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Binary stars are of course more than two stars, but they are also at least two stars. This chapter will review some aspects of the physics governing the evolution of single massive stars. It will also review the uncertainties of key physical ingredients: mass loss, rotation and convection.
Color-magnitude diagrams of open clusters reveal many stars that do not fall on cluster main sequences or red giant branches including blue straggler stars, yellow giants, and sub-subgiants. In fact, as many as a quarter of the evolved stars in older open clusters do not fall on standard single-star isochrones. Rather than being anomalies, these stars are following frequently travelled alternative paths of stellar evolution. Most of these stars are in binary systems, and their origins likely stem from mass transfer, mergers and collisions within binaries. This chapter presents an overview of recent observational and modelling work to understand the processes that shape these alternative stellar evolution pathways, including an HST study of the blue straggler population of NGC 188, an abundance study of the blue stragglers of NGC 6819, establishing yellow giants as evolved blue straggler stars using asteroseismology, exploration of a new class of stars known as sub-subgiants, rotational identification of main sequence blue stragglers with Kepler/K2 and new insights into the angular momentum evolution of blue stragglers.
With stellar masses in the range of eight to several hundreds of solar masses, massive stars are among the most important cosmic engines. Each individual object strongly impact its local environment, and entire populations of massive stars have been driving the evolution of galaxies throughout the history of the Universe. Over the last two decades, it has become increasingly clear that massive stars do not form nor live in isolation but rather as part of a binary or higher-order multiple system. Understanding the life cycle of massive multiple systems, from their birth to their death as supernovae and long-duration gamma ray bursts, is thus one of the most pressing scientific endeavours in modern astrophysics. In this quest, observations offer a critical insight that both guide theoretical developments and challenge the model predications. This chapter provides an overview of the observational constraints of the multiplicity properties of OB stars obtained since 2010.
In 1543, Nicolaus Copernicus published a radical new theory of the heavens. He proposed that the Earth rotates on its axis while the celestial sphere remains stationary. He also placed the Sun at rest near the center of the celestial sphere, while the Earth and other planets orbited around the Sun. Copernicus’ heliocentric theory could account for the motions of the stars, Sun, and planets about as well as Ptolemy’s theory did. It also helped to explain certain features of planetary motion that were mysterious in Ptolemy’s model. However, the idea that the Earth moved was too revolutionary for most of Copernicus’ contemporaries. While Copernicus believed that his model represented the real motions of the universe, most of his readers denied the Earth’s motion and accepted Copernicus' theory as nothing more than a useful mathematical device.
We extend known results concerning crossing numbers by giving the crossing
number of the join product
, where the connected graph
consists of one
-cycle and of two leaves incident with the same vertex of
isolated vertices. The proofs are done with the help of
software that generates all cyclic permutations for a given number
and creates a graph for calculating the distances between
vertices of the graph.
To investigate the necessity of rotational shifts by considering dosimetric impact of rotational errors on stereotactic body radiation therapy (SBRT).
Materials and methods
20 lung patients with the lesion size <5 cm treated with SBRT have been selected for dosimetric analysis. Three-dimensional dose has been rotationally shifted (±1°, ±3°, ±5° for pitch, roll and yaw) and overlaid to the original computed tomography images. The dose–volume histograms of 18-rotational plans of each patient were compared to those of the original plan.
No significant dosimetric differences were observed in target coverage. For all of the cases up to 5° in any couch angle dose differences of D99 and D95 were <3%. Variations of conformity index were observed to be less than 0·05. None of the organ at risk doses exceeded the dose limit. The V20 differences of the ipsilateral and the total lungs were less than 0·4%.
It has been found to be unnecessary to perform rotational shifts up to 5° for lung SBRT treatments; the translational shift is sufficient for the cases used in this study. This method may be applied and tested after planning and before treatment initiation to rule out exceptionally extreme cases.
New observations of Kepler δ Scuti stars show that our understanding of pulsation in these stars is incomplete. A large fraction of A and B stars exhibit rotational modulation in light, suggesting that spots exist in stars with radiative envelopes. Flares are seen in some A stars, as may be expected if starspots are present. Differential rotation shear increases from M to F but decreases for A stars; it reaches a maximum among the γ Doradus variables. Current views of stars with radiative envelopes may need to be reviewed in the light of these observations.
