Accretion disk instabilities

Basic properties of accretion disk instabilities are summarized. We first explain the standard disk model by Shakura and Sunyaev. In this model, the dominant sources of viscosity are assumed to be chaotic magnetic fields and turbulence in gas flow, and the magnitude of viscosity is prescribed by so-called model. It is then possible to build a particular disk model. In the framework of the standard model, accretion disks are stationary, but when some of the basic assumptions are relaxed, various kinds of instabilities appear. In particular, we focus on the thermal limit-cycle instability caused by partial ionization of hydrogen (and helium). We demonstrate that the disk instability model well accounts for the basic observed features of outbursts of dwarf novae and X-ray nova. We then introduce other kinds of instabilities based on the viscosity model. They are suspected to produce time variabilities observed on a wide range of timescales in close binaries and active galactic nuclei.     

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 and evolution in close binaries

The discovery of X-ray binary systems in the 1960's opened up stellar evolution theory by revealing further endpoints in addition to white dwarfs. This review summarises recent progress in studies of stellar-evolutionary processes that lead to X-ray binaries themselves, the mass transfer rates that power them, and the accretion processes which convert this into electromagnetic radiation. Particular attention is paid to the topics of mass transfer fluctuations and of the accretion by magnetic compact stars.     

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).     

Formation and evolution of disk galaxies

I review several of the current issues in the theory of disk galaxy formation. There is still much to be done, observationally and theoretically, before we can expect to approach an understanding of disk galaxies that is reliable enough to make robust predictions about the high redshift universe. This revised version was published online in August 2006 with corrections to the Cover Date.     

Accretion of the asteroids: Implications for their thermal evolution

Thermal models of asteroids generally assume that they accreted either instantaneously or over an extended interval with a prescribed growth rate. It is conventionally assumed that the onset of accretion of chondrite parent bodies was delayed until a substantial fraction of the initial ²⁶Al had decayed. However, this interval is not consistent with the early melting, and differentiation of parent bodies of iron meteorites. Formation time scales are tested by dynamical simulations of accretion from small primary planetesimals. Gravitational accretion yields rapid runaway growth of large planetary embryos until most smaller bodies are depleted. In a given simulation, all asteroid‐sized bodies have comparable growth times, regardless of size. For plausible parameters, growth times are shorter than the lifetime of ²⁶Al, consistent with thermal models that assume instantaneous accretion. Rapid growth after planetesimal formation is consistent with differentiation of parent bodies of iron meteorites, but not with the assumed delay in formation of chondritic bodies. After the initial growth stage, there is an interval of slower evolution until the belt is stirred and the embryos are dynamically removed. During this interval, a fraction of asteroid‐sized bodies experience large accretional impacts, allowing bodies of the same final size to have very different histories of radius versus time. Accretion from small primary planetesimals leaves some fraction of material in bodies small enough to preserve CAIs while avoiding heating by ²⁶Al. Unheated material can be a significant fraction of the mass that remains after large embryos are removed from the Main Belt.     

The chemo-dynamical evolution of a disk galaxy

I present a model for the formation and evolution of a massive disk galaxy, within a growing dark halo whose mass evolves according to cosmological simulations of structure formation. The galactic evolution is simulated with a new three-dimensional chemo-dynamical code, including dark matter, stars and a multi-phase ISM. We follow the evolution from redshift z= 4.85 until the present epoch. The energy release by massive stars and supernovae prevents a rapid collapse of the baryonic matter and delays the maximum star formation until redshift z ≈ 1. The galaxy forms radially from inside-out and vertically from top-to-bottom. Correspondingly, the inner halo is the oldest component, followed by the outer halo, the bar/bulge, the thick and the thin disk. The bulge in the model consists of at least two stellar subpopulations, an early collapse population and a population that formed later in the bar. This revised version was published online in August 2006 with corrections to the Cover Date.     

