The evolution of rotating stars

First, we review the main physical effects to be considered in the building of evolutionary models of rotating stars on the Upper Main-Sequence (MS). The internal rotation law evolves as a result of contraction and expansion, meridional circulation, diffusion processes and mass loss. In turn, differential rotation and mixing exert a feedback on circulation and diffusion, so that a consistent treatment is necessary. We review recent results on the evolution of internal rotation and the surface rotational velocities for stars on the Upper MS, for red giants, supergiants and W-R stars. A fast rotation is enhancing the mass loss by stellar winds and reciprocally high mass loss is removing a lot of angular momentum. The problem of the ``break-up'' or $\Omega$-limit is critically examined in connection with the origin of Be and LBV stars. The effects of rotation on the tracks in the HR diagram, the lifetimes, the isochrones, the blue to red supergiant ratios, the formation of W-R stars, the chemical abundances in massive stars as well as in red giants and AGB stars, are reviewed in relation to recent observations for stars in the Galaxy and Magellanic Clouds. The effects of rotation on the final stages and on the chemical yields are examined, as well as the constraints placed by the periods of pulsars. On the whole, this review points out that stellar evolution is not only a function of mass M and metallicity Z, but of angular velocity $\Omega$ as well.Comment: 78 pages, 7 figures, review for Annual Review of Astronomy and Astrophysics, vol. 38 (2000

The eclipsing LMC star OGLE05155332--6925581: a clue for Double Periodic Variables

We investigate the nature of OGLE05155332-6925581, one of the brightest members of the enigmatic group of Double Periodic Variables (DPVs) recently found in the Magellanic Clouds. The modeling of archival orbital light curves (LCs), along with the analysis of the radial velocities suggest that this object is a semi--detached binary with the less massive star transferring matter to the more massive and less evolved star, in an Algol--like configuration. We find evidence for additional orbital variability and H$\alpha$ emission, likely caused by an accretion disc around the primary star. As in the case of $\beta Lyr$ the circumprimary disc seems to be more luminous than the primary, but we do not detect orbital period changes. We find that the LC follows a loop in the color--magnitude diagram during the long cycle; the system is redder when brighter and the rising phase is bluer than during decline. Infrared excess is also present. The source of the long--term periodicity is not eclipsed, indicating its circumbinary origin. Strong asymmetries, discrete absorption components (DACs) and a $\gamma$ shift are new and essential observational properties in the infrared H I lines. The DACs strength and RV follow a saw--teeth pattern during the orbital cycle. We suggest that the system experiences supercycles of mass outflow feeding a circumbinary disc. Mass exchange and mass loss could produce comparable but opposite effects in the orbital period on a long time scale, resulting in a quasi--constancy of this parameter.Comment: submitted to MNRA

Efficiency of mass transfer in massive close binaries, Tests from double-lined eclipsing binaries in the SMC

One of the major uncertainties in close binary evolution is the efficiency of mass transfer beta: the fraction of transferred mass that is accreted by a secondary star. We attempt to constrain the mass-transfer efficiency for short-period massive binaries undergoing case A mass transfer. We present a grid of about 20,000 detailed binary evolution tracks with primary masses 3.5-35 Msun, orbital periods 1-5 days at a metallicity Z=0.004, assuming both conservative and non-conservative mass transfer. We perform a systematic comparison, using least-squares fitting, of the computed models with a sample of 50 double-lined eclipsing binaries in the Small Magellanic Cloud, for which fundamental stellar parameters have been determined. About 60% of the systems are currently undergoing slow mass transfer. In general we find good agreement between our models and the observed detached systems. However, for many of the semi-detached systems the observed temperature ratio is more extreme than our models predict. For the 17 semi-detached systems that we are able to match, we find a large spread in the best fitting mass-transfer efficiency; no single value of beta can explain all systems. We find a hint that initially wider systems tend to fit better to less conservative models. We show the need for more accurate temperature determinations and we find that determinations of surface abundances of nitrogen and carbon can potentially constrain the mass-transfer efficiency further.Comment: Accepted for publication in A&A 15/03/2007, 16 page