The present paper deals with a general dynamical qualitative study of the rotational motion for cometary-type bodies submitted to gravitational torques. Numerical experiments of the evolution of comet nucleus attitude have been then performed, including the Sun and Jupiter's disturbing torques in the model. Results show small effects of the solar gravitational perturbation for Halley-type orbits. Only a very close-approach with Jupiter induces notable effects. The latter configuration presents some interesting sensitivity to initial conditions.
The physics of massive stars depends (at least) on convection, mass loss by stellar winds, rotation, magnetic fields and multiplicity. We briefly discuss the impact of the first three processes on the stellar yields trying to identify some guidelines for future works.
In the present study, unsteady MHD boundary layer flow of a rotating Walters’-B fluid (viscoelastic fluid) over an infinite vertical porous plate embedded in a uniform porous medium with fluctuating wall temperature and concentration taking Hall and ion-slip effects into consideration is discussed. The MHD flow in the rotating fluid system is induced due to the non-torsional oscillations of the plate in its own plane and the buoyancy forces arises from temperature and concentration differences in field of gravity. The partial differential equations governing the fluid motion are solved analytically by using regular perturbation and variable separable methods by assuming very small viscoelastic parameter. Solution for velocity field in the case when natural frequency due to rotation and Hall current is equals to the frequency of oscillations i.e. in the case of resonance is also obtained. In order to note the influences of various system parameters and to discuss the important flow characteristics, the numerical results for fluid velocity in the non-resonance case, temperature and species concentration are computed and depicted graphically versus boundary layer parameter whereas skin friction, Nusselt number and Sherwood number at the plate are computed and presented in tabular form. An interesting observation recorded that there arises flow reversal in the primary flow direction due to high rotation. When natural frequency is greater than the frequency of oscillations the fluid velocity in the primary flow direction is maximum at the plate whereas incase when natural frequency is smaller than the frequency of oscillations, it is maximum in the neighborhood of the plate.
Massive stars have a strong impact on their surroundings, in particular when they produce a core-collapse supernova at the end of their evolution. In these proceedings, we review the general evolution of massive stars and their properties at collapse as well as the transition between massive and intermediate-mass stars. We also summarise the effects of metallicity and rotation. We then discuss some of the major uncertainties in the modelling of massive stars, with a particular emphasis on the treatment of convection in 1D stellar evolution codes. Finally, we present new 3D hydrodynamic simulations of convection in carbon burning and list key points to take from 3D hydrodynamic studies for the development of new prescriptions for convective boundary mixing in 1D stellar evolution codes.
We give a brief overview of where we stand with respect to some old and new questions bearing on how massive stars evolve and end their lifetime. We focus on the following key points that are further discussed by other contributions during this conference: convection, mass losses, rotation, magnetic field and multiplicity. For purpose of clarity, each of these processes are discussed on its own but we have to keep in mind that they are all interacting between them offering a large variety of outputs, some of them still to be discovered.
Recent spectropolarimetric surveys of bright, hot stars have found that ~10% of OB-type stars contain strong (mostly dipolar) surface magnetic fields (~kG). The prominent paradigm describing the interaction between the stellar winds and the surface magnetic field is the magnetically confined wind shock (MCWS) model. In this model, the stellar wind plasma is forced to move along the closed field loops of the magnetic field, colliding at the magnetic equator, and creating a shock. As the shocked material cools radiatively it will emit X-rays. Therefore, X-ray spectroscopy is a key tool in detecting and characterizing the hot wind material confined by the magnetic fields of these stars. Some B-type stars are found to have very short rotational periods. The effects of the rapid rotation on the X-ray production within the magnetosphere have yet to be explored in detail. The added centrifugal force due to rapid rotation is predicted to cause faster wind outflows along the field lines, leading to higher shock temperatures and harder X-rays. However, this is not observed in all rapidly rotating magnetic B-type stars. In order to address this from a theoretical point of view, we use the X-ray Analytical Dynamical Magnetosphere (XADM) model, originally developed for slow rotators, with an implementation of new rapid rotational physics. Using X-ray spectroscopy from ESA’s XMM-Newton space telescope, we observed 5 rapidly rotating B-types stars to add to the previous list of observations. Comparing the observed X-ray luminosity and hardness ratio to that predicted by the XADM allows us to determine the role the added centrifugal force plays in the magnetospheric X-ray emission of these stars.
