The interaction of a giant planet with a disc with MHD turbulence I: The initial turbulent disc models

This is the first of a series of papers aimed at developing and interpreting simulations of protoplanets interacting with turbulent accretion discs. Here we study the disc models prior to the introduction of a protoplanet.We study models in which a Keplerian domain is unstable to the magnetorotational instability (MRI). Various models with B-fields having zero net flux are considered.We relate the properties of the models to classical viscous disc theory.All models attain a turbulent state with volume averaged stress parameter alpha ~ 0.005. At any particular time the vertically and azimuthally averaged value exhibited large fluctuations in radius. Time averaging over periods exceeding 3 orbital periods at the outer boundary of the disc resulted in a smoother quantity with radial variations within a factor of two or so. The vertically and azimuthally averaged radial velocity showed much larger spatial and temporal fluctuations, requiring additional time averaging for 7-8 orbital periods at the outer boundary to limit them. Comparison with the value derived from the averaged stress using viscous disc theory yielded schematic agreement for feasible averaging times but with some indication that the effects of residual fluctuations remained. The behaviour described above must be borne in mind when considering laminar disc simulations with anomalous Navier--Stokes viscosity. This is because the operation of a viscosity as in classical viscous disc theory with anomalous viscosity coefficient cannot apply to a turbulent disc undergoing rapid changes due to external perturbation. The classical theory can only be used to describe the time averaged behaviour of the parts of the disc that are in a statistically steady condition for long enough for appropriate averaging to be carried out.Comment: 10 pages, 23 figures, accepted for publication in MNRAS. A gzipped postscript version including high resolution figures is available at http://www.maths.qmul.ac.uk/~rp

On non-linear hydrodynamic instability and enhanced transport in differentially rotating flows

In this paper we argue that differential rotation can possibly sustain hydrodynamic turbulence in the absence of magnetic field. We explain why the non-linearities of the hydrodynamic equations (i.e. turbulent diffusion) should not be neglected, either as a simplifying approximation or based on boundary counditions. The consequences of lifting this hypothesis are studied for the flow stability and the enhanced turbulent transport. We develop a simple general model for the energetics of turbulent fluctuations in differentially rotating flows. By taking into account the non-linearities of the equations of motions, we give constraints on the mean flow properties for the possible development of shear instability. The results from recent laboratory experiments on rotating flows show -- in agreement with the model -- that the pertinent parameter for stability appears to be the Rossby number Ro. The laboratory experiments seem to be compatible with Ro 1 in the inviscid or high rotation rates limit. Our results, taken in the inviscid limit, are coherent with the classical linear stability analysis, in the sense that the critical perturbation equals zero on the marginal linear stability curve. We also propose a prescription for turbulent viscosity which generalize the beta-prescription derived in Richard & Zahn 1999.Comment: Accepted for publication in "Astronomy and Astrophysics

Impact of dimensionless numbers on the efficiency of MRI-induced turbulent transport

The magneto-rotational instability is presently the most promising source of turbulent transport in accretion disks. However, some important issues still need to be addressed to quantify the role of MRI in disks; in particular no systematic investigation of the role of the physical dimensionless parameters of the problem on the dimensionless transport has been undertaken yet. First, we complete existing investigations on the field strength dependence by showing that the transport in high magnetic pressure disks close to marginal stability is highly time-dependent and surprisingly efficient. Second, we bring to light a significant dependence of the global transport on the magnetic Prandtl number, with $\alpha\propto Pm^\delta$ for the explored range: $0.12<Pm<8$ and $200<Re<6400$ ($\delta$ being in the range 0.25 to 0.5). We show that the dimensionless transport is not correlated to the dimensionless linear growth rate, contrarily to a largely held expectation. More generally, these results stress the need to control dissipation processes in astrophysical simulations.Comment: 11 pages, 11 figures, accepted to MNRA

An Exact, Three-Dimensional, Time-Dependent Wave Solution in Local Keplerian Flow

We present an exact three-dimensional wave solution to the shearing sheet equations of motion. The existence of this solution argues against transient amplification as a route to turbulence in unmagnetized disks. Moreover, because the solution covers an extensive dynamical range in wavenumber space, it is an excellent test of the dissipative properties of numerical codes.Comment: 22 pages, 4 figures. To appear Apj Dec 1 200

The pure rotation spectrum of ammonia

New experimental means for the study of absorption spectra in the extreme infra-red are described. These have been used in extending our knowledge of the pure rotation spectra to the case of a polyatomic molecule. The absorption spectrum of ammonia has been investigated in the region between 55μ and 130μ, and a very simple structure was found. Six lines were observed which belong to a pure rotation spectrum and are apparently due to changes in the energy of rotation of the ammonia molecule about an axis normal to the line of symmetry, that is, to transitions in which the quantum number j increases by unity. Other lines due to transitions with a change also of τ, the quantum number connected with rotations about the axis of symmetry, are absent. These facts are briefly discussed in connection with the predictions of the wave mechanics with which they are shown to be in accord. The moment of inertia of the ammonia molecule about an axis normal to the line of symmetry is estimated to be 2.77×10^(-40) gm cm^2

Minor head injury in the Republic of Ireland : evaluation of written information given at discharge from emergency departments

Most patients presenting to the emergency department with minor head injuries are discharged with written information. Here the quality of minor head injury discharge leaflets in the Republic of Ireland is evaluated against a nationally accepted template. There was great variability in leaflet content. Most provided minimal information on emergency symptoms but 60% contained no information on post-concussional symptoms. No leaflet was available in audio-format or languages other than English. Information provided in minor head injury leaflets should be improved and standardised across Ireland

The Coming Hangover: Magnified Effects of Sequestration on Research Enterprises

As of March 1, 2013 the US government is taking an $85 billion budget cut. Also referred as the “sequestration”, this automatic spending cut policy might continue for several upcoming years and potentially affect many industries, including the research enterprise. The cut is expected to reflect in the budget of federal agencies that support research activities, such as the National Institutes of Health (NIH) and the National Science Foundation (NSF). For a wide range of structural reasons, discussed in this commentary, the impacts of the budget cut on research enterprises can be magnified

Growth of Hydrodynamic Perturbations in Accretion Disks: Possible Route to Non-Magnetic Turbulence

We study the possible origin of hydrodynamic turbulence in cold accretion disks such as those in star-forming systems and quiescent cataclysmic variables. As these systems are expected to have neutral gas, the turbulent viscosity is likely to be hydrodynamic in origin, not magnetohydrodynamic. Therefore MRI will be sluggish or even absent in such disks. Although there are no exponentially growing eigenmodes in a hydrodynamic disk, because of the non-normal nature of the eigenmodes, a large transient growth in the energy is still possible, which may enable the system to switch to a turbulent state. For a Keplerian disk, we estimate that the energy will grow by a factor of 1000 for a Reynolds number close to a million.Comment: 4 pages; to appear in the Proceedings of COSPAR Colloquium "Spectra & Timing of Compact X-ray Binaries," January 17-20, 2005, Mumbai, India; prepared on the basis of the talk presented by Mukhopadhya