Physics of rotation in stellar models

In these lecture notes, we present the equations presently used in stellar interior models in order to compute the effects of axial rotation. We discuss the hypotheses made. We suggest that the effects of rotation might play a key role at low metallicity.Comment: 32 pages, 7 figures, lectures, CNRS school, will be published by Springe

Structure Formation Inside Triaxial Dark Matter Halos: Galactic Disks, Bulges and Bars

We investigate the formation and evolution of galactic disks immersed in assembling live DM halos. Disk/halo components have been evolved from the cosmological initial conditions and represent the collapse of an isolated density perturbation. The baryons include gas (which participates in star formation [SF]) and stars. The feedback from the stellar energy release onto the ISM has been implemented. We find that (1) The growing triaxial halo figure tumbling is insignificant and the angular momentum (J) is channeled into the internal circulation; (2) Density response of the disk is out of phase with the DM, thus diluting the inner halo flatness and washing out its prolateness; (3) The total J is neathly conserved, even in models accounting for feedback; (4) The specific J for the DM is nearly constant, while that for baryons is decreasing; (5) Early stage of disk formation resembles the cat's cradle -- a small amorphous disk fueled via radial string patterns; (6) The initially puffed up gas component in the disk thins when the SF rate drops below ~5 Mo/yr; (7) About 40%-60% of the baryons remain outside the SF region; (8) Rotation curves appear to be flat and account for the observed disk/halo contributions; (9) A range of bulge-dominated to bulgeless disks was obtained; Lower density threshold for SF leads to a smaller, thicker disk; Gravitational softening in the gas has a substantial effect on various aspects of galaxy evolution and mimics a number of intrinsic processes within the ISM; (10) The models are characterized by an extensive bar-forming activity; (11) Nuclear bars, dynamically coupled and decoupled form in response to the gas inflow along the primary bars.Comment: 18 pages, 16 figures, accepted by the Astrophysical Journal. Minor revisions. The high-resolution figures can be found at http://www.pa.uky.edu/~shlosman/research/galdyn/figs07a

Effects of rotation on the evolution and asteroseismic properties of red giants

The influence of rotation on the properties of red giants is studied in the context of the asteroseismic modelling of these stars. While red giants exhibit low surface rotational velocities, we find that the rotational history of the star has a large impact on its properties during the red giant phase. In particular, for stars massive enough to ignite He burning in non-degenerate conditions, rotational mixing induces a significant increase of the stellar luminosity and shifts the location of the core helium burning phase to a higher luminosity in the HR diagram. This of course results in a change of the seismic properties of red giants at the same evolutionary state. As a consequence the inclusion of rotation significantly changes the fundamental parameters of a red giant star as determined by performing an asteroseismic calibration. In particular rotation decreases the derived stellar mass and increases the age. Depending on the rotation law assumed in the convective envelope and on the initial velocity of the star, non-negligible values of rotational splitting can be reached, which may complicate the observation and identification of non-radial oscillation modes for red giants exhibiting moderate surface rotational velocities. By comparing the effects of rotation and overshooting, we find that the main-sequence widening and the increase of the H-burning lifetime induced by rotation (Vini=150 km/s) are well reproduced by non-rotating models with an overshooting parameter of 0.1, while the increase of luminosity during the post-main sequence evolution is better reproduced by non-rotating models with overshooting parameters twice as large. This is due to the fact that rotation not only increases the size of the convective core but also changes the chemical composition of the radiative zone.Comment: 9 pages, 13 figures, accepted for publication in A&

