Mass-loss rates of Very Massive Stars

We discuss the basic physics of hot-star winds and we provide mass-loss rates for (very) massive stars. Whilst the emphasis is on theoretical concepts and line-force modelling, we also discuss the current state of observations and empirical modelling, and address the issue of wind clumping.Comment: 36 pages, 15 figures, Book Chapter in "Very Massive Stars in the Local Universe", Springer, Ed. Jorick S. Vin

PN fast winds: Temporal structure and stellar rotation

To diagnose the time-variable structure in the fast winds of central stars of planetary nebulae (CSPN), we present an analysis of P Cygni line profiles in FUSE satellite far-UV spectroscopic data. Archival spectra are retrieved to form time-series datasets for the H-rich CSPN NGC 6826, IC 418, IC 2149, IC 4593 and NGC 6543. Despite limitations due to the fragmented sampling of the time-series, we demonstrate that in all 5 CSPN the UV resonance lines are variable primarily due to the occurrence of blueward migrating discrete absorption components (DACs). Empirical (SEI) line-synthesis modelling is used to determine the range of fluctuations in radial optical depth, which are assigned to the temporal changes in large-scale wind structures. We argue that DACs are common in CSPN winds, and their empirical properties are akin to those of similar structures seen in the absorption troughs of massive OB stars. Constraints on PN central star rotation velocities are derived from Fast-Fourier Transform analysis of photospheric lines for our target stars. Favouring the causal role of co-rotating interaction regions, we explore connections between normalised DAC accelerations and rotation rates of PN central stars and O stars. The comparative properties suggest that the same physical mechanism is acting to generate large-scale structure in the line-driven winds in the two different settings.Comment: Accepted for publication in MNRAS; 10 pages, 5 figure

Wind modelling of very massive stars up to 300 solar masses

Some studies have claimed a universal stellar upper-mass limit of 150 Msun. A factor that is often overlooked is that there might be a difference between the current and initial masses of the most massive stars, as a result of mass loss. We present Monte Carlo mass-loss predictions for very massive stars in the range 40-300 Msun, with large luminosities and Eddington factors Gamma. Using our new dynamical approach, we find an upturn in the mass-loss vs. Gamma dependence, at the point where the winds become optically thick. This coincides with the location where wind efficiency numbers surpass the single-scattering limit of Eta = 1, reaching values up to Eta = 2.5. Our modelling suggests a transition from common O-type winds to Wolf-Rayet characteristics at the point where the winds become optically thick. This transitional behaviour is also revealed with respect to the wind acceleration parameter beta, which starts at values below 1 for the optically thin O-stars, and naturally reaches values as high as 1.5-2 for the optically thick Wolf-Rayet models. An additional finding concerns the transition in spectral morphology of the Of and WN characteristic He II line at 4686 Angstrom. When we express our mass-loss predictions as a function of the electron scattering Gamma_e (=L/M) only, we obtain a mass-loss Gamma dependence that is consistent with a previously reported power-law Mdot propto Gamma^5 (Vink 2006) that was based on our semi-empirical modelling approach. When we express Mdot in terms of both Gamma and stellar mass, we find Mdot propto M^0.8 Gamma^4.8 for our high Gamma models. Finally, we confirm that the Gamma-effect on the mass-loss predictions is much stronger than that of an increased helium abundance, calling for a fundamental revision in the way mass loss is incorporated in evolutionary models of the most massive stars.Comment: minor language changes (Astronomy & Astrophysics in press - 11 pages, 10 figures

Wake Development behind Paired Wings with Tip and Root Trailing Vortices: Consequences for Animal Flight Force Estimates

Recent experiments on flapping flight in animals have shown that a variety of unrelated species shed a wake behind left and right wings consisting of both tip and root vortices. Here we present an investigation using Particle Image Velocimetry (PIV) of the behaviour and interaction of trailing vortices shed by paired, fixed wings that simplify and mimic the wake of a flying animal with a non-lifting body. We measured flow velocities at five positions downstream of two adjacent NACA 0012 aerofoils and systematically varied aspect ratio, the gap between the wings (corresponding to the width of a non-lifting body), angle of attack, and the Reynolds number. The range of aspect ratios and Reynolds number where chosen to be relevant to natural fliers and swimmers, and insect flight in particular. We show that the wake behind the paired wings deformed as a consequence of the induced flow distribution such that the wingtip vortices convected downwards while the root vortices twist around each other. Vortex interaction and wake deformation became more pronounced further downstream of the wing, so the positioning of PIV measurement planes in experiments on flying animals has an important effect on subsequent force estimates due to rotating induced flow vectors. Wake deformation was most severe behind wings with lower aspect ratios and when the distance between the wings was small, suggesting that animals that match this description constitute high-risk groups in terms of measurement error. Our results, therefore, have significant implications for experimental design where wake measurements are used to estimate forces generated in animal flight. In particular, the downstream distance of the measurement plane should be minimised, notwithstanding the animal welfare constraints when measuring the wake behind flying animals

Predictions for mass-loss rates and terminal wind velocities of massive O-type stars

