How to adapt broad-band gravitational-wave searches for r-modes

Up to now there has been no search for gravitational waves from the r-modes of neutron stars in spite of the theoretical interest in the subject. Several oddities of r-modes must be addressed to obtain an observational result: The gravitational radiation field is dominated by the mass current (gravitomagnetic) quadrupole rather than the usual mass quadrupole, and the consequent difference in polarization affects detection statistics and parameter estimation. To astrophysically interpret a detection or upper limit it is necessary to convert the wave amplitude to an r-mode amplitude. Also, it is helpful to know indirect limits on gravitational-wave emission to gauge the interest of various searches. Here I address these issues, thereby providing the ingredients to adapt broad-band searches for continuous gravitational waves to obtain r-mode results. I also show that searches of existing data can already have interesting sensitivities to r-modes.Comment: 8 pages, no figure

Conditions for the occurrence of mean-motion resonances in a low mass planetary system

The dynamical interactions that occur in newly formed planetary systems may reflect the conditions occurring in the protoplanetary disk out of which they formed. With this in mind, we explore the attainment and maintenance of orbital resonances by migrating planets in the terrestrial mass range. Migration time scales varying between millions of years and thousands of years are considered. In the former case, for which the migration time is comparable to the lifetime of the protoplanetary gas disk, a 2:1 resonance may be formed. In the latter, relatively rapid migration regime commensurabilities of high degree such as 8:7 or 11:10 may be formed. However, in any one large-scale migration several different commensurabilities may be formed sequentially, each being associated with significant orbital evolution. We also use a simple analytic theory to develop conditions for first order commensurabilities to be formed. These depend on the degree of the commensurability, the imposed migration and circularization rates, and the planet mass ratios. These conditions are found to be consistent with the results of our simulations.Comment: 11 pages with 4 figures, pdflatex, to appear in the proceedings of the conference "Extra-solar Planets in Multi-body Systems: Theory and Observations"; eds. K. Gozdziewski, A. Niedzielski and J. Schneider, EAS Publication Serie

The Local Instability of Steady Astrophysical Flows with non Circular Streamlines with Application to Differentially Rotating Disks with Free Eccentricity

We carry out a general study of the stability of astrophysical flows that appear steady in a uniformly rotating frame. Such a flow might correspond to a stellar pulsation mode or an accretion disk with a free global distortion giving it finite eccentricity. We consider perturbations arbitrarily localized in the neighbourhood of unperturbed fluid streamlines.When conditions do not vary around them, perturbations take the form of oscillatory inertial or gravity modes. However, when conditions do vary so that a circulating fluid element is subject to periodic variations, parametric instability may occur. For nearly circular streamlines, the dense spectra associated with inertial or gravity modes ensure that resonance conditions can always be satisfied when twice the period of circulation round a streamline falls within. We apply our formalism to a differentially rotating disk for which the streamlines are Keplerian ellipses, with free eccentricity up to 0.7, which do not precess in an inertial frame. We show that for small $e,$ the instability involves parametric excitation of two modes with azimuthal mode number differing by unity in magnitude which have a period of twice the period of variation as viewed from a circulating unperturbed fluid element. Instability persists over a widening range of wave numbers with increasing growth rates for larger eccentricities. The nonlinear outcome is studied in a follow up paper which indicates development of small scale subsonic turbulence.Comment: Accepted for publication in Astronomy and Astrophysic

Dust settling in local simulations of turbulent protoplanetary disks

In this paper, we study the effect of MHD turbulence on the dynamics of dust particles in protoplanetary disks. We vary the size of the particles and relate the dust evolution to the turbulent velocity fluctuations. We performed numerical simulations using two Eulerian MHD codes, both based on finite difference techniques: ZEUS--3D and NIRVANA. These were local shearing box simulations incorporating vertical stratification. Both ideal and non ideal MHD simulations with midplane dead zones were carried out. The codes were extended to incorporate different models for the dust as an additional fluid component. Good agreement between results obtained using the different approaches was obtained. The simulations show that a thin layer of very small dust particles is diffusively spread over the full vertical extent of the disk. We show that a simple description obtained using the diffusion equation with a diffusion coefficient simply expressed in terms of the velocity correlations accurately matches the results. Dust settling starts to become apparent for particle sizes of the order of 1 to 10 centimeters for which the gas begins to decouple in a standard solar nebula model at 5.2 AU. However, for particles which are 10 centimeters in size, complete settling toward a very thin midplane layer is prevented by turbulent motions within the disk, even in the presence of a midplane dead zone of significant size. These results indicate that, when present, MHD turbulence affects dust dynamics in protoplanetary disks. We find that the evolution and settling of the dust can be accurately modelled using an advection diffusion equation that incorporates vertical settling. The value of the diffusion coefficient can be calculated from the turbulent velocity field when that is known for a time of several local orbits.Comment: 15 pages, 16 figures, accepted in Astronomy & Astrophysic

