quasi-Keplerian Accretion Disk Research Articles

The Structure of a Quasi-Keplerian Accretion Disk around Magnetized Stars

Abstract In this paper, we present the complete structure of a quasi-Keplerian thin accretion disk with an internal dynamo around a magnetized neutron star. We assume a full quasi-Keplerian disk with the azimuthal velocity deviating from the Keplerian fashion by a factor of ξ (0 < ξ < 2). In our approach, we vertically integrate the radial component of the momentum equation to obtain the radial pressure gradient equation for a thin quasi-Keplerian accretion disk. Our results show that, at large radial distance, the accretion disk behaves in a Keplerian fashion. However, close to the neutron star, pressure gradient force (PGF) largely modifies the disk structure, resulting into sudden dynamical changes in the accretion disk. The corotation radius is shifted inward (outward) for ξ > 1 (for ξ < 1), and the position of the inner edge with respect to the new corotation radius is also relocated accordingly, as compared to the Keplerian model. The resulting PGF torque couples with viscous torque (when ξ < 1) to provide a spin-down torque and a spin-up torque (when ξ > 1) while in the advective state. Therefore, neglecting the PGF, as has been the case in previous models, is a glaring omission. Our result has the potential to explain the observable dynamic consequences of accretion disks around magnetized neutron stars.

ACCRETION DISKS IN TWO-DIMENSIONAL HOYLE-LYTTLETON FLOW

We investigate the flip-flop instability observed in two-dimensional planar hydrodynamic simulations of Hoyle-Lyttleton accretion in the case of an accreting object with a radius much smaller than the nominal accretion radius, as one would expect in astrophysically relevant situations. Contrary to previous results with larger accretors, accretion from a homogenous medium onto a small accretor is characterized by a robust, quasi-Keplerian accretion disk. For gas with a ratio of specific heats of 5/3, such a disk remains locked in one direction for a uniform ambient medium. The accretion flow is more variable for gas with a ratio of specific heats of 4/3, with more dynamical interaction of the disk flow with the bow shock leading to occasional flips in the direction of rotation of the accretion disk. In both cases the accretion of angular momentum is determined by the flow pattern behind the accretion shock rather than by the parameters of the upstream flow.

Axisymmetric general relativistic simulations of the accretion-induced collapse of white dwarfs

(Abridged.) The accretion-induced collapse (AIC) of a white dwarf (WD) may lead to the formation of a protoneutron star and a collapse-driven supernova explosion. This process represents a path alternative to thermonuclear disruption of accreting white dwarfs in Type Ia supernovae. Neutrino and gravitational-wave (GW) observations may provide crucial information necessary to reveal a potential AIC. Motivated by the need for systematic predictions of the GW signature of AIC, we present results from an extensive set of general-relativistic AIC simulations using a microphysical finite-temperature equation of state and an approximate treatment of deleptonization during collapse. Investigating a set of 114 progenitor models in rotational equilibrium, with a wide range of rotational configurations, temperatures and central densities, we extend previous Newtonian studies and find that the GW signal has a generic shape akin to what is known as a "Type III" signal in the literature. We discuss the detectability of the emitted GWs, showing that the signal-to-noise ratio for current or next-generation interferometer detectors could be high enough to detect such events in our Galaxy. Some of our AIC models form massive quasi-Keplerian accretion disks after bounce. In rapidly differentially rotating models, the disk mass can be as large as ~0.8-Msun. Slowly and/or uniformly rotating models produce much smaller disks. Finally, we find that the postbounce cores of rapidly spinning white dwarfs can reach sufficiently rapid rotation to develop a nonaxisymmetric rotational instability.

REVISITING THE “FLIP-FLOP” INSTABILITY OF HOYLE-LYTTLETON ACCRETION

We revisit the flip-flop instability of two-dimensional planar accretion using high-fidelity numerical simulations. By starting from an initially steady-state axisymmetric solution, we are able to follow the growth of this overstability from small amplitudes. In the small-amplitude limit, before any transient accretion disk is formed, the oscillation period of the accretion shock is comparable to the Keplerian period at the Hoyle-Lyttleton accretion radius (R_a), independent of the size of the accreting object. The growth rate of the overstability increases dramatically with decreasing size of the accretor, but is relatively insensitive to the upstream Mach number of the flow. We confirm that the flip-flop does not require any gradient in the upstream flow. Indeed, a small density gradient as used in the discovery simulations has virtually no influence on the growth rate of the overstability. The ratio of specific heats does influence the overstability, with smaller gamma leading to faster growth of the instability. For a relatively large accretor (a radius of 0.037R_a) planar accretion is unstable for gamma = 4/3, but stable for gamma > 1.6. Planar accretion is unstable even for gamma = 5/3 provided the accretor has a radius of < 0.0025R_a. We also confirm that when the accretor is sufficiently small, the secular evolution is described by sudden jumps between states with counter-rotating quasi-Keplerian accretion disks.

