Rotation of Horizontal Branch Stars in Globular Clusters

The rotation of horizontal branch stars places important constraints on angular momentum evolution in evolved stars and therefore rotational mixing on the giant branch. Prompted by new observations of rotation rates of horizontal branch stars, we calculate simple models for the angular momentum evolution of a globular cluster giant star from the base of the giant branch to the star's appearance on the horizontal branch. We include mass loss, and infer the accompanied loss of angular momentum for each of four assumptions about the internal angular momentum profile. These models are compared to observations of horizontal branch rotation rates in M13. We find that rapid rotation on the horizontal branch can be reconciled with slow solid body main sequence rotation if giant branch stars have differential rotation in their convective envelopes and a rapidly rotating core, which is then followed by a redistribution of angular momentum on the horizontal branch. We discuss the physical reasons why these very different properties relative to the solar case may exist in giants. Rapid rotation in the core of the main sequence precursors of the rapidly rotating horizontal branch star, or an angular momentum source on the giant branch is required for all cases if the rotational velocity of turnoff stars is less than 4 km s$^{-1}$. We suggest that the observed range in rotation rates on the horizontal branch is caused by internal angular momentum redistribution which occurs on a timescale comparable to the evolution of the stars on the horizontal branch. The apparent lack of rapid horizontal branch rotators hotter than 12 000 K in M13 could be a consequence of gravitational settling, which inhibits internal angular momentum transport. Alternative explanations and observational tests are discussed.Comment: 32 pages, 7 figures, submitted to the Astrophysical Journa

Models of Individual Blue Stragglers

This chapter describes the current state of models of individual blue stragglers. Stellar collisions, binary mergers (or coalescence), and partial or ongoing mass transfer have all been studied in some detail. The products of stellar collisions retain memory of their parent stars and are not fully mixed. Very high initial rotation rates must be reduced by an unknown process to allow the stars to collapse to the main sequence. The more massive collision products have shorter lifetimes than normal stars of the same mass, while products between low mass stars are long-lived and look very much like normal stars of their mass. Mass transfer can result in a merger, or can produce another binary system with a blue straggler and the remnant of the original primary. The products of binary mass transfer cover a larger portion of the colour-magnitude diagram than collision products for two reasons: there are more possible configurations which produce blue stragglers, and there are differing contributions to the blended light of the system. The effects of rotation may be substantial in both collision and merger products, and could result in significant mixing unless angular momentum is lost shortly after the formation event. Surface abundances may provide ways to distinguish between the formation mechanisms, but care must be taking to model the various mixing mechanisms properly before drawing strong conclusions. Avenues for future work are outlined.Comment: Chapter 12, in Ecology of Blue Straggler Stars, H.M.J. Boffin, G. Carraro & G. Beccari (Eds), Astrophysics and Space Science Library, Springe

Constraining global properties of the Draco dwarf spheroidal galaxy

By fitting a flexible stellar anisotropy model to the observed surface brightness and line-of-sight velocity dispersion profiles of Draco we derive a sequence of cosmologically plausible two-component (stars + dark matter) models for this galaxy. The models are consistent with all the available observations and can have either cuspy Navarro-Frenk-White or flat-cored dark matter density profiles. The dark matter halos either formed relatively recently (at z~2...7) and are massive (up to ~5x10^9 M_Sun), or formed before the end of the reionization of the universe (z~7...11) and are less massive (down to ~7x10^7 M_Sun). Our results thus support either of the two popular solutions of the "missing satellites" problem of Lambda cold dark matter cosmology - that dwarf spheroidals are either very massive, or very old. We carry out high-resolution simulations of the tidal evolution of our two-component Draco models in the potential of the Milky Way. The results of our simulations suggest that the observable properties of Draco have not been appreciably affected by the Galactic tides after 10 Gyr of evolution. We rule out Draco being a "tidal dwarf" - a tidally disrupted dwarf galaxy. Almost radial Draco orbits (with the pericentric distance <15 kpc) are also ruled out by our analysis. The case of a harmonic dark matter core can be consistent with observations only for a very limited choice of Draco orbits (with the apocentric-to-pericentric distances ratio of <2.5).Comment: 18 pages, 14 figures; accepted by Ap

The Dynamical Implications of Multiple Stellar Formation Events in Galactic Globular Clusters

Various galactic globular clusters display abundance anomalies that affect the morphology of their colour-magnitude diagrams. In this paper we consider the possibility of helium enhancement in the anomalous horizontal branch of NGC 2808. We examine the dynamics of a self-enrichment scenario in which an initial generation of stars with a top-heavy initial mass function enriches the interstellar medium with helium via the low-velocity ejecta of its asymptotic giant branch stars. This enriched medium then produces a second generation of stars which are themselves helium-enriched. We use a direct N-body approach to perform five simulations and conclude that such two-generation clusters are both possible and would not differ significantly from their single-generation counterparts on the basis of dynamics. We find, however, that the stellar populations of such clusters would differ from single-generation clusters with a standard initial mass function and in particular would be enhanced in white dwarf stars. We conclude, at least from the standpoint of dynamics, that two-generation globular clusters are feasible.Comment: 24 pages, 7 figures, 3 tables. Accepted for publication in Ap

Monte Carlo Simulations of Globular Cluster Evolution. V. Binary Stellar Evolution

