Shocks and shells in hot star winds

Radiation-driven winds of hot, massive stars showvariability in UV and optical line profiles on time scales of hours to days.Shock heating of wind material is indicated by the observed X-ray emission. We present time-dependent hydrodynamical models of these winds, where flowstructures originate from a strong instability of the radiative driving. Recent calculations (Owocki 1992) of the unstable growth of perturbations were restricted by the assumptions of 1-D spherical symmetry and isothermality of the wind. We drop the latter assumption and include the energy transfer in the wind. This leads to a severe numerical shortcoming, whereby all radiative cooling zones collapse and the shocks become isothermal again. We propose a method to hinder this collapse. Calculations for dense supergiant winds then show: (1) The wind consists of a sequence of narrow and dense shells, which are enclosed by strong reverse shocks (with temperatures of 10⁶ to 10⁷ K) on their starward facing side. (2) Collisions of shells are frequent up to 6 to 7 stellar radii. (3) Radiative cooling is efficient only up to 4 to 6R _*. Beyond these radii, cooling zones behind shocks become broad and alter the wind structure drastically: all reverse shocks disappear, leaving regions ofpreviously heated gas.     

Synthesis of line profiles from models of structured winds

On the basis of a a careful analysis of resonance line formation (both for singlets and doublets) in structured winds, presenttime dependent models of the line driven winds of hot stars (Owocki et al., this volume; Feldmeier, this volume) are shown to be able to explain a number of observational features with respect to variability and structure: they are (in principle) able to reproduce theblack andbroad troughs (without any artificial turbulence velocity) and the blue edge variability observed in saturated resonance lines; they might explain the long lived narrow absorption components often observed in unsaturated lines at high velocities; they predict a relation between the edge velocity of UV-lines and the radiation temperature of the observed X-ray emission.As a first example of the extent to which theoretical models can be constrained by comparisons between observations and profiles calculated by spectrum synthesis from structured winds, we show here that models with deep-seated onset of structure formation ( 1.1R _* ) produce resonance lines which agreequalitatively with observational findings; in contrast, the here presented models with structure formation only well out in the wind ( 1.6R _* ) fail in this respect.     

Erratum: the 2.27 day period of WR-134 (HD 191765)

The original temporal analysis of a 12 night spectral timeseries of WR-134 has been found to be flawed and a re-analysis shows that the line profile variations are indeed periodic. When combined with a 4 night timeseries taken 45 days earlier, a period near 2.27 d is found in periodograms of the Heii 5412 line centroid,rms line width, and line skew variations. When the emission line residuals are ordered as a function of phase, a sinuous feature appears to snake about the line center with an amplitude of ± 500 km s^–1. This is 20 larger than the line centroid amplitude; the calculation of which is heavily weighted by static portions of the line profile. In addition to the snake, emission residuals appear that move away from line center on unbound trajectories and are thought to result from the interaction of a periodic driver with the unstable flow of the radiation driven wind. The nature of the periodic driver is a topic for discussion.     

The equilibrium,stability and evolution of a rotating magnetized gaseous disk

The exact solutions for the equilibrium of rotating gaseous disk with poloidal magnetic field are obtained. The stability of the disk with respect to uniform expansion and contraction is investigated by means of the variational principle. It is shown that if the equilibrium is determined by gravitational and magnetic forces only, the disk is in neutral equilibrium with respect to perturbations of the form r=r. The instability to short-waves perturbations is studied by the quasi-classical method. The analysis shows that if the magnetic field isH>2G, where is the surface density, then these perturbations are stabilized. The configurations of the electrical field induced by the rotation of magnetized disk are found. In conclusion, the questions of the evolution of the disk are discussed in connection with the quasar model when pulsar-like radiation is taken into account.     

Constraints on hot star X-ray source characteristics from combined analysis of X-ray and UV observations

Results from wind ionization calculations are presented which show how the P-Cygni profiles of superionized species such as O VI can provide information about the X-ray source characteristics of early-type stars. Using detailed radiative and atomic physics models, we find that a significant source of X-ray emission from Pup (O4 If) comes from a region in the wind located within roughly 1 to 2 stellar radii of the photosphere. Our results suggest that X-rays sources in which emission occurs exclusively at large radii (r a fewR _* ) are inconsistent with UV P-Cygni profiles for O VI. Instead, we find that X-ray emission from shocks distributed throughout the lower regions of the wind (r 1 – 2R _* ) is consistent with both X-ray and UV data, as well as mass loss rates deduced from radio andH observations.     

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.     

