Direct N-body Modelling of Stellar Populations: Blue Stragglers in M67

We present a state-of-the-art N-body code which includes a detailed treatment of stellar and binary evolution as well as the cluster dynamics. This code is ideal for investigating all aspects relating to the evolution of star clusters and their stellar populations. It is applicable to open and globular clusters of any age. We use the N-body code to model the blue straggler population of the old open cluster M67. Preliminary calculations with our binary population synthesis code show that binary evolution alone cannot explain the observed numbers or properties of the blue stragglers. On the other hand, our N-body model of M67 generates the required number of blue stragglers and provides formation paths for all the various types found in M67. This demonstrates the effectiveness of the cluster environment in modifying the nature of the stars it contains and highlights the importance of combining dynamics with stellar evolution. We also perform a series of N = 10000 simulations in order to quantify the rate of escape of stars from a cluster subject to the Galactic tidal field.Comment: 26 pages, 18 figures, accepted for publication in MNRA

A Complete N-body Model of the Old Open Cluster M67

The old open cluster M67 is an ideal testbed for current cluster evolution models because of its dynamically evolved structure and rich stellar populations that show clear signs of interaction between stellar, binary and cluster evolution. Here we present the first truly direct N-body model for M67, evolved from zero age to 4 Gyr taking full account of cluster dynamics as well as stellar and binary evolution. Our preferred model starts with 12000 single stars and 12000 binaries placed in a Galactic tidal field at 8.0 kpc from the Galactic Centre. Our choices for the initial conditions and for the primordial binary population are explained in detail. At 4 Gyr, the age of M67, the total mass has reduced by 90% as a result of mass loss and stellar escapes. The mass and half-mass radius of luminous stars in the cluster are a good match to observations although the model is more centrally concentrated than observations indicate. The stellar mass and luminosity functions are significantly flattened by preferential escape of low-mass stars. We find that M67 is dynamically old enough that information about the initial mass function is lost, both from the current luminosity function and from the current mass fraction in white dwarfs. The model contains 20 blue stragglers at 4 Gyr which is slightly less than the 28 observed in M67. Nine are in binaries. The blue stragglers were formed by a variety of means and we find formation paths for the whole variety observed in M67. Both the primordial binary population and the dynamical cluster environment play an essential role in shaping the population. A substantial population of short-period primordial binaries (with periods less than a few days) is needed to explain the observed number of blue stragglers in M67.Comment: 32 pages, 17 figures, submitted to MNRA

2MASS J05162881+2607387: A New Low-Mass Double-Lined Eclipsing Binary

We show that the star known as 2MASS J05162881+2607387 (hereafter J0516) is a double-lined eclipsing binary with nearly identical low-mass components. The spectroscopic elements derived from 18 spectra obtained with the High Resolution Spectrograph on the Hobby-Eberly Telescope during the Fall of 2005 are K_1=88.45 +/- 0.48 km/s and K_2=90.43 +/- 0.60 km/s, resulting in a mass ratio of$q=K_1/K_2 = 0.978 +/- 0.018 and minimum masses of M_1 sin^{3}i=0.775 +/- 0.016 solar masses and M_2 sin^{3}i=0.759 +/- 0.012 solar masses, respectively. We have extensive differential photometry of J0516 obtained over several nights between 2004 January-March (epoch 1) and 2004 October-2005 January plus 2006 January (epoch 2) using the 1m telescope at the Mount Laguna Observatory. The source was roughly 0.1 mag brighter in all three bandpasses during epoch 1 when compared to epoch 2. Also, phased light curves from epoch 1 show considerable out-of-eclipse variability, presumably due to bright spots on one or both stars. In contrast, the phased light curves from epoch 2 show little out-of-eclipse variability. The light curves from epoch 2 and the radial velocity curves were analyzed using our ELC code with updated model atmospheres for low-mass stars. We find the following: M_1=0.787 +/- 0.012 solar masses, R_1=0.788 +/- 0.015 solar radii, M_2=0.770 +/- 0.009 solar masses, and R_2=0.817 +/- 0.010 solar radii. The stars in J0516 have radii that are significantly larger than model predictions for their masses, similar to what is seen in a handful of other well-studied low-mass double-lined eclipsing binaries. We compiled all recent mass and radius determinations from low-mass binaries and determine an empirical mass-radius relation of the form R = 0.0324 + 0.9343M + 0.0374M^2, where the quantities are in solar units.Comment: 16 pages, 10 figures (Figure 1 has degraded quality), to appear in Ap