The migrating embryo model for disk evolution

Abstract– A new view of disk evolution is emerging from self‐consistent numerical simulation modeling of the formation of circumstellar disks from the direct collapse of prestellar cloud cores. This has implications for many aspects of star and planet formation, including the growth of dust and high‐temperature processing of materials. A defining result is that the early evolution of a disk is crucially affected by the continuing mass loading from the core envelope, and is driven into recurrent phases of gravitational instability. Nonlinear spiral arms formed during these episodes fragment to form gaseous clumps in the disk. These clumps generally migrate inward due to gravitational torques arising from their interaction with a trailing spiral arm. Occasionally, a clump can open up a gap in the disk and settle into a stable orbit, revealing a direct pathway to the formation of companion stars, brown dwarfs, or giant planets. At other times, when multiple clumps are present, a low mass clump may even be ejected from the system, providing a pathway to the formation of free‐floating brown dwarfs and giant planets in addition to low mass stars. Finally, it has been suggested that the inward migration of gaseous clumps can provide the proper conditions for the transport of high‐temperature processed solids from the outer disk to the inner disk, and even possibly accelerate the formation of terrestrial planets in the inner disk. All of these features arising from clump formation and migration can be tied together conceptually in a migrating embryo model for disk evolution that can complement the well‐known core accretion model for planet formation.     

The evolution of disk galaxies in clusters

We are carrying out a programme to measure the evolution of the stellar and dynamical masses and M/L ratios for a sizeable sample of morphologically-classified disk galaxies in rich galaxy clusters at 0.2 < z < 0.9. Using FORS2 at the VLT we are obtaining rotation curves for the cluster spirals so that their Tully-Fisher relation can be studied as a function of redshift and compared with that of field spirals. We already have rotation curves for ∼ 10 cluster spirals at z = 0.83, and 25 field spirals at lower redshifts and we plan to increase this sample by one order of magnitude. We present here the first results of our study, and discuss the implications of our data in the context of current ideas and models of galaxy formation and evolution. This revised version was published online in September 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.     

Accretion, ablation and propeller evolution in close millisecond pulsar binary systems

A model for the formation and evolution of binary millisecond radio pulsars in systems with low mass companions (<0.1 M_⊙) is investigated using a binary population synthesis technique. Taking into account the non conservative evolution of the system due to mass loss from an accretion disk as a result of propeller action and from the companion via ablation by the pulsar, the transition from the accretion powered to rotation powered phase is investigated. It is shown that the operation of the propeller and ablation mechanisms can be responsible for the formation and evolution of black widow millisecond pulsar systems from the low mass X-ray binary phase at an orbital period of ～0.1 day. For a range of population synthesis input parameters, the results reveal that a population of black widow millisecond pulsars characterized by orbital periods as long as ～0.4 days and companion masses as low as ～0.005 M_⊙ can be produced. The orbital periods and minimum companion mass of this radio millisecond pulsar population critically depend on the thermal bloating of the semi-degenerate hydrogen mass losing component, with longer orbital periods for a greater degree of bloating. Provided that the radius of the companion is increased by about a factor of 2 relative to a fully degenerate, zero temperature configuration, an approximate agreement between observed long orbital periods and theoretical modeling of hydrogen rich donors can be achieved. We find no discrepancy between the estimated birth rates for LMXBs and black widow systems, which on average are ${\sim}1.3\times10^{-5}~{\rm yr}^{-1}$ and $1.3\times10^{-7}~{\rm yr}^{-1}$ respectively.     

The Fresnel space imager as a disk evolution watcher

The Fresnel Diffractive Imaging Arrays form high resolution images by diffraction with low radiometric efficiencies. They are extremely good devices to make high resolution imaging and integral field spectroscopy of bright sources. Thirty meter arrays will provide a spatial resolution of 0.8 mas at Lyman-?? that will open a completely new field of research: the study of matter distribution around disks and their gravitational drives. In this contribution, the potentials of the 3.6 m precursors (or probes) for astrophysical disks and jets research, are described. Main emphasis is made on young planetary disks.     

