The angular momentum loss of low-mass close binary systems

The detailed evolution of low-mass main-sequence stars (M < 1M ) with a compact companion is studied. For angular momentum loss associated with magnetic braking it is found that about 10^–11–10^–12 M yr^–1 in stellar wind loss would be required. This wind is 10²–10³ times stronger than the solar wind, so we believe here magnetic stellar wind is insufficient. It is well known that there is mass outflow in low-mass close binary systems. We believe here that these outflows are centrifugal driven winds from the outer parts of the accretion disks. The winds extract angular momentum from these systems and therefore drive secular evolution. Disk winds are preferred to winds from the secondary, because of the lower disk surface gravity.     

Evolutionary status of the primary component of YZ Cassiopeiae

The models of non-rotating and rotating 2.31M _\ stars of Population I composition have been calculated, starting at the threshold of stability. A 2.31M _\ star was chosen to compare the results with the observational parameters of the primary component of the well-known detached binary YZ Cassiopeiae. The effects of rotation on the internal structure during the evolution of the star were studied by constructing sequences of axisymmetric rotating models under the assumption that angular momentum was conserved according to a predetermined angular velocity distribution depending on the structure of the star.The first section of this paper deals with effects of rotation on the evolutionary behaviours of the 2.31M _\ star through the pre-Main-Sequence evolution as well as the zero-age Main Sequence.In the second section of this paper, the evolutionary studies have been extended up to near-hydrogen exhaustion phase in order to obtain a theoretical model corresponding to the given mass and radius of the primary component of YZ Cassiopeiae. The theoretical models were found to be in a good agreement with observational parameters. The computed rotating models of the primary of YZ Cassiopeiae indicates that its evolutionary age is 6.01×10⁸ years; and the central hydrogen content 0.183 — which means that about 75% of its original value was depleted.     

Mass loss from coronae and its effect upon stellar rotation

The acoustic energy-generation rate from the convective zone was calculated for various models. Results show that chromosphere and corona can be expected around stars with temperature lower than 8000K at the main sequence, and lower than 6500K at logg=2.When a star is rotating rapidly, mass loss from its corona is large, and can be an effective mechanism of braking the stellar rotation. If this mechanism is effective, we can explain the slow rotation of stars later than F2 to be the result of the loss of the angular momentum through a stellar wind that is effective in their main sequence phase. Stars with massM>1.5M lose mass through a stellar wind during their contraction phase. The mass-loss rate is larger than the solar value because of the larger energy input into the chromosphere-corona system and because of the smaller gravitational potential at the surface. T Tauri stars may be the observational counterparts for such stars. As the duration of contraction phase is very short (less than 10⁷ years), the braking mechanism works only in the presence of a strong magnetic field (Ap) or in the presence of a companion (Am).Presented at the Trieste Colloquium on Mass Loss from Stars, September 12–16, 1968.     

Rotation, planets, and the 'second parameter' of the horizontal branch

We analyse the angular momentum evolution from the red giant branch (RGB) to the horizontal branch (HB) and along the HB. Using rotation velocities for stars in the globular cluster M13, we find that the required angular momentum for the fast rotators is up to 1–3 orders of magnitude (depending on some assumptions) larger than that of the Sun. Planets of masses up to 5 times Jupiter's mass and up to an initial orbital separation of ~2 au are sufficient to spin-up the RGB progenitors of most of these fast rotators. Other stars have been spun-up by brown dwarfs or low-mass main-sequence stars. Our results show that the fast rotating HB stars have been probably spun-up by planets, brown dwarfs or low-mass main-sequence stars while they evolved on the RGB. We argue that the angular momentum considerations presented in this paper further support the 'planet second parameter' model. In this model, the 'second parameter' process, which determines the distribution of stars on the HB, is interaction with low-mass companions, in most cases with gas-giant planets, and in a minority of cases with brown dwarfs or low-mass main-sequence stars. The masses and initial orbital separations of the planets (or brown dwarfs or low-mass main-sequence stars) form a rich spectrum of different physical parameters, which manifests itself in the rich varieties of HB morphologies observed in the different globular clusters.     

