Runaway of Line-Driven Winds Towards Critical and Overloaded solutions

Line-driven winds from hot stars and accretion disks are thought to adopt a unique, critical solution which corresponds to maximum mass loss rate and a particular velocity law. We show that in the presence of negative velocity gradients, radiative-acoustic (Abbott) waves can drive shallow wind solutions towards larger velocities and mass loss rates. Perturbations introduced downstream from the wind critical point lead to convergence towards the critical solution. By contrast, low-lying perturbations cause evolution towards a mass-overloaded solution, developing a broad deceleration region in the wind. Such a wind differs fundamentally from the critical solution. For sufficiently deep-seated perturbations, overloaded solutions become time-dependent and develop shocks and shells.Comment: Latex, 2 postscript figures Astrophysical Journal Letters, in pres

Time-dependent modeling of extended thin decretion disks of critically rotating stars

During their evolution massive stars can reach the phase of critical rotation when a further increase in rotational speed is no longer possible. Direct centrifugal ejection from a critically or near-critically rotating surface forms a gaseous equatorial decretion disk. Anomalous viscosity provides the efficient mechanism for transporting the angular momentum outwards. The outer part of the disk can extend up to a very large distance from the parent star. We study the evolution of density, radial and azimuthal velocity, and angular momentum loss rate of equatorial decretion disks out to very distant regions. We investigate how the physical characteristics of the disk depend on the distribution of temperature and viscosity. We calculated stationary models using the Newton-Raphson method. For time-dependent hydrodynamic modeling we developed the numerical code based on an explicit finite difference scheme on an Eulerian grid including full Navier-Stokes shear viscosity. The sonic point distance and the maximum angular momentum loss rate strongly depend on the temperature profile and are almost independent of viscosity. The rotational velocity at large radii rapidly drops accordingly to temperature and viscosity distribution. The total amount of disk mass and the disk angular momentum increase with decreasing temperature and viscosity. The time-dependent one-dimensional models basically confirm the results obtained in the stationary models as well as the assumptions of the analytical approximations. Including full Navier-Stokes viscosity we systematically avoid the rotational velocity sign change at large radii. The unphysical drop of the rotational velocity and angular momentum loss at large radii (present in some models) can be avoided in the models with decreasing temperature and viscosity

Two-dimensional modeling of density and thermal structure of dense circumstellar outflowing disks

Context. Evolution of massive stars is affected by a significant loss of mass either via (nearly) spherically symmetric stellar winds or by aspherical mass-loss mechanisms, namely the outflowing equatorial disks. However, the scenario that leads to the formation of a disk or rings of gas and dust around massive stars is still under debate. Aims. We study the hydrodynamic and thermal structure of optically thick, dense parts of outflowing circumstellar disks that may be formed around various types of critically rotating massive stars, for example, Be stars, B[e] supergiant (sgB[e]) stars or Pop III stars. Methods. We specify the optical depth of the disk along the line-of-sight from stellar poles. Within the optically thick dense region we calculate the vertical disk thermal structure using the diffusion approximation while for the optically thin outer layers we assume a local thermodynamic equilibrium with the impinging stellar irradiation. We use two of our own types of hydrodynamic codes: two-dimensional operator-split numerical code and unsplit code based on the Roe's method. Results. Our models show the geometric distribution and contribution of viscous heating that begins to dominate in the central part of the disk. In the models of dense viscous disks the viscosity increases the central temperature up to several tens of thousands of Kelvins. The high mass-loss rates and high viscosity lead to instabilities with significant waves or bumps in density and temperature in the very inner disk region. Conclusions. The two-dimensional radial-vertical models of dense outflowing disks including the full Navier-Stokes viscosity terms show very high temperatures that are however limited to only the central disk cores inside the optically thick area, while near the edge of the optically thick region the temperature may be low enough for the existence of neutral hydrogen.Comment: 24 pages, 21 figure

Dynamics of Line-Driven Winds from Disks in Cataclysmic Variables. II. Mass Loss Rates and Velocity Laws

We analyze the dynamics of 2D stationary line-driven winds from accretion disks in cataclysmic variables (CVs), by generalizing the Castor, Abbott and Klein theory. In paper 1, we have solved the wind Euler equation, derived its two eigenvalues, and addressed the solution topology and wind geometry. Here, we focus on mass loss and velocity laws. We find that disk winds, even in luminous novalike variables, have low optical depth, even in the strongest driving lines. This suggests that thick-to-thin transitions in these lines occur. For disks with a realistic radial temperature, the mass loss is dominated by gas emanating from the inner decade in r. The total mass loss rate associated with a luminosity 10 Lsun is 10^{-12} Msun/yr, or 10^{-4} of the mass accretion rate. This is one order of magnitude below the lower limit obtained from P Cygni lines, when the ionizing flux shortwards of the Lyman edge is supressed. The difficulties with such small mass loss rates in CVs are principal, and confirm our previous work. We conjecture that this issue may be resolved by detailed nonLTE calculations of the line force within the context of CV disk winds, and/or better accounting for the disk energy distribution and wind ionization structure. We find that the wind velocity profile is well approximated by the empirical law used in kinematical modeling. The acceleration length scale is given by the footpoint radius of the wind streamline in the disk. This suggests an upper limit of 10 Rwd to the acceleration scale, which is smaller by factors of a few as compared to values derived from line fitting.Comment: 14 pages, 3 Postscript figures, also from http://www.pa.uky.edu/~shlosman/publ.html. Astrophysical Journal, submitte