We study the dynamical evolution of globular clusters containing primordial binaries, including full single and binary stellar evolution using our Monte Carlo cluster evolution code updated with an adaptation of the single and binary stellar evolution codes SSE/BSE from Hurley et. al (2000, 2002). We describe the modifications we have made to the code. We present several test calculations and comparisons with existing studies to illustrate the validity of the code. We show that our code finds very good agreement with direct N-body simulations including primordial binaries and stellar evolution. We find significant differences in the evolution of the global properties of the simulated clusters using stellar evolution compared to simulations without any stellar evolution. In particular, we find that the mass loss from stellar evolution acts as a significant energy production channel simply by reducing the total gravitational binding energy and can significantly prolong the initial core contraction phase before reaching the binary-burning quasi steady state of the cluster evolution as noticed in Paper IV. We simulate a large grid of clusters varying the initial cluster mass, binary fraction, and concentration and compare properties of the simulated clusters with those of the observed Galactic globular clusters (GGCs). We find that our simulated cluster properties agree well with the observed GGC properties. We explore in some detail qualitatively different clusters in different phases of their evolution, and construct synthetic Hertzprung-Russell diagrams for these clusters.Comment: 46 preprint pages, 18 figures, 3 tables, submitted to Ap

Stellar Collisions and the Interior Structure of Blue Stragglers

Collisions of main sequence stars occur frequently in dense star clusters. In open and globular clusters, these collisions produce merger remnants that may be observed as blue stragglers. Detailed theoretical models of this process require lengthy hydrodynamic computations in three dimensions. However, a less computationally expensive approach, which we present here, is to approximate the merger process (including shock heating, hydrodynamic mixing, mass ejection, and angular momentum transfer) with simple algorithms based on conservation laws and a basic qualitative understanding of the hydrodynamics. These algorithms have been fine tuned through comparisons with the results of our previous hydrodynamic simulations. We find that the thermodynamic and chemical composition profiles of our simple models agree very well with those from recent SPH (smoothed particle hydrodynamics) calculations of stellar collisions, and the subsequent stellar evolution of our simple models also matches closely that of the more accurate hydrodynamic models. Our algorithms have been implemented in an easy to use software package, which we are making publicly available (see http://vassun.vassar.edu/~lombardi/mmas/). This software could be used in combination with realistic dynamical simulations of star clusters that must take into account stellar collisions.Comment: This revised version has 37 pages, 13 figures, 4 tables; submitted to ApJ; for associated software package, see http://vassun.vassar.edu/~lombardi/mmas/ This revised version presents additional comparisons with SPH results and slightly improved merger recipe

Dynamical age differences among coeval star clusters as revealed by blue stragglers

Globular star clusters that formed at the same cosmic time may have evolved rather differently from a dynamical point of view (because that evolution depends on the internal environment) through a variety of processes that tend progressively to segregate stars more massive than the average towards the cluster centre. Therefore clusters with the same chronological age may have reached quite different stages of their dynamical history (that is, they may have different dynamical ages). Blue straggler stars have masses greater than those at the turn-off point on the main sequence and therefore must be the result of either a collision or a mass-transfer event. Because they are among the most massive and luminous objects in old clusters, they can be used as test particles with which to probe dynamical evolution. Here we report that globular clusters can be grouped into a few distinct families on the basis of the radial distribution of blue stragglers. This grouping corresponds well to an effective ranking of the dynamical stage reached by stellar systems, thereby permitting a direct measure of the cluster dynamical age purely from observed properties.Comment: Published on the 20 December 2012 issue of Natur

Modest-2: A Summary

This is a summary paper of MODEST-2, a workshop held at the Astronomical Institute ``Anton Pannekoek'' in Amsterdam, 16-17 December 2002. MODEST is a loose collaboration of people interested in MOdelling DEnse STellar systems, particularly those interested in modelling these systems using all the available physics (stellar dynamics, stellar evolution, hydrodynamics and the interplay between the three) by defining interfaces between different codes. In this paper, we summarize 1) the main advances in this endeavour since MODEST-1; 2) the main science goals which can be and should be addressed by these types of simulations; and 3) the most pressing theoretical and modelling advances that we identified.Comment: Accepted by New Astronom

The Angular Momentum Evolution of Very Low Mass Stars

We present theoretical models of the angular momentum evolution of very low mass stars (0.1 - 0.5 M_sun) and solar analogues (0.6 - 1.1 M_sun). We investigate the effect of rotation on the effective temperature and luminosity of these stars. We find that the decrease in T_eff and L can be significant at the higher end of our mass range, but becomes negligible below 0.4 M_sun. Formulae for relating T_eff to mass and v_rot are presented. We compare our models to rotational data from young open clusters of different ages to infer the rotational history of low mass stars, and the dependence of initial conditions and rotational evolution on mass. We find that the qualitative conclusions for stars below 0.6 M_sun do not depend on the assumptions about internal angular momentum transport, which makes these low mass stars ideal candidates for the study of the angular momentum loss law and distribution of initial conditions. We find that neither models with solid body nor differential rotation can simultaneously reproduce the observed stellar spin down in the 0.6 to 1.1 M_sun mass range and for stars between 0.1 and 0.6 M_sun. The most likely explanation is that the saturation threshold drops more steeply at low masses than would be predicted with a simple Rossby scaling. In young clusters there is a systematic increase in the mean rotation rate with decreased temperature below 3500 K (0.4 M_sun). This suggests either inefficient angular momentum loss or mass-dependent initial conditions for stars near the fully convective boundary. (abridged)Comment: To appear in the May 10, 2000 Ap