Accretion disk evolution

Three aspects of mass transfer instability models of dwarf novae are examined. The hydrodynamic development of instabilities in the secondary are examined within Roche geometry and shown to extend at least a few degrees away from the line of centres. The form of the outburst light curves observed in SS Cygni are shown to be a natural consequence of mass transfer bursts with a duration either less than, or greater than, the disk viscous timescale. Finally the two-dimensional structure of the disc in the plane of the orbit is studied. As with -disks the viscous evolution time following a burst of mass transfer determines the size of viscosity within the disk. Significant deviations from axial symmetry are found to be present.Paper presented at the IAU Colloquium No. 93 on Cataclysmic Variables. Recent Multi-Frequency Observations and Theoretical Developments, held at Dr. Remeis-Sternwarte Bamberg, F.R.G., 16–19 June, 1986.     

Accretion disk structure in SS Cygni

High-resolution Coude observations of non-axisymmetric line emission from the dwarf nova SS Cygni are presented. By subtracting the constant line component, the asymmetric line emission responsible for the observed phase shift between the absorption and emission line radial velocity curves can be isolated. The extra emission is a large fraction of the total line emission and extends to large velocities (1500 km sec^–1). The phase stability of the emission demands a large-scale structure which is fixed in the frame of the binary. A magnetic origin of the excitation cannot be ruled out but is implausible. A simple explanation is that the accretion stream from the companion star is able to spill over the edge of the disk, introducing emission at non-circular velocities and most likely disturbing the upper layers of the accretion disk.Paper presented at the IAU Colloquium No. 93 on Cataclysmic Variables, Recent Multi-Frequency Observations and Theoretical Development, held at Dr. Remeis-Sternwarte Bamberg, F.R.G., 16–19 June, 1986.     

Accretion disk boundary layers: Their structure and stability

The importance of the boundary layer has been known for some time, (see Lynden-Bell and Pringle, 1974). Yet this region of the disc has never been studied in great depth. We present here some calculations which are undertaken in order to explore some of the complex processes which can go on in this region. It is shown how the structure of the boundary layer is affected by viscosity, how oscillations can occur in the outer disk and boundary layer regions. We also show how they disperse and dissipate.Paper presented at the IAU Colloquium No. 93 on Cataclysmic Variables. Recent Multi-Frequency Observations and Theoretical Developments, held at Dr. Remeis-Sternwarte Bamberg, F.R.G., 16–19 June, 1986.     

Accretion of terrestrial planets from oligarchs in a turbulent disk

We have investigated the final accretion stage of terrestrial planets from Mars-mass protoplanets that formed through oligarchic growth in a disk comparable to the minimum mass solar nebula (MMSN), through N-body simulation including random torques exerted by disk turbulence due to Magneto-Rotational Instability. For the torques, we used the semi-analytical formula developed by Laughlin et al. [Laughlin, G., Steinacker, A., Adams, F.C., 2004. Astrophys. J. 608, 489-496]. The damping of orbital eccentricities (in all runs) and type-I migration (in some runs) due to the tidal interactions with disk gas is also included. Without any effect of disk gas, Earth-mass planets are formed in terrestrial planet regions in a disk comparable to MMSN but with too large orbital eccentricities to be consistent with the present eccentricities of Earth and Venus in our Solar System. With the eccentricity damping caused by the tidal interaction with a remnant gas disk, Earth-mass planets with eccentricities consistent with those of Earth and Venus are formed in a limited range of disk gas surface density (∼10⁻⁴ times MMSN). However, in this case, on average, too many (?6) planets remain in terrestrial planet regions, because the damping leads to isolation between the planets. We have carried out a series of N-body simulations including the random torques with different disk surface density and strength of turbulence. We found that the orbital eccentricities pumped up by the turbulent torques and associated random walks in semimajor axes tend to delay isolation of planets, resulting in more coagulation of planets. The eccentricities are still damped after planets become isolated. As a result, the number of final planets decreases with increase in strength of the turbulence, while Earth-mass planets with small eccentricities are still formed. In the case of relatively strong turbulence, the number of final planets are 4-5 at 0.5-2 AU, which is more consistent with Solar System, for relatively wide range of disk gas surface density (∼¹⁰⁻⁴-¹⁰⁻² times MMSN).     

Linear kinetic theory of instabilities of a gravitatingstellar disk

Linear kinetic theory is developed to describe collective oscillations (and their instabilities) propagating in a rapidly rotating disk of stars, representing a highly flattened galaxy. The analysis is carried out for the special case of a self-gravitating, infinitesimally thin, and spatially inhomogeneous system, taking into account the effects both of thermal movements of stars and of gravitational encounters between stars and giant molecular clouds of an interstellar medium. The star–cloud encounters are described with the use of the Landau collision integral. The dynamics of gravity perturbations with rare interparticle encounters is considered. Such a disk is treated by employing the well elaborated mathematical formalisms from plasma perturbation theory using normal-mode analysis. In particular, the method of solving the Boltzmann equation is applied by integration along paths, neglecting the influence of star–cloud encounters on the distribution of stars in the zeroth-order approximation. We are especially interested in important kinetic effects due to wave–star resonances, which we have little knowledge about. The kinetic effects are introduced via a minor drift motion of stars which is computed from the equations of stellar motion in an unperturbed central force field of a galaxy. The dispersion laws for two main branches of disk's oscillations, that is the classical Jeans branch and an additional gradient branch, are deduced. The resonant Landau-type instabilities of hydrodynamically stable Jeans and gradient gravity perturbations is considered to be a long-term generating mechanism for propagating density waves, thereby leading to spiral-like and/or ring-like patterns in the flat galaxies. This revised version was published online in July 2006 with corrections to the Cover Date.     