Angular momentum transport in pre-main-sequence stars of intermediate mass

Pre-Main-Sequence stars with masses between 2 and 5 M (Herbig Ae/Be stars) have radiative subphotospheric envelopes. However, they possess strong stellar winds and show definite signs of activity which could be linked to surface magnetic field. Therefore, they must lose angular momentum at a significant rate.We investigate the effect of such angular momentum losses on the internal structure of these stars, and on the distribution of angular velocity inside them. This paper presents a preliminary analysis guided by an analogy with laboratory and geophysical fluids. We propose that the friction exerted at the stellar surface by the angular momentum losses produces a mixed layer below the surface, separated from the unperturbed interior by an interface. Using scaling laws established by experimental studies of sheared stratified fluids, we discuss a simplified model for the evolution of the mixed layer.Although this model is still too preliminary to allow quantitative predictions, we show that for a reasonable choice of parameters, the mixed layer penetrates into the stellar interior on a time-scale of 10⁶ years, comparable to the Kelvin time-scale for the Herbig Ae/Be stars.     

Possible effects of internal rotation in low-mass stars

The influence of internal rotation on the evolution of a 0.85M star is investigated by the construction of model sequences. Rotation is treated by a simple one-dimensional approximation. The calculations assume solid-body rotation on the zero-age Main Sequence, followed by conservation of angular momentum in shells. The 4 cases considered have the initial angular velocities 0,2×10^–4, 6×10^–4, and 8×10^–4/sec. All cases but the last are followed to helium ignition. Compared with the non-rotating case, the rotating models are older at Main-Sequence turnoff, develop fast-spinning central regions on the red-giant branch, and ignite helium at higher surface luminosities and at larger helium-core masses. The increases in the last two quantities are roughly proportional to the square of the initial angular velocity.The 6×10^–4 case is followed through the helium core flash to the zero-age horizontal branch. Under the assumption of spherical symmetry, the non-central ignition of helium leads to a sequence of flashes of decreasing amplitude occurring progressively closer to the center. The flashes are weaker than those encountered in previous studies and do not produce mixing.     

Some Comments on the Magnetic Braking of CP Stars

The low rotation velocities of magnetic CP stars are discussed. Arguments against the involvement of the magnetic field in the loss of angular momentum are given: (1) the fields are not strong enough in young stars in the stage of evolution prior to the main sequence; (2) there is no significant statistical correlation between the magnetic field strength and the rotation period of CP stars; (3) stars with short periods have the highest fields; (4) a substantial number of stars with very low magnetic fields (B _e < 500 G) have rotation speeds that are typical of other CP stars; (5) simulations of the magnetic fields by Leroy and the author show that the orientation of dipoles inside rotating stars, both slow and fast, is consistent with an arbitrary orientation of the dipoles; and, (6) slow rotators with P>25 days, which form 12% of the total, probably lie at the edge of the velocity distribution for low mass stars. All of these properties conflict with the hypothesis of magnetic braking of CP stars.     

Dynamical conditions in planets and stars

With the available data in planets, stars and galaxies, it is studied the functions of angular momentaJ(M) and amounts of actionA _c(M) (associated to the non rotational terms in the kinetic energy). The results indicate that independently of how are these functionsJ(M),A _c(M) their ratioA _c/J remains a near invariant. It is independent also from the type of angular momenta: intrinsic spins of the bodies or the total angular (orbital) momenta of the bodies forming a system; for instance, the Solar System and the planets.The relationA _c(M) for the Solar System are analogous to these in the FGK stars of the main sequence, and the relationJ(M) (also for the Solar System) is analogous to the lower possible limit for binary stars.The different types of binary stars from the short period, detached systems to contactary systems, gives a range of functionsJ(M),A _c(M) that are the same that one can expect in stars with planetary systems. According to the detection limits given for planetary companions by Campbell, Walker and Yang (1988) (masses of less than 9 Jupiter masses and orbital periods of less than 50 years) we calculate the limits forJ(M) andA _c(M) This gives a lower limitA _c/J 1 associated to stars with planetary systems as 61 Cygni and to short period detached binaries. The upper limitA _c/J 16 correspond to planetary systems as the ours and probably to cataclysmic binaries. There are reasons to suspect that systems as the ours and in range 4 A _c/J 16 (with a lower limit analogous to contactary binaries as Algols and W Ursa Majoris) must be the most common type of planetary systems. The analogies with the functionsJ(M)A _c(M) for galaxies suggest cosmogonical conditions in the stellar formation.Independently of this, one can have boundary conditions for the Jacobi problem when applied to a collapsing cloud. Namely, from the initial stage (a molecular cloud) to the final stage (a formed stellar system: binary or planetary) the angular momenta and amounts of action decayed to 10^~4 the initial values, but in such a form thatA _c(t)/J(t) remains a near invariant.     

