Appearing in Nature (1999 April 08

No Conclusive Evidence for Transits of Proxima b in MOST photometry

The analysis of Proxima Centauri's radial velocities recently led Anglada-Escud\'e et al. (2016) to claim the presence of a low mass planet orbiting the Sun's nearest star once every 11.2 days. Although the a-priori probability that Proxima b transits its parent star is just 1.5%, the potential impact of such a discovery would be considerable. Independent of recent radial velocity efforts, we observed Proxima Centauri for 12.5 days in 2014 and 31 days in 2015 with the MOST space telescope. We report here that we cannot make a compelling case that Proxima b transits in our precise photometric time series. Imposing an informative prior on the period and phase, we do detect a candidate signal with the expected depth. However, perturbing the phase prior across 100 evenly spaced intervals reveals one strong false-positive and one weaker instance. We estimate a false-positive rate of at least a few percent and a much higher false-negative rate of 20-40%, likely caused by the very high flare rate of Proxima Centauri. Comparing our candidate signal to HATSouth ground-based photometry reveals that the signal is somewhat, but not conclusively, disfavored (1-2 sigmas) leading us to argue that the signal is most likely spurious. We expect that infrared photometric follow-up could more conclusively test the existence of this candidate signal, owing to the suppression of flare activity and the impressive infrared brightness of the parent star.Comment: Accepted to ApJ. Posterior samples, MOST photometry and HATSouth photometry are all available at https://github.com/CoolWorlds/Proxim

The Mass of the Planet-hosting Giant Star Beta Geminorum Determined from its p-mode Oscillation Spectrum

We use precise radial velocity measurements and photometric data to derive the frequency spacing of the p-mode oscillation spectrum of the planet-hosting star Beta Gem. This spacing along with the interferometric radius for this star is used to derive an accurate stellar mass. A long time series of over 60 hours of precise stellar radial velocity measurements of Beta Gem were taken with an iodine absorption cell and the echelle spectrograph mounted on the 2m Alfred Jensch Telescope. Complementary photometric data for this star were also taken with the MOST microsatellite spanning 3.6 d. A Fourier analysis of the radial velocity data reveals the presence of up to 17 significant pulsation modes in the frequency interval 10-250 micro-Hz. Most of these fall on a grid of equally-spaced frequencies having a separation of 7.14 +/- 0.12 micro-Hz. An analysis of 3.6 days of high precision photometry taken with the MOST space telescope shows the presence of up to 16 modes, six of which are consistent with modes found in the spectral (radial velocity) data. This frequency spacing is consistent with high overtone radial pulsations; however, until the pulsation modes are identified we cannot be sure if some of these are nonradial modes or even mixed modes. The radial velocity frequency spacing along with angular diameter measurements of Beta Gem via interferometry results in a stellar mass of M = 1.91 +/- 0.09 solar masses. This value confirms the intermediate mass of the star determined using stellar evolutionary tracks. Beta Gem is confirmed to be an intermediate mass star. Stellar pulsations in giant stars along with interferometric radius measurements can provide accurate determinations of the stellar mass of planet hosting giant stars. These can also be used to calibrate stellar evolutionary tracks.Comment: Accepted by Astronomy and Astrophysic

Toward a Unification of Star Formation Rate Determinations in the Milky Way and Other Galaxies

The star formation rate (SFR) of the Milky Way remains poorly known, with often-quoted values ranging from 1 to 10 solar masses per year. This situation persists despite the potential for the Milky Way to serve as the ultimate SFR calibrator for external galaxies. We show that various estimates for the Galactic SFR are consistent with one another once they have been normalized to the same initial mass function (IMF) and massive star models, converging to 1.9 +/- 0.4 M_sun/yr. However, standard SFR diagnostics are vulnerable to systematics founded in the use of indirect observational tracers sensitive only to high-mass stars. We find that absolute SFRs measured using resolved low/intermediate-mass stellar populations in Galactic H II regions are systematically higher by factors of ~2-3 as compared with calibrations for SFRs measured from mid-IR and radio emission. We discuss some potential explanations for this discrepancy and conclude that it could be allayed if (1) the power-law slope of the IMF for intermediate-mass (1.5 M_sun < m < 5 M_sun) stars were steeper than the Salpeter slope, or (2) a correction factor was applied to the extragalactic 24 micron SFR calibrations to account for the duration of star formation in individual mid-IR-bright H II regions relative to the lifetimes of O stars. Finally, we present some approaches for testing if a Galactic SFR of ~2 M_sun/yr is consistent with what we would measure if we could view the Milky Way as external observers. Using luminous radio supernova remnants and X-ray point sources, we find that the Milky Way deviates from expectations at the 1-3 sigma level, hinting that perhaps the Galactic SFR is overestimated or extragalactic SFRs need to be revised upwards.Comment: Accepted for publication in A

