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

Massive star evolution in close binaries:conditions for homogeneous chemical evolution

We investigate the impact of tidal interactions, before any mass transfer, on various properties of the stellar models. We study the conditions for obtaining homogeneous evolution triggered by tidal interactions, and for avoiding any Roche lobe overflow during the Main-Sequence phase. We consider the case of rotating stars computed with a strong coupling mediated by an interior magnetic field. In models without any tidal interaction (single stars and wide binaries), homogeneous evolution in solid body rotating models is obtained when two conditions are realized: the initial rotation must be high enough, the loss of angular momentum by stellar winds should be modest. This last point favors metal-poor fast rotating stars. In models with tidal interactions, homogeneous evolution is obtained when rotation imposed by synchronization is high enough (typically a time-averaged surface velocities during the Main-Sequence phase above 250 km s$^{-1}$), whatever the mass losses. In close binaries, mixing is stronger at higher than at lower metallicities. Homogeneous evolution is thus favored at higher metallicities. Roche lobe overflow avoidance is favored at lower metallicities due to the fact that stars with less metals remain more compact. We study also the impact of different processes for the angular momentum transport on the surface abundances and velocities in single and close binaries. In models where strong internal coupling is assumed, strong surface enrichments are always associated to high surface velocities in binary or single star models. In contrast, models computed with mild coupling may produce strong surface enrichments associated to low surface velocities. Close binary models may be of interest for explaining homogeneous massive stars, fast rotating Wolf-Rayet stars, and progenitors of long soft gamma ray bursts, even at high metallicities.Comment: 21 pages, 13 figures, 3 tables, accepted for publication in Astronomy and Astrophysic

Presupernova Evolution of Rotating Massive Stars and the Rotation Rate of Pulsars

Rotation in massive stars has been studied on the main sequence and during helium burning for decades, but only recently have realistic numerical simulations followed the transport of angular momentum that occurs during more advanced stages of evolution. The results affect such interesting issues as whether rotation is important to the explosion mechanism, whether supernovae are strong sources of gravitational radiation, the star's nucleosynthesis, and the initial rotation rate of neutron stars and black holes. We find that when only hydrodynamic instabilities (shear, Eddington-Sweet, etc.) are included in the calculation, one obtains neutron stars spinning at close to critical rotation at their surface -- or even formally in excess of critical. When recent estimates of magnetic torques (Spruit 2002) are added, however, the evolved cores spin about an order of magnitude slower. This is still more angular momentum than observed in young pulsars, but too slow for the collapsar model for gamma-ray bursts.Comment: 10 pages, 2 figures, to appear in Proc. IAU 215 "Stellar Rotation

Spindown of massive rotating stars

Models of rapidly rotating massive stars at low metallicities show significantly different evolution and higher metal yields compared to non-rotating stars. We estimate the spin-down time-scale of rapid rotating non-convective stars supporting an alpha-Omega dynamo. The magnetic dynamo gives rise to mass loss in a magnetically controlled stellar wind and hence stellar spin down owing to loss of angular momentum. The dynamo is maintained by strong horizontal rotation-driven turbulence which dominates over the Parker instability. We calculate the spin-down time-scale and find that it could be relatively short, a small fraction of the main-sequence lifetime. The spin-down time-scale decreases dramatically for higher surface rotations suggesting that rapid rotators may only exhibit such high surface velocities for a short time, only a small fraction of their main-sequence lifetime.Comment: Accepted by MNRA

Close binary evolution I. The tidally induced shear mixing in rotating binaries

We study how tides in a binary system induce some specific internal shear mixing, able to substantially modify the evolution of close binaries prior to mass transfer. We construct numerical models accounting for tidal interactions, meridional circulation, transport of angular momentum, shears and horizontal turbulence and consider a variety of orbital periods and initial rotation velocities. Depending on orbital periods and rotation velocities, tidal effects may spin down (spin down Case) or spin up (spin up Case) the axial rotation. In both cases, tides may induce a large internal differential rotation. The resulting tidally induced shear mixing (TISM) is so efficient that the internal distributions of angular velocity and chemical elements are greatly influenced. The evolutionary tracks are modified, and in both cases of spin down and spin up, large amounts of nitrogen can be transported to the stellar surfaces before any binary mass transfer. Meridional circulation, when properly treated as an advection, always tends to counteract the tidal interaction, tending to spin up the surface when it is braked down and vice versa. As a consequence, the times needed for the axial angular velocity to become equal to the orbital angular velocity may be larger than given by typical synchronization timescales. Also, due to meridional circulation some differential rotation remains in tidally locked binary systems.Comment: 10 pages, 18 figures, Accepted for publication in Astronomy and Astrophysic

Mass Limits For Black Hole Formation

We present a series of two-dimensional core-collapse supernova simulations for a range of progenitor masses and different input physics. These models predict a range of supernova energies and compact remnant masses. In particular, we study two mechanisms for black hole formation: prompt collapse and delayed collapse due to fallback. For massive progenitors above 20 solar masses, after a hydrodynamic time for the helium core (a few minutes to a few hours), fallback drives the compact object beyond the maximum neutron star mass causing it to collapse into a black hole. With the current accuracy of the models, progenitors more massive than 40 solar masses form black holes directly with no supernova explosion (if rotating, these black holes may be the progenitors of gamma-ray bursts). We calculate the mass distribution of black holes formed, and compare these predictions to the observations, which represent a small biased subset of the black hole population. Uncertainties in these estimates are discussed.Comment: 15 pages total, 4 figures, Modifications in Conclusion, accepted by Ap

Structure and evolution of rotationally and tidally distorted stars

This paper aims to study the configuration of two components caused by rotational and tidal distortions in the model of a binary system. The potentials of the two distorted components can be approximated to 2nd-degree harmonics. Furthermore, both the accretion luminosity ($\sigma_{i}$) and the irradiative luminosity are included in stellar structure equations. The equilibrium structure of rotationally and tidally distorted star is exactly a triaxial ellipsoids. A formula describing the isobars is presented, and the rotational velocity and the gravitational acceleration at the primary surface simulated. The results show the distortion at the outer layers of the primary increases with temporal variation and system evolution. Besides, it was observed that the luminosity accretion is unstable, and the curve of the energy-generation rate fluctuates after the main sequence in rotation sequences. The luminosity in rotation sequences is slightly weaker than that in non-rotation sequences. As a result, the volume expands slowly. Polar ejection is intensified by the tidal effect. The ejection of an equatorial ring may be favoured by both the opacity effect and the $g_{e}(\theta,\varphi)$-effect in the binary system.Comment: 10 pages, 17 figures,Accepted by Astronomy and Astrophysic

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