Using rotation, magnetic activity and lithium to estimate the ages of low mass stars

The rotation rate, level of magnetic activity and surface lithium abundance are age-dependent quantities in stars of about a solar mass and below. The physical reasons for the evolution of these phenomena are qualitatively understood, but accurate quantitative models remain dependent on empirical calibration using the Sun and stars of known age, chiefly in clusters. In this work I review the status of these "empirical age indicators", outlining the astrophysics of their time dependence, describing the measurements, assessing the precision (and accuracy) of age estimates when applied to individual stars, and identifying their principle limitations in terms of the mass and age ranges over which they are useful. Finally, I discuss the "lithium depletion boundary" technique which, in contrast to the empirical methods, appears to provide robust, almost model-independent ages that are both precise and accurate, but which is only applicable to coeval groups of stars.Comment: 38 pages; contribution to the proceedings of the 23rd Evry Schatzman School on Stellar Astrophysics, "The Ages of Stars", Roscoff 2013, EAS Publications Series, eds. C. Charbonnel et al. This version has minor corrections/additions to the bibliograph

The effect of starspots on the radii of low-mass pre-main sequence stars

A polytropic model is used to investigate the effects of dark photospheric spots on the evolution and radii of magnetically active, low-mass (M<0.5Msun), pre-main sequence (PMS) stars. Spots slow the contraction along Hayashi tracks and inflate the radii of PMS stars by a factor of (1-beta)^{-N} compared to unspotted stars of the same luminosity, where beta is the equivalent covering fraction of dark starspots and N \simeq 0.45+/-0.05. This is a much stronger inflation than predicted by the models of Spruit & Weiss (1986) for main sequence stars with the same beta, where N \sim 0.2 to 0.3. These models have been compared to radii determined for very magnetically active K- and M-dwarfs in the young Pleiades and NGC 2516 clusters, and the radii of tidally-locked, low-mass eclipsing binary components. The binary components and ZAMS K-dwarfs have radii inflated by \sim 10 per cent compared to an empirical radius-luminosity relation that is defined by magnetically inactive field dwarfs with interferometrically measured radii; low-mass M-type PMS stars, that are still on their Hayashi tracks, are inflated by up to \sim 40 per cent. If this were attributable to starspots alone, we estimate that an effective spot coverage of 0.35 < beta < 0.51 is required. Alternatively, global inhibition of convective flux transport by dynamo-generated fields may play a role. However, we find greater consistency with the starspot models when comparing the loci of active young stars and inactive field stars in colour-magnitude diagrams, particularly for the highly inflated PMS stars, where the large, uniform temperature reduction required in globally inhibited convection models would cause the stars to be much redder than observed.Comment: MNRAS in press, 13 page

On the lithium abundance dispersion in late-type Pleiades stars

I present the results of a programme to monitor the strengths of the Li I 6708A, K I 7699A and chromospheric Halpha lines in a group of cool Pleiades stars. Consistent instrumentation and analysis techniques are used to show that there is no Li I variability on timescales of 1 year that could possibly account for the apparent spread in Li abundances seen in Pleiades stars between effective temperatures of 4800-5200K. Comparison with published data reveals tentative evidence for variability on 10 year timescales, but at a very low level. The lack of chromospheric activity variability above levels of 20 to 30 percent makes it difficult however, to rule out evenly distributed magnetic activity regions causing a scatter in the Li I line strengths at a given abundance. The similar star to star scatter of K I line strengths in these and published data reinforces the conclusion that it is still unsafe to attribute the Li I line strength dispersion to a large variation in Li depletion at a given mass.Comment: Latex 7 pages, 3 postscript figures to appear in MNRA

Ages and Age Spreads in Young Stellar Clusters

I review progress towards understanding the time-scales of star and cluster formation and of the absolute ages of young stars. I focus in particular on the areas in which Francesco Palla made highly significant contributions - interpretation of the Hertzsprung-Russell diagrams of young clusters and the role of photospheric lithium as an age diagnostic.Comment: To appear in "Francesco's Legacy: Star Formation in Space and Time", Memorie della SAIt, in press. Eds. R. Cesaroni, E. Corbelli and D. Galli. 5p

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

Synthesis of the Beryllium 3131A Spectral Region

The Beryllium spectral region of the Sun, Procyon and 4 stars in the open cluster NGC6633 up to Teff = 7500K have been synthesised using ATLAS9 model atmospheres and the MOOG spectral synthesis program. The line list used for these syntheses has been modified from the ATLAS9 line list to improve the quality of the fits in light of the improved opacities in the new version of the MOOG code. Significant changes have been made to the Mn I line at ATLAS9 wavelength 3131.037A and an OH line has been added at 3131.358A. In addition there are a number of minor changes to gf-values throughout the synthesised region thus improving the fit for the spectra across the temperature range considerably.Comment: 4 pages, 3 figures. To appear in the proceedings of the Workshop "ATLAS 12 and related codes", Trieste, July 11-15, 200