Low-mass red giants and masses of NPNs

The evolutionary track of low-mass red giant stars (0.7–0.9M ) is computed with the aim to demonstrate the conditions under which low-mass white dwarfs (WDs) can form through the evolution of single stars. Also, the influence of the mixing length to the scale height ratio on the radius of the star is calculated and the coupling between the mixing-length and the mass-loss rate parameters is investigated. Our conclusions are that the uncertainties in mass-loss and mixing-length to scale-height ratio leave enough parameter space to allow the formation of low-mass WD via single star evolution. We also conclude that the gap between proto-WD stars without any nebula and stars with well-defined nebulae is bridged by stars which have a dilute gas cloud around them which cannot be observed as a nebula.     

Hydrodynamic processes of angular momentum transport in the interior of a rotating massive hydrogen-burning star

The evolution of a rotating star with a mass of 16M _⊙ at the hydrogen burning phase is considered together with the hydrodynamic processes of angular momentum transport in its interior. Shear turbulence is shown to limit the amplitude of the latitudinal variations in mean molecular weight on a surface of constant pressure in a layer with variable chemical composition. The resulting nonuniformity in the mean molecular weight distribution and the turbulent energy transport along the surface of constant pressure reduce the absolute value of the meridional circulation velocity. Nevertheless, meridional circulation remains the main mechanism of angular momentum transport in the radial direction in a layer with variable chemical composition. The intensity of the processes of angular momentum transport by meridional circulation and shear turbulence is determined by the angular momentum of the star. At a fairly high angular momentum, more specifically, at J = 3.69 × 10⁵² g cm² s^?1, the star during the second half of the hydrogen-burning phase in its convective core has characteristics typical of classical early Be stars.     

Unseen matter and angular momentum in the Milky Way and other galaxies: Simple two-component models

Simple two-component (dark+bright) models are built up for the Milky Way, where both the density distribution and the rotation curve are deduced from known observations. The derived dark to bright mass ratio turns out to be in the range 10, in close agreement with the results of more refined approaches, with a weak dependence on the geometry of the model. The related angular momentum appears to be well in agreement with theoretical predictions, if proto-galaxies gain angular momentum via either gravitational interactions or peculiar velocities of their own sub-units, according to a logarithmic distribution of the squared fractional angular momenta close to a Maxwellian one. The rougher assumption that the whole system is represented by a rigidly rotating polytrope leads to dark components rounder than _D 0.7 if proto-galaxies gain angular momentum via gravitational interactions, and to much more flattened dark components if proto-galaxies gain angular momentum via peculiar velocities of their own sub-units and few (4) sub-units are present at the beginning. To fit the observed positions of several galaxies on the (Oê _B q _B ) plane-ê _B representing the ellipticity andq _B close to the ratio of maximum rotational to central peculiar velocity, averaged for all the inclinations to the line of sight — galaxies are modelled by two-component (dark+bright) rigidly rotating, concentric, co-polar, homogeneous spheroids and the Galaxy is assumed to be a typical system. An acceptable fit is produced only under the assumption that protogalaxies gain their angular momentum in late stages of evolution, i.e., after having decoupled from the Hubble flow.     

Effect of partial mixing of matter on the hydrodynamic angular momentum transport processes in massive main-sequence stars

We consider the evolution of a rotating star with a mass of 16M _⊙ and an angular momentum of 3.25 × 10⁵² g cm² s^?1, along with the hydrodynamic transport of angular momentum and chemical elements in its interiors. When the partial mixing of matter of the turbulent radiative envelope and the convective core is taken into account, the efficiency of the angular momentum transport by meridional circulation in the stellar interiors and the duration of the hydrogen burning phase increase. Depending on the Schmidt number in the turbulent radiative stellar envelope, the ratio of the equatorial rotational velocity to the circular one increases with time in the process of stellar evolution and can become typical of early-type Be stars during an additional evolution time of the star on the main sequence. Partial mixing of matter is a necessary condition under which the hydrodynamic transport processes can increase the angular momentum of the outer stellar layer to an extent that the equatorial rotational velocity begins to increase during the second half of the evolutionary phase of the star on the main sequence, as shown by observations of the brightest stars in open star clusters with ages of 10–25 Myr. When the turbulent Schmidt number is 0.4, the equatorial rotational velocity of the star increases during the second half of the hydrogen burning phase in the convective core from 330 to 450 km s^?1.     

