Linear Analysis of the Hall Effect in Protostellar Disks

The effects of Hall electromotive forces (HEMFs) on the linear stability of protostellar disks are examined. Earlier work on this topic focused on axial field and perturbation wavenumbers. Here we treat the problem more generally. Both axisymmetric and nonaxisymmetric cases are investigated. Though seldom explicitly included in calculations, HEMFs appear to be important whenever Ohmic dissipation is. They allow for the appearance of electron whistler waves, and since these have right-handed polarization, a helicity factor is also introduced into the stability problem. This factor is the product of the components of the angular velocity and magnetic field along the perturbation wavenumber, and it is destabilizing when negative. Unless the field and angular velocity are exactly aligned, it is always possible to find destabilizing wavenumbers. HEMFs can destabilize any differential rotation law, even those with angular velocity increasing outward. Regardless of the sign of the angular velocity gradient, the maximum growth rate is always given in magnitude by the local Oort A value of the disk, as in the standard magnetorotational instability. The role of Hall EMFs may prove crucial to understanding how turbulence is maintained in the ``low state'' of eruptive disk systems.Comment: 34 pages, 10 figures, AAS LaTEx, v.4.0. Submitted to Ap

Discs and Planetary Formation

The formation, structure and evolution of protoplanetary discs is considered. The formation of giant planets within the environment of these models is also discussed.Comment: 22 pages, LaTeX (including 6 figures), uses paspconf.sty, epsf.sty and rotate.sty, to be published in Proceedings of the EC Summer School on 'Astrophysical Discs', eds J. A. Sellwood and J. Goodman, ASP Conf. Serie

Tidally-induced warps in protostellar discs

We review results on the dynamics of warped gaseous discs. We consider tidal perturbation of a Keplerian disc by a companion star orbiting in a plane inclined to the disc. The perturbation induces the precession of the disc, and thus of any jet it could drive. In some conditions the precession rate is uniform, and as a result the disc settles into a warp mode. The tidal torque also leads to the truncation of the disc, to the evolution of the inclination angle (not necessarily towards alignment of the disc and orbital planes) and to a transport of angular momentum in the disc. We note that the spectral energy distribution of such a warped disc is different from that of a flat disc. We conclude by listing observational effects of warps in protostellar discs.Comment: 10 pages, LaTeX (including 1 figure), uses paspconf.sty and epsf.sty, to be published in Proceedings of the EC Summer School on 'Astrophysical Discs', eds J. A. Sellwood and J. Goodman, ASP Conf. Serie

The response of accretion disks to bending waves: angular momentum transport and resonances

We investigate the linear tidal perturbation of a viscous Keplerian disk by a companion star orbiting in a plane inclined to the disk. We consider m=1 perturbations with odd symmetry with respect to the z=0 midplane. Since the response of a viscous disk is not in phase with the perturbing potential, a tidal torque is exerted on the disk, resulting in a decrease of its angular momentum. This tidal torque is found to be comparable to the horizontal viscous stress acting on the background flow when the perturbed velocities in the disk are on the order of the sound speed. If these velocities remain subsonic, the tidal torque can exceed the horizontal viscous stress only if the viscous parameter \alpha which couples to the vertical shear is larger than that coupled to the horizontal shear. In protostellar disks, bending waves are found to propagate deep into the disk inner parts. If the waves are reflected at the center, resonances occur when the frequency of the tidal waves is equal to that of some free normal global bending mode of the disk. If such resonances exist, tidal interactions may then be important even when the binary separation is large. Out of resonance, the torque associated with the secular perturbation is generally much larger than that associated with the finite frequency perturbations. As long as the waves are damped before they reach the center, the torque associated with the finite frequency perturbations does not depend on the viscosity. These calculations are relevant to disks around young stars and maybe also to disks in X-ray binary systems. (abridged

Tidally-induced angular momentum transport in disks

We discuss the transport of angular momentum induced by tidal effects in a disk surrounding a star in a pre-main sequence binary system. We consider the effect of both density and bending waves. Although tidal effects are important for truncating protostellar disks and for determining their size, it is unlikely that tidally-induced angular momentum transport plays a dominant role in the evolution of protostellar disks. Where the disk is magnetized, transport of angular momentum is probably governed by MHD turbulence. In a non self-gravitating laminar disk, the amount of transport provided by tidal waves is probably too small to account for the lifetime of protostellar disks. In addition, tidal effects tend to be localized in the disk outer regions

The TRAPPIST-1 system: Orbital evolution, tidal dissipation, formation and habitability