The equations of motion of an artificial satellite in nonsingular variables

The equations of motion of an artificial satellite are given in nonsingular variables. Any term in the geopotential is considered as well as luni-solar perturbations up to an arbitrary power ofr/r, r being the geocentric distance of the disturbing body. Resonances with tesseral harmonics and with the Moon or Sun are also considered. By neglecting the shadow effect, the disturbing function for solar radiation is also developed in nonsingular variables for the long periodic perturbations. Formulas are developed for implementation of the theory in actual computations.     

Coalescing neutron stars as gamma ray bursters?

We investigate the dynamics and evolution of coalescing neutron stars. The three-dimensional Newtonian equations of hydrodynamics are integrated by the Piecewise Parabolic Method on an equidistant Cartesian grid. The code is purely Newtonian, but does include the emission of gravitational waves and their back-reaction. The properties of neutron star matter are described by the equation of state of Lattimer and Swesty (1991). Energy loss by all types of neutrinos and changes of the electron fraction due to the emission of electron neutrinos and antineutrinos are taken into account by an elaborate neutrino leakage scheme. We simulate the coalescence of two identical, cool neutron stars with a baryonic mass of 1.6M and a radius of 15 km and with an initial center-to-center distance of 42 km. The initial distributions of density and electron concentration are given from a model of a cold neutron star in hydrostatic equilibrium. We investigate three cases which differ by the initial velocity distribution in the neutron stars. The orbit decays due to gravitational-wave emission and after one revolution the stars are so close that dynamical instability sets in. Within 1 ms the neutron stars merge into a rapidly spinning (P 1 ms), high-density body ( 10¹⁴ g/cm³) with a surrounding thick disk of material with densities 10¹⁰ – 10¹² g/cm³ and orbital velocities of 0.3-0.5 c. The peak emission of gravitational waves has a maximum luminosity of a few times 10⁵⁵ erg/s and is reached for about 1 ms. The amplitudes of the gravitational waves are close to 3 10^–23 at a distance of 1 Gpc and the typical frequency is near the dynamical value of the orbital motion of the merging neutron stars of 2 KHz. In a post-processing step, the rate of neutrino-antineutrino annihilation is calculated from the neutrino luminosities generated during the hydrodynamical simulations. We find the integral annihilation rate to be a few 10⁵⁰ erg/s during the phase of strongest neutrino emission, which is too small to generate the observed bursts considering the fact that the merged object of about 3M will most likely collapse to a black hole within milliseconds.     

The interpretation of flows in molecular clouds

Stellar winds interacting with gas in dense molecular clouds produce flows which may be initially energy or momentum driven. A criterion for this is derived which depends sensitively on the wind velocity. Flows may change from one regime to another depending on the gas distribution about the wind source and these changes are discussed for power law density distributions. In general, the flows observed in CO associated with infrared point sources seem to be in the energy driven regime. By combining CO observations with radio continuum flux measurements, wind parameters are derived for several of these sources. There is some evidence from the derived parameters that high (L _*2×10³ L ) luminosity sources have radiatively-driven winds. Lower luminosity source winds are driven by some agency as yet unknow. We suggest that the widths of infrared lines from wind sources seriously underestimate the wind terminal velocities.     

X-ray emission in wind instability simulations

We estimate X-ray emission by shock-heated regions in hot star winds, using temperature and density profiles calculated by time-dependent dynamical models; the shocks result from the instability of the line scattering force that drives the wind. For main sequence late O and early B stars, the model X-ray flux is generally well below the observed flux, though the shape of the model spectrum is approximately consistent with observations. For the early O supergiant Pup, the model spectral shape again agrees with observation; the total flux predicted by models is well above the observed flux, though significant uncertainties remain.     

A quantitative analysis of the prototype [WCL] star CPD-56° 8032

We present a detailed, quantitative study of the standard [WC10] Wolf-Rayet central star CPD-56^o 8032 based on new high resolution AAT UCLES observations and the Hillier (1990) WR standard model. Our analysis of CPD-56^o 8032 gives the wind properties (T _*=34500K, lg (L/L )=3.8, lg (M/M a^–1)=–5.4,v =225 km s^–1) and chemistry (C/He=0.5, O/He=0.1, by number), the latter suggesting an intimate relationship with the Ovi PN central stars and the PG 1159-035 objects. A comparison between the wind properties of CPD-56^o 8032 and Sk-66^o 40 (WN 10) indicates that low excitation, low wind velocity WR winds are common to both low mass PN central stars (WC sequence) and high mass post-LBV's (WN sequence).     

Critical parameters for supermassive objects in general relativity

Evolutionary tracks up to the point of dynamical instability are obtained for isentropic objects with rest masses ranging from 10² M to 10⁷ M . Accurate values for the red shift, specific entropy, luminosity and effective temperature at the onset of collapse are given.     

