Philip D. Nicholson

Tidal friction in early-type stars

The tidal torque on an early-type star is concentrated near the boundary between the convective core and radiative envelope and a train of gravity waves is excited there. The angular momentum which the torque removes from the fluid is transported outward by the gravity waves, which carry negative angular momentum. Before the surface layers are despun to synchronous rotation, the gravity waves propagate to just below the photosphere where they suffer radiative damping and are partially reflected. It is here that the negative angular momentum is deposited and the primary tidal despinning takes place. The surface layers cannot be spun down below synchronous rotation because as a train of gravity waves approaches a corotation resonance its group velocity and wavelength tend to zero, its amplitude diverges, and it is completely absorbed. Thus, tidal despinning to synchronous rotation proceeds from the outside toward the inside of the star. Our picture provides a neat explanation for the otherwise puzzling discovery by Giuricin, Mardirossian, and Mezzetti that Zahns theory for tidal evolution in early-type close binaries seems to be compatible with the observed rates of orbit circularization while significantly underestimating the observed rates of spin synchronization.

Turbulent viscosity and Jupiter's tidal Q☆

A recent estimate of tidal dissipation by turbulent viscosity in Jupiters convective interior predicts that the current value of the planets tidal Q ∼ 5 × 10^6. We point out a fundamental error in this calculation, and show that turbulent dissipation alone implies that at present Q ∼ 5 × 10^(13). Our reduced estimate for the rate of tidal dissipation shows conclusively that tidal torques have produced only negligible modifications of the orbits of the Galilean satellites over the age of the solar system.

Tides in rotating fluids

We consider the tidal disturbance forced in a differentially rotating fluid by a rigidly rotating external potential. The fluid is assumed to be inviscid, insulated, and self-gravitating, and to have laminar unperturbed and perturbed velocity fields. The external potential may exert a steady torque on the fluid which is of second order in Its strength. However, to this order, we prove that there are no secular changes in the angular momenta of fluid particles, except possibly at corotation where the angular velocity, Ω(r,θ), is equal to the pattern speed of the potential, Ω_p. A corollary of our theorem is that, except at corotation, all of the angular momentum transferred to the fluid by the external potential must be transported away by internal stresses. In the applications of which we are aware, these stresses are associated with waves.

The upper atmosphere of Uranus: A critical test of isotropic turbulence models

Abstract Observations of the 15 August 1980 Uranus occultation of KM 12, obtained from Cerro Tololo InterAmerican Observatory, European Southern Observatory, and Cerro Las Campanas Observatory, are used to compare the atmospheric structure at points separated by ∼140 km along the planetary limb. The results reveal striking, but by no means perfect, correlation of the light curves, ruling out isotropic turbulence as the cause of the light curve spikes. The atmosphere is strongly layered, and any acceptable turbulence model must accommodate the axial ratios of ⪆60 which are observed. The mean temperature of the atmosphere is 150 ± 15°K for the region near number density 10 14 cm −3 . Derived temperature variations of vertical scale ∼ 130km and amplitude ±5°K are in agreement for all stations, and correlated spikes correspond to low-amplitude temperature variations with a vertical scale of several kilometers.

Maps of the rings of Uranus at a wavelength of 2.2 microns

Maps of the ring system of Uranus, as seen in reflected sunlight at a wavelength of 2.2 μm, are presented for May 1978 and July 1979. Large azimuthal brightness variations revealed by these maps are consistent with the variable width established for the ϵ ring from occultation studies and support the existing elliptical model for this ring. An upper limit of ∼0.010 is placed on the normal optical depth of any broad (∼5000 km wide) axisymmetric ring component. There exists, however, an unexplained east-west asymmetry in the May 1978 map. In addition, multiaperture broadband infrared photometry of Uranus is reported, from which the geometric albedo of the planet at wavelengths of 1.25, 1.65, and 2.2 μm and the geometric albedo of the rings at 2.2 μm are derived.