Accretion disk spectra of super-luminal jet sources and ultra-luminous compact X-ray sources in nearby spiral galaxies

The Ultra-luminous Compact X-ray Sources (ULXs)in nearby spiral galaxies and the Galactic super-luminaljet sources sharethe common spectral characteristic that they haveextremely high disk temperatures which cannot be explainedin the framework of the standard accretion disk modelin the Schwarzschild metric. We have calculated an extreme Kerr disk model to examine if the Kerr disk model can instead explain the observed `too hot' accretion disk spectra.We found that the Kerr disk spectrum becomes significantly hardercompared to the Schwarzschild disk only when the disk is highlyinclined.For super-luminal jet sources, which are known to beinclined systems, the Kerr disk model may thuswork if we choose proper values for the black hole angular momentum. For the ULXs, however, the Kerr disk interpretation will be problematic,as is is highly unlikely that their accretion disks are preferentiallyinclined.     

Parker instability in a self-gravitating magnetized gas disk: II. Competition between gravitational and convective instabilities

Under influence of external gravity generated by Galactic all components excluding ISM, a magnetized gas disk may experience both Parker and convective instabilities. Growth rate of the convective instability increases with decreasing perturbation wavelength, and the convective motion makes sheet-like structures all over before the Parker instability forms structures of any meaningful size in the disk. Yet the Parker instability is thought to be an ideal route to form large-scale condensations in the Galaxy. In search of a means to curb convective activities in the Galactic ISM disk, the external gravity is replaced by self-gravity as a driving force of the Parker instability and the gravitational instability is invoked to reinforce the Parker instability. Perturbation of interchange mode is known to trigger convective instability in such disk and the one of undular mode to activate the Parker instability, while the gravitational instability can be triggered by both modes. Therefore, the resulting Jeans instability would help the Parker instability to overcome disrupting behavior of the convection. Dynamical properties of the disk can be characterized by ratio α of magnetic to gas pressure, adiabatic exponent γ, scale height H of the ISM, and disk thickness z_a. A linear stability analysis has been done to the disk, and the maximum growth rate of the Parker–Jeans instability is compared with that of the convective instability. The latter may or may not be higher than the former, depending on the disk parameters. The Parker–Jeans instability has chances to override the convective instability, when the disk is thicker than a certain value. In the disk thinner than the critical one, the Jeans instability can always suppress the convection. Since the growth rate of the convective instability is proportional to local gravitational acceleration, thereby in the general Galactic gravity, the convective instability works actively only in upper regions, we expect chaotic features to appear in regions of low density far from Galactic mid-plane.     

Turbulence in Accretion Disks

An accretion disk is an inevitable part of the star forming process. Recent years have witnessed dramatic progress in our understanding of how turbulence arises and transports angular momentum in astrophysical accretion disks. The key conceptual point is that the combination of a subthermal magnetic field and outwardly decreasing differential rotation is subject to the magnetorotational instability. This rapidly generates magnetohydrodynamical (MHD) turbulence, leading to greatly enhanced angular momentum transport. Purely hydrodynamic disks, on the other hand, are stable. Disks that are too cool to couple effectively to the magnetic field will not be turbulent. Fully global three dimensional MHD simulations are now beginning to probe the properties of accretion disks from first principles.     

Stability of Accretion Models

A critical analysis of standard accretion models is presented. We consider the stability of models in the theories of disc accretion onto black holes and spherical/disc accretion onto a magnetosphere. We take into account realistic physics processes and geometry (inner magnetic field in the accreted plasma, finite conductivity, finite length of the field lines, finite rotation of the accreted object, and magnetic shear on the boundary between the magnetosphere and accreted plasma). The influence of these factors leads to radical changes of both the accretion as whole and the energy release in the accreting system. Strong current-sheet and Z-pinch-like structures should arise over the polar region of the accreting object. Particle acceleration in the electric fields of current discharges in these regions may be a source of efficient conversion of energy into nonthermal particles and of the emission observed from many accreting objects.     

