Showing papers by "Ronald E. Taam published in 1994"

The conductive propagation of nuclear flames. II. Convectively bounded flames in C + O and O + Ne + Mg cores

Abstract: We determine the speeds, and many other physical properties, of flame fronts that propagate inward into degenerate and semidegenerate cores of carbon and oxygen (CO) and neon and oxygen (NeOMg) white dwarfs when such flames are bounded on their exterior by a convective region. Combustion in such fronts, per se, is incomplete, with only a small part of the initial mass function burned. A condition of balanced power is set up in the star where the rate of energy emitted as neutrinos from the convective region equals the power available from the unburned fuel that crosses the burning front. The propagation of the burning front itself is in turn limited by the temperature at the base of the convective shell, while cannot greatly exceed the adiabatic value. Solving for consistency between these two conditions gives a unique speed for the flame. Typical values for CO white dwarfs are a few hundredths of a centimeter per second. Flames in NeOMg mixtures are slower. Tables are presented in a form that can easily be implemented in stellar evolution codes and yield the rate at which the convective shell advances into the interior. Combining these velocities with the local equations for stellar structure, we find a minimum density for each gravitational potential below with the local equations for stellar structure, we find a minimum density for each gravitational potential below which the flame cannot propagate, and must die. Although detailed stellar models will have to be constructed to reslove some issues conclusively, our results that a CO white dwarf inginted at its edge will not burn carbon all the way to its center unless the mass of the white dwarf exceeds 0.8 solar mass. On the other hand, it is difficult to ignite carbon burning by compression alone anywhere in a white dwarf whose mass does not exceed 1.0 solar mass. Thus, compressionally ignited shell carbon burning in an accerting CO dwarf almost certainly propagates all the way to the center of the star. Implications for neutron star formation, and Type Ia supernova models, are briefly discussed. These are also applicable to massive stars in the about 10-12 solar mass range which ignite neon burning off center.

Double-core evolution. 5: Three-dimensional effects in the merger of a red giant with a dwarf companion

Abstract: The evolution of the common envelope phase of a binary system consisting of a 4.67 solar mass red giant and a 0.94 solar mass dwarf is studied using smoothed particle hydrodynamics. We demonstrate that the three-dimensional effects associated with the gravitational tidal torques lead to a rapid decay of the orbit on timescales approximately less than 1 yr. The relative orbit of the two cores in the common envelope is initally eccentric and tends to circularize as the orbital separation of the two cores decreases. The angular momentum lost from the orbital motion is distributed throughout the common envelope, and the double core does not evolve to a state of co-rotation for the evolutionary time followed. The energy dissipated from the relative orbit and deposited in the common envelope results in the ejection of approximately 13% of the mass of the envelope. The mass is ejected in all directions, but there is a preference for mass ejection in the orbital plane of the binary system. For example, approximately 80% of the ejected mass lies within 30 deg of the binary orbital plane. Because gravitational forces are long range, most of the energy and angular momentum is imparted to a small fraction of the common envelope resulting in an efficiency of the mass ejection process of approximately 15%. The core of the red giant executes significant displacement with respect to the center of mass of the system and contributes nearly equally to the total energy dissipation rate during the latter phases of the evolution. The degree of departure from synchronism of the initial binary system can be an important property of the system which can affect the outcome of the common envelope phase.

Variability of Accretion Disks Surrounding Black Holes ----- the Role of Inertial-Acoustic Mode Instabilities

Abstract: The global nonlinear time-dependent evolution of the inertial-acoustic mode instability in accretion disks surrounding black holes has been investigated. The viscous stress is assumed to be proportional to the gas pressure only, i.e.\,, $\tau = - \alpha p_g$. It is found that an oscillatory instability exists in the inner regions of disks ($r < 10 r_g$, where $r_g$ is the Schwarzschild radius) for sufficiently large $\alpha$ ($\gapprox 0.2$), and for mass accretion rates less than about 0.3 times the Eddington value. The variations of the integrated bolometric luminosity from the disk, $\Delta L/L$, are less than 3\%. A power spectrum analysis of these variations reveals a power spectrum which can be fit to a power law function of the frequency $P \propto f^{-\gamma}$, with index $\gamma \sim 1.4-2.3$ and a low frequency feature at about 4 Hz in one case. In addition, a narrow peak centered at a frequency corresponding to the maximum epicyclic frequency of the disk at $\sim 100-130$ Hz and its first harmonic is also seen. The low frequency modulations are remarkably similar to those observed in black hole candidate systems. The possible existence of a scattering corona in the inner region of the disk and/or to other processes contributing to the power at high frequencies in the inner region of the accretion disk may make the detection of the high frequency component difficult.