Corotation Resonance and Diskoseismology Modes of Black Hole Accretion Disks

We demonstrate that the corotation resonance affects only some non-axisymmetric g-mode oscillations of thin accretion disks, since it is located within their capture zones. Using a more general (weaker radial WKB approximation) formulation of the governing equations, such g-modes, treated as perfect fluid perturbations, are shown to formally diverge at the position of the corotation resonance. A small amount of viscosity adds a small imaginary part to the eigenfrequency which has been shown to induce a secular instability (mode growth) if it acts hydrodynamically. The g-mode corotation resonance divergence disappears, but the mode magnitude can remain largest at the place of the corotation resonance. For the known g-modes with moderate values of the radial mode number and axial mode number (and any vertical mode number), the corotation resonance lies well outside their trapping region (and inside the innermost stable circular orbit), so the observationally relevant modes are unaffected by the resonance. The axisymmetric g-mode has been seen by Reynolds & Miller in a recent inviscid hydrodynamic accretion disk global numerical simulation. We also point out that the g-mode eigenfrequencies are approximately proportional to m for axial mode numbers |m|>0.Comment: 16 pages, no figures. Submitted to The Astrophysical Journa

Precession of collimated outflows from young stellar objects

We consider several protostellar systems where either a precessing jet or at least two misaligned jets have been observed. We assume that the precession of jets is caused by tidal interactions in noncoplanar binary systems. For Cep E, V1331 Cyg and RNO 15-FIR the inferred orbital separations and disk radii are in the range 4-160 AU and 1-80 AU, respectively, consistent with those expected for pre-main sequence stars. Furthermore, we assume or use the fact that the source of misaligned outflows is a binary, and evaluate the lengthscale over which the jets should precess as a result of tidal interactions. For T Tau, HH1 VLA 1/2 and HH 24 SVS63, it may be possible to detect a bending of the jets rather than 'wiggling'. In HH 111 IRS and L1551 IRS5, 'wiggling' may be detected on the current observed scale. Our results are consistent with the existence of noncoplanar binary systems in which tidal interactions induce jets to precess.Comment: 5 pages (including 1 figure), LaTeX, uses emulateapj.sty, to be published in ApJ Letters, also available at http://www.ucolick.org/~ct/home.html and http://www.tls-tautenburg.de/research/research.htm

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

Global m=1 modes and migration of protoplanetary cores in eccentric protoplanetary discs

We calculate global $m=1$ modes with low pattern speed corresponding to introducing a finite eccentricity into a protoplanetary disc. We consider disc models which are either isolated or contain one or two protoplanets orbiting in an inner cavity. Global modes that are strongly coupled to inner protoplanets are found to have disc orbits which tend to have apsidal lines antialigned with respect to those of the inner protoplanets. Other modes corresponding to free disc modes may be global over a large range of length scales and accordingly be long lived. We consider the motion of a protoplanet in the earth mass range embedded in an eccentric disc and determine the equilibrium orbits which maintain fixed apsidal alignment with respect to the disc gas orbits. Equilibrium eccentricities are found to be comparable or possibly exceed the disc eccentricity. We then approximately calculate the tidal interaction with the disc in order to estimate the orbital migration rate. Results are found to deviate from the case of axisymmetric disc with near circular protoplanet orbit once eccentricities of protoplanet and disc orbits become comparable to the disc aspect ratio in magnitude. Aligned protoplanet orbits with very similar eccentricity to that of the gas disc are found to undergo litle eccentricity change while undergoing inward migration in general. However, for significantly larger orbital eccentricities, migration may be significantly reduced or even reverse from inwards to outwards. Thus the existence of global non circular motions in discs with radial excursions comparable to the semi-thickness may have important consequences for the migration and survival of protoplanetary cores in the earth mass range.Comment: Accepted for publication by A &

On the orbital evolution and growth of protoplanets embedded in a gaseous disc

We present a new computation of the linear tidal interaction of a protoplanetary core with a thin gaseous disc in which it is fully embedded. For the first time a discussion of the orbital evolution of cores with eccentricity (e) significantly larger than the gas-disc scale height to radius ratio (H/r) is given. We find that the direction of orbital migration reverses for e>1.1H/r. This occurs as a result of the orbital crossing of resonances in the disc that do not overlap the orbit when the eccentricity is very small. Simple expressions giving approximate fits to the eccentricity damping rate and the orbital migration rate are presented. We go on to calculate the rate of increase of the mean eccentricity for a system of protoplanetary cores due to dynamical relaxation. By equating the eccentricity damping time-scale with the dynamical relaxation time-scale we deduce that an equilibrium between eccentricity damping and excitation through scattering is attained on a 10^3 to 10^4 yr time-scale, at 1au. The equilibrium thickness of the protoplanet distribution is such that it is generally well confined within the gas disc. By use of a three dimensional N-body code we simulate the evolution of a system of protoplanetary cores, incorporating our eccentricity damping and migration rates. Assuming that collisions lead to agglomeration, we find that the vertical confinement of the protoplanet distribution permits cores to build up from 0.1 to 1 earth mass in only ~10^4 yr, within 1au. The time-scale required to achieve this is comparable to the migration time-scale. We deduce that it is not possible to build up a massive enough core to form a gas giant planet before orbital migration ultimately results in the preferential delivery of all such bodies to the neighbourhood of the central star. [Abridged]Comment: Latex in MNRAS style, 13 pages with 6 figures, also available from http://www.maths.qmw.ac.uk/~jdl

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