We study the dynamical evolution of the TRAPPIST-1 system under the influence of orbital circularization through tidal interaction with the central star. We find that systems with parameters close to the observed one evolve into a state where consecutive planets are linked by first order resonances and consecutive triples, apart from planets c, d and e, by connected three body Laplace resonances. The system expands with period ratios increasing and mean eccentricities decreasing with time. This evolution is largely driven by tides acting on the innermost planets which then influence the outer ones. In order that deviations from commensurability become significant only on $Gy$ time scales or longer, we require that the tidal parameter associated with the planets has to be such that $Q' > \sim 10^{2-3}.$ At the same time, if we start with two subsystems, with the inner three planets comprising the inner one, $Q'$ associated with the planets has to be on the order (and not significantly exceeding) $10^{2-3}$ for the two subsystems to interact and end up in the observed configuration. This scenario is also supported by modelling of the evolution through disk migration which indicates that the whole system cannot have migrated inwards together. Also in order to avoid large departures from commensurabilities, the system cannot have stalled at a disk inner edge for significant time periods. We discuss the habitability consequences of the tidal dissipation implied by our modelling, concluding that planets d, e and f are potentially in habitable zones.Comment: 27 pages, 15 figures, accepted for publication in MNRA

Bending Instabilities in Magnetized Accretion Discs

We study the global bending modes of a thin annular disc subject to both an internally generated magnetic field and a magnetic field due to a dipole embedded in the central star with axis aligned with the disc rotation axis. When there is a significant inner region of the disc corotating with the star, we find spectra of unstable bending modes. These may lead to elevation of the disc above the original symmetry plane facilitating accretion along the magnetospheric field lines. The resulting non-axisymmetric disc configuration may result in the creation of hot spots on the stellar surface and the periodic photometric variations observed in many classical T Tauri stars (CTTS). Time-dependent behaviour may occur including the shadowing of the central source in magnetic accretors even when the dipole and rotation axes are aligned.Comment: Accepted by MNRAS. 18 pages, 11 figures. LaTeX2e in the MN style. PostScript and HTML files are also available from http://www-star.qmw.ac.uk/~va/ or by e-mail: [email protected]

Orbital evolution of a planet on an inclined orbit interacting with a disc

We study the dynamics of a planet on an orbit inclined with respect to a disc. If the initial inclination of the orbit is larger than some critical value, the gravitational force exerted by the disc on the planet leads to a Kozai cycle in which the eccentricity of the orbit is pumped up to large values and oscillates with time in antiphase with the inclination. On the other hand, both the inclination and the eccentricity are damped by the frictional force that the planet is subject to when it crosses the disc. We show that, by maintaining either the inclination or the eccentricity at large values, the Kozai effect provides a way of delaying alignment with the disc and circularization of the orbit. We find the critical value to be characteristically as small as about 20 degrees. Typically, Neptune or lower mass planets would remain on inclined and eccentric orbits over the disc lifetime, whereas orbits of Jupiter or higher mass planets would align and circularize. This could play a significant role in planet formation scenarios.Comment: 28 pages, 8 figures, accepted for publication in MNRA

On the global warping of a thin self-gravitating near Keplerian gaseous disk with application to the disk in NGC 4258

On the global warping of a thin self-gravitating near Keplerian gaseous disk with application to the disk in NGC 4258Comment: 36 pages (including 4 figures), Latex, to appear in Ap

On the energy dissipation rate at the inner edge of circumbinary discs

We study, by means of numerical simulations and analysis, the details of the accretion process from a disc onto a binary system. We show that energy is dissipated at the edge of a circumbinary disc and this is associated with the tidal torque that maintains the cavity: angular momentum is transferred from the binary to the disc through the action of compressional shocks and viscous friction. These shocks can be viewed as being produced by fluid elements which drift into the cavity and, before being accreted, are accelerated onto trajectories that send them back to impact the disc. The rate of energy dissipation is approximately equal to the product of potential energy per unit mass at the disc's inner edge and the accretion rate, estimated from the disc parameters just beyond the cavity edge, that would occur without the binary. For very thin discs, the actual accretion rate onto the binary may be significantly less. We calculate the energy emitted by a circumbinary disc taking into account energy dissipation at the inner edge and also irradiation arising there from reprocessing of light from the stars. We find that, for tight PMS binaries, the SED is dominated by emission from the inner edge at wavelengths between 1-4 and 10 $\mu$m. This may apply to systems like CoRoT 223992193 and V1481 Ori.This is the final version of the article. It first appeared from Oxford University Press via https://doi.org/10.1093/mnras/stw248