Turbulent Disks are Never Stable: Fragmentation and Turbulence-Promoted Planet Formation

A fundamental assumption in our understanding of disks is that when the Toomre Q>>1, the disk is stable against fragmentation into self-gravitating objects (and so cannot form planets via direct collapse). But if disks are turbulent, this neglects a spectrum of stochastic density fluctuations that can produce rare, high-density mass concentrations. Here, we use a recently-developed analytic framework to predict the statistics of these fluctuations, i.e. the rate of fragmentation and mass spectrum of fragments formed in a turbulent Keplerian disk. Turbulent disks are never completely stable: we calculate the (always finite) probability of forming self-gravitating structures via stochastic turbulent density fluctuations in such disks. Modest sub-sonic turbulence above Mach number ~0.1 can produce a few stochastic fragmentation or 'direct collapse' events over ~Myr timescales, even if Q>>1 and cooling is slow (t_cool>>t_orbit). In trans-sonic turbulence this extends to Q~100. We derive the true Q-criterion needed to suppress such events, which scales exponentially with Mach number. We specify to turbulence driven by MRI, convection, or spiral waves, and derive equivalent criteria in terms of Q and the cooling time. Cooling times >~50*t_dyn may be required to completely suppress fragmentation. These gravoturbulent events produce mass spectra peaked near ~M_disk*(Q*M_disk/M_star)^2 (rocky-to-giant planet masses, increasing with distance from the star). We apply this to protoplanetary disk models and show that even minimum mass solar nebulae could experience stochastic collapse events, provided a source of turbulence.Comment: 15 pages, 5 figures (+appendix), accepted to ApJ (added clarifications and discussion to match accepted version

The Phoenix survey: the pairing fraction of faint radio sources

The significance of tidal interactions in the evolution of the faint radio population (sub-mJy) is studied using a deep and homogeneous radio survey (1.4 GHz), covering an area of 3.14 deg$^2$ and complete to a flux density of 0.4 mJy. Optical photometric and spectroscopic data are also available for this sample. A statistical approach is employed to identify candidate physical associations between radio sources and optically selected `field' galaxies. We find an excess of close pairs around optically identified faint radio sources, albeit at a low significance level, implying that the pairing fraction of the sub-mJy radio sources is similar to that of `field' galaxies (at the same magnitude limit) but higher than that of local galaxies.Comment: 5 pages, 4 figures. Accepted for publication in MNRAS Letter

General Rotorcraft Aeromechanical Stability Program (GRASP) version 1.03: User's manual

The Rotorcraft Dynamics Division, Aeroflightdynamics Directorate, U.S. Army Aviation Research and Technology Activity has developed the General Rotorcraft Aeromechanical Stability Program (GRASP) to perform calculations that will assess the stability of rotorcraft in hovering flight and ground contact conditions. The program is designed to be state-of-the-art, hybrid, finite-element/multibody code that can be applied to all existing and future helicopter configurations. While GRASP was specifically designed to solve rotorcraft stability problems, its innovative structure and formulation allow for application to a wide range of structures. This manual describes the preparation of the input file required by Version 1.03 of GRASP, the procedures used to invoke GRASP on the NASA Ames Research Center CRAY X-MP 48 computer, and the interpretation of the output produced by GRASP. The parameters used by the input file are defined, and summaries of the input file and the job control language are included