Disk Instabilities and Cooling Fronts

Accretion disk outbursts, and their subsequent decline, offer a unique opportunity to constrain the physics of angular momentum transport in hot accretion disks. Recent work has centered on the claim by Cannizzo et al. that the exponential decay of luminosity following an outburst in black hole accretion disk systems is only consistent with a particular form for the dimensionless viscosity, $\alpha=35(c_s/r\Omega)^{3/2}$. This result can be understood in terms of a simple model of the evolution of cooling fronts in accretion disks. In particular, the cooling front speed during decline is $\sim \alpha_F c_{s,F}(c_{s,F}/r\Omega)^{n}$, where $F$ denotes the position of the cooling front, and the exact value of $n$ depends on the hot state opacity, (although generally $n\approx 1/2$). Setting this speed proportional to $r$ constrains the functional form of $\alpha$ in the hot phase of the disk, which sets it apart from previous arguments based on the relative durations of outburst and quiescence. However, it remains uncertain how well we know the exponent $n$. In addition, more work is needed to clarify the role of irradiation in these systems and its effect on the cooling front evolution.Comment: 10 pages, uses aipproc.st

Fast Magnetic Reconnection and Spontaneous Stochasticity

Magnetic field-lines in astrophysical plasmas are expected to be frozen-in at scales larger than the ion gyroradius. The rapid reconnection of magnetic flux structures with dimensions vastly larger than the gyroradius requires a breakdown in the standard Alfv\'en flux-freezing law. We attribute this breakdown to ubiquitous MHD plasma turbulence with power-law scaling ranges of velocity and magnetic energy spectra. Lagrangian particle trajectories in such environments become "spontaneously stochastic", so that infinitely-many magnetic field-lines are advected to each point and must be averaged to obtain the resultant magnetic field. The relative distance between initial magnetic field lines which arrive to the same final point depends upon the properties of two-particle turbulent dispersion. We develop predictions based on the phenomenological Goldreich & Sridhar theory of strong MHD turbulence and on weak MHD turbulence theory. We recover the predictions of the Lazarian & Vishniac theory for the reconnection rate of large-scale magnetic structures. Lazarian & Vishniac also invoked "spontaneous stochasticity", but of the field-lines rather than of the Lagrangian trajectories. More recent theories of fast magnetic reconnection appeal to microscopic plasma processes that lead to additional terms in the generalized Ohm's law, such as the collisionless Hall term. We estimate quantitatively the effect of such processes on the inertial-range turbulence dynamics and find them to be negligible in most astrophysical environments. For example, the predictions of the Lazarian-Vishniac theory are unchanged in Hall MHD turbulence with an extended inertial range, whenever the ion skin depth $\delta_i$ is much smaller than the turbulent integral length or injection-scale $L_i.$Comment: 31 pages, 5 figure

Gravitational Instabilities In A Protoplanetary Disk Including The Effects Of Magnetic-Fields

We investigate the gravitational instability of a thin, Keplerian protoplanetary disk including the effects of a largely azimuthal magnetic field. The model follows that of our previous work (Noh, Vishniac, & Cochran 1991) except for the inclusion of a magnetic field. The disk is assumed to consist of neutral and ionized gas and neutral dust which are coupled by gravity and friction. The growth rates and eigenfunctions are calculated numerically using nonaxisymmetric linear perturbation methods. The results show that the growth rate has a maximum at some intermediate azimuthal number m, but for each value of m it is reduced relative to the unmagnetized case. The effects of the magnetic field appear more strongly on small scales. As the strength of the equilibrium magnetic field increases the growth rates decrease, and the maximum instability occurs at a lower value of m due to the increasing magnetic pressure. The response of each component to the magnetic field is discussed using the behavior of the eigenfunctions in the radial direction. With the inclusion of the magnetic field, the effects of the ionization fraction and friction on the growth rates also appear to be important for high m modes. Increasing the ionization fraction or the friction suppresses instability, but only slightly changes the maximally unstable azimuthal scales. The enhanced growth rates due to a dust component for which thermal pressure is negligible are somewhat reduced by the inclusion of a magnetic field. The effects of different boundary conditions (reflecting and transmitting) on the growth rates are also shown.NASA NAGW 2418Astronom

