On the frequency of close binary systems among very low-mass stars and brown dwarfs

We have used Monte Carlo simulation techniques and published radial velocity surveys to constrain the frequency of very low-mass star (VLMS) and brown dwarf (BD) binary systems and their separation (a) distribution. Gaussian models for the separation distribution with a peak at a = 4 au and 0.6 =< sigma(log(a/au)) =< 1.0 correctly predict the number of observed binaries, yielding a close (a<2.6 au) binary frequency of 17-30 per cent and an overall VLMS/BD binary frequency of 32-45 per cent. We find that the available N-body models of VLMS/BD formation from dynamically decaying protostellar multiple systems are excluded at >99 per cent confidence because they predict too few close binary VLMS/BDs. The large number of close binaries and high overall binary frequency are also very inconsistent with recent smoothed particle hydrodynamical modelling and argue against a dynamical origin for VLMS/BDs.Comment: Accepted for publication in MNRAS letters. 5 pages, 2 figure

The Value of the Application Photograph as a Teacher-Selecting Instrument

The purpose of this study is to discover information which may contribute to a better understanding of the value of application photographs for prospective teaching positions. Specifically, this study is concerned with the following aspects: (1) the extent to which superintendents of schools use photographs in teacher selection; (2) the influence in which three physical characteristics, namely, size, contrast, and expression, may have upon teacher selection; and (3) the value which the superintendent of schools places on the photograph as an instrument of teacher selection

An XMM-Newton observation of the young open cluster NGC 2547: coronal activity at 30 Myr

We report XMM-Newton observations of the young open cluster NGC 2547 which allow us to characterise coronal activity in solar-type stars at an age of 30 Myr. X-ray emission peaks among G-stars at luminosities (0.3-3keV) of Lx~10^{30.5} erg/s and declines to Lx<=10^{29.0} erg/s among M-stars. Coronal spectra show evidence for multi-temperature differential emission measures and low coronal metal abundances (Z~0.3). The G- and K-type stars follow the same relationship between X-ray activity and Rossby number established in older clusters and field stars, although most solar-type stars in NGC 2547 exhibit saturated/super-saturated X-ray activity levels. Median levels of Lx and Lx/Lbol in the solar-type stars of NGC 2547 are similar to T-Tauri stars of the Orion Nebula cluster (ONC), but an order of magnitude higher than in the older Pleiades. The spread in X-ray activity levels among solar-type stars in NGC 2547 is much smaller than in older or younger clusters. Coronal temperatures increase with Lx, Lx/Lbol and surface X-ray flux. Active solar-type stars in NGC 2547 have coronal temperatures between those in the ONC and the most active older ZAMS stars. A flaring rate (for total flare energies [0.3-3keV] >10^{34} erg) of 1 every 350^{+350}_{-120} ks was found for solar-type stars, similar to rates found in the ONC and Pleiades. Comparison with ROSAT HRI data taken 7 years previously reveals that only 10-15 percent of solar-type stars or stars with Lx>3x10^{29} erg/s exhibit X-ray variability by more than a factor of two. The similar levels of X-ray activity and rate of occurrence for large flares in NGC 2547 and the ONC demonstrate that the X-ray radiation environment around young solar-type stars remains relatively constant over their first 30 Myr (abridged).Comment: Accepted for publication in MNRAS. Electronic tables available from the autho

Pre-main-sequence isochrones -- II. Revising star and planet formation timescales

We have derived ages for 13 young (<30 Myr) star-forming regions and find they are up to a factor two older than the ages typically adopted in the literature. This result has wide-ranging implications, including that circumstellar discs survive longer (~10-12 Myr) and that the average Class I lifetime is greater (~1 Myr) than currently believed. For each star-forming region we derived two ages from colour-magnitude diagrams. First we fitted models of the evolution between the zero-age main-sequence and terminal-age main-sequence to derive a homogeneous set of main-sequence ages, distances and reddenings with statistically meaningful uncertainties. Our second age for each star-forming region was derived by fitting pre-main-sequence stars to new semi-empirical model isochrones. For the first time (for a set of clusters younger than 50 Myr) we find broad agreement between these two ages, and since these are derived from two distinct mass regimes that rely on different aspects of stellar physics, it gives us confidence in the new age scale. This agreement is largely due to our adoption of empirical colour-Teff relations and bolometric corrections for pre-main-sequence stars cooler than 4000 K. The revised ages for the star-forming regions in our sample are: ~2 Myr for NGC 6611 (Eagle Nebula; M 16), IC 5146 (Cocoon Nebula), NGC 6530 (Lagoon Nebula; M 8), and NGC 2244 (Rosette Nebula); ~6 Myr for {\sigma} Ori, Cep OB3b, and IC 348; ~10 Myr for {\lambda} Ori (Collinder 69); ~11 Myr for NGC 2169; ~12 Myr for NGC 2362; ~13 Myr for NGC 7160; ~14 Myr for {\chi} Per (NGC 884); and ~20 Myr for NGC 1960 (M 36).Comment: 28 pages, 18 figures, 34 tables, accepted for publication in MNRAS. All photometric catalogues presented in this paper are available online at the Cluster Collaboration homepage http://www.astro.ex.ac.uk/people/timn/Catalogues

