Interpenetrating streams of solids and gas in a Keplerian disk produce a local, linear instability. The two components mutually interact via aerodynamic drag, which generates radial drift and triggers unstable modes. The secular instability does not require self-gravity, yet it generates growing particle density perturbations that could seed planetesimal formation. Growth rates are slower than dynamical, but faster than radial drift, timescales. Growth rates, like streaming velocities, are maximized for marginal coupling (stopping times comparable dynamical times). Fastest growth occurs when the solid to gas density ratio is order unity and feedback is strongest. Curiously, growth is strongly suppressed when the densities are too nearly equal. The relation between background drift and wave properties is explained by analogy with Howard's semicircle theorem. The three-dimensional, two-fluid equations describe a sixth order (in the complex frequency) dispersion relation. A terminal velocity approximation allows simplification to an approximate cubic dispersion relation. To describe the simplest manifestation of this instability, we ignore complicating (but possibly relevant) factors like vertical stratification, dispersion of particle sizes, turbulence, and self-gravity. We consider applications to planetesimal formation and compare our work to other studies of particle-gas dynamics.Comment: 26 pages, 8 figures, submitted to Ap

The outer parts of standard steady‐state accretion discs around quasi‐stellar objects (QSOs) are prone to self‐gravity, and they might be expected to fragment into stars rather than feed the central black hole. Possible solutions to this well‐known problem are examined with an emphasis on general dynamic constraints. Irradiation by the QSO is insufficient for stability even if the outer disc is strongly warped. Marginal local gravitational instability enhances viscous transport but extends the stable regions only modestly. Compton cooling in the observed QSO radiation field rules out hot thick discs unless the local accretion rate is vastly super‐Eddington. The formation of stars or stellar‐mass black holes, and the release of energy in these objects by fusion or accretion, may help to stabilize the remaining gas in an otherwise standard disc. But at fixed mass accretion rate, the energy inputs required for stability increase with radius; beyond a parsec, they approach the total QSO luminosity and are probably unsustainable by stars. Magnetic torques from a wind or corona, and gravitational torques from bars or global spirals, may increase the accretion speed and reduce the density of the disc. But dynamical arguments suggest that the accretion speed is at most sonic, so that instability still sets in beyond about a parsec. Alternatively, the QSO could be fed by stellar collisions in a very dense stellar cluster, but the velocity dispersion would have to be much higher than observed in nearby galactic nuclei containing quiescent black holes. In view of these difficulties, we suggest that QSO discs do not extend beyond a thousand Schwarzschild radii or so. Then they must be frequently replenished with gas of small specific angular momentum.

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Recent observations have shown that globular clusters contain a significant binary population. This is a dramatic change from the conventional view of even a decade ago, which held that globular clusters formed without any binaries at all, since the observed X-ray binaries were understood to be formed through dynamical capture. Over the last few years, a number of different observational techniques have resulted in the detection of a substantial number of binaries most of which are believed to be primordial. When the many selection effects are taken into account, these detections translate into a binary abundance in globular clusters that may be somewhat smaller than those in the Galactic disk and halo, but not by a large factor. Within the current uncertainties, it is even possible that the primordial binary abundance in globular clusters is comparable to that in the Galactic disk. We discuss different successful optical search techniques, based on radial-velocity variables, photometric variables, and the positions of stars in the color-magnitude diagram. In addition, we review searches in other wavelengths, which have turned up low-mass X-ray binaries and more recently a variety of radio 981

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