Further considerations on contracting solar nebula

Prentice (1978a) in his modern Laplacian theory of the origin of the solar system has established the scenario of the formation of the solar system on the basis of the usual laws of conservation of mass and angular momentum and the concept of supersonic turbulent convection that he has developed. In this, he finds the ratio of the orbital radii of successively disposed gaseous rings to be a constant - 1.69. This serves to provide a physical understanding of the Titius-Bode law of planetary distances. In an attempt to understand the law in an alternative way, Rawal (1984) starts with the concept of Roche limit. He assumes that during the collapse of the solar nebula, the halts at various radii are brought about by the supersonic turbulent convection developed by Prentice and arrives at the relation: R _p= Ra^p, where R _pare the radii of the solar nebula at various halts during the collapse, R the radius of the present Sun and a = 1.442. a is referred here as the Roche constant. In this context, it is shown here that Kepler's third law of planetary system assumes the form: T _p = T ₀(a^3/2)^p, where T _p are the orbital periods at the radii R _p, T ₀ - 0.1216d - 3 h, and a the Roche constant. We are inclined to interpret T ₀' to be the rotation period of the Sun at the time of its formation when it attained the present radius. It is also shown that the oribital periods T _pcorresponding to the radii R _psubmit themselves to the Laplace's resonance relation.     

Expanding and superdense astrophysical systems in general relativistic hierarchical cosmology

A semi-continuous hierarchy, (i.e., one in which there are galaxies outside clusters, clusters outside superclusters etc.), is examined using an expression of the field equations of general relativity in a form due to Podurets, Misner and Sharp. It is shown (a) that for a sufficiently populous hierarchy, the thinning factor( _i+1/ _i [r _i /r _i+1] is approximately equal to the exponentN in a continuous density law (=aR ^–N) provided (r _i /r _i+1)^3-1; (b) that a hierarchical Universe will not look decidedly asymmetric to an observer like a human being because such salient observers live close to the densest elements of the hierarchy (viz stars), the probability of the Universe looking spherically symmetric (dipole anisotropy0.1 to such an observer being of order unity; (c) the existence of a semi-continuous or continuous hierarchy (Peebles) requires that 2 if galaxies, not presently bound to clusters were once members of such systems; (d) there are now in existence no less than ten arguments for believing 2, though recent number counts by Sandageet al. seem to be in contradiction to such a value; (e) Hubble's law, withH independent of distance, can be proved approximately in a relativistic hierarchy provided (i)N=2, (ii)2GM(R)/c ² R1; (iii)Rc (iv)M0 in a system of massM, sizeR (f) Hubble's law holds also in a hierarchy with density jumps; (g)H100 km s^–1 Mpc^–1; (h) objects forming the stellar level of the hierarchy (in a cosmology of the Wilson type) must once have had 2GM/c ² R1; (i) there is a finite pressurep=2Ga in all astrophysical systems (a=R ^N ,N2); (j) for the Galaxy, theory predictsp _G7×10^–12 dyn cm^–2, observation givesp _G5×10^–12 dyn cm^–2; (k) if the mass-defect (or excess binding energy) hypothesis is taken as a postulate, all non-collapsed astrophysical systems must be non-static, and any non-static, p0 systems must in any case be losing mass; (1) the predicted mass-loss rate from the Sun is 10¹² g s^–1, compared to 10¹¹ g s^–1 in the observed solar wind; (m) the mass-loss rates known by observation imply timescales of 5×10⁹ years for the Sun and 10¹⁰ years for other astrophysical systems; (n) degenerate superdense objects composed of fermions must haveN-2 if they were ever at their Schwarzschild radii and comprised a finite numberN _B of baryons; (o)N _B10⁵⁷N for degenerate fermion and boson systems; (p)285-4; (q) the metric coefficients for superdense bodies give equations of motion that imply equal maximum luminosities for all evolving superdense bodies (L _max10⁵⁹ erg s^–1); (r) larger bodies have longer time-scales of energy radiation atL _max (10^–5 s for stars,1 h for QSO's) (s) expansion velocities are c soon after the initial loss of equilibrium in a superdense object; (t) if the density parametera(t) in aR ^–N isa=a (non-atomic constants of physicsc, G, A), andA, thenN=2; (u) N2 is necessary to giveMM at the stellar level of the hierarchy;(v) systems larger than, and including, galaxies must have formed by clumping of smaller systems and not (as advocated by Wertz and others) in a multiple big bang.     