Strong lensing probability in TeVeS theory

We recalculate the strong lensing probability as a function of the image separation in TeVeS (tensor-vector-scalar) cosmology, which is a relativistic version of MOND (MOdified Newtonian Dynamics). The lens is modeled by the Hernquist profile. We assume an open cosmology with $\Omega_b=0.04$ and $\Omega_\Lambda=0.5$ and three different kinds of interpolating functions. Two different galaxy stellar mass functions (GSMF) are adopted: PHJ (Panter-Heavens-Jimenez, 2004) determined from SDSS data release one and Fontana (Fontana et al., 2006) from GOODS-MUSIC catalog. We compare our results with both the predicted probabilities for lenses by Singular Isothermal Sphere (SIS) galaxy halos in LCDM (lambda cold dark matter) with Schechter-fit velocity function, and the observational results of the well defined combined sample of Cosmic Lens All-Sky Survey (CLASS) and Jodrell Bank/Very Large Array Astrometric Survey (JVAS). It turns out that the interpolating function $\mu(x)=x/(1+x)$ combined with Fontana GSMF matches the results from CLASS/JVAS quite well.Comment: 15 pages, 3 figures, 1 table. Published in JCA

Unilateral elongated styloid process: a case report

An unusual case of a unilaterally elongated styloid process with a length of 5.8 cm was found on a dry skull of a male cadaver. During his life the subject was complaining for reported ipsilateral otalgia presumably due to nerve compression from the elongated styloid process. The symptomatology appeared by such an anatomical variant as well as relative literature is discussed in this paper

Anisotropy in the Hubble constant as observed in the HST Extragalactic Distance Scale Key Project results

Based on general relativity, it can be argued that deviations from a uniform Hubble flow should be thought of as variations in the Universe's expansion velocity field, rather than being thought of as peculiar velocities with respect to a uniformly expanding space. The aim of this paper is to use the observed motions of galaxies to map out variations in the Universe's expansion, and more importantly, to investigate whether real variations in the Hubble expansion are detectable given the observational uncertainties. All-sky maps of the observed variation in the expansion are produced using measurements obtained along specific lines-of-sight and smearing them across the sky using a Gaussian profile. A map is produced for the final results of the HST Extragalactic Distance Scale Key Project for the Hubble constant, a comparison map is produced from a set of essentially independent data, and Monte Carlo techniques are used to analyse the statistical significance of the variation in the maps. A statistically significant difference in expansion rate of 9 km/s/Mpc is found to occur across the sky. Comparing maps of the sky at different distances appears to indicate two distinct sets of extrema with even stronger statistically significant variations. Within our supercluster, variations tend to occur near the supergalactic plane, and beyond our supercluster, variations tend to occur away from the supergalactic plane. Comparison with bulk flow studies shows some concordance, yet also suggests the bulk flow studies may suffer confusion, failing to discern the influence of multiple perturbations.Comment: 23 pages, 5 figures, to be published in New Astronom

Optimal skeleton huffman trees revisited

A skeleton Huffman tree is a Huffman tree in which all disjoint maximal perfect subtrees are shrunk into leaves. Skeleton Huffman trees, besides saving storage space, are also used for faster decoding and for speeding up Huffman-shaped wavelet trees. In 2017 Klein et al. introduced an optimal skeleton tree: for given symbol frequencies, it has the least number of nodes among all optimal prefix-free code trees (not necessarily Huffman’s) with shrunk perfect subtrees. Klein et al. described a simple algorithm that, for fixed codeword lengths, finds a skeleton tree with the least number of nodes; with this algorithm one can process each set of optimal codeword lengths to find an optimal skeleton tree. However, there are exponentially many such sets in the worst case. We describe an (formula presented)-time algorithm that, given n symbol frequencies, constructs an optimal skeleton tree and its corresponding optimal code. © Springer Nature Switzerland AG 2020.Supported by the Russian Science Foundation (RSF), project 18-71-00002