Observations of various solar-type stars along decades showed that they could have magnetic cycles, just like our Sun. These observations yield a relation between the rotation period Prot and the cycle length Pcycle of these stars. Two distinct branches for the cycling stars were identified: active and inactive, classified according to stellar activity level and rotation rate. In this work, we determined the magnetic activity cycle for 6 active stars observed by the Kepler telescope. The method adopted here estimates the activity from the excess in the residuals of the transit light curves. This excess is obtained by subtracting a spotless model transit from the light curve, and then integrating over all the residuals during the transit. The presence of long term periodicity is estimated from the analysis of a Lomb-Scargle periodogram of the complete time series. Finally, we investigate the rotation-cycle period relation for the stars analysed here.
We here discuss the various dynamo models which have been designed to explain the generation and evolution of large-scale magnetic fields in stars. We focus on the models that have been applied to the Sun and can be tested for other solar-type stars now that modern observational techniques provide us with detailed stellar magnetic field observations. Mean-field flux-transport dynamo models have been developed for decades to explain the solar cycle and applications to more rapidly-rotating stars are discussed. Tremendous recent progress has been made on 3D global convective dynamo models. They do not however for now produce regular flux emergence that could be responsible for surface active regions and questions about the role of these active regions in the dynamo mechanism are still difficult to address with such models. We finally discuss 3D kinematic dynamo models which could constitute a promising combined approach, in which data assimilation could be applied.
The role of tachoclines, the thin shear layers that separate solid body from differential rotation in the interior of late-type stars, in stellar dynamos is still controversial. In this work we discuss their relevance in view of recent results from global dynamo simulations performed with the EULAG-MHD code. The models have solar-like stratification and different rotation rates (i.e., different Rossby number). Three arguments supporting the key role of tachoclines are presented: the solar dynamo cycle period, the origin of torsional oscillations and the scaling law of stellar magnetic fields as function of the Rossby number. This scaling shows a regime where the field strength increases with the rotation and a saturated regime for fast rotating stars. These properties are better reproduced by models that consider the convection zone and a fraction of the radiative core, naturally developing a tachocline, than by those that consider only the convection zone.
The role played by rotationally-induced mixing in the diffusion-based models for non-magnetic chemically peculiar stars is investigated. This paper focuses on one specific rotationally controlled mixing mechanism, namely thermally-driven meridional circulation. Its effects on the time evolution of chemical abundances are illustrated by means of three specific examples. The first two concern the diffusion model for FmAm stars, where it is shown that while circulation has a determining influence on the settling of Helium, it has no significant effect on the diffusion of heavier metals once the He superficial convection zone has disappeared. The third example is concerned with the diffusion/mass loss model for λBootis stars. It is shown that the inclusion of circulation prevents the appearance of generalized underabundances at any epoch of the evolution, indicating that the diffusion/mass loss model for these objects must be abandoned.
We present a selection of results from a large set of numerical simulations of the spin-down of a solar-type star containing a large scale magnetic field in its radiative interior. Our computations are dynamical, in that they take into account both the generation of the toroidal component by the wind-induced shear endits back-reaction on the azimuthal flow. Our results demonstrate the existence of classes of internal magnetic fields that can accomodate rapid spin-down near the ZAMS, and yield weak internal differential rotation by the solar age.
The material used to form the CEMP-no stars presents signatures of processing by the CNO cycle and by He-burning from a previous stellar generation called spinstars. We compare the composition of the ejecta (wind + supernova) of a spinstar model to observed abundances of CEMP-no stars. We show that observed abundances as well as the isotope ratio 12C/13C may be reproduced by the spinstar ejecta if we assume different mass cuts when adding the supernova material to the wind ejecta.