Populations of rotating stars II. Rapid rotators and their link to Be-type stars

Even though it is broadly accepted that single Be stars are rapidly rotating stars surrounded by a flat rotating circumstellar disk, there is still a debate about how fast these stars rotate and also about the mechanisms involved in the angular-momentum and mass input in the disk. We study the properties of stars that rotate near their critical-rotation rate and investigate the properties of the disks formed by equatorial mass ejections. We used the most recent Geneva stellar evolutionary tracks for rapidly rotating stars that reach the critical limit and used a simple model for the disk structure. We obtain that for a 9 Msun star at solar metallicity, the minimum average velocity during the Main Sequence phase to reach the critical velocity is around 330 km/s, whereas it would be 390 km/s at the metallicity of the Small Magellanic Cloud (SMC). Red giants or supergiants originating from very rapid rotators rotate six times faster and show N/C ratios three times higher than those originating from slowly rotating stars. This difference becomes stronger at lower metallicity. It might therefore be very interesting to study the red giants in clusters that show a large number of Be stars on the MS band. On the basis of our single-star models, we show that the observed Be-star fraction with cluster age is compatible with the existence of a temperature-dependent lower limit in the velocity rate required for a star to become a Be star. The mass, extension, and diffusion time of the disks produced when the star is losing mass at the critical velocity, obtained from simple parametrized expressions, are not too far from those estimated for disks around Be-type stars. At a given metallicity, the mass and the extension of the disk increase with the initial mass and with age on the MS phase. Denser disks are expected in low-metallicity regions.Comment: Accepted for publication in A&A, language edite

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

Quantitative Estimates of Environmental Effects on the Star Formation Rate of Disk Galaxies in Clusters of Galaxies

A simple model is constructed to evaluate the change of star formation rate of a disk galaxy due to environmental effects in clusters of galaxies. Three effects, (1) tidal force from the potential well of the cluster, (2) increase of external pressure when the galaxy plows into the intracluster medium, (3) high-speed encounters between galaxies, are investigated. General analysis indicates that the star formation rate increases significantly when the pressure of molecular clouds rises above $\sim 3\times 10^5 cm^{-3} K$ in $\sim 10^8$ yr. The tidal force from the potential well of the cluster increases pressures of molecular clouds in a disk galaxy infalling towards the cluster center. Before the galaxy reaches the cluster center, the star formation rate reaches a maximum. The peak is three to four times larger than the initial value. If this is the main mechanism of the Butcher-Oemler effect, blue galaxies are expected to be located within $\sim 300$ kpc from the center of the cluster. However this prediction is inconsistent with the recent observations. The increase of external pressure when the galaxy plows into the intracluster medium does not change star formation rate of a disk galaxy significantly. The velocity perturbation induced by a single high-speed encounter between galaxies is too small to affect star formation rate of a disk galaxy, while successive high-speed encounters (galaxy harassment) trigger star formation activity because of the accumulation of gas in the galaxy center. Therefore, the galaxy harassment remains as the candidate for a mechanism of the Butcher-Oemler effect.Comment: 12 pages, 13 figures. To be published in Ap

Rest-Frame Ultraviolet Spectra of z~3 Lyman Break Galaxies

We present the results of a systematic study of the rest-frame UV spectroscopic properties of Lyman Break Galaxies (LBGs). The database of almost 1000 LBG spectra proves useful for constructing high S/N composite spectra. The composite spectrum of the entire sample reveals a wealth of features attributable to hot stars, HII regions, dust, and outflowing neutral and ionized gas. By grouping the database according to galaxy parameters such as Lyman-alpha equivalent width, UV spectral slope, and interstellar kinematics, we isolate some of the major trends in LBG spectra which are least compromised by selection effects. We find that LBGs with stronger Lyman-alpha emission have bluer UV continua, weaker low-ionization interstellar absorption lines, smaller kinematic offsets between Lyman-alpha and the interstellar absorption lines, and lower star-formation rates. There is a decoupling between the dependence of low- and high-ionization outflow features on other spectral properties. Most of the above trends can be explained in terms of the properties of the large-scale outflows seen in LBGs. According to this scenario, the appearance of LBG spectra is determined by a combination of the covering fraction of outflowing neutral gas which contains dust, and the range of velocities over which this gas is absorbing. Higher sensitivity and spectral resolution observations are still required for a full understanding of the covering fraction and velocity dispersion of the outflowing neutral gas in LBGs, and its relationship to the escape fraction of Lyman continuum radiation in galaxies at z~3.Comment: 28 pages including 17 figures. Accepted for publication in Ap