Accretion disc evolution in cataclysmic variables (the 1988 international time project in La Palma

A summary of data collected during a sixty night international campaign devoted to cataclysmic variables is presented.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

The evolution of the water distribution in a viscous protoplanetary disk

Astronomical observations have shown that protoplanetary disks are dynamic objects through which mass is transported and accreted by the central star. This transport causes the disks to decrease in mass and cool over time, and such evolution is expected to have occurred in our own solar nebula. Age dating of meteorite constituents shows that their creation, evolution, and accumulation occupied several Myr, and over this time disk properties would evolve significantly. Moreover, on this timescale, solid particles decouple from the gas in the disk and their evolution follows a different path. It is in this context that we must understand how our own solar nebula evolved and what effects this evolution had on the primitive materials contained within it. Here we present a model which tracks how the distribution of water changes in an evolving disk as the water-bearing species experience condensation, accretion, transport, collisional destruction, and vaporization. Because solids are transported in a disk at different rates depending on their sizes, the motions will lead to water being concentrated in some regions of a disk and depleted in others. These enhancements and depletions are consistent with the conditions needed to explain some aspects of the chemistry of chondritic meteorites and formation of giant planets. The levels of concentration and depletion, as well as their locations, depend strongly on the combined effects of the gaseous disk evolution, the formation of rapidly migrating rubble, and the growth of immobile planetesimals. Understanding how these processes operate simultaneously is critical to developing our models for meteorite parent body formation in the Solar System and giant planet formation throughout the galaxy. We present examples of evolution under a range of plausible assumptions and demonstrate how the chemical evolution of the inner region of a protoplanetary disk is intimately connected to the physical processes which occur in the outer regions.     

Toward a more consistent evolution model for the local galactic disk

Infall models for the evolution of the local galactic disk were studied and confronted with a large number of observational constraints from the solar vicinity, inclusive of the white dwarf luminosity function. The models are characterized as follows: 1. The key-functions (SFR, IMF, gas infall rate) are not prescribed by simple laws, but are directly derived from observational constraints. 2. A scatter in the metallicity at fixed age is considered which partly reflects inhomogeous chemical evolution. 3. Special attention is drawn to the internal consistency of the models. 4. In addition to infall of low-metallicity gas, metal-enriched outflows are allowed. The “best” model is characterized by a disk age of ≈︁ 12 Gyr, a SFR which is decreasing over the first half and is nearly constant over the second half of the disk evolution, and by a similar temporal run of the gas infall rate. Moderate metal-enriched outflow can not be excluded.     

Eccentricity evolution of giant planet orbits due to circumstellar disk torques

The extrasolar planets discovered to date possess unexpected orbital elements. Most orbit their host stars with larger eccentricities and smaller semi-major axes than similarly sized planets in our own Solar System do. It is generally agreed that the interaction between giant planets and circumstellar disks (Type II migration) drives these planets inward to small radii, but the effect of these same disks on orbital eccentricity, ?, is controversial. Several recent analytic calculations suggest that disk-planet interactions can excite eccentricity, while numerical studies generally produce eccentricity damping. This paper addresses this controversy using a quasi-analytic approach, drawing on several preceding analytic studies. This work refines the current treatment of eccentricity evolution by removing several approximations from the calculation of disk torques. We encounter neither uniform damping nor uniform excitation of orbital eccentricity, but rather a function d?/dt that varies in both sign and magnitude depending on eccentricity and other Solar System properties. Most significantly, we find that for every combination of disk and planet properties investigated herein, corotation torques produce negative values of d?/dt for some range in ? within the interval [0.1, 0.5]. If corotation torques are saturated, this region of eccentricity damping disappears, and excitation occurs on a short timescale of less than 0.08 Myr. Thus, our study does not produce eccentricity excitation on a timescale of a few Myr—we obtain either eccentricity excitation on a short time scale, or eccentricity damping on a longer time scale. Finally, we discuss the implications of this result for producing the observed range in extrasolar planet eccentricity.     

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.