Evaluating irreversible social harms

In this paper we investigate how irreversible social harms should be evaluated from an ethical perspective. First, we define a general notion of irreversibility, drawing on discussions in ecology and economics. This notion is relational in the sense that 'irreversibility' is always 'irreversibility for a certain party'. We also note that a change may be more or less difficult to reverse, with full reversibility and irreversibility as two extremes. Second, we examine what can make an irreversible change a harm, and why these kinds of harms have particular ethical significance. Here we draw on discussions from ethics, particularly regarding the Capability Approach. We also show how our notion of irreversibility connects to, and can add to, discussions in the fields of development studies and disaster management, particularly on the concept of resilience. Third, we suggest how potentially irreversible harms can be recognised and dealt with in policy-making. Finally, we show how our framework can be applied by evaluating the land acquisition process of two biofuel producers in Tanzania

A more detailed look at the Opacities for Enriched Carbon and Oxygen Mixtures

We have included opacity tables in our stellar evolution code that enable us to accurately model the structure of stars composed of mixtures with carbon and oxygen independently enhanced relative to solar. We present tests to demonstrate the effects of the new tables. Two of these are practical examples, the effect on the evolution of a thermally pulsing asymptotic giant branch star and a Wolf-Rayet Star. The changes are small but perceptible.Comment: 6 pages, 3 figures, 5 tables. Refereed version with corrections resubmitted to MNRA

Third Dredge-up in Low Mass Stars: Solving the LMC Carbon Star Mystery

A long standing problem with asymptotic giant branch (AGB) star models has been their inability to produce the low-luminosity carbon stars in the Large and Small Magellanic Clouds. Dredge-up must begin earlier and extend deeper. We find this for the first time in our models of LMC metallicity. Such features are not found in our models of SMC metallicity. The fully implicit and simultaneous stellar evolution code STARS has been used to calculate the evolution of AGB stars with metallicities of Z=0.008 and Z=0.004, corresponding to the observed metallicities of the Large and Small Magellanic Clouds, respecitively. Third dredge-up occurs in stars of 1Msol and above and carbon stars were found for models between 1Msol and 3Msol. We use the detailed models as input physics for a population synthesis code and generate carbon star luminosity functions. We now find that we are able to reproduce the carbon star luminosity function of the LMC without any manipulation of our models. The SMC carbon star luminosity function still cannot be produced from our detailed models unless the minimum core mass for third dredge-up is reduced by 0.06Msol.Comment: 6 pages, 5 figures. Accepted for publication in MNRA

Modelling the observed properties of carbon-enhanced metal-poor stars using binary population synthesis

The stellar population in the Galactic halo is characterised by a large fraction of CEMP stars. Most CEMP stars are enriched in $s$-elements (CEMP-$s$ stars), and some of these are also enriched in $r$-elements (CEMP-$s/r$ stars). One formation scenario proposed for CEMP stars invokes wind mass transfer in the past from a TP-AGB primary star to a less massive companion star which is presently observed. We generate low-metallicity populations of binary stars to reproduce the observed CEMP-star fraction. In addition, we aim to constrain our wind mass-transfer model and investigate under which conditions our synthetic populations reproduce observed abundance distributions. We compare the CEMP fractions and the abundance distributions determined from our synthetic populations with observations. Several physical parameters of the binary stellar population of the halo are uncertain, e.g. the initial mass function, the mass-ratio and orbital-period distributions, and the binary fraction. We vary the assumptions in our model about these parameters, as well as the wind mass-transfer process, and study the consequent variations of our synthetic CEMP population. The CEMP fractions calculated in our synthetic populations vary between 7% and 17%, a range consistent with the CEMP fractions among very metal-poor stars recently derived from the SDSS/SEGUE data sample. The results of our comparison between the modelled and observed abundance distributions are different for CEMP-$s/r$ stars and for CEMP-$s$ stars. For the latter, our simulations qualitatively reproduce the observed distributions of C, Na, Sr, Ba, Eu, and Pb. Contrarily, for CEMP-$s/r$ stars our model cannot reproduce the large abundances of neutron-rich elements such as Ba, Eu, and Pb. This result is consistent with previous studies, and suggests that CEMP-$s/r$ stars experienced a different nucleosynthesis history to CEMP-$s$ stars.Comment: 17 pages, 11 figures, accepted for publication on Astronomy and Astrophysic