A VLT/FLAMES survey for massive binaries in Westerlund 1: II. Dynamical constraints on magnetar progenitor masses from the eclipsing binary W13

Context. Westerlund 1 is a young, massive Galactic starbust cluster that contains a rich coeaval population of Wolf-Rayet stars, hot- and cool-phase transitional supergiants, and a magnetar. Aims. We use spectroscopic and photometric observations of the eclipsing double-lined binary W13 to derive dynamical masses for the two compnents, in order to determine limits for the progenitor masses of the magnetar CXOU J164710.2-455216 and the population of evolved stars in Wd1. Methods. We use eleven epochs of high-resolution VLT/FLAMES spectroscopy to construct a radial velocity curve for W13. R-band photometry is used to constrain the inclination of the system. Results. W13 has an orbital period of $9.27090\pm0015$ days and near-contact configuration. The shallow photometric eclipse rules out an inclination greater than 65°, leading to lower limits for the masses of the emission-line optical primary and supergiant optical secondary of $21.4\pm2.6M_{\odot}$ and $32.8\pm4.0M_{\odot}$ respectively, rising to $23.2_{-3.0}^{+3.3}M_{\odot}$ and $35.4_{-4.6}^{+5.0}M_{\odot}$ for our best-fit inclination $62_{-4}^{+3}$ degrees. Comparison with theoretical models of Wolf-Rayet binary evolution suggest the emission-line object had an initial mass in excess of $\sim35M_{\odot}$, with the most likely model featuring highly non-conservative late-Case A/Case B mass transfer and an initial mass in excess of $40M_{\odot}$. Conclusions. This result confirms the high progenitor mass of the magnetar CXOU J164710.2-455216 inferred from its membership in Wd1, and represents the first dynamical constraint on the progenitor mass of any magnetar. The red supergiants in Wd1 must have similar progenitor masses to W13 and are therefore amongst the most massive stars to undergo a red supergiant phase, representing a challenge for population models that suggest stars in this mass range end their redwards evolution as yellow hypergiants

Observational constraints from models of close binary evolution

The evolution of a system of 9 MO + 5.4 MO is computed from Zero Age Main Sequence through an early case B of mass exchange, up to the second phase of mass transfer after core helium burning. Both components are calculated simultaneously. The evolution is divided into several physically different phases. The characteristics of the models in each of these phases are transformed into corresponding ‘observable’ quantities. The outlook of the system for photometric observations is discussed, for an idealized case. The influence of the mass of the loser, mli, and the initial mass ratio qi is considered.</jats:p

Who is Who in Algol-Land ? - Part II -

AbstractIn part I (De Greve and Packet) we have investigated the occurrence of reversed phases of mass-transfer during Case A evolution in close binaries. If the initial period of a system is shorter than 1 - 2 days (Early Case A) the reversed phase starts before core hydrogen exhaustion of the gainer (part I). This type of evolution is characterized by at least two phases of slow mass-transfer.We have computed the evolution of four Early Case A systems with initial masses of the loser equal to 3 Mo and 5 Mo. These four systems start mass-exchange when Xc of the primary has decreased to 0.525 (75% of its initial value). They all experience two phases of slow mass-transfer.We find that both phases have about the same duration for all systems. The mass ratios are clearly distinct, being closer to unity during the first phase. In the Hertzsprung-Russell, mass-radius and mass-luminosity diagrams both components remain close to the main-sequence band during slow mass-transfer. Evolution as an Algol is ended when both components overflow their outer critical surface after a second reversal of the mass-transfer.Observed Algol systems evolving in Early Case A are scarce. A search thruogh the catalogue by Giuricin et al. gives us the following candidates: X Tri, SX Aur and V Pup. Based on their mass ratios, SX Aur can tentatively be assigned to the first phase of slow mass transfer and X Tri to the second phase. For V Pup (which is more massive) this choice can not be made with certainty.</jats:p