Low-frequency quasi-periodic oscillations in low-mass X-ray binaries and galactic black hole candidates

Abstract: We consider the inner regions of accretion disks surrounding black holes and neutron stars and investigate the nonlinear time-dependent evolution of thermal-viscous instabilities. The viscous stress is assumed to be proportional to the gas pressure with the viscosity parameter formulated as alpha = min alpha (sub zero) (h/r) (exp n), alpha(sub max), where h is the local scale height, r is the distance from the central compact object, and n, alpha(sub zero) and alpha(sub max) are constants. It is found that the disk is unstable for alpha sufficiently sensitive to h (n greater than or equal to 1.2). The instabilities are globally coherent in the entire unstable region of the disk, and, depeding on the viscosity parameters, the time variability of the mass accretion rates are manifested as periodic or quasi-periodic oscillations. We show that, the low-frequency (approximately 0.04 Hz) quasi-periodic oscillations (QPOs) discovered recently in some of the black hole candidates (Cyg X-1 and GRO J0422+32) and a low-mass X-ray binary (Rapid Burster MXB 1730-335) may be explicable by the thermal-viscous instabilities in accretion disks. The observations of QPOs place constraints on the viscosity parameters and suggest that (n, alpha(sub zero) approximately (1.6, 30) for the Rapid Burster with a 1.4 solar mass neutron star. In the case of black hole candidates, the dependence of alpha on h/r is less steep corresponding to n approximately 1.2-1.3 for black holes less than 10 solar mass.

The Vertical Structure and Stability of Accretion Disks Surrounding Black Holes and Neutron Stars

Abstract: The structure and stability of the inner regions of accretion disks surrounding neutron stars and black holes have been investigated. Within the framework of the alpha viscosity prescription for optically thick disks, we assume the viscous stress scales with gas pressure only, and the alpha parameter, which is less than or equal to unity, is formulated as alpha(sub 0)(h/r)(exp n), where h is the local scale height and n and alpha(sub 0) are constants. We neglect advective energy transport associated with radial motions and construct the vertical structure of the disks by assuming a Keplerian rotation law and local hydrostatic and thermal equilibrium. The vertical structures have been calculated with and without convective energy transport, and it has been demonstrated that convection is important especially for mass accretion rates, M-dot, greater than about 0.1 times the Eddington value, M-dot(sub Edd). Although the efficiency of convection is not high, convection significantly modifies the vertical structure of the disk (as compared with a purely radiative model) and leads to lower temperatures at a given M-dot. The results show that the disk can be locally unstable and that for n greater than or = 0.75, an S-shaped relation can exist between M-dot and the column density, sigma, at a given radius. While the lower stable branch (derivative of M-dot/derivative of sigma greater than 0) and middle unstable branch (derivative of M-dot/derivative of sigma less than 0) represent structures for which the gas and radiation pressure dominate respectively, the stable upper branch (derivative of M-dot/derivative of sigma greater than 0) is a consequence of the saturation of alpha. This saturation of alpha can occur for large alpha(sub 0) and at M-dot less than or = M-dot(sub Edd). The instability is found to occur at higher mass accretion rates for neutron stars than for black holes. In particular, the disk is locally unstable for M-dot greater than or = 0.5 M-dot(sub Edd) for neutron stars and for M-dot greater than or = M-dot(sub Edd) for black holes for a viscosity prescription characterized by n = 1 and alpha(sub 0) = 10.

The vertical structure and stability of accretion disks surrounding black holes and neutron stars

Abstract: The structure and stability of the inner regions of accretion disks surrounding neutron stars and black holes have been studied. Within the framework of the α viscosity prescription for optically thick disks, we assume the viscous stress scales with gas pressure only, and the α parameter, which is less than or equal to unity, is formulated as α0(h/r)n, where h is the local scale height and n and α0 are constants. We neglect advective energy transport associated with radial motions and construct the vertical disk structures by assuming a Keplerian rotation law and local hydrostatic and thermal equilibrium. The vertical structures have been calculated with and without convective energy transport, and it is found that convection is important especially for mass accretion rates greater than about 0.1 times the Eddington value, MEdd. Although convective efficiency is low, convection does help to stabilize the disk. The results show that the disk can be locally unstable and that for n≳0.75, an S‐shaped relatio...