Comments on "Angular Momentum Transport in Quasi-Keplerian Accretion Disks"

Subramanian, Pujari and Becker (2004) claim that the correct expression for the angular momentum transport in an accretion disc, which is proportional to dΩ/dR, can be derived on the basis of the analysis of the epicyclic motion of gas parcels in adjacent eddies in the disc. We study their argument and show that their derivation contains several fundamental errors: 1) the biased choice of the desired formula from an infinite number of formulae; 2) the biased choice of parcel trajectories; and 3) confusion regarding the reference frames. Following 1) we could derive, for example, a (invalid) formula in which the angular momentum transport is proportional to dv Φ /dR, and from 2) we could even prove that the angular momentum transport is either inward or null. We present the correct approach to the problem of angular momentum transport in an accretion disc in terms of mean free path theory.

Presupernova evolution of accreting white dwarfs with rotation

We discuss the effects of rotation on the evolution of accreting carbon-oxygen white dwarfs, with the emphasis on possible consequences in Type Ia supernova (SN Ia) progenitors. Starting with a slowly rotating white dwarf, we simulate the accretion of matter and angular momentum from a quasi-Keplerian accretion disk. The role of the various rotationally induced hydrodynamic instabilities for the transport of angular momentum inside the white dwarf is investigated. We find that the dynamical shear instability is the most important one in the highly degenerate core. Our results imply that accreting white dwarfs rotate differentially throughout,with a shear rate close to the threshold value for the onset of the dynamical shear instability. As the latter depends on the temperature of the white dwarf, the thermal evolution of the white dwarf core is found to be relevant for the angular momentum redistribution. As found previously, significant rotation is shown to lead to carbon ignition masses well above 1.4 Msun. Our models suggest a wide range of white dwarf explosion masses, which could be responsible for some aspects of the diversity observed in SNe Ia. We analyze the potential role of the bar-mode and the r-mode instability in rapidly rotating white dwarfs, which may impose angular momentum loss by gravitational wave radiation. We discuss the consequences of the resulting spin-down for the fate of the white dwarf, and the possibility to detect the emitted gravitational waves at frequencies of 0.1 >... 1.0 Hz in nearby galaxies with LISA. Possible implications of fast and differentially rotating white dwarf cores for the flame propagation in exploding white dwarfs are also briefly discussed.

Angular momentum transport in quasi-Keplerian accretion disks

We reexamine arguments advanced by Hayashi & Matsuda (2001), who claim that several simple, physically motivated derivations based on mean free path theory for calculating the viscous torque in a quasi-Keplerian accretion disk yield results that are inconsistent with the generally accepted model. If correct, the ideas proposed by Hayashi & Matsuda would radically alter our understanding of the nature of the angular momentum transport in the disk, which is a central feature of accretion disk theory. However, in this paper we point out several fallacies in their arguments and show that there indeed exists a simple derivation based on mean free path theory that yields an expression for the viscous torque that is proportional to the radial derivative of the angular velocity in the accretion disk, as expected. The derivation is based on the analysis of the epicyclic motion of gas parcels in adjacent eddies in the disk.

The vertical structure of T Tauri accretion disks

We present a self-consistent analytical model for the computation of the physical conditions in a steady quasi-Keplerian accretion disk. The method, based on the thin disk approximation, considers the disk as concentric cylinders in which we treat the vertical transfer as in a plane-parallel medium. The formalism generalizes a work by Hubeny (1990), linking the disk temperature distribution to the local energy dissipation and leads to analytical formulae for the temperature distribution which help to understand the behaviour of the radiation propagated inside the disks. One of the main features of our new model is that it can take into account many heating sources. We apply the method first to two sources: viscous dissipation and stellar irradiation. We show that other heating sources like horizontal transfer or irradiation from the ambiant medium can also be taken into account. Using the analytical formulation in the case of a modified Shakura & Sunyaev radial distribution that allow the accretion rate to be partly self-similar in the inner region, and, for an alpha and beta prescription of the viscosity, we obtain two-dimensional maps of the temperature, pressure and density in the close environment of low mass young stars. We use these maps to derive the observational properties of the disks such as spectral energy distributions, high resolution spatial images or visibilities in order to underline their different behaviours under different input models.