A lithium depletion boundary age of 22 Myr for NGC 1960

We present a deep Cousins RI photometric survey of the open cluster NGC 1960, complete to R_C \simeq 22, I_C \simeq 21, that is used to select a sample of very low-mass cluster candidates. Gemini spectroscopy of a subset of these is used to confirm membership and locate the age-dependent "lithium depletion boundary" (LDB) --the luminosity at which lithium remains unburned in its low-mass stars. The LDB implies a cluster age of 22 +/-4 Myr and is quite insensitive to choice of evolutionary model. NGC 1960 is the youngest cluster for which a LDB age has been estimated and possesses a well populated upper main sequence and a rich low-mass pre-main sequence. The LDB age determined here agrees well with precise age estimates made for the same cluster based on isochrone fits to its high- and low-mass populations. The concordance between these three age estimation techniques, that rely on different facets of stellar astrophysics at very different masses, is an important step towards calibrating the absolute ages of young open clusters and lends confidence to ages determined using any one of them.Comment: Accepted for publication in MNRA

Low-mass members of the young cluster IC 4665 and pre-main-sequence lithium depletion

We have used fibre spectroscopy to establish cluster membership and examine pre-main-sequence (PMS) lithium depletion for low-mass stars (spectral types F to M) in the sparse young (~30 Myr) cluster IC 4665. We present a filtered candidate list of 40 stars that should contain 75 per cent of single cluster members with V of 11.5 to 18 in the central square degree of the cluster. Whilst F- and G-type stars in IC 4665 have depleted little or no lithium, the K- and early M-type stars have depleted more Li than expected when compared with similar stars in other clusters of known age. An empirical age estimate based on Li-depletion among the late-type stars of IC 4665 would suggest it is older than 100 Myr. This disagrees entirely with ages determined either from the nuclear turn-off, from isochronal matches to low-mass stars or from the re-appearance of lithium previously found in much lower mass stars (the ``lithium depletion boundary''). We suggest that other parameters besides age, perhaps composition or rotation, are very influential in determining the degree of PMS Li-depletion in stars with M greater than 0.5 Msun. Further work is required to identify and assess the effects of these additional parameters, particularly to probe conditions at the interface between the sub-photospheric convection zone and developing radiative core. Until then, PMS Li depletion in F- to early M-type stars cannot be confidently used as a precise age indicator in young clusters, kinematic groups or individual field stars.Comment: Accepted for publication in MNRA

No evidence for intense, cold accretion onto YSOs from measurements of Li in T-Tauri stars

We have used medium resolution spectra to search for evidence that proto-stellar objects accrete at high rates during their early 'assembly phase'. Models predict that depleted lithium and reduced luminosity in T-Tauri stars are key signatures of 'cold' high-rate accretion occurring early in a star's evolution. We found no evidence in 168 stars in NGC 2264 and the Orion Nebula Cluster for strong lithium depletion through analysis of veiling corrected 6708 angstrom lithium spectral line strengths. This suggests that 'cold' accretion at high rates (M_dot > 5 x 10-4 M_sol yr-1) occurs in the assembly phase of fewer than 0.5 per cent of 0.3 < M < 1.9 M_sol stars. We also find that the dispersion in the strength of the 6708 angstrom lithium line might imply an age spread that is similar in magnitude to the apparent age spread implied by the luminosity dispersion seen in colour magnitude diagrams. Evidence for weak lithium depletion (< 10 per cent in equivalent width) that is correlated with luminosity is also apparent, but we are unable to determine whether age spreads or accretion at rates less than 5 x 10-4 M_sol yr-1 are responsible.Comment: 13 pages, 10 figures; Accepted for publication in Monthly Notices of the Royal Astronomical Society, 2013 June 0

Eigenvalues of matrices with tree graphs

AbstractWhen the undirected graph of a real square matrix is a tree of forest, we establish finitely computable tests yielding information about the magnitudes and multiplicities to the eigenvalues of the matrix. Applying these tests to system designs expressed as signed directed graphs can be sufficient to guarantee controllability of the associated linear dynamical systems