A tidal theory for the origin of the solar nebula

There are two angular momentum (AM) problems associated with the formation of stars in general and the solar system in particular. The first is how to dispose of the AM possessed by turbulent protostellar clouds. Two-dimensional calculations of the gravitational infall of rotating gas clouds by several authors now indicate that stars are formed in groups or clusters rather than as single entities. Added evidence comes from observation of probable regions of star formation and young clusters, plus the fact that most stars are presently members of binaries or other multiples. Thus the first problem is solved by postulating the fragmentation of massive clouds with most of the AM ending up in the relative orbits. These clusters are notoriously unstable and evolve with the ejection of single stars like the Sun.The second problem is the uneven distribution of AM with mass in the solar system. It turns out that the collapse time for the majority of the infalling material is comparable to the time necessary for significant dynamical interaction of the protostellar fragment with its neighbors. It is found here through calculations utilizing very simplified numerical models that the last few tens of percent of infalling material can easily have sufficient AM transferred to it by the tidal action of passing protostars to form a solar nebula and ensure alignment of the solar spin. The most important parameter is the degree of central condensation: fragments without several tenthsM in a central core tend to be torn apart by encounters, or at least stimulated into binary fission. A stabilizing central mass maintains its identity and acquires a rotating envelope of material.Paper presented at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.     

Main sequence for rotating stars of intermediate mass

We have investigated the evolutionary behaviour of intermediate mass (2, 3, 4, 5, and 7M ) Population I stars, assuming two different rates of rotation at the threshold of stability.In the first part of the study, stars are assumed to start with a critical rotation (fast rotation model) and to progress to the point of rotational instability. The stars evolve by losing mass and become rotationally unstable before they reach the zero-age Main Sequence. It is argued that multiple star systems might be formed through the evolution of rapidly rotating stars. An expression for the rotational mass loss rate is derived as a function of the physical parameters of stars.In the second part of the study, stars are assumed to rotate at a rate below the critical value (slow rotation model). The evolution of slowly rotating stars is followed as far as zero-age Main Sequence on the theoretical Hertzsprung-Russell diagram and compared with that of normal stars. The evolutionary paths are found to be more or less similar to those of normal stars; but their positions on the Main Sequence are characterized by effective temperatures and luminosities lower than those of normal stars. The zero-age Main-Sequence times of these stars are longer than those of normal stars. The rotational rates obtained for the zero-age Main Sequence are in good agreement with observed values.     

Pregalactic-primordial low-mass stars

The Main-Sequence positions as well as the evolutionary behavior of Population III stars up to an evolution age of 2×10¹⁰ yr, taking this time as the age of the Universe, have been investigated in the mass range 0.2 and 0.8M . While Population III stars with masses greater than 0.3M develop a radiative core during the approach to the Main Sequence, stars with masses smaller than 0.3M reach the Main Sequence as a wholly convective stars. Population III stars with masses greater than 0.5M show a brightening of at most 2.2 in bolometric magnitude when the evolution is terminated as compared to the value which corresponds to zero-age Main Sequence. The positions of stars with masses smaller than 0.5M remain almost the same in the H-R diagram.If Population III stars have formed over a range of redshifts, 6相似文献   

The angular momentum problem and magnetic braking during star formation: Exact solutions for an aligned and a perpendicular rotator

The problems of fragmentation, angular momentum, and magnetic flux during star formation are reviewed briefly. Then the resolution of the angular momentum problem through magnetic braking is studied rigorously.A disk-like interstellar cloud of uniform density _cl is given an initial angular velocity _o about its axis of symmetry, which isaligned with an initially uniform, frozen-in magnetic field. Torsional Alfvén waves transport angular momentum from the cloud to the external medium, which has a uniform density _ext . The angular velocity of the cloud ( _cl ) is determined analytically as a function of space and time for different ratios _cl / _ext (the only free parameter in the equations), representing different stages of contraction. Despite dissimilar transient response of the cloud (or fragment) structure to different initial conditions, the characteristic time for magnetic braking of the rotation of the cloud (or fragment) as a whole is remarkably insensitive to the initial conditions and independent of the stage of contraction. The latter conclusion is in agreement with an approximate result obtained recently (Mouschovias, 1978; 1979a).A cylindrical cloud (or fragment) of uniform density is also imparted an initial angular velocity about its axis of symmetry with respect to the external medium. The frozen-in magnetic field is now initially radial andperpendicular to the axis of symmetry. In this case magnetic braking becomes more efficient upon contraction. It is more efficient than the aligned rotator case typically by one order of magnitude. The angular momentum problem can be resolved in about 10⁶ yr during the early stages of cloud contraction. Planetary systems, such as the Sun-Jupiter pair, become dynamically possible. A stage exists in which a cloud (or fragment) is in retrograde rotation with respect to its surroundings. This provides the first and only observable prediction of magnetic braking in action. It also constitutes a natural explantation of retrograde rotation in stellar and planetary systems.This work was supported in part by the National Science Foundation under grant NSF AST-77-23568.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