Shock instabilities

It is well known that adiabatic shocks in ordinary gases are stable to both tranverse and longitudinal perturbations, but this need not be true if there are significant thermal effects due to chemical reactions or cooling processes. For example, detonation waves in gases are observed to form cellular structures if the chemical reaction is sufficiently temperature sensitive and a similar instability occurs in radiative shocks in the ISM if their speed exceeds 150 km s^–1. This means that interstellar shocks will be subject to this radiative instability in many cases. The temperature sensitivity of the nuclear reactions in Type I supernovae is also such that we would expect detonation waves in these objects to have a cellular structure.     

Accretion process of the moon

Recent geochemical and geophysical data suggest that the initial temperature of the Moon was strongly peaked toward the lunar surface. To explain such an initial temperature distribution, a simple model of accretion process of the Moon is presented. The model assumes that the Moon was formed from the accumulation of the solid particles or gases in the isolated, closed cloud. Two equations are derived to calculate the accretion rate and surface temperature of the accreting Moon. Numerical calculations are made for a wide range of the parameters particle concentration and particle velocity in the cloud. A limited set of the parameters gives the initial temperature profiles as required by geochemical and geophysical data. These models of the proto-moon cloud indicate that the lunar outershell, about 400 km thick, was partially or completely molten just after the accretion of the Moon and that the Moon should have been formed in a period shorter than 1000 yr. If the Moon formed at a position nearer to the Earth than its present one, the Moon might have been formed in a period of less than one year.On leave from Geophysical Institute, University of Tokyo.Contribution No. 2104, Division of Geological and Planetary Sciences, California Institute of Technology.     

Accretion by isolated neutron stars

Accretion of interstellar material by an isolated neutron star is discussed. The point I address here is the interaction between the accretion flow and the stellar magnetosphere. I show that the interchange instabilities of the magnetospheric boundary under the conditions of interest are basically suppressed. The entry of the material into the magnetosphere is governed by diffusion. Due to this reason the persistent accretion luminosity of isolated neutron stars is limited to <4×10²⁶ erg s⁻¹. These objects can also appear as X-ray bursters with the burst durations of ∼30 min and repetition time of ∼10⁵ yr. This indicates that the number of the accreting isolated neutron stars which could be observed with recent and modern X-ray missions is a few orders of magnitude smaller than that previously estimated.      

Periodic Orbits and Accretion Disks

The effect of the radiation pressure on the periodic motion of a small particle around one ‘primary’ body of the restricted photogravitational three-body problem is examined. Simple periodic orbits are used to determine the maximum size of the accretion disk in close binary systems. This revised version was published online in July 2006 with corrections to the Cover Date.     

Time-Scale for Accretion of Matter

Mass accretion is the key factor for evolution of galaxies. It can occur through secular evolution, when gas in the outer parts is driven inwards by dynamical instabilities, such as spirals or bars. This secular evolution proceeds very slowly when spontaneous, and can be accelerated when triggered by companions. Accretion can also occur directly through merging of small companions, or more violent interaction and coalescence. We discuss the relative importance of both processes, their time-scale and frequency along a Hubble time. Signatures of both processes can be found in the Milky Way. It is however likely that our Galaxy had already gathered the bulk of its mass about 8–10 Gyr ago, as is expected in hierarchical galaxy formation scenarios. This revised version was published online in July 2006 with corrections to the Cover Date.     

On penetrative instabilities

The investigation of instabilities in a penetrative atmosphere discussed in our earlier paper (Pandeyet al., 1979) is extended to include thermal dissipation in a more realistic approximation. It is shown that the convective modes are not very sensitive to the presence of an overlying stable layer. The overstabilization of gravity modes is, however, found to occur under very stringent conditions, while the acoustic overstability is enhanced by the presence of an overlying stable layer.     

Relativistic Jets from Accretion Disks

The jets observed to emanate from many compact accreting objects may arise from the twisting of a magnetic field threading a differentially rotating accretion disk which acts to magnetically extract angular momentum and energy from the disk. Two main regimes have been discussed, hydromagnetic jets, which have a significant mass flux and have energy and angular momentum carried by both matter and electromagnetic field and, Poynting jets, where the mass flux is small and energy and angular momentum are carried predominantly by the electromagnetic field. Here, we describe recent theoretical work on the formation of relativistic Poynting jets from magnetized accretion disks. Further, we describe new relativistic, fully electromagnetic, particle-in-cell (PIC) simulations of the formation of jets from accretion disks. Analog Z-pinch experiments may help to understand the origin of astrophysical jets.     

Accretion in magnetic cataclysmic variables

We discuss the arguments in favour of the suggestion that polars (AM Her systems) and intermediate polars (IP's) have magnetic fields of the same order of magnitude, and form one single class of objects. The period distribution of magnetic catclysmic variables is well explained if they evolve the same way as non magnetic systems, IP's becoming AM Her systems after crossing the gap. We discuss some consequences of the limited magnetic moment distribution (10³³10³⁴ G cm^–3) in magnetic CV's, in particular for the existence of accretion discs in those systems.Paper presented at the IAU Colloquium No. 93 on Cataclysmic Variables. Recent Multi-Frequency Observations and Theoretical Developments, held at Dr. Remeis-Sternwarte Bamberg, F.R.G., 16–19 June, 1986.