Conserving Local Magnetic Helicity in Numerical Simulations

Magnetic helicity is robustly conserved in systems with large magnetic Reynolds numbers, including most systems of astrophysical interest. This plays a major role in suppressing the kinematic large scale dynamo and driving the large scale dynamo through the magnetic helicity flux. Numerical simulations of astrophysical systems typically lack sufficient resolution to enforce global magnetic helicity over several dynamical times. Errors in the internal distribution of magnetic helicity are equally serious and possibly larger. Here we propose an algorithm for enforcing strict local conservation of magnetic helicity in the Coulomb gauge in numerical simulations.Comment: Comments are welcom

The distribution of dark matter, galaxies, and the intergalactic medium in a cold dark matter dominated universe

The evolution and distribution of galaxies and the intergalactic medium (IGM) have been studied, along with collisionless dark matter in a Universe dominated by cold dark matter. The Einstein-deSitter universe with omega sub 0 = 1 and h = 0.5 was considered (here h = H sub 0 bar 100/kms/Mpc and H sub 0 is the present value of the Hubble constant). It is assumed that initially dark matter composes 90 pct and baryonic matter composes 10 pct of total mass, and that the primordial baryonic matter is comprised of H and He, with the abundance of He equal to 10 pct of H by number. Galaxies are allowed to form out of the IGM, if the total density and baryonic density satisfy an overdensity criterion. Subsequently, the newly formed galaxies release 10 to the 60th ergs of energy into the IGM over a period of 10 to the 8th years. Calculations have been performed with 32 to the 3rd dark matter particles and 32 to the 3rd cells in a cube with comoving side length L = 9.6/h Mpc. Dark matter particles and galaxies have been followed with an N-body code, while the IGM has been followed with a fluid code

The Growth Rate of Tidally Excited Waves in Accretion Disks

Accretion disks in close binary systems are subject to a tidally driven parametric instability which leads to the growth of internal waves near the outer edges of such disks (Goodman 1993). These waves are important in understanding the torque exerted on a disk by tidal forces and may play a role in the structure of the disk at small radii. Here we calculate the growth rate of this instability, including the effects of vertical structure and fluid compressibility. We find growth rates which are only slightly different from Goodman's original results, except that near the vertical resonance radius the growth rate can have an extremely broad and strong peak when the disk is stably stratified in the vertical direction. Higher order modes, in the sense of increasing number of vertical nodes, have similar growth rates. Our results differ from a previous calculation along these lines by Lubow et al. (1993). The difference is mostly due to their neglect of radial gradients in the tidally distorted streamlines.Comment: LaTeX (aastex

New Regime of MHD Turbulence: Cascade Below Viscous Cutoff

In astrophysical situations, e.g. in the interstellar medium (ISM), neutrals can provide viscous damping on scales much larger than the magnetic diffusion scale. Through numerical simulations, we have found that the magnetic field can have a rich structure below the dissipation cutoff scale. This implies that magnetic fields in the ISM can have structures on scales much smaller than parsec scales. Our results show that the magnetic energy contained in a wavenumber band is independent of the wavenumber and magnetic structures are intermittent and extremely anisotropic. We discuss the relation between our results and the formation of the tiny-scale atomic structure (TSAS).Comment: ApJ Letters, accepted (Feb. 10, 2002; ApJ, 566, L...); 10 pages, 3 figure

The Anisotropy of MHD Alfv\'{e}nic Turbulence

We perform direct 3-dimensional numerical simulations for magnetohydrodynamic (MHD) turbulence in a periodic box of size $2\pi$ threaded by strong uniform magnetic fields. We use a pseudo-spectral code with hyperviscosity and hyperdiffusivity to solve the incompressible MHD equations. We analyze the structure of the eddies as a function of scale. A straightforward calculation of anisotropy in wavevector space shows that the anisotropy is scale-{\it independent}. We discuss why this is {\it not} the true scaling law and how the curvature of large-scale magnetic fields affects the power spectrum and leads to the wrong conclusion. When we correct for this effect, we find that the anisotropy of eddies depends on their size: smaller eddies are more elongated than larger ones along {\it local} magnetic field lines. The results are consistent with the scaling law $\tilde{k}_{\parallel} \sim \tilde{k}_{\perp}^{2/3}$ proposed by Goldreich and Sridhar (1995, 1997). Here $\tilde{k}_{\|}$ (and $\tilde{k}_{\perp}$) are wavenumbers measured relative to the local magnetic field direction. However, we see some systematic deviations which may be a sign of limitations to the model, or our inability to fully resolve the inertial range of turbulence in our simulations.Comment: 13 pages (11 NEW figures), ApJ, in press (Aug 10, 2000?