Nodal and periastron precession of inclined orbits in the field of a rotating black hole

The inclination of low-eccentricity orbits is shown to significantly affect orbital parameters, in particular, the Keplerian, nodal precession, and periastron rotation frequencies, which are interpreted in terms of observable quantities. For the nodal precession and periastron rotation frequencies of low-eccentricity orbits in a Kerr field, we derive a Taylor expansion in terms of the Kerr parameter at arbitrary orbital inclinations to the black-hole spin axis and at arbitrary radial coordinates. The particle radius, energy, and angular momentum in the marginally stable circular orbits are calculated as functions of the Kerr parameter j and parameter s in the form of Taylor expansions in terms of j to within O[j ⁶]. By analyzing our numerical results, we give compact approximation formulas for the nodal precession frequency of the marginally stable circular orbits at various s in the entire range of the Kerr parameter.     

Extragalactic Astronomy with the VLTI: a new window on the Universe

Interferometry in the optical and near infrared has so far played a marginal role in Extragalactic Astronomy. Active Galactic Nuclei are the brightest and most compact extragalactic sources, nonetheless only a very limited number could be studied with speckle interferometry and none with long baseline interferometry. The VLTI will allow the study of moderately faint extragalactic objects with very high spatial resolution thus opening a new window on the universe. With this paper we focus on three scientific cases to show how AMBER and MIDI can be used to tackle open issues in extragalactic astronomy. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dynamics of co-ignimbrite plumes generated from pyroclastic flows of Mount St. Helens (7 August 1980)

 Four co-ignimbrite plumes were generated along the flow path of the pyroclastic flow of 7 August 1980 at Mount St. Helens. Three of the plumes were generated in discrete pulses which can be linked to changes in slope along the channel. One plume was generated at the mouth of the channel where the flow decelerated markedly as it moved onto the lower slopes of the pumice plain. Plume generation here may be triggered by enhanced mixing due to a hydraulic jump associated with an abrupt slope change. Measurements of plume ascent velocity and width show that the co-ignimbrite plumes increased in velocity with height. The plumes have initial velocities of 1–2 m/s. Two of the plumes reached a velocity maximum (4.6 and 8.8 m/s, respectively, at heights of 270 and 315 m above the flow) and thereafter decelerated. The other plumes reached velocities of 6.2 and 13 m/s. The four plumes become systematically less energetic downstream as measured by their ascent rates, which can be interpreted as a consequence of decreasing interaction of the pyroclastic flow front with the atmosphere. Theoretical models of both co-ignimbrite plumes and discrete co-ignimbrite clouds assume that there is no initial momentum, and both are able to predict the observed acceleration stage. The rising plumes mix with and heat air and sediment out particles causing their buoyancy to increase. Theoretical models agree well with observations and suggest that the initial motion of the ascending material is best described as a discrete thermal cloud which expands as it entrains air, whereas the subsequent motion of the head may become influenced by material supplied from the following plume. The models agree well with observations for an initial temperature of the ash and air mixture in the range of 500–600 K, which is in turn consistent with the measured initial ash temperature of around 920 K. Ash masses of 3.4×10⁵ to 1.8×10⁶ kg are estimated. Received: 11 January 1996 / Accepted: 7 October 1996