Free-convection effects on MHD flow past a porous plate with step function change in suction velocity

Free convection effects on MHD flow past a semi infinite porous flat plate is studied when the time dependent suction velocity changes in step function form. The solution of the problem is obtained in closed form for the fluid with unit Prandtl number. It is observed that for both cooling and heating of the plate the suction velocity enhances the velocity field. The heat transfer is higher with increase in suction velocity.Notations B intensity of magnetic field - G Grashof number - H magnetic field parameter,H=(M+1/4) ^1/2–1/2 - M magnetic field parameter - N _u Nusselt number - P Prandtl number of the fluid - r suction parameter - T temperature of the fluid - T _w temperature of the plate - T temperature of the fluid at infinity - t time - t non-dimensional time - u velocity of the fluid parallel to the plate - u non-dimensional velocity - U velocity of the free stream - suction velocity - ₁ suction velocity att0 - ₂ suction velocity att>0 - x,y coordinate axes parallel and normal to the plate, respectively - y non-dimensional distance normal to the plate - coefficient of volume expansion - thermal diffusivity - kinematic viscosity - electric conductivity of the fluid - density of the fluid - non-dimensional temperature of the fluid - shear stress at the plate - non dimensional shear stress - erf error function - erfc complementary error function     

The inclination changes in the problem of two triaxial rigid spheroids

The first-order perturbations of a system of two triaxial rigid spheroids under Hori-Lie transformation are investigated. The time dependence of the configuration of the three angular momentum vectors, two rotational and one orbital, is studied. The problem is simplified by the introduction of a new time parameter , such thatt is the hyperelliptic function of . The projectionsH ₁ andH ₂ of the rotational momentum vectors into the direction of the total angular momentum vector of the system are then harmonic or exponential functions of . The trajectory in theH ₁,H ₂ plane is a part of an ellipse or hyperbola respectively. If this conical section intersects a certain critical contourC, the system is bounced back along the original trajectory. The motion of the relative configuration of the angular momentum vectors is periodical except in a special aperiodic case. The expressions for the periods are given.     

Effect of Krein signatures on the stability of relative equilibria

We consider the linear stability of the equilibrium points of the generic rotating potentials U(r), U(r, ), U(r, and U(r, , . The stability analysis is performed using the concept of Krein's signature. This signature is calculated for all eigenvalues of the above potentials. Thereby, the Lagrangian points of the restricted three-body problem and the synchronous satellites of oblate and prolate planets are also studied. We find also the new positions of the eigenvalues for perturbations of the original L ₄ and L ₅ points of Mars, Jupiter, Saturn, Uranus and Neptune. Finally, we study the problem with the mass ratio µ close to the critical value and the stability of geostationary satellites perturbed by the Moon.     

Possible effects of anisotropy ofG on celestial orbits

Will (1971) has discussed a possible anisotropy in the gravitational constantG. Suppose that the attractive gravitational force between two particles of massesm ₁ andm ₂ is given by the usual expressionF=–Gm ₁ m ₂ r/r ³, wherer is the separation vector. Ifc is the velocity of light in vacuo and if 1 _r r/r, he expresses the anisotropy byG=G [1+(v·1 r/c)²], whereG is a constant,v is identified practically as the velocity of the Sun around the galaxy, and 1. Will's suggestion is to look for such an effect in the laboratory.The purpose of the present paper is to look for such an effect in the solar system, wherem ₁ andm ₂ become the masses of the Sun and a planet or of the Earth and the Moon. For simplicity I consider only those planets whose orbits are close to the ecliptic, so that the angle betweenv and the plane of the ecliptic is about 59°.With the above force, the resulting two-body problem is completely solvable. The results are these. If =1, there is an increase in mean motion of 7 parts in 10⁸, a periodic fluctuation in true longitude with period half that of the orbit and amplitude ranging possibly from 0.01 to 0.02, and periodic fluctuations in the radius vector, with period also one half that for the orbit. The amplitudes are: 2.7 km for Mercury, 5.1 km for Venus, 7.0 km for Mars, 18 m for the Moon about the Earth, and 28 cm for a close artificial satellite with inclination 23°. The more conservative estimate <0.0115 would reduce these values by the factor 70.     

Stochastic models of stellar winds in T Tauri-stars

We consider the conditions in which emission lines of hydrogen, ionized calcium and ionized magnesium are formed in the spectra of T Tauri-stars. It is well known that there is a problem in interpreting the two-component profiles which are frequently observed in H, Caii K, and Mgii k lines. This problem can be solved if we abandon an assumption which is customarily made in modelling stellar winds: namely, the approximation of a continuous medium. Our calculations indicate that line profiles similar to those which are observed can be obtained by making very simple assumptions about spherical-symmetry and quasistationary gas flow provided that the following conditions are also stratified: (i) the stellar wind consists of separate gas structure (blobs) with a volume-filling factorq of order 0.1; (ii) the blobs decelerate in the outer regions of the wind.The first of these conditions indicates that the outflow of the gas from the surface of a T Tauri-star is extremely inhomogeneous. At any instant, only about 1/10 of the stellar surface acts as a source of stellar wind. Although this conclusion is at first sight very unexpected, it is nevertheless entirely logical if the outflow of gas from the star originates in magnetic activity on the stellar surface.