Mass loss forms an important aspect of the evolution of massive stars, as well as for the enrichment of the surrounding ISM. Our goal is to predict accurate mass-loss rates and terminal wind velocities. These quantities can be compared to empirical values, thereby testing radiation-driven wind models. One specific issue is that of the "weak-wind problem", where empirically derived mass-loss rates fall orders of magnitude short of predicted values. We employ an established Monte Carlo model and a recently suggested new line acceleration formalism to solve the wind dynamics consistently. We provide a new grid of mass-loss rates and terminal wind velocities of O stars, and compare the values to empirical results. Our models fail to provide mass-loss rates for main-sequence stars below a luminosity of log(L/Lsun) = 5.2, where we run into a fundamental limit. At luminosities below this critical value there is insufficient momentum transferred in the region below the sonic point to kick-start the acceleration. This problem occurs at the location of the onset of the weak-wind problem. For O dwarfs, the boundary between being able to start a wind, and failing to do so, is at spectral type O6/O6.5. The direct cause of this failure is a combination of the lower luminosity and a lack of Fe V lines at the wind base. This might indicate that another mechanism is required to provide the necessary driving to initiate the wind. For stars more luminous than log(L/Lsun) = 5.2, our new mass-loss rates are in excellent agreement with the mass-loss prescription by Vink et al. 2000. This implies that the main assumption entering the method of the Vink et al. prescriptions - i.e. that the momentum equation is not explicitly solved for - does not compromise the reliability of the Vink et al. results for this part of parameter space (Abridged).Comment: 10 pages, 10 figures, Astronomy & Astrophysics (in press

3-D radiative transfer in clumped hot star winds I. Influence of clumping on the resonance line formation

The true mass-loss rates from massive stars are important for many branches of astrophysics. For the correct modeling of the resonance lines, which are among the key diagnostics of stellar mass-loss, the stellar wind clumping turned out to be very important. In order to incorporate clumping into radiative transfer calculation, 3-D models are required. Various properties of the clumps may have strong impact on the resonance line formation and, therefore, on the determination of empirical mass-loss rates. We incorporate the 3-D nature of the stellar wind clumping into radiative transfer calculations and investigate how different model parameters influence the resonance line formation. We develop a full 3-D Monte Carlo radiative transfer code for inhomogeneous expanding stellar winds. The number density of clumps follows the mass conservation. For the first time, realistic 3-D models that describe the dense as well as the tenuous wind components are used to model the formation of resonance lines in a clumped stellar wind. At the same time, non-monotonic velocity fields are accounted for. The 3-D density and velocity wind inhomogeneities show very strong impact on the resonance line formation. The different parameters describing the clumping and the velocity field results in different line strengths and profiles. We present a set of representative models for various sets of model parameters and investigate how the resonance lines are affected. Our 3-D models show that the line opacity is reduced for larger clump separation and for more shallow velocity gradients within the clumps. Our new model demonstrates that to obtain empirically correct mass-loss rates from the UV resonance lines, the wind clumping and its 3-D nature must be taken into account.Comment: Astronomy and Astrophysics, accepted for publicatio

Enhanced flight performance by genetic manipulation of wing shape in Drosophila

Insect wing shapes are remarkably diverse and the combination of shape and kinematics determines both aerial capabilities and power requirements. However, the contribution of any specific morphological feature to performance is not known. Using targeted RNA interference to modify wing shape far beyond the natural variation found within the population of a single species, we show a direct effect on flight performance that can be explained by physical modelling of the novel wing geometry. Our data show that altering the expression of a single gene can significantly enhance aerial agility and that the Drosophila wing shape is not, therefore, optimized for certain flight performance characteristics that are known to be important. Our technique points in a new direction for experiments on the evolution of performance specialities in animals

Evolution and Nucleosynthesis of Very Massive Stars

In this chapter, after a brief introduction and overview of stellar evolution, we discuss the evolution and nucleosynthesis of very massive stars (VMS: M>100 solar masses) in the context of recent stellar evolution model calculations. This chapter covers the following aspects: general properties, evolution of surface properties, late central evolution, and nucleosynthesis including their dependence on metallicity, mass loss and rotation. Since very massive stars have very large convective cores during the main-sequence phase, their evolution is not so much affected by rotational mixing, but more by mass loss through stellar winds. Their evolution is never far from a homogeneous evolution even without rotational mixing. All VMS at metallicities close to solar end their life as WC(-WO) type Wolf-Rayet stars. Due to very important mass loss through stellar winds, these stars may have luminosities during the advanced phases of their evolution similar to stars with initial masses between 60 and 120 solar masses. A distinctive feature which may be used to disentangle Wolf-Rayet stars originating from VMS from those originating from lower initial masses is the enhanced abundances of neon and magnesium at the surface of WC stars. At solar metallicity, mass loss is so strong that even if a star is born with several hundred solar masses, it will end its life with less than 50 solar masses (using current mass loss prescriptions). At the metallicity of the LMC and lower, on the other hand, mass loss is weaker and might enable star to undergo pair-instability supernovae.Comment: 42 pages, 20 figures, Book Chapter in "Very Massive Stars in the Local Universe", Springer, Ed. Jorick S. Vin

Exploration of the rotational power consumption of a rigid flapping wing

Accepted versio