Stellar analogs of solar magnetic activity

The techniques and principal results of observational studies of stellar activity are summarized. Both chromospheric and coronal emission clearly track surface magnetic field properties, but it is not well known how the detailed relation between the emission and surface magnetic fields varies with spectral type. For lower Main-Sequence stars of the same spectral type, there is clear evidence of a close relationship between mean activity level and rotation period P _rot. There is also less definitive evidence for a similar dependence on convective overturn time _c , such that activity depends on the single parameter Ro = P _rot/ _c . For single stars, stellar rotation, and magnetic activity both decline smoothly with age. This implies a feedback between angular momentum loss rate and activity level. Temporal variations in mean stellar activity level mimic the solar cycle only for old stars like the Sun, being much more irregular for younger stars. The characteristic timescale of the variations (the cycle period) appears to depend on Ro for old stars, but shows no clear dependence on either rotation rate or spectral type for younger stars. Further data on mean activity and its variation for a large number of lower Main-Sequence stars should contribute significantly to our understanding of the causes of stellar magnetic activity.     

Effect of the rotation and tidal dissipation history of stars on the evolution of close-in planets

Since 20 years, a large population of close-in planets orbiting various classes of low-mass stars (from M-type to A-type stars) has been discovered. In such systems, the dissipation of the kinetic energy of tidal flows in the host star may modify its rotational evolution and shape the orbital architecture of the surrounding planetary system. In this context, recent observational and theoretical works demonstrated that the amplitude of this dissipation can vary over several orders of magnitude as a function of stellar mass, age and rotation. In addition, stellar spin-up occurring during the Pre-Main-Sequence (PMS) phase because of the contraction of stars and their spin-down because of the torque applied by magnetized stellar winds strongly impact angular momentum exchanges within star–planet systems. Therefore, it is now necessary to take into account the structural and rotational evolution of stars when studying the orbital evolution of close-in planets. At the same time, the presence of planets may modify the rotational dynamics of the host stars and as a consequence their evolution, magnetic activity and mixing. In this work, we present the first study of the dynamics of close-in planets of various masses orbiting low-mass stars (from \(0.6~M_\odot \) to \(1.2~M_\odot \)) where we compute the simultaneous evolution of the star’s structure, rotation and tidal dissipation in its external convective envelope. We demonstrate that tidal friction due to the stellar dynamical tide, i.e. tidal inertial waves excited in the convection zone, can be larger by several orders of magnitude than the one of the equilibrium tide currently used in Celestial Mechanics, especially during the PMS phase. Moreover, because of this stronger tidal friction in the star, the orbital migration of the planet is now more pronounced and depends more on the stellar mass, rotation and age. This would very weakly affect the planets in the habitable zone because they are located at orbital distances such that stellar tide-induced migration happens on very long timescales. We also demonstrate that the rotational evolution of host stars is only weakly affected by the presence of planets except for massive companions.     

Gamma-ray bursts from nearby neutron stars

We interpret the puzzling-ray bursts as emitted by cooling sparks from the surface of spasmodically accreting, old neutron stars. Their spiky, anisotropic radiation is oriented w.r.t. the galactic disk via interstellar accretion, whose orbital angular momentum tends to counteralign with the galactic spin; in this way, larger source numbers in directions of the galactic disk are compensated by smaller beaming probabilities, resulting in a near-isotropic arrival distribution, as observed by BATSE. The source distances range between 10 pc and 500 pc. Their radiated energies are of order 10³⁵ erg, corresponding to accreted clumps (blades) of typical mass 10¹⁵ g per burst. Magnetic surface field strengths range between 10¹⁰ and 10¹² G, somewhat weaker than those of newborn neutron stars.     

Pulsating sdB Stars: A New Approach to Probing their Interiors

Horizontal branch stars should show significant differential rotation with depth. Models that assume systematic angular momentum exchange in the convective envelope and local conservation of angular momentum in the core produce HB models that preserve a rapidly rotating core. A direct probe of core rotation is available. The nonradial pulsations of the EC14026 stars frequently show rich pulsation spectra. Thus their pulsations probe the internal rotation of these stars, and should show the effects of rapid rotation in their cores. Using models of sdB stars that include angular momentum evolution, we explore this possibility and show that some of the sdB pulsators may indeed have rapidly rotating cores.